aijst volume 1 no 1 april 2012

ISSN : 2088-9860

Volume 1. Number 1,

April 2012

ACEH INTERNATIONAL JOURNAL OF SCIENCE AND TECHNOLOGY

Volume 1, Nomor 1, April 2012

ISSN 2088-9860

Contents

Performance Evaluation of An Innovative-VaporCompression-Desalination System. 1 - 13 Mirna R. Lubis, and Mark T. Holtzaple Grey Model for Stream Flow Prediction

14 - 19

Vishnu B., and Syamala P. A Study on Learning Pre-Algebra Using Interactive Multimedia Courseware Within Collaborative Learning Set-Up and E-Mail Interactions.

20 - 25

Mohd Sazali Khalid, Sulaiman Yamin, and Sri Adelila Sari Electrochemistry Study on PVC-LiClO4 Polymer Electrolyte Supported by Bengkulu Natural Bentonite for Lithium Battery

26 - 29

Ghufira, Sal P. Yudha, Eka Angasa, and Jhoni Ariesta

Functional Data Analysis of Multi-Angular Hyperspectral Data on Vegetation 30 - 39 Sugianto, and Shawn Laffan

Aceh International Journal of Science and Technology, 1 (1): 1-13 April 2012

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Performance Evaluation of An Innovative-Vapor- Compression-Desalination System

1Mirna R. Lubis and 2Mark T. Holtzaple

1Chemical Engineering Department, Engineering Faculty, Syiah Kuala University Jl. Syech Abdurrauf No. 7, Darussalam, Banda Aceh, 23111

2Artie McFerin Department of Chemical Engineering TAMU, College Station, Texas 1Email: [email protected]

Abstract – Two dominant desalination methods are reverse osmosis (RO) and multi-stage flash (MSF). RO requires large capital investment and maintenance, whereas MSF is too energy-intensive. Innovative system of vapor compression desalination is proposed in this study. Comprehensive mathematics model for evaporator is also described. From literature study, it is indicated that very high overall-heat-transfer coefficient for evaporator can be obtained at specific condition by using dropwise condensation in the steam side, and pool boiling in the liquid side. Smooth titanium surface is selected in order to increase dropwise condensation, and resist corrosion. To maximize energy efficiency, a cogeneration scheme of a combined cycle consisting of gas turbine, boiler heat recovery, and steam turbine that drives compressor is used. The resource for combined cycle is relatively too high for the compressor requirement. Excess power can be used to generate electricity for internal and/or external consumptions, and sold to open market. Four evaporator stages are used. Evaporator is fed by seawater, with assumption of 3.5% salt contents. Boiling brine (7% salt) is boiled in low pressure side of the heat exchanger, and condensed vapor is condensed in high pressure side of the heat exchanger. Condensed steam flows at velocity of 1.52 m/s, so that it maximize the heat transfer coefficient. This unit is designed in order to produce 10 million gallon/day, and assumed it is financed with 5%, 30 years of passive obligation. Three cases are evaluated in order to determine recommended condition to obtain the lowest fixed capital investment. Based on the evaluation, it is possible to establish four-stage unit of mechanical vapor compression distillation with capital $31,723,885. Keywords: Desalination, dropwise condensation, heat exchanger, StarRotor compressor, vapor compression distillation.

Introduction

Desalination aims to produce potable water form seawater, brackish water, or treated waste water. Among water treatment technologies, it is one of the most efficient thermal distillation processes used to reduce the broadest range of water contaminant. Mechanical vapor compression is modern method that produces potable water with acceptable energy efficiency (Ejjeh, 2001). Following World War II, the vapor compression distillers were used in oil production in remote area. Larger unit could produce 200,000 gallons per day. The installations had four identical units operating in parallel. The original design had one rotor fitted with a set of blades having the inducer section in a single piece. The up-graded design is based on two rotors housing the inducer blades allowing for more efficient configuration. A number of modifications have been incorporated on the shroud, vapor ducts, diffusion section, instrumentation, and the number of evaporators to improve the performance.

Sheet-shell heat exchanger is key technology in the mechanical-vapor-compression-desalination system. The heat exchanger consists of new assembly, which combines conventional plate-and-frame appearance and shell-and-tube heat exchanger. The heat exchanger could be used in order to exchange sensible heat as well as latent heat. Latent heat exchanger could be part of multi effect evaporator that operates at lower temperature and pressure. Alternatively, the evaporator could be part of vapor compression evaporator. Multi effect evaporator used operates at lower pressure and temperature. Steam from high pressure evaporator boils water in adjacent low pressure. The compressor draws vapor from the low pressure evaporator, forces, and returns it to high pressure evaporator. The salt water has to be degassed before it is fed into evaporator.

Low pressure steam from steam turbine discharge could be added to evaporator where pressure from discharged steam and the evaporator is the most suitable. While overall heat transfer coefficient is obtained, the heat exchanger's surface could be known, and also the cost. The disadvantages of the mechanical vapor compression system (Al-Juwayhel, 1997) include use of high electrical energy, flow rate limitations on the vapor compression range, maintenance and spare part requirements. The disadvantage limits the use of the mechanical vapor compression


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system in countries with limited fossil, nuclear, or hydro. It also limits the operation of the mechanical vapor compression system to low brine temperature. This results in a larger heat transfer area for the heat exchanger, which increases the energy requirement, and therefore the investment cost. Because the critical cost parameter is fixed cost (amortization) and energy cost (Anonymous, 2000), this research focus is in order to reduce energy requirement by introducing multi-effect evaporator, and developing new latent heat exchanger. Holtzapple and Noyes (2004) arrange system illustrated in their Disclosure of Invention (Figure 1). Degassed feed is fed to evaporator that operates at the highest pressure (Evaporator 4). The system uses "combined cycle" machine, consisting of gas turbine (Brayton cycle) and steam turbine (Rankine cycle). Waste heat from gas turbine is used to make steam, so that it strengthens the steam turbine. Both gas turbine and steam turbine will strengthen the compressor.

Holtzapple and Noyes (2004) have arranged new sheet shell heat exchanger (Lubis, 2011) as used in this research. The configuration has short diagonal cut that enables the formation of small peak. At high pressure chamber, the baffle causes flow area more decreased, which enables relatively constant velocity through the heat exchanger. The flow finally compress out gasses that are condensable. Channel number per pass is selected in order to achieve low pressure drop. In low pressure chamber, liquid enters from bottom part, and boils because of heat exchange through the wall. Vapor resulted exits from the top.

For high pressure side of sheet-shell heat exchanger, the objective is in order to produce dropwise condensation. This could be increased by using titanium layers toward carbon steel as proposed in this research, surface coated by gold (Griffith and Lee, 1967) or titanium plate (Rose, 1967). Titanium surface also reduce impurities and avoid corrosion because of seawater (Rose, 1967). Holtzapple and Noyes (2004) targets T = 5.56oC as temperature difference in every heat exchanger of vapor compression evaporator. An extensive review on this matter (Haslego and Polley, 2002) shows that this number is suitable temperature difference. Furthermore, literature (O'Bara et al., 1967) suggested average velocity of 1.52 m/s at high-pressure steam side.

Experiment conducted by Dollof et al. (1969) indicated influence of pressure (and vapor temperature) on heat transfer coefficient of steam side. O'Bara, Killian, and Roblee also indicated that Ts = 2.3oC, large heat transfer coefficient is obtained at vapor velocity around 1.52 m/s. Ruckenstein and Metiu (1965) have used a model to estimate heat transfer coefficient for dropwise condensation on solid surface. Their model considers heat moved through drops and film, which dynamically break the solid surface. The heat transfer coefficient is proportional to drop fraction toward total area and thermal conductivity of liquid film as much of 0.3934 Btu/(h·ft·oF). Based on study that has been carried out, this research is aimed to analyze performance of a desalination system that has been designed by considering all designed data above and consists of four evaporators in order to determine capital investment of saturated steam compression. Over the past several years, the cost of desalting still cannot compete with the cost of fresh water that it requires minimal treatment to make it potable. Though many methods have been proposed to desalt seawater, only a few have been developed commercially. Therefore, the investment proposed in this research is expected to be able to give contribution to production of a unit of potable water with low cost. Materials and Methods

Degassed seawater is fed to evaporators that relate in parallel in order to obtain evaporator temperature requirement (Figure 1). The flow is between 147.5 kg/s and 144.57 kg/s. Four evaporator stages are used, each with various T = 2, 4, 6oF and 7% brine (S = 70 g/kg). This S is substituted in activity formula (Emerson and Jamieson, 1967) as follows:

(1) where; p = vapor pressure of salt water p0 = vapor pressure of water h = -2.1609 × 10-4 j = -3.5012 × 10-7 S = salinity (70 g salt/kg seawater)

Figure 2 shows the nomenclature to identify temperature and pressure of each stage of the evaporator. In order to ensure dropwise condensation, maximum pressure at steam side is set as much of 827.4 kPa gauge (120 psig). This value was chosen to give agreement with results obtained by other investigators (Dolloff et al., 1969). Saturated steam is fed to the first stage at 120 psig (176.7oC) and recovered from the final stage at 158.63oC. For T = 6oF, temperature at point C becomes 6oF less than temperature at point A, whereas vapor pressure of water is 8,471 atm from steam table.


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Figure 1. Desalination System (Holtzapple and Noyes, 2004)

Therefore, the pressure in point C can be calculated from equation 1. The pressure obtained is the same as

the pressure at point A in stage 2. Similarly, pressure and temperature in each stage can be determined for each temperature difference. The flow rate is calculated for every evaporator as required by production. Estimated range of seawater temperature is 21.1 – 26.2oC. The number of condensation as required by flow rate or production is calculated in accordance with mass balance. The seawater feed is 3.5% salt (xf = 35 g/kg) and the following brine concentration (xb) is obtained: 20, 50, 70, dan 100 g/kg. The fouling factor is not available (the surface is assumed clean by raising brush balls. The heat transfer coefficient ia around 0.14 MW/(m2 · K). In this experiment, sea water moves at velocity of 1.52 m/s in gauge tubes ¾ in, with condensing steam at the outside. The material construction code is API-ASME code.

Titanium plate surface with thickness of 0.007 in is used in order to achieve dropwise condensation, the evaporator is constructed with elastomeric gasket, and carbon steel vessel coated with epoxy or titanium layers to protect it from corrosion on seawater side. The distance of center to center among adjacent plates is 0.25 inch. Standard plate dimension is 2.4 m × 2.4 m. Vessel shell thickness is 29.6 mm. It is based on recommended design equation for a vessel under internal pressure (Peters et al., 2003) as follows:

(2) where; P = Maximum allowable pressure = 910.1 kPa ri = Inside radius of shell before corrosion allowance is added = 2 m Sm = Maximum allowable working stress (88.350 kPa for carbon steel SEA J412) Ej = Efficiency of joints = 0.85 (spot examined joints) Cc = Allowance for corrosion = 0


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m v C A m s

vapor steam

E

D B m b m w

Figure 2. Flows in latent heat exchanger

The sensible heat exchanger for the evaporator inlet flow and the entering seawater feed is divided in two

parts: one corresponds to the sensible heat exchanger between the exiting distillate and 50% of the seawater feed, and the other corresponds to the sensible heat transfer between the exiting brine and 50% of the seawater feed. To determine the price of the sensible heat exchanger, first a mass balance and an enthalpy balance are performed for each evaporator. The data are used to compute both the sensible heat exchanger area and the latent heat exchanger area. For dry centrifugal compressor, isentropic compressor work is calculated as follows:

(3) where; W = compressor work (J/kg) p1 = input compressor pressure (Pa) p2 = output compressor pressure (Pa) v1 = specific volume of steam at compressor inlet (m3/kg) k = isentropic constant = Cp / Cv = 1.3 or steam H2 = specific enthalpy of compressor exit (J/kg) H1 = specific enthalpy of compressor inlet (J/kg) c = isentropic efficiency of compressor = 0.85 (assumed)

Work supplied to the compressor increases the pressure and temperature. The compressor is relatively small at flow that is passed, so that it is adiabatic, it means a small number of energy is lost while heat exchange is out of the compressor. The objective is in order to increase gas pressure by using work as less as possible, which is possibly completed by making the compression process reversible. Work required in reversibly isothermal compression is less than that carried out in reversibly adiabatic compression. If the steam temperature is maintained close to the suction temperature by injecting water, the process becomes close to isothermal. Conventional centrifugal compressor does not enable water injection because high velocity blades could be damaged because of collision with the drops. Therefore, this research uses StarRotor compressor that operates at lower velocity and has strong component that could be resistant to liquid injection. StarRotor compressor uses gerotor that is positive shear apparatus. For water injection case, compressor work W is calculated (Holtzapple and Noyes, 2004) as follows:

(4) where;

= vapor enthalpy at compressor output (2) (J/kg) = vapor enthalpy at compressor input (1) (J/kg)

= liquid enthalpy at compressor input (J/kg)


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c = compressor efficiency = 0.85 (assumed) x = the amount of water injection that evaporates in compressor.

(5) where;

= entropy of liquid water at compressor inlet (J/(kg·K)) = entropy of steam at compressor inlet (J/(kg·K)) = entropy of steam at compressor exit (J/(kg·K)) Gas turbine is used in order to supply the compressor and generator work requirement. The Mars® gas

turbine is selected because it has been engineered for very high reliability and durability as well as ease of maintenance. Like Solar's other gas turbine families, Mars gas turbines are available for compressor, generator, and mechanical-drive applications. The gas turbine power output is 11,190 kW with fuel requirements of 10,600 kJ/kWh. Steam turbine is selected according to the steam turbine operating conditions such as inlet temperature steam at 673.15 K and 4.2403 MPa, outlet temperature steam at 319.26 K and 0.010135 MPa. After an isentropic expansion, the saturated vapor quality can be calculated as follows:

(6) where; x = saturated vapor quality Sl = entropy of superheated steam (kJ/(kg·K)) S2l = entropy of saturated liquid (kJ/(kg·K)) S2v = entropy of saturated steam (kJ/(kg·K)) The energy recovered from the steam turbine is as follows:

(7) where; W = energy recovered from steam turbine H1t = enthalpy of superheated steam (kJ/kg) H2t = xH2v + (1 – x)H2l (kj/kg) Therefore the total power for the proposed combined-cycle system is power from gas turbine added by power from steam turbine. To determine the price of Heat Recovery Boiler and Pumps, both are selected to handle a total of 0.876 m3/s of seawater (3.5% concentrated feed). This rate is based on distilled flow produced i.e. 50% of the seawater feed or 10,000,000 gallons/day (3.45 × 106 lbm/h or 0.4356 m3/s). The shaft work of each pump is calculated as follows:

(8)


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where; W0 = shaft work (kW) H = total dynamic head (kPa) mv = mass flow rate (kg/s) ρseawater = 1,021.90 kg/m3 pump = pump efficiency = 0.85 Distillate and brine discharges from the sensible heat exchanger do not need pumping. Even though both flows lose pressure in the heat exchanger, they still can flow out. The discharge pressure required is the sum of the pressure drop in the sensible heat exchanger plus the vapor pressure in the latent heat exchanger. The price is obtained from Reference (Ettouney et al., 2002). All pumps receive a correction factor of 1.6 because the pressure exceeds 1,035 kPa. In addition, a factor of 1.26 is used for anti-corrosion material for all pumps used in the seawater environment. Based on design and formula of the desalination system, performance and the capital cost are analyzed while producing water as much of 10 million gallon/day. Results and Discussion

Figure 3 indicates overall heat transfer coefficient that is accordance with condensation temperature and temperature difference of heat transfer, T, between condensing steam side and boiling liquid side. Overall heat transfer coefficient U approaches optimal maximum value 53,585 Btu/(h·ft2·oF) at overall temperature difference T = 6oF. Even though high heat transfer coefficient value could be obtained in theory, constant value of 24,900 Btu/(h·ft2·oF) has been used in technical design. To verify this value, an investigation is being prepared by the author.

Data presented in this research is obtained by using 10 million gal/day of seawater feed. This unit has heat exchanger sheets that are made of titanium 0.007 inch. Data obtained from this research results in heat transfer coefficient value (U) that is suitable to analytical estimation. Once the overall heat transfer coefficient is obtained, the area of the heat exchanger can be known and consequently its cost. Because of the low temperature differential, the compression energy cost is low. The unit has been used sporadically. Testing this unit with tap water and sodium chloride solution 5000 ppm causes very thin scale layers of calcium carbonate precipitates in vaporizing side of the rotors of the last two effects. There is no effort is made in order to separate scale from the surface. High brine concentration in the last two effects also gives additional resistant to heat flow across the film solution as a result of viscosity increasing and thermal conductivity decreasing of the brine. This factor is believed to cause U values are a little lower than that predicted. Figure 4 indicates system limit for overall energy balance. Compressor work (W) will enter to the system and go

out as thermal energy that is brought out by distillate and the brine . Therefore, energy balance is:

Assume T = Tb = Ts


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Figure 3. Calculated overall heat transfer coefficient

This temperature difference states temperature increasing of distillate and brine. In addition, this increasing is

approached temperature in sensible heat exchanger. The temperature difference is proportional to W/m; the proporsionality constant is indicated in Table 1. The result is observed so that at concentration of 7% and low T (among 2 and 6oF), the work requirement of compressor shaft is between 14 and 29 MJ/m3 that is acceptable range. Compressor in this unit is centrifugal StarRotor compressor. It is selected because while compared to centrifugal compressor, StarRotor gerotor compressor has technical benefit as follows: StarRotor gerotor compressor is cheaper ($450.000 vs $3.000.000). StarRotor gerotor compressor could retain toward water injection that makes the compression close to

isothermal that requires less work. StarRotor gerotor compressor could be designed in accordance with particular compression requirement. StarRotor gerotor compressor is efficient throughout broad range of operational condition.

The volumetric capacity is directly proportional to velocity and rather inversely proportional to pressure increasing because of back leakage of vapor in room between horse and its lobe. Three cases have been studied as indicated in Table 2.

Figure 4. Overall energy balance

Total mass balance: ms + mb = mf (6)


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Salt mass balance: mf xf = mb xb (7) Where;

Table 1. Proporsionality constant in temperature change equation

xf (g/kg) xb (g/kg) Cpb (kJ/(kg · K)) Cps (kJ/(kg · K))

35 50 3.917 4.209 0.07491

35 70 3.822 4.209 0.12450

35 100 3.689 4.209 0.16197

35 150 3.521 4.209 0.18937


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Table 2. Cases used in vapor compression Cases A B C

Tcond (oF) 6 4 2

Tsens (oF) 5.85 4.5 3.15

Salinity (g/kg) 70 70 70

Number of stages 4 4 4

Compressor energy (kJ/m3 distillate)

28.873 20.329 14.320

Basically, input energy to compressor motor consists of energy lost in electrical motor, energy lost in steering

belt, energy lost because of friction, and energy given to steam during compression. Figure 5 indicated compressor work for dry compressor at condenser temperature 176.7 oC as salinity function for six conditions: 0 oC, 1 oC, 2o C, 3 oC, 4 oC, and 5 oC. For every vapor compressed by compressor in 4-stage system, the unit produces 70 g/kg brine, so that at 6oF (3.3 oC) energy required by every product unit from the 4-stage unit is 30.2 kWh/thousand gallon (29 MJ/m3 distillate). The temperature is appropriate to reduce the energy because the lower condenser temperature, the higher compression energy required.

Figure 6 indicates compressor work for dry compressor at condenser temperature of 120oC. For 70 g/kg brine salinity produced at 3.3 oC, the compression work required is as much of 32.7 kWh/thousand gallon. Comparing the result to that at condenser temperature 176.7 oC, it is recommended to operate vapor compression unit at máximum temperature that is 176.7 oC in order to reduce compression energy. However, wet compressor has less work requirement, so that only wet compressor is assessed in Cases B and C. For case B, the work compressor is indicated in Figure 7. It is necessary to note here that a mechanical-vapor-compression unit of conventional single stage, and vapor compression unit of four stages that operate at the same temperature difference, compressor energy at multi stages is less than the energy in single stage because of salinity increasing in every stage compared to that of mechanical-vapor compression unit of conventional single stage. This fact indirectly states that work required by every product unit from four-stage vapor compression unit is less than that of conventional single-stage of mechanical-vapor-compression unit for the same T value regardless the evaporator type. As example of work calculation, assume situation required in order to recover 93 percent of water from various feed salinity in mechanical-vapor-compression unit that operates at average temperature 176.7 oC. For simplicity and data availability on sea salt solution, the feed is assumed to have sea water composition. Then, the situation will need compression energy that can be calculated by using Equation 4 and the results are indicated in Figure 7.

For case C, correlation of number of stages to inlet volume of compressor is indicated in Figure 8. Inlet volume of compressor is in the range of 67.16 m3 vapor/m3 distillate up to 222.97 m3 vapor/m3 distillate. It seems here that the inlet volume of compressor is around 118.6 m3 vapor/m3 liquid and higher while the stage number is less than 2. This is caused by the fact that energy consumption by rotors descends as a result of the high condensate rate, and specific energy consumed by the rotors descends as indicated in Figure 9. Comparing Figure 9 to Figure 7, it is clear that for 4 stages, compressor shaft work at T of latent heat exchanger 2 oF is less than that for single stage at T = 4 oF. However, it is not efficient to use the condition to operate unit of mechanical vapor compression distillation because the area of distillate sensible heat exchanger becomes larger. Figure 8 also indicates that for case C, it is not appropriate to use 4 stages because, it is clearly seen that the optimum condition to use minimum gas flow is while the number of stages is two.


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Figure 5. Compression work of desalination at condenser temperature of 176.7 oC

Figure 6. Compression work of desalination at condenser temperature 120 oC

Figure 7. Work of wet compressor shaft (T of latent heat exchanger = 4 oF, Seawater feed = 3.5%, Brine = 7%, Inlet T of heat exchanger = 174 oC)


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Figure 8. Gas flow at inlet compressor (T of latent heat exchanger = 2 oF, Seawater feed = 3.5%, Brine = 7%, Inlet T of heat exchanger = 175.5 oC)

Figure 9. Work of wet compressor shaft (T of latent heat exchanger = 2 oF, Seawater feed = 3.5%, Brine solution = 7%, Inlet T of heat exchanger = 446.53 K)

Figure 9 indicates correlation of number of stages to compressor work required to produce distillate water

with brine concentration 70 g/kg seawater. For 4 stages, the compressor shaft work is as much of 14,320 kJ/m3, whereas for single stage, compressor work is as much of 13,915 kJ/m3. If rotor design is developed, and brine salinity is as much of 5%, specific energy consumption by the rotors calculated from equation 4 is believed to be able to achieve 11,535 kJ/m3 or less, and total specific energy consumption by compressor and the rotors will be lower while using seawater whose salinity is as much of 3.5%. However, the area of latent heat exchanger required for temperature difference of 2 oF is quite larger than that for temperature difference 4 oF, which means the condition becomes more costly. Therefore, fixed capital investment is calculated only for case B which is considered as the most efficient condition for the system. Table 3 summarizes equipment required in innovative vapor-compression-desalination unit for recommended case B. This table gives utility requirement for this unit operating. The unit consists of four latent heat exchangers, four sensible heat exchangers for brine and distillate, and four pumps. Table 3 also indicates Lang Factor component used as much of 5.19 in order to estimate total Project cost from equipment cost. However, factor 2.2 is generally used for total project cost, equipment cost, and pipeline installed in order to determine unexpected cost. The cost is not estimation because it is a base for fund proposal. The cost resource is in accordance with technical estimation.


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Table 3. Summary of equipment and utility requirement for 10 million gallon/day of desalination unit

Code Name Description Purchasing Cost ($)

Utility Natural gas (kJ/kWh)

Electricity (kW)

Cooling Water

L Latent Heat Exchanger (4)

41,064 ft2 290,324

B Sensible Brine Heat Exchanger

218,939 ft2 1,547,901

D Sensible Distillate Heat Exchanger

239,077 ft2 1,690,277

P Seawater Feed Pump (4)

1480 kPa 147.05 kg/sec

80,000 992.75

GT Gas Turbine 800,000 10,600 11,190 DS Degassing System 25,000 C Compressor 450,000 8,760

ST Steam Turbine 300,000 5,032

G Generator 110,000 7,714

C Condenser 19,000 0.198 m3/s

HRB Heat Recovery Boiler (unburnt)

800,000

Total Equipment 6,112,502

Fixed Capital Investment = 5.19 × 6,112,502 = $31,723,885

Conclusions In order to design the sensible heat exchanger, first mass balance and energy balance are carried out for every evaporator. According to literatur data, dropwise condensation at steam side and pool boiling at liquid side enables to obtain overall heat transfer coefficient up to 53,585 Btu/(h·ft2·oF) in specific working condition. To enable dropwise condensation, recommended steam velocity should not higher than 1.52 m/s, and steam pressure should not more than 828 kPa gauge. Design of innovative heat exchanger/evaporator has been analyzed so that it can be implemented in desalination system with capital $31,723,885. This can be achieved by using thin sheet of titanium with smooth surface as its heat transfer surface. In addition, temperature difference as a result of flow across evaporator surface should be 4 oF. Nomenclatures Cc - Allowance for corrosion = 0 Cps - Specific heat of distillate [J/(kgm · K)] or [Btu/(lbm · oR)] Cpb - Specific heat of brine [J/(kgm · K)] or [Btu/(lbm · oR)] Ej - Efficiency of joints = 0.85 (spot examined joints) H1 - Specific enthalpy of compressor inlet (J/kg) H2 - Specific enthalpy of compressor exit (J/kg) H1t - Enthalpy of superheated steam (kJ/kg)

- Liquid enthalpy at compressor inlet (1) (J/kgm) or (Btu/lbm) - Vapor enthalpy at compressor inlet (1) (J/kgm) or (Btu/lbm) - Vapor enthalpy at compressor exit (2) (J/kgm) or (Btu/lbm)

h - Empirical constant = -2.1609 × 10-4 j - Empirical constant = -3.5012 × 10-7 k - Isentropic constant = Cp / Cv = 1.3 or steam mb - Rate of exiting brine flow (kg/h) or (lbm/h) mf - Rate of seawater feed flow (kg/h) or (lbm/h) ms - Rate of steam flow and condénsate (kg/h) or (lbm/h) p - Vapor pressure of salt water at the same temperature (N/m2) or (psi) p0 - Vapor pressure of water p1 - Input compressor pressure (Pa) p2 - Output compressor pressure (Pa)


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P - Maximum allowable pressure = 910.1 kPa ri - Inside radius of shell before corrosion allowance is added = 2 m S - Salinity (g salt/kg seawater) Sl - Entropy of superheated steam (kJ/(kg·K)) S2l - Entropy of saturated liquid (kJ/(kg·K)) S2v - Entropy of saturated steam (kJ/(kg·K)) Sm - Maximum allowable working stress (88.350 kPa for carbon steel SEA J412)

- Entropy of liquid water at compressor inlet (J/(kg·K)) - Entropy of steam at compressor inlet (J/(kg·K)) - Entropy of steam at compressor exit (J/(kg·K))

Tb - Boiling temperature of the seawater (K) or (oF) Tf - Temperature of the seawater feed (K) or (oF) Ts - Steam temperature (K) or (oR) x - Fraction amount of injection wáter that evaporates in the compressor xb - Fraction amount of salt in brine xf - Fraction amount of salt in seawater feed T - Overall heat transfer temperature differential (K) or (oF) Tcond - Overall heat transfer temperature differential in latent heat exchanger (K or oF) Tsens - Overall heat transfer temperature differential in sensible heat exchanger (K, oF) v1 - Specific volume of steam at compressor inlet (m3/kg) W - Compressor work (J/kg) Wt - Energy recovered from steam turbine x - Saturated vapor quality c - Compressor efficiency Acknowledgements

The writer gratefully thanks to Dr. Jorge Horacio Juan Lara Ruiz from Texas A&M University for all support and very valuable discussion regarding this research. References Al-Juwayhel, F., El-Dessouky, H., and Ettouney, H. (1997). Analysis of single-effect evaporator desalination systems

combined with vapor compression heat pumps. Desalination, 114: 253-275. Anonymous. (2000). Examining the economics of seawater desalination using the DEEP code. Technical Document

1186, International atomic Energy Agency, Vienna, Austria. Anonymous. (2005). Solar turbines, mars 100 compressor Set. http://mysolar.cat.com/cda/layout?m=41428&x=7,

13 December 2007. Dolloff, J. B., Metzger, N. H., and Roblee, L. H. S. Jr. (1969). Dropwise condensation of steam at elevated pressures.

Chem. Eng. Sci., 24: 571-583. Ejjeh, G. (2001). Desalination, a reliable source of new water. International Desalination Association, Belgium. Ettouney, H. M.,. El-Dessouky, H. T., and Gowing, P. J. (2002). Evaluating the economics of desalination. CEP

magazine, http://cepmagazine.org, 31 December 2002. Emerson, W. H., and Jamieson, D. T. (1967). Some physical properties of sea water in various concentrations.

Desalination, 3: 213-224. Griffith, P., and Lee, M. S. (1967). The effect of surface thermal properties and finish on dropwise condensation.

Int. J. Heat Mass Transfer, 10: 697. Haslego, C., and Polley, G. (2002). Compact heat exchanger Part 1: Designing plate and frame heat exchangers, CEP

magazine, http://cepmagazine.org, 30 September 2002. Holtzapple, M., and Noyes, G. (2004). Advanced vapor-compression evaporator and heat exchanger system.

Disclosure of Invention, Department of Chemical Engineering, Texas A&M University. Lubis, M. R. (2011). Desalination using vapor-compression distillation. Lambert Academic Publishing, Germany. O'Bara, J. T., Killian, E. S., and Roblee, L. H. S. Jr. (1969). Dropwise condensation of steam at atmospheric and

above pressures. Chem. Eng. Sci., 22: 1305. Peters, M. S., Timmerhaus, K. D., and West, R. E. (2003). Plant design and economics for chemical engineers, 5th

ed., McGraw Hill, New York, NY. Rose, J. W. (1967). On the mechanism of dropwise condensation. Int. J. Heat Mass Transfer, 10: 755. Ruckestein, E., and Metiu, H. (1965). On dropwise condensation on a solid surface. Chem. Eng. Sci., 20: 173.


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Grey Model for Stream Flow Prediction

1 Vishnu B. and 2 Syamala P. 1 Department of Land & Water Res. Eng., Kerala Agri. Univ., KCAET, Tavanur, India.

2 Department of Civil Engineering, National Institute of Technology Calicut, Kozhikkode, India. [email protected], [email protected]

Abstract – Design, operation and planning of water resources, irrigation and water supply systems require estimation of stream flow. A grey system or stochastic approach is required for dealing with the hydrological complexities of mid and long-term stream flow prediction. Generally relatively long period data series of stream flow records is required for the prediction using stochastic methods. In developing countries like India, availability of long period hydrological records is a problem. Grey system theory is applicable in the case of unclear inner relationship, uncertain mechanisms and insufficient information and requires only small samples for parameter estimation. Stream flow records of Bharathapuzha river basin, Kerala, India is subjected to grey analysis. Model parameters were estimated using least-squares method. Statistical indices for the developed models indicate their ability to predict stream flow in the river under study with reasonable accuracy. Keywords: GM Model, grey system theory, stream flow, India.

Introduction

Design and operation of water resources systems requires reasonably accurate prediction of stream flow. Planning irrigation and water supply for optimal water use also require estimation of river flow amounts. Since the analysis and prediction of stream flow at mid and long-term time scales are usually influenced by various uncertain factors like climate change, human activities etc., a stochastic or a grey system approach is required for dealing with this hydrological complexity (Gupta and Duckstein, 1975; Viertl, 1990; Deng, 1985; Xia, 1985,1989,1990). In situations where a large sample set is not easily available, a system may be considered in the status of poor, uncertain and incomplete information and is known as a grey system (Deng, 1989). Model parameter estimation of grey systems requires smaller samples compared to nondeterministic methods of probability statistics which require large samples. Hence grey systems approach is preferable to stochastic approach for dealing with the hydrological variability,especially in cases where there is non-availability of adequate hydrological records. In developing countries like India, where there is a paucity of reliable long period hydrological data, an approach of prediction requiring less amounts of hydrological data and fewer parameters is of more practical use than complex hydrological models.

Systems with partially known and partially unknown information are termed as grey systems (Liu and Lin, 2006). The hydrological processes responsible for the stream flow can be considered as grey processes due to their randomness. The randomness of the time series data may be reduced by the accumulated generating operation (AGO) (Deng, 1989). A once or twice accumulation of raw time series is normally enough to support the differential equation characterizing the grey system under consideration (Yu et al., 2001) and the next output from the model can be obtained by simply solving this equation (Trivedi and Singh, 2005). In the present study grey system theory is applied for the prediction of stream flow in Bharathapuzha river basin, Kerala, India. Materials and Methods Study area

Bharathapuzha is the second longest river in the south-west coast of India with a length of 252 km. The river basin of Bharathapuzha (10– 11 N, 76 - 77 E) is the largest of Kerala and has a total catchment area of 6186 km2 spread in Kerala and Tamilnadu states of India. Malampuzha reservoir supplying irrigation water is situated in this river and the river is a major source of water. River flow data compiled at Kelappaji College of Agricultural Engineering and Technology, Tavanur, Kerala from various sources like Central Water Commission, India, Water Resources and Irrigation Departments of Kerala have been used for the study. Grey system model

Xia (1989) detailed the application of grey system theory proposed by Deng (1982) to hydrology. It has multifaceted use to solve problems that are uncertain or incomplete in information. The grey prediction method is the most important method of grey theory to analyze and predict future data from the known past and present data. It has the advantage of building a model with few and uncertain data. Its unique feature is the development of a model for prediction from discrete time data with first order differential equation.


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Grey modeling (GM) generally involves GM(1, 1), GM(1, N) and GM(0, N) models. GM(h, N) represents hth order derivate model and N is the number of variables. Wen (2004) showed that grey models for order (h) greater than one does not exist. The first-order grey differential equation is adopted in this study because it may be able to depict the normal rapid response of watersheds to rainfall (Yu et al., 2001) and is less complicated to solve. The disorder and randomness of original data is reduced by ‘grey generation’, a data pre-processing method, to obtain regular sequential order of the original series. The grey generation is done using the accumulated generating operation (AGO) and the inverse accumulated generating operation (IAGO) produces the predictions for the original data series in the model.

The disorder and randomness of original data is reduced by ‘grey generation’, a data pre-processing method, to obtain regular sequential order of the original series. The grey generation is done using the accumulated generating operation (AGO) and the inverse accumulated generating operation (IAGO) produces the predictions for the original data series in the model. Let original time series data taken consecutively at equal time interval be expressed as

(1) Where is a sequence of raw data values and is the number of raw data values, which should be greater than 3. As per Deng, 1989 the following is the GM(1,1) model to predict the future value

where is an integer variable such that . The first order AGO of X is as follows (2)

Where is the sequence obtained through accumulating generation; that is, (3)

Where is an index variable that can take values from 1 to n and is the summation index which runs from 1 through . A first-order differential grey model may be expressed as a whitened linear differential equation:

(4)

Where ‘t’ is time and ‘a’ and ‘b’ are grey parameters. The parameters ‘a’, called developing coefficient and ‘b’, the grey input, are estimated by the least-squares method. A first-order differential grey model may be expressed as a whitened linear differential equation:

(5)

Where: is the first order inverse AGO (1-IAGO) and k represents time index. For discrete data in Equation (4) (Lee and Wang, 1998),

(6) Where is the background value which is taken to be the mean of the entries in Substituting Equation (5) and Equation (6) in Equation (4), the grey difference equation is represented as:

(7) As the data set starts at time t=1, Equation (7) may be expressed as

(8)

Equation (8) can be represented in matrix notation as Y=Uβ (9) The parameter vector β can be estimated by least-squares method as

(10) where is the estimate of β, is the transpose of matrix and is the inverse matrix of matrix. The predicted values for the data X1 from the AGO is

(11) where, time index k=0,1,2, …., n-1 From the predicted values of accumulated stream flow for different periods, the predicted values of stream flow can be estimated by applying inverse AGO (IAGO) to the Equation (11)

(12) or

(13)


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Results and Discussion The differential grey model as shown in Equation (13) was developed for stream flow data from the

Bharathapuzha watershed using grey system theory. The river is having considerable stream flow during months from June to December, the months in which the basin receives rainfall. Hence the stream flows in these seven months only were considered for the analysis. The stream flows at four river gaging stations, viz. Kuttippuram, Thrithala and Cheruthuruthy along the main river from downstream upwards in that order and one gauging station Thiruvegapura on a tributary, were analyzed. The least-squares method was applied for the estimation of the model parameters, which are given in Table. 1. It can be observed that the model parameters vary from one gauging station to other owing to the variation in watershed characteristics. The parameter ‘a’ indicates the grey response function in decay of the storage capacity and physiographical factors of the grey process in the watershed. The other factor ‘b’ explains the factors other than the above mentioned watershed characteristics responsible for variation in stream flow.

Table 1. Grey model parameters estimated using least-squares method

Gauging Station Grey Parameters A b

Kuttippuram 0.3335 1094.5155 Thrithala 0.4033 598.6059 Cheruthuruthy 0.3602 489.1365 Thiruvegapura 0.2969 339.1772

Figure 1. Observed and predicted stream flow at Kuttippuram gauging station

Figure 2. Observed and predicted stream flow at Thrithala gauging station


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Figure 3. Observed and predicted stream flow at Cheruthuruthy gauging station

Figure 4. Observed and predicted stream flow at Thiruvegapura gauging station

Table 1. Proporsionality constant in temperature change equation

Gauging Station RMSE1 NSE2 CC3 TIC4

Kuttippuram 61.5441 0.9245 0.9619 0.0659

Thrithala 34.7194 0.9502 0.9750 0.0705

Cheruthuruthy 32.0506 0.9043 0.9514 0.0798

Thiruvegapura 25.0713 0.9309 0.9656 0.0766 1. RMSE-root mean square error, 2. NSE-Nash–Sutcliffe model efficiency, 3. CC-correlation coefficient, 4. TIC-Thiel's inequality coefficient

The observed and predicted stream flow hydrographs are shown in Figure 1 to Figure 4. It can be observed from these figures that the actual and estimated values, especially the peak value, are in fairly good agreement. There is a close agreement in the rising limb of the observed and predicted stream flow graphs. Even though the recession segments of the observed and predicted stream flow hydrographs follow the same trend, the fluctuations in the observed values were smoothened out in the predicted curve. The model performance is evaluated by a number of statistical indices such as root mean square error (RMSE), Nash–Sutcliffe model efficiency coefficient (NSE),


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correlation coefficient (CC) and Thiel’s inequality coefficient (TIC). These indices for the grey prediction models for different gauging stations are given in Table 2. Coefficient of correlation values near to one indicates good correlation. The Nash–Sutcliffe model efficiency values are closer to one, indicating good model accuracy. The Thiel’s inequality coefficient’s values (TIC) are closer to zero, indicating a better forecast method. All the quantitative statistical performance indicators show the suitability of the grey system prediction models to the study area. Conclusion

Grey system prediction models derived for the study area were able to predict stream flows revealing close agreement with the observed flows as could be seen from their plot. The statistical model performance indicators confirmed the ability of the models to predict stream flows with accuracy in the area under study. The grey system analysis seems to be a boon to areas with scarcity of reliable long duration hydrological records. Nomenclatures

AGO = accumulated generating operation IAGO = inverse accumulated generating operation

GM(h, N) = hth order derivate Grey Model with N number of variables

= original time series data taken consecutively at equal time interval

= sequence of raw data values (i.e. time series data like rainfall)

= number of observed time series data

= the future predicted value of

= sequence obtained through accumulating generation

= an integer variable such that

= index variable that can take values from 1 to n

= the background value which is taken to be the mean of the entries in

= summation index which runs from 1 through ‘t’ = time ‘a’ = grey parameter called “developing coefficient” which is a grey response

function in decay of the storage capacity and physiographical factors of the grey process in the watershed.

‘b’ = grey parameter called “the grey input” which is a grey response function explaining factors of watershed characteristics responsible for variation in stream flow other than that of ‘a’.

= first order inverse AGO (1-IAGO)

= time index variable that can take values from 1 to n

; k=0,.., n-1 = predicted values of ; k=0,.., n-1 = predicted values of

RMSE = root mean square error NSE = Nash–Sutcliffe model efficiency

CC = correlation coefficient TIC = Thiel's inequality coefficient

Mm3 = million meter cube (106 m3)


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References Deng, J. (1982). Control problem of grey system. System & Control Letter, 1(5): 288-294 Deng, J. (1985). Special issue of grey system approach. Fuzzy Mathematic, 5(2): 1-25 Deng, J. (1989). Introduction to grey system theory. Journal of Grey System, 1(1): 1-24. Gupta, V.K., and Duckstein, L. (1975). A stochastic analysis of extreme droughts. Water Resources Research, 11(2):

221-228. Lee, R. H., and Wang, R. Y. (1998). Parameter estimation with colored noise effect for differential hydrological grey

model. Journal of Hydrology, 208: 1-15. Liu, S., and Lin, Y. (2006). Grey Information. Springer Verlag Inc., London. Trivedi, H.V., and Singh, J.K. (2005). Application of Grey System Theory in the Development of a Runoff

Prediction Model. Biosystems Engineering, 92 (4): 521-526. Viertl, R. (1990). Statistical inference for fuzzy data in environmetrics. Environmetrics, 1(1): 37-42. Wen, K. L. (2004). The grey system analysis and its application in gas breakdown and VAR compensator finding.

Journal of Computational Cognition, 2(1): 21-44. Xia, J. (1985). Conceptual model of hydrologic nonlinear system and grey parameters identification. Wuhan Institute

Hydraulic Electrical Engineering, 2(55). Xia, J. (1989). Research and application of grey system theory to hydrology. Journal of Grey System, 1(1): 43-52. Xia, J. (1990). A grey system approach applied to catchment hydrology. In: The Hydrological Basis for Water

Resources Management. IAHS Publ. No. 197. Yu, P. S., Chen, C.J., Chen, S.J., and Lin, S.C. (2001). Application of grey model toward runoff forecasting. Journal

of the American Water Resource Association, 37(1): 151-166.

Aceh International Journal of Science and Technology, 1(1): 20-25 April 2012

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A Study on Learning Pre-Algebra Using Interactive Multimedia Courseware Within Collaborative Learning Set-Up

and E-Mail Interactions

1Mohd Sazali Khalid, 2Sulaiman Yamin, and 3Sri Adelila Sari 1,2Universiti Tun Hussein Onn Malaysia, 3Faculty of Teacher Training and Education Syiah Kuala University

[email protected], [email protected], [email protected] Abstract – Many students at diploma level are weak in mathematics even after spending eleven years in Malaysian education system. However, throughout the world there are research studies been done with mixed results using technology and collaborative learning. The objective of this paper is to analyze the effect of learning pre-algebra using interactive courseware with collaborative learning by using STAD set ups with interactive courseware using e-mail facilities during team discussion only. Quasi experimental type research was used. The gain score (differences between post and pre test) between the two equivalent groups were obtained. Diploma Information Technology first year students in two different intake years 2009 and 2010 in UTHM were employed. ‘t-test’ results revealed the second group using e-mail is statistically significantly inferior to the group using purely interactive multimedia courseware CDiCL only with STAD team discussion. On average participants experienced higher gain scores in the first group (Mean = 3.28, SE=0.433), than participants in the second group (M=0.77, SE=0.354). This difference was statistically significant (t (74) = 4.51, p<0.05); however, it did show a medium effect size of r = 0.45. Some clinical interviews and audio-video recordings were taken to support that teams prefer using conventional collaborative learning method with more group discussions rather than e-mails and facebook in solving problem. Keywords: mathematics information technology, algebra, CDiCL, facebook.

Introduction Many students at certificate and diploma level are weak in mathematics even after spending eleven years in Malaysian education system. Computing courses in Malaysian tertiary institutions of higher learning take mathematics as the core subject where tutorials are sometimes spent as remedial. However, there are research being done using technology and collaborative learning with mixed results (Khalid et al., 2010a; Mays, 2005). According to a Tracer Study Polytechnic MOHE Malaysia in 2006, IT graduates were employed mainly in services industries where decision makings has to be made fast in the Kuala Lumpur stock exchange for example, was the most valuable asset sought for by prospective employers. To develop this a curriculum of mathematics in IT era was designed. Anecdotally, in year 2000 FTMM (Fakulti Teknologi Maklumat dan Multimedia) was operating as a department called JTMM under Faculty Engineering Technology, in KUiTTHO (Kolej Universiti Teknologi Tun Hussein Onn). As a result Diploma Mathematics IT 1 adopted UTM’s Diploma Computer Science syllabus and curriculum. Discrete Mathematics topics and tutorial (pen and paper) was the order since most of the mathematics lecturers graduated from UTM. In 2004 KUiTTHO was officially upgraded into the 17th full fledged public university in Malaysia called UTHM and JTMM became a faculty called FTMM which introduced Mathematics IT 1 and Mathematics IT 2 for the first year diploma students with all the mathematics topics still intact plus the introduction of laboratory activities (Khalid et al., 2006). The objective was to let the students see mathematics applications in information technology. License packages like SPSS and Matlab were incorporated into the syllabus since it took more rigorous statistical approach with probability distributions, permutations and hypothesis testing. Problem Based Learning (PBL) was tried in UTHM using Republic Polytechnic Singapore experience as the yardstick. Current issues

At diploma level many lecturers from the local universities found that mathematics was not rigorously understood even though the students who successfully entered the university programs with high grade score in SPM (equivalent to GCSE ‘O’ levels). For example statistics from Kelantan State Education Department (2003 – 2006) revealed the average rate of passes SPM Mathematics was 75% only. This means that 25% failed mathematics at SPM level. In spite of 75% passes, some of them were found to be struggling in mathematics, statistics and quantitative methods once they entered Diploma and degree studies especially on topics involving algebra (Khalid, 1990). Something must be done some how quickly since e-learning has become the in-things of today. More over algebra is the gate to many advance mathematical topics in the universities.

Many researches were done about the above problem with mixed results (Healy, 1998; Heid, 2002; Zain et al., 2006). In Malaysia, many young teachers complained that they could not deliver mathematics concepts very well in English which started 2003 during PPSMI. (Tan, 2007). PPSMI was introduced at Primary Year 1, Form 1 and Lower 6


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at the public schools. It was found that many senior teachers who were trained in English medium schools took administrative duties while the young teachers (aged 45 below) who had learnt and fully trained in mathematics in Malaysian language beginning 1979. Hassan (2008) studied on learners and teachers style using computers. He correctly pinpointed one thing - both parties have different strength and weaknesses as far as learning and teaching styles which did not match for the optimum benefit for the students’ side.

During PPSMI, in order to hasten many ideas, the Ministry introduced critical allowance schemes, computer notebooks for mathematics and science teachers and many kind of ICT courses were offered during the school holidays. At the earlier stages when this scheme was introduced many teachers were happy. But soon many reports came where computers were stolen from schools and some teachers misused the computers. Besides, many parents perceived that tuition in mathematics was more effective than schools. This is because young teachers are inexperienced (Puteh, 2003). Currently, all teachers are paying so much attention to examination results. The whole country was so obsessed with how many ‘As’ each school and candidate can get every time the examination result was announced . From this result the school is categorized into cluster schools and these schools are going to be treated differently from the ministry in terms of annual ‘budget’, staff recruitment and other incentives. One of them is they can hire their own set of teachers (PTA Talk in KISAS) and the school enjoyed better treatment. Unknowingly, sometimes creative teachers are temporarily sidelined. A creative teacher is defined as someone who is braved enough to teach differently from the syllabus (Schifter and Fosnot, 1993). Once the school is very focused to excel only in the public examination it was found the standard of questions posed by the teachers were steroetyped. What is asked are mostly public examination questions and nothing else. Without critical and challenging questions it is hard to produce holistic learning that produces first class engineers, scientists and professionals (Idris, 2006). Noraini claimed that students who were taught mathematics in visual mode understood mathematics better. But Healy (1998) disagreed when many visual aided students understood mathematics from the surface level only and this was insufficient for higher college mathematics.

One of the main features of cluster and smart schools is the employment of ICT in teaching mathematics and sciences. Advantages of computer-aided-instruction are increased student engagement and motivation, providing students with a greater level of individualized instruction (Barrow et al., 2008). Since mathematics is synonym to drilling and practice, ICT is looked as the rescue to teaching problems especially in remedial work. According to MOE INTEL 2007 report, USA experienced 20 – 30 percent remedial classes at high colleges and first year degree programs. When Malaysia is facing with remedial classes in polytechnics and colleges communities MOHE, it seems that USA, a developed country, is experiencing that too (Barrow et al., 2008).

Drilling and practicing is taken quite well at schools because item analysis by Mun and Tiong (2005) found that 50% of the PMR and UPSR questions set 2003 – 2006 was categorically put as simple, 30% are medium difficulty and 20% are challenging. Many ‘naughty’ teachers know that by drilling their students at easy and middle type of questions would suffice their students to pass in any public exam. As a result many students are not exposed at all to harder critical thinking skills since many teachers rushed with the syllabus. Once they are at the university the students look so lost. They cannot help themselves with internet to find important facts in mathematics. What was seen they used ICT not for studying related subjects but reading gossips.

Understanding the above issue FTMM was braved to introduce Mathematics IT syllabus for two semesters in Diploma Information Technology (DIT) Year 1. Assessment of this subject is 60: 40 favouring coursework than final examination. This style of evaluation and assessment is identical to polytechnic education assessment system in this country since the students in DIT programs were graduates from the polytechnics and college community MOHE. Smart school came with ICT technology. Zain et al. (2006) complained that not all school heads know how to instruct the teachers in using CD-ROMS supplied by Technology Education Department, MOE. These so called principals always focus on exam results while CD-ROM put forward many ideas that can come later. So it seems there is lacking in using teaching aids like CD at schools. MOE Project Report (2007) suggested the schools to introduce ICT into mathematics and science subjects beginning primary and secondary schools in order to create talented pool of engineers, scientists and entrepreneurs but they have some problems including time tabling in schools and getting smoother accessibility towards teachers in running ICT courses during school holidays. They suggested group blocking on certain specific day from the time table in order to reduce technical problem carrying ICT tools into classrooms. But the success of smart schools depends heavily on teachers’ attitude. Attitude, motivation are all related in working successfully among teams in society (Shane and Von Glinov, 2008). Here Shane and Von Glinov did not encourage any team to appoint a leader who has limited ability in a specified skill. Now Facebook is getting more popular not only among youngsters in social networking but also among teachers. They shared messages, pictures, video clips and they can use it for studying purposes. e -mails are popular too. Now how can we implement mathematics education using ICT in Malaysia. Thus a curriculum and syllabus for Mathematics IT came into UTHM. The objectives of this study is to analyze the effect of learning pre-algebra using interactive courseware with collaborative learning set up against a group that use mainly e-mails and facebook and determine whether e-mails and facebook help mathematics learning.


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Materials and Methods The structure of the experiment is shown in Figure 1. This structure was agreed since calculus came during Week 7

and Week 8 of 1DIT Mathematics I.T. syllabus. Between Week 3 to Week 6 they were exposed to more algebra, Discrete Mathematics and Series. CDiCL (Compact Disk interactive Collaborative Learning) used ADDIE methodology under multimedia interactive courseware development. It was tested in Polytechnic Kota Bharu, Kelantan and a secondary school in Pasir Mas, Kelantan in 2006. (Khalid, 2010). The content of the CD has more than 10 topics under pre-algebra, factorization and simplification. It was recommended that CDiCL would be more effective if it was used with lower size team of 3. Managing the class was much easier.

Figure 1. Basic Structure of the experimentation

Results and Discussion Quasi-experimental design was employed where it was not possible to randomize any student to participate. Group

I (Control using CDiCL and CL only) n=30; 22 girls 8 boys. The students were academically equivalent as their entry was controlled by MOHE. Learning processes

First week, they were explained about the study to compare effectiveness studying mathematics IT using CD-ROM and CL against another group learning mathematics using e-mail only). They were asked to sit for PRE-TEST and after ninth week the POST TEST was conducted. Both tests had similar questions. Marks from pre and post test are taken as coursework marks in their diploma program. They are divided into two different groups size 18 and 12 of them. The first group came at 0800 am and the second group came at 0900am. They were required to learn pre-algebra skills using CD-ROM called CDiCL which has 20 different modules. Each session they must cover at least 2 – 3 modules while solving word problem in between. This was to maintain focus all along the session. The instructor selected the team using math results from SPM. Each team has 5 members and they solved it collaboratively using STAD (Student Team Assessment Division) set up which has a leader, assistant leader, reporter, manager and time keeper. At the end of each session they must submit a report. Computing time is about 20 – 40 minutes *only. The rest of the session is used by the instructor (the first author) to explain recommended solution during the CL work.

Group II (using e-mails and facebook) - Experimented group (n=45) 30 girls 15 boys.First week, they were explained about the study to compare effectiveness studying Diploma Mathematics IT using e-mails and facebook against learning mathematics using CDiCL. They were asked to sit for PRE-TEST and after ninth week POST TEST was conducted. Marks from pre and post test were taken as coursework marks in their diploma program. Both tests have identical questions. They were divided into two different groups size 25 and 20 of them. The first group came at 0800 am and the second group came at 0900 am beginning 2nd week to the 9th week. They were required to learn pre-algebra skills using CDiCL that was already uploaded on the server. Each session they must cover at least 2 – 3 modules while solving word problem in between. This was to maintain their focus. During the learning process they were allowed e-mail facilities and facebook within 20 – 40 minutes only. To enhance e-mailing work half of each team sat in different room. The team members was selected using results from SPM (Sijil Pelajaran Malaysia). Each team has 5 members. However to reduce face to face discussion between peers in any team, few members of any team must come at 0900 am session but the team leader must come at 0800 am session. To prove their work, each team must submit a report to the lecturer. This was easily done by looking at the lecturers’ weekly e-mail activities. Computing time is about 20 – 40 minutes * per session. The rest of the time was used by the lecturer (the first author) to explain mathematics solutions during their e-mail and Facebook encounters. Learning outcome

The students obtained all their marked pre and post test after the 9th week with full elaboration by the first author. The recommended answers were put on paper for students’ notes. Results

The result was analysed using SPSS version 16.0. Descriptive and some basic statistics t-test was used in analyzing the effectiveness of these two groups. The first author was teaching both sets of students 2008 and 2009. This is to

|…………….|…………………………………………….|……………| Week 0 Week1 Week 9 Week 10

Pre-Test

CDiCL with elaboration(n=30)

Email & Facebook (n=45)

Post-Test Stop

Entry


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reduce biasness and any discrepancies (extraneous variables) in the teaching values. The first author has more than 20 years experience teaching mathematics at diploma level (Kota Bharu Polytechnic and UTHM). In order to explain the result, we are going to use Table 1 as a guide.

Table 1. Framework for explaining the outcomes

Input Process Output Teaching method (the INDEPENDENT VARIABLE)

Elaborated explanations, quality and quantity of explanations from CDiCL quality of interactions – Peer-to-peer; student-lecturer from Collaborative Learning Perceptions of peers and lecturers; E-mails, facebooks

Quantity of learning –score from test - DEPENDENT VARIABLE – gain score.

In this section two types of results are shown. Quantitative and qualitative results Quantitative results

Descriptive statistics in terms of the Gain score (difference between post and pre test score) is shown in Table 2. Here the control group mean is three times than the experimental group even though standard deviation between them is almost equal. This implies that they are equivalent in ability since all entries into UTHM were processed by MOHE in Kuala Lumpur. Since two groups of students were tested, an independent‘t-test’ statistics was employed. Table 3 has the details.

Table 2. Descriptive statistics of the two different participating groups

Table 3. Results of Independent Equal Variance t-test

From Table 3, Levene’s test produced non-significant (i.e. p >0.05) then the null hypothesis was accepted that

the difference between the variance is zero - which implies the variance are roughly the same and the assumption is tenable. For these data, Levene’s test is non-significant so we read the test statistics in the row labeled Equal Variance assumed. This again implies homogeneity of variances is met by looking at the mean difference of 2.51 and the standard error difference of 0.554. In the case of 2-tailed test of p equals to 0.0031 which is smaller than 0.05, we could conclude there was a significant difference between these two groups of 1DIT students in UTHM. In terms of the experiment we can infer that students are not equally excited to use a courseware CDiCL delivered through the server with some collaborative learning against another group of DIT students using e-mails and Facebook. Calculating the effect size, a score of 0.45 was obtained which is substantial (Field, 2000). Qualitative results

While doing the experiments, the following data were obtained through clinical interviews and audio video recordings (Table 4). This is to triangulate the above quantitative findings. What could be gained from this qualitative data was firstly many students enjoyed using e-mails and facebook since this was the trend among

Method Mean St. Error Group 1(control) CDiCL n=30

3.28 2.372 0.433

Group 2( Facebook and e-mails) n=45

0.77 2.314 0.345

Levene’s Test for equality of variance

t-test for equality of Means

Gain Score

F Sig. t df Sig.(2-tailed)

Mean Difference

Std. Error Difference

Equal variances assumed

Group1 1.078 0.303 4.51 74 .0031 2.51 0.554

Equal variances not assumed

Group2 - - 4.67 68.27 .002 2.51 0.554


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youngsters. However their mood could easily change if they faced difficulties in getting feedback from peers and handling problems to use symbols and notations in e-mail and facebook modes.

Table 4. Advantages and disadvantages of methods

Items and characteristics Advantages Disadvantages

CD-ROM known as CDiCL Easy to understand and control

Boring / not the state of the art

Collaborative learning for they are sitting in pairs

Peer to peer discussion on word problem. More members talking in malay. The mathematics concepts are relayed in malay by the instructor too.

The worthiness of their discussion depends on the readiness of the members in each team i.e., the discussion is more fruitful and effective in solving more word problems.

e-mails only; FB; they sit by themselves alone

It looked more conducive, the state of the art.

Interesting but lonely. The student cannot walk all over the places to discuss. They just e-mail their problems and suggested solution. Problem symbols and notations (noted).

e-mail They can write anything they like but malay was more used in their e-mails and this created nice conditions.

They cannot talk as freely as what they used to do all this time. They can only emails or Facebook. New experience.

Facebook They looked happier. They can see their friends faces.

They think more in giving opinions and criticisms.

Discussion

In this study 75 Diploma Information Technology from UTHM students took part and they were put into two different groups. One studied in 2008/09 session and the other one 2009/10 session. The first group used CDiCL courseware with collaborative learning set up while the second group practiced electronic mails and Facebook to learn algebra topics. The first author was the only mathematics instructor among the two groups. From the result section, e-mail group did not do so well as compared to CDiCL and collaborative learning group. The average gain score obtained from the e-mail group and Facebook is lower than the old collaborative learning group using CDiCL. This implies that stability among group members of 3 is important to be achieved as face to face discussion is more fruitful than e-mails and facebook during mathematics learning. And this concurs with Zain et al. (2006), Tan (2007), Hassan (2008) and Shane and Glinov (2008). May be the members lost their focus once they got facebook as the facility to learn since the students suddenly changed their mood to study using online computers facing symbol problems and this concurs with MOE INTEL 2007 report. Word problem solving exercises could be more effective in malay language (Khalid, 2010b) and this was so not well demonstrated by the second group using e-mails and facebook.

The contribution of this paper is that we could see students can do higher mathematics if they were trained to experience new things than their normal classrooms i.e., conventional encounters. This came with some creativity and innovation from lecturers’ sides i.e., trying collaborative learning method besides the use of teaching aid – CdiCL as a start. Their work in the computer laboratory must be guided with some sort of ‘word problem’ solving tasks within specified time per session in order for them to learn higher mathematics using youtube in future. The experiment in FTMM UTHM DIT Year 1 was differently done than schools that participated in MOE INTEL 2007 program where in UTHM more ‘solid questions‘ were prepared as the main guide in the computer laboratory work. In MOE Intel report 2007 some students complained they were more advanced than the teachers in getting correct web sites for learning purposes. The only limitation was this study had used UTHM diploma students only as sample and they were still new to this style of learning in the first semester. Perhaps if this approach is tried in degree programs with bigger size of samples running across different faculties in UTHM and/or in different universities, the result could be more applicable for the usage of future teaching and learning strategies. Another obstacle was to understand algebra the sample had used English and Malay when mathematics algebra itself has its own language and concepts as well. From interview, few students complained – their understanding in algebra did not match with their marks at all and they did face symbol problems in Facebook and e-mail interactions. In sum, these students had gained few learning and teachings skills from this study to be used in the coming semesters.

Conclusion

This study had used quasi-experimental method with two batches of Diploma IT students 2008/09 and 2009/10 in UTHM (N=75). It presented a pedagogical approach i.e., using computers in learning mathematics in Collaborative Learning set-up as compared to learning using e-mails and facebook. The former group did better from social interaction between teams as found in their gain scores (difference in marks between Post and Pre Tests) as compared to the latter. New learning and teaching experience were obtained among the participants and symbols and notation problems were faced during e-mails and Facebook interactions.


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Acknowledgement

Vice Chancellor UTHM and Dean FTMM/FSKTM for allowing us conducting this study. Special thanks goes to 1DIT students batch 2008/09 and 2009/10 for participating. Technicians Mr Razzaly and Mr Mohd AlHafiz were very instrument in producing successful environment for this study. Madames Siti Mahfuzoh Wasikon, Noraini Ibrahim and Miss Nurul Nadzirah Hairani 3BIT were acknowledged in preparing this paper. References Barrow, L., Debraggio, E., and Rouse, C.E. (2008). Failing in mathematics.(url address:

http://www.voxeu.org/index.php?q=node/2722 ) accessed on 26 July 2011. Field, A. (2000). Discovering Statistics using SPSS. 2nd Ed. London: Sage Healy, J.M. (1998). Failure to connect: How computers affect our children’s minds – for better and worse. USA:

Simon and Schuster. Heid, M.K. (2002). Computer algebra systems in secondary mathematics classes: The Time To Act is Now!”.

Mathematics Teacher, 95(9): 662-667 Hassan, R. (2008). How do learners respond to computer Based learning material which has been designed to suit

their particular learning style. Ph.D thesis. Warwick University, UK. (Unpublished) Idris, N. (2006). Teaching and learning of mathematics. Making sense and developing cognitive abilities. Utusan

Publications and Distributors Sdn Bhd, Kuala Lumpur. (Unpublished). Mays, H. (2005). Using the results of diagnostically testing to promote mathematical pedagogical knowkedge.

Teacher Education: local and global. Australian Teacher Education Association 33rd Annual Conference proceedings., pp 310-316, ATEA, Australia.

MOE Intel Project Report. (2007). School adoption project phase 1. Ministry of Education Malaysia and Intel Malaysia. 1st edition. Kuala Lumpur: Educational Technology Division, MOE , and Intel Malaysia. ISBN 978-983-3244-87-4.

Khalid, M.S,, Hassan, H., Arbaiy, N., Afip, Z.A., and Abdullah, N.A. (2006). Statistical mathematics – laboratory activities. Teaching module. Parit Raja: UTHM Publication.

Khalid, M.S., Alias, M., Razally, W., Yamin, S., and Herawan, T. (2010a). The effect of using an interactive multimedia courseware within a collaborative learning environment on learning pre-algebra concepts. Procedia Social & Behavioural Sciences, 8: 571-579.

Khalid, M.S, K. (2010b). A study using interactive multimedia courseware in learning pre-algebra among polytechnic students in Malaysia. PhD thesis UTHM, Parit Raja. (Unpublished).

Mun, C., and Tiong, O.C. (2005). Siri Teks Referens SPM 4&5. Pearson Longman, Petaling Jaya. Field, A .(2000). Discovering statistics using SPSS for windows (2nd Edition). Sage, London. Healy, J.M. (1998). Failure to connect: How computers affect our children’s minds – for better and worse. Simon

and Schuster, USA. Pusat Perkembangan Kurikulum (2001). Kemahiran Berfikir dalam Pengajaran dan Pembelajaran. Kuala Lumpur:

Kementerian Pendidikan Malaysia. Puteh, M. (2003). Factors associated with mathematics anxiety. UPSI, Tanjung Malim. Schifter, D., and Fosnot, C. T. (1993). Reconstructing mathematics education. Stories of Teachers Meeting. The

Challenge of Reform. Teachers College Press, New York. Shane, M., and Glinov, V. (2008). Organization behavior. 4th Ed. Mc Graw, Boston. Tan, M. (2007). Teaching mathematics and science in English in Malaysian Schools: Profiles of Teacher Learning

within the context of educational reform. Proceedings of COSMED 2nd International Conference Math and Science Education. Penang: Nov 2007: 142 – 151.

Tracer Study. (2006). Projek kajian graduan politeknik Kementerian Pendidikan Malaysia bagi tahun 2003 – 2005 Accessed.ttp://www.politeknik.edu.my/WebSept07/PENERBITAN/TRACER_STUDY_2006/laporan_final_2006.pdf on 5 May 2009

Zain, M.Z.M., Majid, O., Luan, W.S., Fong, S.F., Atan, H., and Idrus, R.M. (2006). Computers in Malaysian smart school: The changing of technologies and mindsets. Malaysian Journal of Educational Technology, 6(2): 61-70.


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Electrochemistry Study on PVC-LiClO4 Polymer Electrolyte Supported by Bengkulu Natural Bentonite

for Lithium Battery

1Ghufira, 2Sal P. Yudha, 3Eka Angasa, and 4Jhoni Ariesta Chemistry Department, University of Bengkulu

[email protected], [email protected], [email protected], [email protected] Abstract – In this research bentonite was used as filler to produce polymer electrolyte (PVC-LiClO4). Some weight variation of bentonite have been made by addition, such as 0% wt/wt; 5% wt/wt ; 10% wt/wt ; 15% wt/wt ; 20% wt/wt ; and 25% wt/wt of bentonite to the mixture of 0,5 gram of PVC and 0,125 gram of LiClO4. Ionic conductivity of polymer electrolyte was tested using impedance spectroscopy. The result of the research was showed that a mixture of PVC-Bentonite(10% wt/wt)-LiClO4 gives the highest ionic conductivity (4,86 x 10-3 S.Cm-1). This result indicated that the presence of natural bentonite can be used as a filler in the current composite polymer electrolyte and can increase the ionic conductivity of the polymer electrolyte. Keywords: Polymer electrolyte, bentonite, ionic conductivity, natural inorganic filler.

Introduction

Solid-state lithium polymer batteries may be one of the best choices for electrochemical power source of the future characterized by its high energy densities, good cyclability, reliability and safety. PEO-LiX based polymer electrolytes had received extensive attention, for its potential capability to be used as candidate material for the traditional liquid electrolytes, since Wright et al. found that the complex of PEO and alkaline salts had the ability of ionic conductivity in 1973 (Jingyu, 2004). Lithium ion polymer battery is made from lithium ion which holding to polymer electrolyte. There are many research has done to synthesis polymer electrolyte, but filler matrices are synthetic organic polymer which is more expensive than inorganic chemicals (Ahmad, 2009). Biodegradable polymer electrolyte was developed to reduce environmental pollutions. A research using LiClO4 which is dopped to acetic sellulose has been synthesized as biodegradable polymer electrolyte (Sivakumar, 2007). Another biodegradable polymer electrolyte is based on PCL (Poly(ε-caprolalactone)) with PC (polycarbonate) as plastisizer and lithium salts. PCL is synthetic polymer that can degrade in aqueous medium or in contact with microorganisms. Pure PCL/LiClO4 was investigated as a biodegradable solid polymer electrolyte. This polymer showed a wide electrochemical stability window (5.5V vs. Li), good mechanical properties, and total biodegradation in soil compost at 60 days (Fonseca, 2007).

Polyvinyl chloride (PVC) is thermoplastic polymer, inert and wide range products with low cost of production. PVC is available as resin with hard or flexible characteristics, usually used by plastisized or prepared in a mixture or heterogeneously dopped with inorganic particles. PVC has been used as a doping in blend of LiPF6 and LiCF3SO3 salts system.(Subban, 2004). Rajendran (2008) investigated the blend-based polymer electrolyte consisting of polyvinyl chloride (PVC) and polyethylene glycol (PEG) as host polymers and lithium perchlorate (LiClO4) as the complexing salt and TiO2 as ceramic filler. The conductivity results indicate that the incorporation of ceramic filler up to a certain concentration (15 wt.%) increases the ionic conductivity and have mechanical stability.

Zeolite is microporous material with large surface area, having two dimensional channel and high Lewis acid characteristics. A research with ZSM-5 as filler has been investigated by Jingyu (2004). ZSM-5 is synthetic zeolite which usually used in industry. ZSM-5 have dimensional structure, high activity and selectivity for some reactions, selective on molecular shape and not easy to deactivated (Mustaim, 1997). Jingyu (2004) reported that ZSM-5 as filler in composite polymer electrolyte PEO-LiClO4-LiZSM5 could enhance the ionic conductivity. The addition of ZSM-5 could improve the Li+ transference number of the CPE effectively. Based on the current results, we would like to explain a development using natural resources such as Bengkulu bentonite. In this work we studied the effect of the addition of bentonite of Bengkulu natural resources as filler in polymer electrolyte PVC-LiClO4. The ionic conductivity measured by impedance spectroscopy. Materials and Methods

Natural bentonite was taken from Desa Taba Terunjam Kecamatan Karang Tinggi Bengkulu Tengah, polyvynil chloride (PVC MW. 43.000) from Sigma Aldrich, tetrahydrofuran (THF) and LiClO4 from Merck were


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used as received. Destilled water was available at Chemistry Laboratory, Faculty of Mathematics and Natural Science, University of Bengkulu. Instrumentation

Balance, magnetic stirrer, glass apparatus pH meter were available at Laboratory of Chemistry, Department of Chemistry, Faculty of Mathematics and Natural Science, University of Bengkulu (Unib). Procedure Preparation of Bentonite

Raw bentonite was taken from natural deposit in desa Taba Terunjam Kecamatan Karang Tinggi Bengkulu Tengah and there was no special treatments when it was taken. Raw bentonite from natural deposit was cleaned and grinded into small pieces. The cleaned benonite then washed using aquabidest to neutralize the acidity and dried under the sun shine, which after the bentonite was crushed into powder and filtered to get homogeny particle size. It was stored in desicator till it used. Preparation and characterization of Polymer Electrolyte PVC-Bentonite-LiCiO4

Briefly, 0,5 g polyvynil chloride (PVC : molecular weight = 43.000) was added into 25 mL of tetrahydrofuran (THF). The mixture then stirred at room temperature for 15 minutes to get homogeneous solution. 0,125 g LiClO4 and bentonite were added into reactor and was stirred at room temperature for 24 hours. Bentonite was added in variety of %wt (5 %, 10 %, 15 %, 20 %, 25 %) of total weight of solid chemicals. The homogen mixture then poured into petridish and dried at ambient temperature. The polymer electrolyte film then stored in desicator before the ionic conductivity measurement. Ionic conductivity was measured using impedance spectoroscopy HIOKI 3522-50 LCR HiTESTER. Results and Discussion

Bentonite with homogen particle size (53 µm) was used to synthesize polymer electrolyte PVC-bentonite-LiClO4. Bentonite was added in variety (0 %; 5 %; 10 %; 15 %; 20 %; 25 %) of total weight PVC + LiClO4. Polyvynil chloride (PVC : molecular weight = 43.000) was added into 25 mL of tetrahydro furan (THF). The mixture then stirred at room temperature to get homogen solution. 0,125 g LiClO4 and bentonite were added into reactor and was stirred at room temperature for 24 hours. In polar solvent, like water, bentonite will be suspended (Lubis, 2007). Bentonite also suspended in THF which is polar solvent. According to Daintith (1990), the suspension is a mixture comprising solid particles suspended in fluid. In this case the solid particle is bentonite and the solution are PVC, THF and LiClO4. After the blend was homogen, it poured into petridish and dried at room temperature. The polymer electrolyte film then stored in desicator before the ionic conductivity measurement. Dried polymer electrolyte films are shown in Figure 1.

Figure 1. PVC-bentonite- LiClO4 films with different % wt of bentonite (a) 0 % (b) 5 % (c) 10 % (d) 15 % (e) 20 % (f) 25 %

Ionic conductivity of Polymer Electrolyte PVC-Bentonite-LiCiO4

Ionic conductivity of polymer electrolyte PVC-bentonite-LiClO4 was measured using impedance spectroscopy. In this study nafion NR212 was used as reference.Table 1 and Table 2 are shown ionic conductivity of nafion NR212 Dupont and polymer electrolyte PVC-bentonite-LiClO4 respectively. In Table 1 the average ionic conductivity of Nafion NR212 was 7,70 x 10-2 S.Cm-1.

a b c

d e f


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Table 1. Ionic conductivity of Nafion NR212 Dupont

Nafion NR212 was used as reference because nafion polymer having good chemical stability and ionic

exchange in the same time. Nafion NR212 are widely used as proton exchange membrane in fuel cell. Bentonite is aluminium or magnesium silicate compound in crystal form with variety content of lime, alkali, and iron and hydrated water. Based on the mineral analysis, most of bentonite is montmorillonite and the rest are kaolinite, Illit, feldspar, gypsum, volcanic ash, calcium carbonate, quartz and other minerals. So it also called as montmorillonite mineral. LiClO4 selected as the salt in this study because it has high solubility in various solvents, did not undergo oxidation at the anode, has a better conductivity than LiF3CSO3 and LiBF4, as shown in the results of research on the polymer poly (-caprolactone) (Fonseca,2007), and relatively stable against reduction than LiPF6 (Zhang, 2001).

In the Table 2 ionic conductivity of polymer electrolyte with 0 % - 10 % of bentonite were increase, but the ionic conductivity of polymer electrolyte with 15 % - 25 % of bentonite were decrease. Polymer electrolyte with 10 % of bentonite giving the highest ionic conductivity with 4,86 x 10-3 S.Cm-1, and the lowest is polymer electrolyte with 0 % of bentonite with 2,21 x 10-4 S.Cm-1. This result indicate that bentonite as natural filler can increase ionic conductivity of polymer electrolyte PVC-LiClO4. Introduction of bentonite filler into polymer electrolyte system will make the electrolyte more amorf and promote more free lithium ion (Li+) into the system. Bentonite itself is negatif charge, so it has possibility to promote cation exchange. The charge happened because of isomorph substitution.

Table 2. Ionic conductivity of PVC-Bentonit-LiClO4

Sample Average Thickness (Mm) Conductivity (Siemen.Cm-1) Average Conductivity

(Siemen.Cm-1) 0% 0,276 2,46 x 10-4 2,28 x 10-4 - 2,37 x 10-4 5% 0,347 6,01 x 10-4 6,10 x 10-4 6,14 x 10-4 6,08 x 10-4 10% 0,444 4,69 x 10-3 4,89 x 10-3 4,99 x 10-3 4,86 x 10-3 15% 0,391 1,67 x 10-3 1,70 x 10-3 1,66 x 10-3 1,68 x 10-3 20% 0,441 4,98 x 10-4 4,65 x 10-4 5,33 x 10-4 4,99 x 10-4 25% 0,335 - 9,78 x 10-4 9,74 x 10-4 9,76 x 10-4

The addition of bentonite with 10 % of total weight, made the polymer electrolyte has the same number of

cation with LiClO4, because Li+ in LiClO4 removed to coordination system in polymer. Ion Li+ exchange will decrease isolated hydroxyl level, but H bond will increase. It shows that Li+ coordinated by octahedral structure of bentonite through atom O of free Al-O-H group or free Si-O-H group. It makes stronger interaction between bentonite and PVC-LiClO4 and the ionic conductivity will increase. Figure 2 show that bentonite particle is porous particle. The size of the particle is 53 µm and it spread evenly througout the polymer electrolyte film. Bentonite particle were succesfully introduced to polymer electrolyte PVC-LiClO4 system as seen in Figure 2(b).

Ionic conductivity was decreased with addition of 15 % - 25 % wt bentonite. It seems the addition of bentonite made the system saturated by agglomeration of bentonite and decreasing the movement of ion in polymer chain. Membrane with higher ionic conductivity (> 1.10-5 S.cm-1) can be used as fuel cell. It can be used as environmental friendly fuel cell because no polution occured. Based on the result, polymer electrolyte PVC-Bentonite-LiClO4 can be recommended as fuel cell with high ionic conductivity (4.86 . 10-3 S.cm-1) it shows that bentonite from Bengkulu can be used as natural filler to increase ionic conductivity of solid polymer electrolyte.

Figure 2. SEM image of PVC-bentonite (10 % wt)-LiClO4 (a) 500 magnification (b) 2500 magnification

Sample Average Thickness (Mm) Conductivity (Siemen.Cm-1) Average Conductivity

(Siemen.Cm-1)

NAFION NR212 Dupont 0,056 7,83 x 10-2 7,57 x 10-2 7,70 x 10-2 7,70 x 10-2

(b) (a)


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Conclusion Six different polymer electrolyte systems consisting of PVC–bentonite–LiClO4 (bentonite = 0, 5, 10, 15, 20,

25 wt.%) have been studied. Of the five films, the film with 10 % wt of bentonite is found to be the best on the basis of conductivity. The conductivity of the polymer electrolyte is found as 4.86 x 10-3 S cm−1. Hence, natural bentonite look very promising to be used as natural filler in polymer electrolyte systems. Acknowledgement

This research was supported by Kementerian Pendidikan Nasional (Kemdiknas) Indonesia via Direktorat Jenderal Pendidikan Tinggi (DIKTI) Jakarta. This research dedicated to our colleague Mrs. Juniarti Isnaini (in memoriam) References Ahmad, A., Yusri, MA.R., Siti Azizah, M.N., and Reduan, M.A.B. (2009). Preparation and characterization of PVC-

Al2O3-LiClO4 composite polymeric electrolyte. Sains Malaysia, 38: 483-487. Daintith, J. (1990). Kamus lengkap kimia, edisi baru. Erlangga, Jakarta. Fonseca, C.P., Cavalcante, F.J.R., Amaral F.A., Zani Souza, C.A., and Neves, S. (2007). Thermal and conduction

properties of a-PCL-biodegradable gel polymer electrolyte with LiClO4, LiF3CSO3 and LiBF4 salts. Int. J. Electrochem. Sci., 2: 52-63.

Jingyu, X., Xiaomei, M., Mengzhong, C., Xiaobin, H., Zhen, Z., and Xiaozhen, T. (2004). Electrochemistry study on PEO-LiClO4-ZSM5 composite polymeric electrolyte. Chinese Science Bulletin, 49: 785-789.

Le Pluart, L., Duchet, J., Santereau, H., Halley, P., and Gerard, J.F. (2003). Rheological properties of organoclay suspensions in epoxy network precursors. Applied Clay Science, 25(3-4): 207-219.

Lubis, S. (2007). Preparasi bentonit terpilar alumina dari bentonit alam dan pemanfaatannya sebagai katalis pada reaksi dehidrasi etanol, 1-Propanol serta 2-Propanol. Jurnal Rekayasa Kimia dan Lingkungan, 6(2): 77-81.

Manoratne, C.H., Rajapakse, R.M.G., and Dissanayake, M.A.K.L. (2006). Ionic conductivity of Poly(ethylene oxide) (PEO)-Montmorillonite (MMT) Nanocomposite prepared by intercalation from aqueous medium. Int. J. Electrochem. Science, 1: 32-46.

Mustaim. (1997). Konversi zeolit alam menjadi ZSM-5. Master Theses Institut Teknologi Bandung, Bandung. Ozer, B.B.P. (2008). Development of carbon black-layered clay/epoxy nanocomposites. The Science and Engineering

of Izmir Institute of Technology, Turki. Rajendran, S.,M., Prabhu, R., and Rani, M.U. (2008). Characterization of PVC/PEMA based polymer blend

Electrolytes. Int. J. Electrochem. Sci., 3: 282-290 Sivakumar, M., Subadevi, R., Rajendran, S., Wu, H.C., and Wu, N.L. (2007). Compositional effect od PVdF-PEMA

blend gel polymer electrolytes for lithium polymer batteries. European Polymer Journal, 43: 4464-4473. Subban, R.H.Y., Yahya, M.Z.A., Puteh, R., and Arof, A.K. (2004). Two percolations model for conductivity-salt.

Indonesian Journal of Physics, 14: 51-53. Zhang, X., Pugh, J.K., and Ross, N. (2001). Evidence for epoxide formation from the electrochemical reduction of

ethylene carbonate. Electrochemical and Solid-State. Letters, 4(6): A82-A84.


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Functional Data Analysis of Multi-Angular Hyperspectral Data on Vegetation

1Sugianto, and 2Shawn Laffan

1Remote Sensing and GIS Laboratory, Syiah Kuala University, Banda Aceh 23111, Indonesia, 2School of Biological Earth and Environmental Science, The University of New South Wales, Australia.

__________________________________________________________________________________

Abstract - The surface reflectance anisotropy can be estimated by directional reflectance analysis through the collection of multi-angular spectral data. Proper characterization of the surface anisotropy is an important element in the successful interpretation of remotely sensed signals. A signal received by a sensor from a vegetation canopy is affected by several factors. One of them is the sensor zenith angle. Functional data analysis can be used to assess the distribution and variation of spectral reflectance due to sensor zenith angle. This paper examines the effect of sensor zenith angles on the spectral reflectance of vegetation, example on cotton leaves. The spectra were acquired in a green house trial in order to address the question ‘how much information can be obtained from multi-angular hyperspectral remote sensing of vegetation?’ The goals of the functional data analysis applied in this paper is to examine the Functional Data Analysis approach was applied to analysis multi-angular hyperspectral data on cotton, highlighting various characteristics of cotton spectra due to sensor view angles, and to infer directional variation in an outcome or dependent variable with different zenith angles. Keywords: Functional data analysis, multi angular hyperspectral, zenith angle.

__________________________________________________________________________________ Introduction

The physical interpretation of hyperspectral remote sensing for vegetation has been hampered by anisotropic surface reflectance (Bruegge et al., 2000). This is because vegetation properties are not generally perfectly diffuse reflectors, and sunlight reflected from vegetation exhibits a significant degree of anisotropy (Settle, 2004). The surface reflectance anisotropy can be estimated by directional reflectance analysis through the collection of multi-angular spectral data (Chooping et al., 2003; D'Urso et al., 2003; Widen, 2004). Proper characterization of the surface anisotropy is an important element in the successful interpretation of remotely sensed signals. However, proper characterization of surface anisotropy needs perfect measurement of illumination and modelling. This is not an easy task in remote sensing. It involves consideration of factors such as land surface properties, sensor view angles, reflectance and scattering, and sun incident angles.

This problem has received attention in remote sensing through research on multi-angular measurement of hyperspectral data. The effect of sensor viewing geometry on vegetation spectra can be assessed by measuring the spectral reflectance of the target at different sensor positions. A handheld spectroradiometer can be mounted on a goniometer, a hemispherical structure, to simulate multiple viewing angles and sensor positions. The importance of directional spectral reflectance is that different zenith angles can create variation in spectral reflectance, inhibiting the analysis of the spectral characteristics.

Recent developments in multi-angular space borne hyperspectral remote sensing provide directional spectral reflectance of the vegetation canopies. The first step, however, is to measure the multi-angular spectral reflectance at ground level. Crucial factors that need to be considered when collecting multi-angular hyperspectral data are how the data is distributed along the wavelength, the variance of the data, and what additional information can be generated by collecting spectra from multiple angles.

Data obtained with a spectroradiometer can be used to model the spectral reflectance. However, there are still assumptions that need to be considered in dealing with spectral data collected from the field such as variation and distribution of the data due to viewing sensor geometry. Sensor viewing geometry is related to the sun illumination. Handling this factor can be achieved by measuring multi-angular spectral reflectance and analysing them in functional relationship between factors affecting them and the spectral reflectance characteristics of the targets. The functional data analysis implemented in this research includes an assessment of the effect of smoothing basis functions, functional principal component analysis, functional linear modelling and functional analysis of variance (Ramsay and Silverman 1997, 2002) There are two types of analysis presented in this paper, wavelength basis and zenith- angle basis.


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Materials and Methods Goniometer setting and cotton spectral collection

A field goniometer was used with mounted of spectradiometer. A goniometer is a mechanised device that characterises radiance as a function of angle and allows the operator to acquire spectra at different zenith angles. The spectroradiometer was put one meter above the canopy attached to goniometer with a 10° instantaneous field of view (IFOV). The spectroradiometer used is an Analytical Spectral Devices (ASD) Fieldspec UV-NIR CCD spectroradiometer (ASD, 1999). The ASD spectroradiometer records a spectrum from 325 - 1075 nm (Visible to Near Infra Red wavelenght). This device is post-dispersive, meaning it can be exposed much higher levels of ambient light outside laboratory controlled conditions. The average band interval is 1.5 nm. For the purposes of this research, a subset of spectra is used, selecting the spectral wavelength range 400 to 950 nm (412 bands).

The cotton plant used in the trial is Siokra V-16 cultivar. This cultivar is a conventional and non-genetically modified variety (CSD, 2003), The cultivar were grown in a greenhouse experiment at the University of New South Wales. The temperature and humidity were maintained at 18-30°C with 55-70% humidity during the experimental growing season. The 25 cm diameter-pots were used to grow the cultivar. Watering was monitored to replicate water consumption during the growing period of the cotton cultivar at the field at Iffley Farm, between 410 mm and 610 mm during a seven-month growing period. Water consumption of cotton increases significantly through the plants’ development, during vegetative and generative period, and then decreases near harvest time. The cotton spectra were collected using the ASD spectroradiometer attached to the field goniometer (Figure 1). Calibration was performed for each measurement using a spectralon® standard reflectance (ASD,1999).

Figure 1. Illustration of the goniometer set up for multi-angular spectral data collection

To prevent unwanted background scattering and absorption from the surrounding area, a black plastic cover was

placed underneath the canopy and over the surrounding area to minimise reflectance from the surrounding area. The spectroradiometer was located one metre above the foliage. A 10° spectroradiometer foreoptic was used to create a FOV area of 240.46 cm². Spectral reflectance readings were taken as the average of 25 readings and repeated five times for each view angle position relative to the target. The azimuth and zenith angles position of the sensor were determined using a compass and clinometers attached to the spectroradiometer.

Spectral measurement was conducted under natural light conditions between 10 AM and 2 PM during clear sky conditions. The hot spot effect was avoided by not measuring the spectra where sensor zenith angle and solar zenith angle were at the same position. The solar azimuth angle was assumed to have small variation during spectral data collection in this time. The direction of zenith angles to collect multi-angular reflectance was set facing northeast (45° azimuth) to southwest (225° azimuth). The angle between northeast to nadir is denoted using a positive sign and nadir to southwest direction is denoted using a negative sign. The zenith angles are 50°, 40°, 30°, 20°, 10°, 0°, -10°, -20°, -30°, -40°, and -50°, where 0° is the nadir position.

Two factors need to be considered with the analysis of spectral reflectance data during functional data conversion, wavelength and zenith angle basis function analyses. The wavelength basis function treats the reflectance value as a function of bands (or channels). For the wavelength basis, the x value is the wavelength and y value is the reflectance. For the zenith angle function, the x axis is the angle and the y axis is the reflectance. Figure 2 illustrates the difference between the analysis of wavelength and zenith angle basis functions. The wavelength functions treat the wavelength as the major component that affects the reflectance for individual zenith angles. Thus, every band can be retrieved in the plot at any individual zenith angle, such as at -50°, 50°, 0°, 40° and so on. Zenith basis functions assume that the zenith angle is the main factor that affects the reflectance for individual bands. We used a 20-basis function to represent the functional spectra for wavelength basis analysis, and 5-basis function to represent the functional spectra for zenith function for the January and February data.

spec

1 M

r

spec

1 M

r

Zenith Direction

Azimuth Direction


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(a) (b)

Figure 2. Illustration of functional curve representation of the hyperspectral data, wavelength (a), zenith basis (b) basis analysis

Functional data analysis routines

The descriptive statistic functions consist of the mean and standard deviation functions of the cotton spectra was calculated. The mean and standard deviation of the two data sets were plotted to show the variance of the curve functions of the cotton spectra. Variance-covariance functions and the functional derivatives of the cotton spectra was generated in FDA (Ramsay and Ramsay, 2002; Ramsay and Silverman, 1997). The purpose of the descriptive statistics is to assess the nature of the data by observing the mean value and standard deviation function plots, variance-covariance function, and first and second derivative of the cotton spectra acquired with different zenith angles. The derivative of cotton spectra was set for wavelength basis analysis. The variance-covariance function was calculated for sensor zenith basis analysis.

The basis function for spectral smoothing was applied using B-spline smoothing in FDA to the wavelength basis analysis (413 values), but not for zenith basis analysis due to the limited number of data points (11 angles). In order to examine the smallest factors of smoothing for spectral curves of vegetation, different numbers of basis function (K) were assessed namely 5, 10, 15, 20, 30, 50 and 100 for the wavelength analysis. Then, the effect of the smoothing was examined by visual comparison of the smoothed spectra to the original spectrum, and by comparing the residual noise spectrum with each smoothing method to find the best fit to the data.

The four principal components along with the residual and harmonic data were calculated. The main objective is to demonstrate the features of the functional principal component analysis results by recounting the variance value for each principal component of the cotton spectra, which, when plotted, will expose the dynamics of multi-angular spectra. A functional linear model can be used to make predictions, and so it was applied to the cotton spectral data to assess the effect of azimuth and zenith angles on spectral reflectance by comparing the functional linear curve, and followed by functional Analysis of Variance (fANOVA) to test the significance of the model. Direction of scanning (e.g. forward (negative zenith) and backward) from the nadir positions was used to display the directional spectra in a functional linear model. It is assumed that the different sensor positions at each zenith angle will relate to different spectral reflectance at nadir. This method was applied for wavelength basis analysis.

Results and Discussion The effect of sensor zenith angle on spectral plots

The spectral reflectance signature of the cotton spectra acquired at different sensor zenith angles shows a vertical ‘shift’ (increase or decrease) of spectral reflectance values in the visible to NIR. Some wavelength regions above 900 nm have excessive noise. This spectral signature consists of 413 bands and 11 different zenith angles. It is clear that forward direction (positive angles) tend to have higher spectral reflectance value in the Red-NIR regions. The functional spectral reflectance for all eleven-zenith angles with a total of 412 bands for both January and February data, fitted with 20-basis functions, are shown in Figure 4. Each curve represents a functional data object for each zenith angle (different color and line types) of cotton spectra for the spectrum range and gives a trend of spectral reflectance over different angles.

There is variance across the zenith angles, with lower variance in the January data when compared to February data. For the January data, at zenith angles 0° (nadir), -10° and 10°, the first three functional spectra have high reflectance in the red to near infrared wavelengths (the red-edge) (see Figure 4). For the data from February, 0º, -10º and -50º, all show a shift in spectral reflectance in the Red –NIR. When compared, the 50° azimuth of the January and February data is similar, less than 0.4 or 40% reflectance for the cotton spectra. Noise is visible at above 900 nm, particularly for the February data. As is common for green vegetation, reflectance in the visible range was quite low, with peak response in the green. In the case of data collected from different angles using the goniometer, the range in reflectance for the visible region is important, showing directional variation in the visible to near infrared region.


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The functional mean and functional standard deviation for the 11-zenith angles is shown in Figure 5. The functional mean and functional standard deviation for both datasets are similar except for a slight difference at 900 nm in the January data. Both datasets have the same tendency and distribution, which is not surprising because the spectral results come from the same plant at different dates of acquisition. The functional derivative analysis of cotton plant spectra indicates spectral variation due to sensor zenith angles. The reflectance at +10° and 0° (nadir) are higher for both dates of spectral collection (Figure 6). The first derivative has shown some critical absorption of the wavelength for cotton for vegetation discrimination such as green, red and near infrared regions.

Figure 3. Typical spectral signature of cotton plant acquired at difference zenith angles before the FDA process.

Figure 4. Spectral functional at different zenith angles using 20-basis for January and February data

Figure 5. Functional mean and standard deviation of cotton spectra across the eleven zenith angles.


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Figure 6. First derivative curve showing spectral variables for different zenith angles of cotton spectra acquired on 06 January and 06 February 2003

Basis function for spectra smoothing

Figures 7 and 8 show the smoothing results of multi-angle cotton spectra using different basis functions. The lower limit function determines the lowest function that can be applied to the data sets and still affect the smoothing basis, but not perfectly fit the dataset. The upper limit determines the number of basis functions that can show a perfect fit to the dataset, but not exceed the number of data points that need to be smoothed. In this experiment, the lowest basis function that can be applied to the data is five. Applying the 5-basis function show very smooth curve along the spectrum range, and the spectral data was shifted to a model far from the real data value, resulting in a poor representation of the absorption features of the vegetation spectra. Using 10-basis functions, the curve starts to follow the real data values. The function that is smoothed has limited curvature, depending on the number of basis functions used. The greater the basis used up to 20-basis, the closer the curve line follows the original data values. The 50 basis curves provide no more variation than the 20-basis curves. In this example, the 50-basis function can be considered as the upper limit for this data set. It is still possible to apply higher bases, but a basis of 412 must not be exceeded as this is the maximum number of range data value for the dataset. Since the plots (Figures 7 and 8) are on the same scale, it can be seen that the range of variation in the polynomial closely matches the range of variation in the data. With the use of a 20-basis function, the line model fits approximately well to the real data, but there are still some points where the line model strays from the real data values. The use of a 30-basis function, the line model fits well to the real data. In addition, a 30-basis function is not much different to 50- and 100- basis functions. The 20-basis is sufficient to represent smoothed spectra.

Figure 7. Spectral curves with different basis function models (January data),

the 20 basis function curves give a good approximation of the data.


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Figure 8. Spectral curves with different basis function models (February data),

the 20 basis function curves give a good approximation of the data.

The fitting basis function of spectral data (Figures 9 and 10) shows the construction of a smoothing curve of B-splines with given coefficients. The use of the same basis functions (5-basis) on different zenith angles shows a variation in the residual fit (Figure 9) from 0.05 at Znt 8 (-40°) to 0.09 at Znt 6. The results show that different residual numbers could determine the level of fit to the particular zenith angle. These findings indicate that the specific basis function needed for smoothing purposes depends on two factors: (1) the level of noise or variations of spectral data determines what basis function is required. More variation in the spectrum requires greater basis functions in order to obtain a better fit for the smoothed model to the original data, (2) the selection of basis for individual spectra can determine how well the smoothing line fits the data. The greater the number of basis functions used for a particular spectrum, the better the approximate models fits the data.

(a) (b) (c) (d) (e) (f) (g) (h) (i)

(a) (b)

(c) (d) Figure 9. Fitting the curve at 0° (nadir) view angle (Znt 6) for different basis; 5-basis (a),

10-basis (b), 20-basis (c), and 50-basis (d) (January data. RMSr=Root mean square residual.

5-basis model

20-basis model

50-basis model

10-basis model


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Figures 10 shows the comparison of fitting spectral curves using 5-basis function for the four zenith angles(Znt 5,

Znt 6, Znt 7, Znt 8, representing -10°, 0°, +10° and +20° respectively) and 30-basis function for smoothing at Znt 6 (0° nadir). The use 30-basis function for all zenith angles has zero residual for the January spectra. This result shows that level of noise due to the sensor view angles could be identified by examining the residual. The noise not only comes from sensor, but also from environmental conditions that may affect the spectral reflectance. In this example, the February spectra are noisier than the January spectra. The use of 30-basis functions on the January data displays no residual, but the February data still has residual value with 30 basis functions. The 30-basis function was used for the remaining analyses in this chapter.

Through functional basis analysis, a 30-basis function was found to be the best for smoothing the data with minimal residual. Using lower a basis than 30 for the cotton spectra provided a poorer fit of the functional model to the original data. Values above the 30-basis function resulted in no further change to the approximate functional model. Thus, more than 30-basis is considered overfit to the curve. Various basis function test worked for wavelength basis analysis. For zenith basis analysis, 5-basis function still works well in representing an approximation of the basis function model. However, fitting the model to the original data was not properly fitted. The main important point for basis function for smoothing of cotton spectral data is that the smoothing using basis function can be estimated by inverting mathematical models of the Bidirectional Reflectance Different Function against directional reflectance data sampled at several different sensor view angles as with the soils.

. (a)

(b)

Figure 10. Fitting the curve at different view angle (Znt 5-to 8; 50°, 0°, -50° and -40°)

for the same basis (5-basis) (a). The 30-basis functions for Znt 6 (0°) (b) show zero residual; a perfect fitting for January data.


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Functional principal component analyses (FPCA)

Figure 11 shows the bivariate plot of the principal component score for the first four principal components of January and February data; the second principal component was plotted against first, third against first, fourth against first and second against third. The harmonic values, a summary statistic used in analyses of frequency data display a clearly unordered pattern. Four principal component directions (eigenvectors) and the percent of total variation of each direction are shown. In each case, the solid curve (black) is the overall mean spectra for the given wavelength range and the circle (green) and dashed (red) curves shows the effect of adding and subtracting a multiple of each principal component to clarify the effect of the components.

(a) (b)

Figure 11. Results of the fPCA (PCA 1 to PCA 4) on the multi-angular spectral data on cotton. Note the first principal component direction of first fPCA explains most of the variation 93.6% (January) (a), and 96.1% (February) (b) in the data.

The shape of first fPCA indicates that most of the variation of the data occurs at the two angle measurements.

The first principal component direction, fPCA, explains most of the variation, about 93.6% and 96.4% respectively for the January and February data. The variation occurs for all wavelengths, especially in the 700 to 900 nm. The fPCA value is essentially the common spectral variation over different zenith angles, and is due to the specific reflectance or absorption along the wavelength range for vegetation. The second principal component function, which accounts for 5.8% and 2.6% respectively for January and February, picks up the differences between high and low reflectance values regarding the NIR regions. The third and the fourth components account for less than one percent of the variation. These could be spurious and therefore do not provide useful information, contributing to error effects in the spectral analysis. An important aspect of PCA is the examination of the score function of each curve on each component. Each angle is identified by the level given to the angles, as described earlier. Some positions of the score have been adjusted to the same degree of score component-scale to improve legibility. Variation of spectral data was almost indistinguishable from the harmonic score values. The -10°, 10° and 0° appear in the same order for the first three harmonic comparisons. The rest of data points are clustered in the adjacent values, except for harmonic 2 versus harmonic 3 (Figure 12). The -10°, 0° are in the upper right corner for January data because they have a higher reflectance value in the Red-NIR than most of the other zenith angles (on PCA 1). Similarly, the -50°, 20°, 0° and -30° February data are higher in spectral reflectance in this region than most of the other zenith angles.

The results of functional principle component analysis of the wavelength basis analysis vary for each date of collection and sensor zenith angles. The first functional principle component of zenith angles accounts for 93.6% and 96.4% respectively for January and February data. The variation of the first fPCA was high in the NIR reflectance. This region basically is sensitive reflectance location for most green vegetation. The second fPCA accounts for 5.8% and 2.6% respectively for January and February, picking up the differences between high and low reflectance values with respect to the NIR regions.


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This second fPCA still provide the information of spectral reflectance, especially below 700 nm wavelengths. Vegetation pigment and chloroplast play important role in this region (Lichtenthaler et al., 1996; Yoder and Pettigrew-Crosby, 1995). Thus, the second fPCA provides important information on plant physiology. The third and the fourth fPCA account for less than one percent of the variation. These results could be spurious and so do not provide useful information which is contributed to a large error effect in the spectral analysis. The key point of using fPCA for January and February data of cotton spectra is that the variation for both data is not much different in the distribution of variance explained for the first four fPCA. February data has a slightly higher variance for the first fPCA.

Figure 12. Principal component scores of second fPCA versus first fPCA, third fPCA versus first fPCA, fourth fPCA

versus first fPCA and second fPCA versus third fPCA for January and February 2003 data. Conclusions

Various characteristics of cotton spectra due to sensor view angles have been considered in the results, which indicate directional variation as an outcome of the dependent variable with different zenith angles. Two principal approaches have been used to represent cotton plant spectra in the FDA process: wavelength and zenith angles. These result in different curve function output, the basis function, functional analysis of variance and the linear model of multi-angular cotton spectra. The spectral noise produced by the sensor presented in a smoothed curve approximation has different RMS residual, depending on the basis function and zenith angles. The use of different numbers of basis functions clearly affects the fit of the spectral curves obtained from eleven-zenith angles. One implication of the findings from this directional analysis of multi-angular spectra of cotton is that the spectral reflectance data can be considered as functions. By using a functional approach for modelling, the smoothing, predicting and analysis of the cotton spectra can be achieved. However, the main implication is that there is only a very small amount of additional information provided by multi-angular measurements within the range of zenith angles assessed. Acknowledgements

We thank to Geoff Mcdonald for helping me during this research. Yanni Zakaria and John Owen for their assistance in computer matters at the University of New South Wales.

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