abe 5646-4162 course overview & introduction to systems...
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ABE 5646-4162Course Overview &
Introduction to Systems Analysis ConceptsFrazier-Rogers Hall Room 283
Dr. James W. Jones and
Dr. Senthold AssengAgricultural and Biological Engineering Dept.
P.O. Box 110570Gainesville, FL 32611-0570
Phone: (352) 392-1864 ext 289Fax: (352) 392-4092
Email: [email protected] & [email protected]
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Objectives1) To learn to basic modeling and simulation methods
for biological and agricultural systems• Systems Approach• Model development• Example models• Numerical Simulation
2) To learn methods for working with dynamic models• Model evaluation• Sensitivity analysis• Parameter estimation• Applications
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Overall FormatThe course will contain two components. For about the first 1/3 of the course, students will be exposed to basic concepts of systems analysis, modeling and computer simulation of agricultural and biological systems. Emphasis will be placed on continuous simulation of dynamic models with examples that give students a broad exposure to dynamic models. Most of the reading material for this part of the course will be made available by the instructor via the course web site. Much of the basic information will be from the book by Keen and Spain (1992), which is now out of print. Students will also be referred to a new book for examples of biological models: Datta, A.K. and V. Rakesh. 2010. An Introduction to Modeling of Transport Processes: Applications to Biomedical Systems. Cambridge University Press.
The second part of the course will introduce students to various methods for working with dynamic models, starting with sensitivity analysis, going into parameter estimation and model evaluation. An overview of applications of models in agricultural and biological systems will be given. The text for this part of the course is the book by Wallach et al. (2006) entitled “Working with Dynamic Crop Models: Evaluation, Analysis, Parameterization, and Applications”. During this part of the class, students will also be exposed to uncertainties in models associated with uncertainties in model parameters, inputs, and structure.
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OutlineWeek Description Reading Material
1 Course OverviewIntroduction to SystemsDiagrams used in Systems AnalysisModeling ConceptsForrestor Diagram Conceptual Model, Example ModelAssumptions in Model Development
Jones & Luyten (1998)
2 Computer Simulation of Dynamic ModelsFinite Difference, continuous states, discrete time Simple Methods
EulerTrapezoidRunge-Kutta
Choice of time stepErrors in Numerical Simulation
Jones and LuytenThornley & Johnson, 1990, pp. 13-31Keen & Spain (1992) Ch 5
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OutlineWeek Description Reading Material
3 Back to Modeling – Biological & Physical Models• Growth• Heat flow and temperature• Passive Diffusion • Inhibited growth•Michaelis-Menten model of enzyme reactions• Kinetics of biochemical reactions • Homogenous Population of organisms • Chemostat microbial growth (batch, continuous flow)
Keen & Spain (1992) Ch. 1-2, 6-8
4 Additional Modeling Concepts• Compartment models of biogeochemical systems• Lags in dynamic biological models• Adding an age dimension in biological models• Adding spatial dimensions in dynamic models
Keen & Spain (1992) Ch. 7, 9, 13, 14
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OutlineWeek Description Reading Material
5 Modeling Temperature Effects on Biological Systems• Effects on chemical reaction rates• Effects on biological activity, general• Effects on developmental processes in plants and other biological organisms• Degree-day models: basis for and use of
Keen & Spain (1992) Ch. 12Handout; degree-days
6 Crop Modeling• State variables• Development• Dry matter growth
- photosynthesis, respiration- Light Use Efficiency (LUE)
• Partitioning of dry matter
Jones & Luyten (1998) Salazar Papers on Node development & on GrowthWallach et al. (2006) Chapter 9Jones et al. (2003)
7 Mid Term Exam
Introduction to Working with Dynamic <crop> ModelsTwo forms of <crop> models
---
Wallach et al. (2006) Ch 1
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OutlineWeek Description Reading Material
8 Review of Basic Statistics, Random VariablesWhy these are important in simulationExamplesDistributionsExpectationWorking with Statistics in Simulation
Approximation of distributions from numerical outputsExpected Values (Mean, Variance, Covariance – 2 methods)Random Sampling, Monte Carlo Methods
Bayesian Statistics
Wallach et al. (2006) Ch 1, AppendixOther References
9 Introduction to the R Programming environment, with exercises Handout
10 Spring Break (March 5-12)
11 Evaluating [Crop] Models•Comparing a model with data
- Graphical, errors- Measures of agreement (bias in mean, variance)- Evaluation of predictive quality
• Cross validation• Bootstrap estimation
Wallach et al. (2006) Ch 2
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OutlineWeek Description Reading Material
12 Uncertainty and Sensitivity Analysis• Uncertainty of parameters, inputs• Model output analysis, probability distributions • Local sensitivity analysis (absolute, relative)• Global Sensitivity Analysis
- Monte Carlo sampling- Analysis of output variance (ANOVA)
Wallach et al. (2006) Ch 3Jones Handout
13 Parameter Estimation• Least Squares (non-linear)• Choice of parameters• Multiple variable observations• Monte Carlo methods
- Metropolis-Hastings- GLUE- Parameter uncertainty and correlation
Wallach et al. (2006) Ch 4
14 Optimization with Simulation ModelsData Assimilation with Dynamic Models
Wallach et al. (2006)Ch 5, 6
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Outline
Week Description Reading Material
15-16Apr 19
Special Project PresentationsReview for Final Exam
Apr 20Apr 20
Last Day of ClassesFinal Project Reports due on or before this date
Tuesday, Apr 26, 12:30 – 2:30 pmFinal Exam - ABE 5646 (Exam 26C)
ROG 283
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Grading
• Homework 30%• Mid-term Exam 20%• Final Exam 20%• Project 30%
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Class LecturesLectures will be held on Tuesday during class
periods 2 and 3 (8:30 – 10:25 am) and on Thursday during class period 2 (8:30 – 9:20 am). The additional class period allocated for the course (period 3 on Thursdays) will be used as needed for presenting additional material or for discussions and reviews.
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Textbook and other Reading Material
TEXTBOOK• Wallach, D., D. Makowski, and J. W. Jones (eds.). 2006. Working with
Dynamic Crop Models: Evaluation, Analysis, Parameterization, and Applications. Elsevier. New York. ISBN 0-444-52135-6.
HANDOUTS will include pages from:• Keen, R. E. and J. D. Spain. 1992. Computer Simulation in Biology: A
Basic Introduction. Wiley-Liss Inc. New York. (Selected Chapters – Book out of print)
• Jones, J.W. and Luyten, J.C. 1998. Simulation of Biological Processes. In: Peart, R.M. and Curry, R.B. (eds). Agricultural Systems Modeling and Simulation. Marcel Dekker Inc. ISBN 0-827-0041-4.
• Thornley, John H. M. and Ian R. Johnson. 2000. Plant and Crop Modeling: A Mathematical Approach to Plant and Crop Physiology. Oxford University Press. New York. Blackburn Press (Second Printing).
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Other Reading Material• Datta, A.K. and V. Rakesh. 2010. An Introduction to Modeling of Transport
Processes: Applications to Biomedical Systems. Cambridge University Press. • Dent, J. B., M. J. Blackie, and S. R. Harrison. 1979. Systems Simulation in
Agriculture. Applied Science Publishers LTD. London. 180 pp.• Forrestor, J. W. 1961. Industrial Dynamics. John Wiley. New York.• Merva, G. E. 1995. Physical Principles of the Plant Biosystem. ASAE Textbook
Number 9. ASAE, St. Joseph, MI, 272 pp.• Penning de Vries, F.W.T., et al. 1989. Simulation of Ecophysiological Processes
of Growth in Several Annual Crops. Pudoc, Wageningen.• Peart, R. M., and R. B. Curry. 1998. Agricultural Systems Modeling and
Simulation. Marcel Dekker, Inc. New York. 696 pp.• Takakura, T. and J. E. Son. 2004. Simulation of Biological and Environmental
Processes. Kyushu University Pres,Fukuoka-shi, Japan (ISBN 4-87378-848-X)• Tsuji, G. Y., G. Hoogenboom, and P. K. Thornton (eds.). 1998. Understanding
Options for Agricultural Production. Kluwer Academic Publishers. Boston.
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Introduction to Systems Analysis
• Terminology• Systems Diagrams• Dynamic Models and Modeling• Systems Analysis Approach• Dynamic Models• Forrestor Diagrams• Example system, diagram, equations
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Some Perspectives of Systems Approach in Agricultural and
Biological/Ecological Systems
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• Agricultural Science is not a science unless it predicts and tests its predictions (P. G. Cox, 1996)
• Understanding Prediction Control, Manage(H. Nix, 1983)
• A wealth of research information exists concerningthe possibilities for change, the options available and the likely effects of a range of land use practices. However, it is less clear how this information is ofuse to, or can be filtered into, decision makingprocesses. (J. Park and R. A. F. Seaton, 1996)
Information Needs in a Systems Approach
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Systems Approach
Application/Analysis
Control/Management/
Decision SupportResearch
Model Development
Increased Understanding
Model
Test Predictions
Prediction
Research for Understanding
Problem Solving
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Incorporating Crop Models into Traditional Agronomic Research
ComputerExperiments
Question, Problem
Hypotheses
Experiments
Analysis
Conclusions, DecisionsRecommendations
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Hierarchy is Important in Biological/Ecological/Agricultural Systems
“WORLD”
FARMING AREAS
CROP ECOSYSTEMS
ELEMENTS
MICRO-COMPONENTS
CORN, PASTURE, ...
STOMATA, BIO-CHEM. PATHWAYS...
INDIVIDUAL PLANTS, ...
COMPONENTSLEAVES, STEMS, ROOTS, ...
REGIONS
MANAGEMENT
/
RESEARCH
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Terminology (Jones & Luyten, 1998)
• System: a collection of components and their interrelationships that have been grouped together for the purpose of studying some part of the real world
– Biological systems tend to hierarchically organized and can be studied at a number of levels
• Environment: everything except the components of the system• System Boundary: abstraction of the limits of the system components,
separating them from the environment• Model: a mathematical representation of a system• Modeling: process of developing the representation of a system• Computer Simulation: includes processes necessary for
operationalizing or solving a model to mimic real system behavior– Developing computer logic and flow diagrams, writing the computer code
and implementing the code on a computer are tasks
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Terminology (Jones & Luyten, 1998)• Inputs: factors in the environment that influence the behavior of the
system but are not influenced by the system – (Exogenous variables, driving variables, forcing functions)– May vary with time (rainfall, temperature, light, tide, etc…)
• Outputs: represent the characteristic behavior of the system that is of interest to the modeler (crop biomass, yield, meHg concentration)
• Parameters and Constants: characteristics of the components of the model that are constant through simulated time
– Constants - Molecular weight of glucose, gravitational constant, number of seconds in a day, days in January
– Parameters – daily caloric requirement, water use efficiency, soil water resistance, respiration loss
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System Diagrams
• Help analysts design a model • Communicate model structure, components to
others• Show relationships among components• Help analysts organize concepts, assumptions• Help in development of mathematical model • There are different diagram types
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Dynamic Models
• Play important role in systems analysis• Derived from understanding of system• Physical, biological, economic • Simplification of reality
– “All models are wrong, but some are useful” G. E. P. Box quote
• General form -)}),(),({)( ptutXf
dttdX=
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Terminology (Jones & Luyten, 1998)
• State Variables: quantities that describe the conditions of system components– Change with time in dynamic models as system components interact with
each other and the environment– Soil water content, crop biomass, elephant happiness…
• Process Model: interrelationships between components in a system, and therefore between state variables in the system, exist because of various processes– Continuous models: characterized by state variables that can change
smoothly over small time intervals and are not restricted to integers– Discrete models: characterized by state variables that can change in
integers over time intervals (# of live births), populations etc…
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Terminology (Jones & Luyten, 1998)• Verification: the evaluation of the accuracy with which
the computer code represents the mathematical model and the programmer's intentions– Checking of mathematics, units, programming logic and code
errors– Does the model work like I expect it to?
• Calibration: making adjustments to the model parameters to give the best fit between simulated results and results obtained from measurements
• Validation: process of comparing simulated results to real system data not previously used in any calibration or parameter estimation process.– Is the model sufficiently accurate for its application?– As defined by objectives of the simulation study
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Systems Approach• Statement of Objectives
– Critical step, often overlooked– What to develop? Who are the users?– Better understanding? vs. Solving the problem?
• Definition of the System– System boundary, inputs, outputs
• Literature Review and Data Analysis• Model Development (Design, Code, Parameters)• Sensitivity Analysis• Model Accuracy Evaluation (gaining confidence
in the model)• Model Application
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Cropping System Diagram
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Modeling• Continuous systems modeling is a process-oriented approach for
describing system behavior• Three types of processes
– Transport– Transformation– Storage
• Processes are described by two types of variables– Extensive (storage & flow-through quantities, i.e. mass, volume, heat,
money)– Intensive (represent the driving forces for the extensive variables, i.e.,
force, pressure, temperature, etc.)– Example: heat flow through a wall is described by its heat conduction
(extensive) and the temperature differential (intensive)– Extensive variables are measured at a point, intensive variables are
measured across an object– In biological systems, these are hard to determine!
• Complex states or storage quantities• Scale of model may prevent the use of a real intensive variable, leading to
empirical descriptions of flow rates
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Modeling continued• Compartment Models
– Primary emphasis on flows and storages of system variables
– First order differential equations can be derived from compartment structure
• Forrester (1961) is most commonly used diagramming system
∑∑ −=k
kij
jii OI
dtdX
,,i.e. Change in level per unit time = Sum of Flow Rates into compartment i minus Sum of Flow Rates out of compartment i
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Forrester Diagrams (1961)
a) Levelb) Ratec) Sourced) Auxiliary Variablee) Pathway for materialf) Pathway for
information flow
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Two Water Tank Example
V1 = A1 * H1
V2 = A2 * H2
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System2 Storage Compartments(i = 2)3 Flows(j = 3)
∑∑ −=k
kij
jii OI
dtdV
,,
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)()( 2,11 tfti
dtdV
−=
)()(2,12 tOtf
dtdV
−=
112,1 2)( gHCtf =
22 2)( gHCtO =
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Two Water Tank Example)()( 2,1
1 tftidt
dV−=
)()(2,12 tOtf
dtdV
−=
112,1 2)( gHCtf =
22 2)( gHCtO =
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Two Water Tank Example
1
11
1 2)(AVgCti
dtdV
−=
2
22
1
11
2 22AVgC
AVgC
dtdV
−=
substituting Hi=Vi/Ai for each tank
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Two Water Tank Example Equations
1
11
1 2)(AVgCti
dtdV
−=
2
222,1
2 2)(AVgCtf
dtdV
−=
∑∑ −=k
kij
jii OI
dtdX
,,
Standard Forrester Form
General Functional Form
)}),(),({)( ptutXfdt
tdX=
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Some Key Points
• Assumptions about compartments• Assumptions about rates• Rate equations – based on physics, chemistry laws
or empirical• Two compartments led to two equations and two
state variables• Could have many flows, but state variable number
always equals the number of storage compartments
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Complexity of System Models
• Modeling approach (diagrams, mathematical representation as first order differential equations, numerical solution/simulation) works with simple to complex models
• What characterizes a simple vs. complex system model?
• What are some difficulties associated with this approach?
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CropDevelopmentPhotoperoidResponse
Thermal Time
TransplantingShock
Crop GrowthProcesses
Leaf GrowthStem GrowthRoot Growth
Panicle GrowthGrain Growth
PartitioningRules
PlantWaterStatus
GrowthStage
Genetic InformationDaylength
Temperature
Solar RadiationTemperature
AlbedoCO2
PrecipitationIrrigation
Bund HeightWater Table Depth
Urea
Urea
Urea
Urea
Runoffloss
Aquatic PhotosyntheticActivity
Evaporation
Transpiration
NHLoss
3
AvailableP
NH Soln3
NH Soln4
NH Soln4
NH Soln4
Nh Soil4
+
+
+NH Soln4+
+
{
{
}
}
DiffusionPercolation
Adsorption/desorptionCECDiffusion
Adsorption/desorption
Mineralization/Immobilization
C/NWaterTemp.
Lignin/NFresh Organic Matter
Stable Organic MatterRoot Residue
Water andN Uptake
Urea Hydrolysis RateTemp.Org. C
pHInhibitors
DiffusionPercolation
DiffusionPercolation
DiffusionPercolation
Urea HydrolysisRate
Urea HydrolysisRate
Leaching Loss
Runoffloss
DiffusionPercolation
DiffusionPercolation
DiffusionPercolation
Leaching Loss
Flood
water
Oxidi
zed
Soil
Zone
Redu
ced
Soil
Laye
rs
NO3
NO3
-
NO3-
NO3-
-
Nitrification Rate
DenitrificationRate
Soluble CTemp.
Water filledPorosity
pH
Plant N
Root
N
Tops
N
Plant NStatus
Grain Yield
Redis
tributi
onRa
te
ET
Root WaterUptake
NH4+
pHTemp.
Water FilledPorosityInhibitors
DenitrificationLoss
Grain N
Straw
Straw N
FloodwaterpH & Temp.
Runoffloss
Crop ResidueSoil Organic C
Total Soil N
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Systems Dynamics Software!• Commercial Tools
– Stella: http://www.iseesystems.com/– Vensim: http://www.vensim.com/– Powersim: http://www.powersim.com/– MATLAB: http://www.mathworks.com/
• Free Tools– The R programming Language– VisSim
• http://www.VisSim.com/– Mapsys:
• http://www.simtegra.com/system-dynamics-modeling-software.html– Consideo
• http://www.consideo.de/english/index.html– Netlogo: (agent-based simulation)
• http://ccl.northwestern.edu/netlogo/
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Introduction to Systems Approach and Modeling in Agricultural &
Biological Systems