1_charachteristics of sensors

Instrumentation and Experimental Design

Engi 7930 Spring 2015

1.Charachteristics of Sensors1.1 Generalized Measurement System

1.2 Calibration1.3 Standards

1.4 Specifications of sensors1.5 Types of sensors

Introduction

Instrumentation engineering is the practice related to the use of measuring instruments to monitor or control a process.

Related to many disciplines:

Avionics Ocean Instrumentation Medical Instrumentation

Introduction

Instrumentation engineering is the practice related to the use of measuring instruments to monitor or control a process.

Instrumentation for Mechanical Engineers

Proximity, level sensingTemperature, pressure and flowMotion sensingForce, torque sensingVibration analysis

Underlying concepts and general theory applies across domains

Introduction

A sensor is a device which provides measurements.

A measurement assigns a specific value to a physical variable (measurand). E.g. Temperature, Force, etc.

Components of a basic sensor/measurement system can be divided as follows:

= () Sensor

Sensing Element

SignalManipulation

Indicator Or recorder

Physical World

Introduction

The sensing element has a physical characteristic which significantly changes in response to the measurand.

Signal manipulation performs the task of converting the output of the sensing element to make it suitable for indication.

The indicator provides a scale for reading the measurement.

Sensing Element

SignalManipulation


Physical World

Introduction

Example: Common bulb thermometer

Measurand : temperature of the environment

Sensing element : mercury bulbPhysical phenomenon : thermal expansion of

mercurySignal manipulation : capillary tube to

amplify expansionIndication : visual scale

Sensing Element

SignalManipulation


Physical World

Generalized Measurement system

Modern measurement systems mostly operate using electrical signals. This allows to exploit digital storage, communication, and control functionalities.

The generalized measurement model given below summarizes components of a typical measurement system.


Sensor stage: Uses a natural phenomenon to extract information of a physical variable.

Transducer stage: converts the sensed information to a measurable (electrical) signal.

Signal conditioning: Performs amplification and filtering of signal to desired levels and specifications.

Sampling : Performs analog to digital conversion of the signal.


Estimation: Performs statistical estimation of the measurand, using a set of measurements from one or many sensors.

Communicate: establishes standard protocols for communication with other devices to ultimately perform indicating, storing, or controlling functions.


Example: Load cell (Lab1)

1. Sensing element: A cantilevered beam which changes the resistance of an attached strain gauge.

2. Transducer stage: A Wheatstone bridge converts the change in resistance to a measurable voltage signal

3. Signal conditioning: An instrumentation amplifier performs the necessary amplification of the signal

= 1

2

6

2


Example: Weighing scale (Lab1)

4. Sampling : An NI USB 6008 DAQ performs the analog to digital conversion.

5. Estimation: The mean of the measured value is taken to reduce noise. Voltage is used to estimate the load

6. Indicate: A graphical indicator is used to show the estimated measurand


Parameters and variables

Independent variable: variables of the system that can be changed independently of other variables ().

Dependant variables: variables which are affected by changes in one or more other variables (, )

Parameters : defines a functional relationship between variables (, , , , , ).

Controlled variable : variables that can be held constant during a measurement ().

= 1

2

6

2


Parameters and variables

Extraneous variable : variables that cannot be held constant but affects the measurand. (Temperature affects , )o Noise: Random variation of

the value of the measured signal (thermal noise)

o Interference: Produces undesirable deterministic trends on the measured value, because of extraneous variables (Temperature drift)

Noise

Interference+ Noise

Calibration

Calibration is the process of establishing the relationship between the measured physical variable () and the output value of the sensor ().

Static calibration: the input is held constant and the output is measured after it converges to a value. I.e. The dynamic behaviour is not considered.

Performed by applying known values of the measurand and recording the output in order to identify a functional relationship = (). The value denotes the expected value of the measurement for a given measurand ().

Calibration

A Static calibration curve:

= ()

Calibration:find

Calibration

Dynamics Calibration: The dynamic behaviour of the system is established using time varying input signals. E.g. Finding the transfer function of a sensor which is presumably a linear time invariant system.

Dynamic calibration plot of ADXL001 accelerometer :

Calibration

Types of tests

Sequential test applies a sequential variation in input value over the desired input range. This allows to capture any trends in the measurement such as hysteresis, temperature drifts etc.

Random tests use a measurement matrix that sets a random order in the value of the independent variable applied. Random tests allow to break trends in the measurement occurring due to extraneous variables.

Calibration

Types of tests

Repetitions are repeated measurements made in a single test run. Repetitions allows to better estimate a quantity which is corrupted by noise.

Replications are measurements made in different test runs under same operating conditions. Replication permits to asses how well a set of conditions can be duplicated. (captures more extraneous effects than repetitions)

Dynamic tests are performed to asses the dynamic response of a system. I.e, step test, frequency tests

Sensor Specifications

1. Static sensitivity (K): The slope of a static calibration curve. may or may not be constant over the range of input values.

2. Range: The minimum and maximum limits of both the input ( , ) and the output ( , ) that the sensor is intended to operate.

3. Span : input span = output span (FS) =

= () =

=1


4. Resolution (): smallest increment in the measurand that can be measured.

5. Bias: The shift of the static calibration curve from zero.

0 100 200 300 400 500 600 700 800 900 10000

1

2

3

4

5

6

7Caliberation plot - Lab 1

Load (g)

Vout

(V)

Vo= 0.00612W + 0.33596

Sensitivity :0.00612 V/g

Bias :0.33596 V

Range :0.33 to 6.45V

Span :6.12 V


6.Error (): The difference between the measured value and the true value of the measurement. Since true value is not known the expected value is used.

7. Accuracy (): The accuracy is the maximum error expected from a measurement system when calibrated and used in a specified manner. Consists systematic errors (interference) and random errors (Noise).

shown as absolute error bounds =

shown as a percentage = ||

100

shown as statistical bounds (using variance 2) = 2

100

Error (e)= measured value - true value =


0 100 200 300 400 500 600 700 800 900 1000-0.01

-0.008

-0.006

-0.004

-0.002

0

0.002

0.004

0.006

0.008

0.01

Load (g)

Outp

ut

err

or(

V)

Deviation plot - Lab 1

Accuracy in F.S (abs) : 0.11534 %

Accuracy in F.S (stat) : 0.13752 %

Bias error :-0.00000

Nonlinearity error :


8. Hysteresis errors (): The difference in values found in going up scale and down scale in a sequential application of the input values.

Component ErrorsBias error: This is the constant shift of the measured value from the expected value. Minimized in calibration.


i. For each level of , defined as (), find the average error of all replications going up the scale and down the scale. i.e, ,

ii. Define individual hysteresis errors for each .

iii. Hysteresis error is the maximum among all `s expressed as a percentage of full scale.

% = ||

100

() = .


9. Nonlinearity (): The error between the output and the linear approximation of the sensor. Different calculations exist. The Terminal based linearity is measured as follows:

i Average the error for each level of . . , ()

ii Draw a line going through the

terminal points of the deviation plot.

iii | | is the maximum deviation

of from the line.

Linearity error: % = ||

100


10. Precision(): Measure of random variation of errors. This is termed as repeatability, when the sensor is tested for a relatively short term experiment. Termed reproducibility when tested for replications considering many extraneous factors. I.e, different labs, different batches, different operators.

Precision as absolute bounds:

i. For each level of , find the span of error. =max m

ii. Precision error is the maximum of these spans among different s, expressed in %FSO.

% =||

100


Precision- As statistical bounds

i. For each level of , find the sample standard deviation of the errors.. . , ()

ii. Take the maximum of these standard deviations. = max(())

iii. The 95% confidence level of precision expressed in %FSO is reported.

% =2

100

( + ) 0.6827( 2 + 2) 0.9545( 3 + 3) 0.9973


11. Bias, sensitivity errors: The bias and sensitivity of the sensor can change due to temperature, aging etc. The expected error bounds of bias () and sensitivity () are reported as part of sensor specifications.


12. Loading errors: The sensing element undergoes an energy transfer with the physical world. This causes the measured physical quantity to change from its initial value.

This phenomenon occurs between each connecting stages of a measurement system.


Dynamic characteristics

1. Bandwidth: specifies the minimum and maximum frequency that the sensor produces constant sensitivity (flat amplitude ratio). Usually a 3dB specification is used. (~70% sensitivity change).

2. Transient response: Transient response characteristics of the sensor (time constant, rise time, settling time, overshoot )

Formally introduced in Topic 2: Dynamic response and frequency analysis


Dynamic characteristics

3. Power spectral density: method of determining the frequency content of a random signal. While the mean and variance are measures of magnitude of a random signal, in order to measure how rapidly changing a random signal is, PSD spectrum is found.

Formally introduced in Topic 2: Dynamic response and frequency analysis


Datasheet of ADXL 335 accelerometer

Standards

Standards

Static calibration used known values of the input variables which are presumably known to be accurate. These known values are referred to as standards.

Standards are related to dimensions and units.

Dimensions define some aspect of a physical variable. Units defines a quantitative measure of a dimension. SI standard defines 7 basic dimensions and units.

Standards

Standards

For each basic unit a primary standard is defined which exactly quantifies the unit. (with zero error)

Dimension SI Units Primary Standard

Mass (kilogram) kg Mass of Platinum Irradium bar maintained at IBWM Severs, France

Time (second) s Time elapsed during 9,192,631,770 periods of the radiation emitted between two excitation levels of the fundamental state of cesium-133

Length (meter) m Length traveled by light in 3.335641 109

Temperature (Kelvin) K Different standards are used depending on the scale. E.g. triple point of hydrogen 13.81 K

Current (Ampere) A The current that produces 2 107between two parallel conductor

Standards

The primary standards are difficult to obtain for calibration. Therefore secondary derived standards can be used. The accuracy of the standard deteriorates down the hierarchy.

Therefore the error of the standard used for calibration () also deteriorates the accuracy of a sensor.

Total Error

A conservative estimate of the overall instrument error is the 2-norm of all component errors.

All component errors should be expressed in the same manner before applying the equation. I.e., accuracy bounds, percentage accuracy, or statistical bounds.

Discussed further in Topic 4: Uncertainty propagation

= (2 +

2 + 2 +

2 + 2 +

2)

Questions

1. Select the type of test best suited to establish each specification shown below.

Hysteresis:

Accuracy:

Bandwidth:

Time constant:

Select your answer from the following options:

Random test, Step test, Sequential test, Frequency test

Questions

2. Classify the following component errors to systematic errors (interference) and random errors.

Precision:

Bias drift:

Sensitivity drift:

Nonlinearity:

Hysteresis:

Loading:

Resolution:

Repeatability:

Reproducibility:

Questions

3. Find the sensitivity, bias, range, accuracy, repeatability, and nonlinearity, of the sensor using the data set given in table.

x y

Load(N) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5

20 7.84 7.93 7.96 7.83 7.89

80 32.33 32.38 32.42 32.3 32.44

40 15.96 16 15.91 15.85 15.93

100 40.79 40.82 40.86 40.72 40.83

0 0.01 -0.02 0.08 0.05 -0.07

60 24.07 24.04 24.16 24.17 24.04

Questions

x y y_pred e |e|Load(N) Voltage(V) Kx+b y-y_pred abs(e)

20 7.84 7.9449 -0.1049 0.104980 32.33 32.4249 -0.0949 0.094940 15.96 16.1049 -0.1449 0.1449

100 40.79 40.5849 0.2051 0.20510 0.01 -0.2151 0.2251 0.2251

60 24.07 24.2649 -0.1949 0.194920 7.93 7.9449 -0.0149 0.014980 32.38 32.4249 -0.0449 0.044940 16 16.1049 -0.1049 0.1049

100 40.82 40.5849 0.2351 0.2351

y = 0.408x - 0.2151R = 0.9998

-5

0

5

10

15

20

25

30

35

40

45

0 20 40 60 80 100 120

Calibration plot

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

0.4

0 20 40 60 80 100 120

Deviation plot

Questions

x y y_max y_min y_avg y_pred e_repeat e_avg |e_avg|

Load(N) Cycle 1 Cycle 2 Cycle 3 Cycle 4 Cycle 5max(y_row)

min(y_row)

average(y_row) K*x+b

y_max-y_min

y_avg-y_pred

abs(e_avg)

20 7.84 7.93 7.96 7.83 7.89 7.96 7.83 7.89 7.9449 0.13 -0.0549 0.0549

80 32.33 32.38 32.42 32.3 32.44 32.44 32.3 32.37432.424

9 0.14 -0.0509 0.0509

40 15.96 16 15.91 15.85 15.93 16 15.85 15.9316.104

9 0.15 -0.1749 0.1749

100 40.79 40.82 40.86 40.72 40.83 40.86 40.72 40.80440.584

9 0.14 0.2191 0.2191

0 0.01 -0.02 0.08 0.05 -0.07 0.08 -0.07 0.01-

0.2151 0.15 0.2251 0.2251

60 24.07 24.04 24.16 24.17 24.04 24.17 24.04 24.09624.264

9 0.13 -0.1689 0.1689

SpecificationsOutput range -0.07 40.86VOutput span 40.93VSensitivity 0.408V/NBias -0.2151VAccuracy %FSO 0.720987%

Component errorsNonlinearity error %eL 0.977278%Precision error %eR 0.366479%Total of components %eT 1.043734%

1_charachteristics of sensors

Documents

typical measurement

generalized measurement

signal conditioning

filtering of signal

measurable electrical

instrumentation amplifier

basic sensormeasurement

physical variable measurand