ANN BASED INTELLIGENT PRESSURE SENSOR IN NOISY ENVIRONMENT KULDEEP SINGH 212EC3163

ANN BASED INTELLIGENT PRESSURE SENSOR IN NOISY ENVIRONMENT KULDEEP SINGH 212EC3163

ANN BASED INTELLIGENT PRESSURE

SENSOR IN NOISY ENVIRONMENT

A THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

Master of Technology

In

Electronics and Instrumentation Engineering

By

KULDEEP SINGH

212EC3163

Department of Electronics and Communication Engineering

National Institute Of Technology Rourkela

ANN BASED INTELLIGENT PRESSURE

SENSOR IN NOISY ENVIRONMENT

A THESIS SUBMITTED IN PARTIAL FULFILLMENT

OF THE REQUIREMENTS FOR THE DEGREE OF

Master of Technology

In

Electronics and Instrumentation Engineering

By

KULDEEP SINGH

212EC3163

Under the supervision of

Prof. U.K.Sahoo

Department of Electronics and Communication Engineering

National Institute Of Technology Rourkela

National Institute Of Technology

Rourkela

CERTIFICATE

This is to certify that the thesis entitled, “

ANN BASED INTELLIGENT PRESSURE SENSOR IN

NOISY ENVIRONMENT” submitted by Mr. KULDEEP SINGH in partial fulfillment of the requirements for the award of Master of Technology Degree in Electronics & communication

Engineering with specialization in “Electronics and Instrumentation Engineering” at the National

Institute of Technology, Rourkela is an authentic work carried out by him under my supervision and guidance.

To the best of my knowledge, the matter embodied in the thesis has not been submitted to any other University / Institute for the award of any Degree or Diploma.

Date: Prof. U. K. SAHOO

Department Of Electronics and Communication Eng.

National Institute of Technology

Rourkela-769008

ACKNOWLEDGEMENTS

This project is by far one of the most significant accomplishment in my life and it would not be possible without peoples who supported me and believed in me.

I would like to extend my gratitude and my sincere thanks to my honorable, esteemed supervisor Prof. U.K. SAHOO. He is not only a great lecturer with deeper vision but also and most importantly a kind person. I sincerely thank for his exemplary guidance and encouragement in my life. His trust and support inspired me in the most important moments of making right decisions and I am glad to work with him.

I would like to thank all my teachers Prof. T. K. Dan, Prof. U .C. Pati ,Prof. S. Meher,

Prof. A.K.Sahoo for providing a solid background for my studies and my research work thereafter.

All of them have been great sources of inspiration to me and I really thank them a lot for supporting so much.

I would like to thank all my friends and especially my classmates and lab mates for their wonderful support for each and every thing ,and I think without them it was really not going to be very easy for me to complete my work. I’ve really enjoyed their company so much during my stay at NIT, Rourkela.

KULDEEP SINGH

ABSTRACT

There are so many problems that arise due to nonlinearity, direct digital readout is one of them i.e. with the help of such devices taking the direct digital readout is not possible. Therefore we are bound to operate the instrument in their linear range of the characteristics only ,in other words we can say that the usable range of the instrument is getting restricted due to this problem. not only the usable range ,but also the accuracy of the instrument is affected if we are not able to use the full range of the instrument. One more factor important to mention is the variation of nonlinearity from instrument to instrument place to place and time to time ,sometimes it depends on some uncertain factors which are not possible to predict. Here capacitive pressure sensor(CPS) is the topic of discussion for adaptive linearization. We can introduce an intelligent inverse model in series with the nonlinear instrument or a sensor to reduce the nonlinearity present there.

A switched capacitor circuit (SCC) is used to convert the change in capacitance of the CPS.

Because of the change in applied pressure the capacitance of the CPS changes, this change in capacitance of the CPS due to applied pressure is converted into proportional voltage which can then be applied to an ANN model to estimate the pressure applied.

This model gives satisfactory performance for wide temperature range (-20 to 70 ) and signal to noise ratio of 40 dB and above.

Contents

Figure2 1 Typical structure of the CPS 2 ......7

CHAPTER 1 ...............................................................................................................................9

INTRODUCTION ...................................................................................................................9

Developing direct model: ................................................................................................... 10

Developing inverse model: ................................................................................................ 10

Sensor: .............................................................................................................................. 11

Elements of generalized measurement system: ................................................................... 12

Functional elements of an instrumentation system: ............................................................... 14

Properties of a sensor or measurement system: .................................................................. 15

Dynamic characteristics of the instrument:......................................................................... 18

Speed of response: ............................................................................................................. 19

ANN(ARTIFICIAL NEURAL NETWORK): ........................................................................ 20

Environmental parameters: .................................................................................................... 24

Literature survey: .................................................................................................................. 24

Problem formulation:............................................................................................................. 27

CHAPTER 2 ............................................................................................................................. 30

Direct and inverse modelling of the CPS by using intelligent ................................................. 30 techniques: ............................................................................................................................ 30

Capacitive pressure sensor (CPS): ......................................................................................... 31

MODEL OF THE CPS: ..................................................................................................... 31

SWITCHED CAPACITOR CIRCUIT: .............................................................................. 35

Development of an intelligent model of the CPS: .................................................................. 36

Direct modelling:................................................................................................................... 36

Inverse modeling: .................................................................................................................. 37

Simulation studies: ................................................................................................................ 38

The MLP based direct modeling: ........................................................................................... 38

The MLP based inverse modelling:........................................................................................ 39

Conclusion: ........................................................................................................................... 44

LIST OF FIGURES

Figure 1. 1 Sensing process ....................................................................................................... 11

Figure 1. 2 Block diagram of generalized measurement system ................................................. 12

Figure 1. 3 Primary Sensing element ......................................................................................... 13

Figure 1. 4 Process after primary sensing element Variable conversion element: ....................... 13

Figure 1. 5 General structure of an instrumentation system ........................................................ 14

Figure 1. 6 Reproducibility ........................................................................................................ 16

Figure 1. 7 Zero drift ................................................................................................................. 17

Figure 1. 8 Zonal drift ............................................................................................................... 17

Figure 1. 9 Span drift ................................................................................................................. 18

Figure 1. 10 Neural network structure........................................................................................ 20

Figure 1. 11 Nonlinear model of a neuron.................................................................................. 21

Figure2 1 Typical structure of the CPS 31

Figure2 2 Graph of capacitance as a function of applied pressure .............................................. 34

Figure2 3 Graph between normalized voltage and normalized pressure ..................................... 35

Figure2 4 A scheme of direct modeling of a CPS and SCC using ANN based model ................. 37

Figure2 5 Development of an inverse ANN model of CPS ........................................................ 37

Figure2 6 Plots of true and estimated forward characteristics of the CPS at and by MLP ......... 39

Figure2 7 Plot of forward, inverse and overall characteristics of the CPS by MLP at ................. 40

Figure2 8 Plot of forward, inverse and overall characteristics of the CPS by MLP at ................. 40

Figure2 9 Plot of forward, inverse and overall characteristics of the CPS by MLP at ................. 41

List of abbreviation

ANN

MLP

- artificial neural network

- multilayer perceptron

BP Algorithm - back propagation algorithm

RBFNN - radial basis function based neural network

FLANN - functional link artificial neural network

CPS - capacitive pressure sensor

SCC - Switched capacitor circuit

CFLANN

LMS - Least mean square

CHAPTER 1

INTRODUCTION

There are number of instrumentation systems and sensors that exhibit nonlinear input-output characteristics, such sensors are restricted to be used within their linear operating range otherwise they will present erroneous data at the output. There are so many reasons behind the systems nonlinearity. The factors which introduce nonlinearity or at least affect the performance of the sensor are as follows

1. Variation in environmental conditions such as change in temperature, pressure, humidity etc. (since these factors vary from place to place.)

2. Aging of the instrument or sensor is another factor which introduces nonlinearity.

There are so many problems that arise due to nonlinearity, direct digital readout is one of them i.e. with the help of such devices taking the direct digital readout is not possible. Therefore we are bound to operate the instrument in their linear range of the characteristics only ,in other words we can say that the usable range of the instrument is getting restricted due to this problem. not only the usable range ,but also the accuracy of the instrument is affected if we are not able to use the full range of the instrument. One more factor important to mention is the variation of nonlinearity from instrument to instrument place to place and time to time ,sometimes it depends on some uncertain factors which are not possible to predict. Here capacitive pressure sensor(CPS) is the topic of discussion for adaptive linearization. We can introduce an intelligent inverse model in series with the nonlinear instrument or a sensor to reduce the nonlinearity present there. On introduction of such an inverse model it permits two things

1. Accurate measurement

2. Use of full dynamic range of the instrument

Although there exists some nonlinearity compensators which are of fixed type, but these compensators are not suitable for the nonlinear devices which vary with time. Hence adaptive techniques by using Artificial Neural Network (ANN) preferred for such cases.

Hence the major work done in the present thesis is as

1. Developing direct model

2. Developing inverse model

Developing direct model:

It is nothing but the development of the adaptive system identification model for the capacitive pressure sensor to analyze the inherent dynamic nonlinearity present in input and output characteristics of the sensor (this nonlinearity may be due to variation in temperature or another parameter but we are considering only temperature problem)

Developing inverse model:

It is development of the inverse model which is supposed to be cascaded in series with the direct model of the CPS to compensate the nonlinearity of the sensor.

The above mentioned models can be modelled by using

1. Multilayer perceptron ( MLP)

2. Radial Basis Function based Neural Network (RBFNN)

3. Functional Link Artificial Neural Network (FLANN)

4. Artificial Neural Network (ANN)

These models when cascaded in series with the sensor or instrument required, offer extended linearity.

A switched capacitor circuit (SCC) is used to convert the change in capacitance of the CPS.

Because of the change in applied pressure the capacitance of the CPS changes, this change in capacitance of the CPS due to applied pressure is converted into proportional voltage which can then be applied to an ANN model to estimate the pressure applied.

Here in present thesis multilayer perceptron is utilized to model the CPS characteristics ,since there are due advantages of this model which are as follows

1. Direct digital readout of the applied pressure is possible

2. More flexible than others

3. More accurate in changing and noisy environment

This model gives satisfactory performance for wide temperature range (-20 to 70 ) and signal to noise ratio of 40 dB and above.

Sensor:

A device which detects or measures a physical property and records, indicates, or otherwise responds to it ,is known to be a sensor .

Figure 1. 1 Sensing process

There are some basic differences of sensor with a transducer which can be explained as – sensor sense change in input energy given to it and produces a change another form of energy or same form of energy while transducer changes a particular measuring variable into an usable output.

Elements of generalized measurement system:

Figure 1. 2 Block diagram of generalized measurement system

The generalized measurement system or a sensor consists of following elements

1. Primary sensing element

2. Variable conversion element

3. Variable manipulation element

4. Data transmission element

5. Data presentation element

Primary sensing element:

Figure 1. 3 Primary Sensing element

The quantity under measurement makes its first contact with the primary sensing element in other words we can say that the measurand is first detected by the primary sensor .the output of the primary sensing element is given to the next stage of the measurement system which is variable conversion element.

Figure 1. 4 Process after primary sensing element Variable conversion element:

The signal coming out of the primary sensing element may be electrical signal of any form like it may be a voltage ,current, frequency signal or may be a function of any other electrical parameter.

If the signal coming out of the primary sensing element is not suitable to be given into the variable manipulation element we need this block (in some cases we don’t need this block ). This block

makes the output of the sensing element suitable to be operated in manipulation element preserving the information of the signal.

Variable manipulation element:

This block manipulates the signal preserving the original nature of the signal, this block along with the variable conversion element is also called as data conditioning element or signal conditioning element.

Data transmission element:

When the elements of a measurement system are separated physically from each other then it is necessary to transmit the information from one block to another or sometimes from one place to place. This kind of function is implemented with the help of data presentation element.

Data presentation element:

The information about the physical variable to be measured is supposed to be conveyed to the observer in some suitable form so that it may be easy to interpret, such a job is done by data presentation element. It may be some recorder or any display device.

Functional elements of an instrumentation system:

Figure 1. 5 General structure of an instrumentation system

Properties of a sensor or measurement system:

The characteristics of a sensor or any measurement system can be broadly categorized into two which are as

1. Static characteristic

2. Dynamic characteristics

Static characteristic:

The characteristics of a sensor which do not vary with time is called as static characteristic this can again be categorized as

1. Accuracy

2. Sensitivity

3. Reproducibility

4. Drift

5. Static error

6. Dead zone

Accuracy:

Accuracy is defined as the deviation of the measured value from the true value or we can say that it is the closeness of the measured value to the true value.

In the above equation

In case of multi error systems the rooy mean square approach is more practical where total performance error can be can be given as

Sensitivity:

It is defined as inverse of the full scale value of the measurand .

s = 1/full scale value

Reproducibility:

Reproducibility of a sensor is defined as the capability of that sensor or measuring instrument to generate the same result again and again in respond to the same input . one more term associated with the precision is repeatability which is nothing but the

Figure 1. 6 Reproducibility

Drift:

It is the gradual shift in the measured value with a given input .drift may be of following types

1. Zero drift

2. zonal drift

Figure 1. 7 Zero drift

3. span drift or sensityvity drift

Figure 1. 8 Zonal drift

Figure 1. 9 Span drift

static error:

It is defined as the difference between measured value and actual value of the quantity being measured .

Dead zone:

The range or zone of an instrument for which the instrument is not going to respond to a given input is known to be the dead zone.In other words we can say that it is the largest change of input quantity for which there is no output.

Dynamic characteristics of the instrument:

Such characteristics of the instrument which vary with respect to time is known to the dynamic charateristic of the instrument, these are as follows

1. Speed of response

2. Fidelity

3. Lag

4. Dynamic error

Speed of response:

It is defined as the rapidity with which an instrument responds to thechanges in the input.the speed of response for an instrument shows how active and fast the system is

.

Fidelity:

Fidelity of an instrument is defined to be the degree to which that is capable of faithfully reproducing the changes in the input.

Lag:

Each and every system needs some time to respond to the changes in input,which we call lag.lag is defined as the retardation or delay in response to the changes in input of a system

Lag is of two types

1. Retardation lag

2. Time delay

Retardation lag:

Here in this case the measurement system starts responding to the changes in the input as soon as there is change in the measured quantity.

Time delay:

This kind of lag causes dynamic error,here the measurement system starts responding to the input once it is given to the system just after the dead time.

Dynamic error:

Dynamic error is the error defined as the difference between the true valueof the quantity whcich is being measured with changing time and the measured value .here static error is not considered.

ANN(ARTIFICIAL NEURAL NETWORK):

Figure 1. 10 Neural network structure

Models of a neuron:

A neuron which we call an information processing unit is nothing but a fundamental operation to the neural network. The block diagram of neuron is as shown below.

Figure 1. 11 Nonlinear model of a neuron

As shown in above block diagram the model of the neuron consist of

1) Connecting links

2) Summing element

3) Activation function

Connecting link:

Generally the connecting links of the neuron are characterized by the weight or the strength.

Summing element:

The purpose of the summing element is to add the incoming signals having the weight of the synapses of the neuron.

Activation function:

Since it squashes the amplitude range of the output signal to some definite value, hence we also call it a squashing function. The purpose of the activation function is to limit the amplitude of the output of the neuron.

Multilayer perceptron:

It is a kind of multilayer feed forward network, which consists of a set of source nodes (also known as sensory units). These sensory units constitute the

(a) Input layer

(b) One or more than one hidden layers

(c) And the output layer

The input signal here propagates (on a layer by layer basis) in forward direction. The benefit with the multilayer perceptron is that it has been successful to solve diverse problems. It is done by training them in supervised manner and the algorithm used is a popular algorithm known to be error back propagation algorithm. The error back propagation algorithm is based on error correction learning rule. The error back propagation algorithm is implemented in two passes which are explained in the following section.

Back propagation algorithm:

Back propagation is an abbreviation for “backward propagation of errors.” Back propagation algorithm is a method of training an ANN in combination with an optimization method. By this method we calculate the gradient of a loss function with respect to all weights in the network. since it requires a known, desired output for each input value to calculate the gradient of loss function.

Hence we consider it a supervised learning, although we can use it in case of unsupervised learning. The condition with the BP algorithm is that the activation function which is used by the artificial neurons must be differentiable.

Back propagation learning algorithm can be categorized into two phases which are as

1. Propagation

2. Weight update

Phase 1: propagation

The propagation step of this algorithm involves following steps

1. Forward propagation

2. Backward propagation

(a) Forward propagation of a training pattern’s input through the network to generate the propagation’s output activations.

(b) Backward propagation of the propagation’s output activations through the neural network by using the training pattern target to generate the deltas of all output and hidden neurons.

Phase 2: weight update

The synapse follow these steps for each weight

1. To find the gradient of the weight get the product of its output deltas and input activations.

2. Then subtract a part of the gradient from the weight.The percentage which is subtracted from the weight affects the speed of the learning as well as the quality of the learning. This we call learning rate, the training rate is directly proportional to this ratio i.e. greater the ratio faster will be the training of the neurons, but lower ratio will result into more accurate training. The sign of the gradient of a weight shows increment of the error, this is why the updating of the weight must be in opposite direction.

Environmental parameters:

Other than the characteristics of the instrument or a sensor there are some environmental parameters which affect the performance of the sensor ,these are temperature,humidity,pressure etc. Aging is also one of the very important factors to affect the performance of the sensor.Here in this thesis mainly one parameter i.e.temperature is considered to study the performance of the sensor.

Literature survey:

Capacitive pressure sensor is a pressure sensor which is having some due advantages over other pressure sensors .some advantages of capacitive pressure sensor are as follows

1. Low power dissipation

2. Higher sensityvity

3. Less sensitive to environmental effects

4. Robust structure

Because of above mentioned advantages of the capacitive pressure sensor ,it has very wide range of applications . Capacitive pressure sensor senses the pressure applied to it because of the deflection of its diapragm .due to the deflection of the diapragm the capacitance of the capacitive pressure sensor’s chamber changes resulting in change in pressure of the sensor.

Since most of the sensors are having in built non-linearity or nonlinear input output characteristics hence direct digital read out from such sensors is very difficult to get.becuase of this problem we use the sensors in their linear operating range .

Although CPS is having so many advantages as mentioned above but the output characteristics of this pressure sensor is also nonlinear. Also the sensityvity of the pressure sensor near the linear operating range of sensor is not so enough to ignore the stray capacitance effect.because of the nonlinearities present in the sensors we face so many problems ,some of them may be summerised as

1. Difficulty in on chip interface

2. Difficulty in calibration

3. Difficulty in direct digital read out

These above mentioned difficulties arises due to the nonlinearity present in the sensor

,wchich may have creeped in due to variation in environmental conditions or may be because of aging of the sensor ,hence to avoid the above mentioned difficulties our sensor should have linear

input-output charcteristics and also it should be independent of the environmental changes as well as aging .

There are so many methods to compensate the nonlinear response characteristics of the sensor like switched capacitor charge balancing technique,a ROM based look up table,nonlinear encoding scheme etc.The sensor should have not only the linear charcateristics but also it should fulfill the demand of low cost and other required features.Piezo-resistive pressure sensor (bridge based integrated pressure sensor) fulfills the demand of having low cost and small range linear input-output characteristics. Piezo-resistive pressure sensor finds application in biomedical instrumentation ,it (a thin diapragm diffused piezo-resistive pressure sensor )was developed using monolithic IC techniques.the reason behind using integrated circuit technology is that it provides many advantagesin fabrication of pressure sensors particularly the capability to control the geometry accurately on small dimension.such kind of advantages provide reliabilty with stability.

Pressure sensors having their principle of operation on the piezo-resistive effecthave some advantages over their counterpart depending upon other pressure sensitive effects .The advantages are that these transducers operate at low stress level and the resistance change which they exhibit is linear function of pressure and it is quiet sensitive to pressure changes for a wide range.

For estimating the nonlinearity and to get the direct digital read out from a pressure sensor

(here we are considering the CPS ),an ANN based modelling technique is proposed .the problem with this technique is that when we don’t consider the change in ambient tepmerature into account

,this is quite satisfactory but if the change in temperature is taken into account (if the temperaure changes frequently),then the problem becomes two dimensional making the situation more complex .now we need complex signal processing to asses this problem.for such kind of problems two below mentioned techniques are used with some success

1. Micro-comuter based 2-dimensional look–up table

2. Approach based on oversampling ∆-Σ demodulator method

3. Complex signal processing

If we take the temperature into considering 2-layer multi-layer perceptron(MLP) based

ANN model is proposed here in this thesis to auto calibrate and to compensate the nonlinearity ofa CPS model with the consideratin of variation in ambient teperature.here we use a switched capacitor circuit (SCC) after CPS ,the switched capacitor circuit converts the change in capacitance of the CPS into proportional volatge.the temperature range here is taken as from -

20

0

C to 70

0

C ,all of first we train the network for this temperature range .there are two training modes in this scheme

1. Series training mode

2. Parallel training mode

In case of direct modelling the ANN is trained in parallel mode for estimating the capacitance of the CPS ,but in case of inverse modelling the ANN is trained in series mode for estimating the capacitnce of the CPS i.e. applied pressure which will in this case be independent of the ambient temperature .

Problem formulation:

As we already discussed the problems associated with nonlinearity of the sensors, the nonlinearity present in the sensor limits the performance of the sensor ,few of them are as

1. It limits the dynamic range of the sensor or devices in use ,this introduces some other problems as the difficulty in direct digital readout of the output for the whole range of the sensor.

2. It also limits the utilization of the full potential of the sensor

3. Effect on accuracy of the measurement

To avoid these problems all of first we need to eliminate the nonlinearity present in the sensor which is the real challenge for designing and implementing the intelligent sensors. In few of the cases the nonlinearity present is of fixed type i.e. it does not vary with time, then in that case we can use the existing nonlinearity compensation techniques. but it becomes more complex when the nonlinearity of the sensors vary with time which is the real case in practice ,more than this the varying behavior of the nonlinearity of the sensor which is generally unknown makes the situation worse. As we know that for inverse model we connect it in series with the device ,hence the adaptive inverse model of the concerned sensor which is CPS here is connected in series with the sensor, so that we can compensate for the nonlinearity present in the device and the direct digital readout may be possible in the required sensor for the complete range of the sensor. A scheme of direct modelling and inverse modeling can be developed by using different ANN structure. The motive of the direct modelling is calibration of inputs and to estimate the internal parameters of the CPS. The direct model is developed to get an ANN model of the sensor (CPS) in such a way that we may match the output of the CPS and the ANN closely. the motive of the inverse modelling is to estimate the applied input pressure .once the model of the CPS is developed ,the output of the

CPS provides a voltage signal which is proportional to the change in capacitance (the change in capacitance is due to change in applied pressure).The CPS is interfaced with switched capacitor circuit (SCC). There are so many techniques to develop the adaptive inverse model of the CPS

few of them are as Least Mean Square (LMS) algorithm, Recursive Least Square (RLS )algorithm etc.

CHAPTER 2

Direct and inverse modelling of the CPS by using intelligent techniques:

The capacitive pressure sensor (CPS) finds many applications because of its advantages as we mentioned earlier in previous chapter, here the capacitance of the chamber changes with change in pressure or with application of pressure .but along with the advantages of the CPS we face some difficulties in modelling the CPS which are as

1. There exist nonlinearity in the transfer function of the CPS, this checks the direct digital readout and limits the dynamic range of the sensor.

2. Accuracy of measurement in the sensor, this is much affected by aging of the sensors and also by variations in environmental conditions

Usually the nonlinearities introduced by above mentioned factors varies with time and cannot be predicted since it depends upon so many indefinite factors.

Here we will deal with the design and development of models of the CPS which are as direct model and inverse model .the direct model of the CPS which is much similar with as system identification in control system develops the electronic model of the CPS. this is developed by using ANN techniques in such a way that output of the sensor and that of the model may be identical. Then the inverse model developed compensates the nonlinearity of the sensor. This is similar to channel equalization technique in digital communication to cancel the adversarial effects of the channel.

Capacitive pressure sensor (CPS):

MODEL OF THE CPS:

The commonly used structure of the CPS is shown as following. Here we keep one of the plates of the CPS fixed which is made up of metal disc and the other plate is a flexible circular diaphragm which is clamped around its circumference. The dielectric material is air i.e. the value of dielectric constant is kept as one (

1

). Since the diaphragm is one of the elastic sensing elements

,

it bends with the application of pressure.

The deflection of the diaphragm

d

Figure2 1 Typical structure of the CPS

as a function of its radius r is given as

d

(

r

)

3

16

1

r

R

2

2

1

Eh

3

2

(1.1)

Where R is the radius of the circular diaphragm ,h is the thickness of the diaphragm, r is the radius of the diaphragm, µ is the Poisson ratio and E is the elasticity of the diaphragm

The capacitance of the CPS or we can say that of the chamber is given as

C

(

P

)



0

0

R d

0

2

r

d

(

r

)

dr

(1.2)

Where

o

is the permittivity of the free space

r

is the relative permittivity

From equations (1.1) and (1.2) the value of the capacitance as a function of fractional pressure can be expressed as

C

C

0

1

x

𝑡𝑎𝑛ℎ

−1

(√𝑥) (1.3)

Where

x

P

P

max

(≤1)

and

P

max

16

3

1

E

2

t

3

d

0

R

4

(1.5)

P

max

is the maximum pressure which can be applied and it causes a center deflection i.e. equivalent to chamber depth zero (P=0),

C

0

R

2

0

r

d

0

(1.6)

We can write the capacitance as a function of the fractional pressure

 

C

0

1

x

1

x

C

0

 

 

(1.7)

Where

 

C

0

1

1

x

.

x

(1.8)

The parameters

 and

P

max can be determined by measuring the capacitance of the pressure sensor.

The capacitance of the capacitor as a function of the fractional pressure can be plotted as shown below

Figure2 2 Graph of capacitance as a function of applied pressure

Input-output relationship of CPS with temperature and pressure as its inputs:

The output equation of the CPS as a function of the pressure (P) and temperature (T) is given as ,

C

N

 

(1.9)

C

0

,

C g T

0 1

 

 

,

0

  

2

T

(2.0)

Where pressure i.e.

P

0 at reference temperature

When pressure is applied to the sensor ,the change in capacitance

,

C

0

.

Where

P

N

1

1

P

N

Where

=sensitivity parameter of the CPS and it varies with the geometrical structure of the CPS and normalized pressure

P

N

P

P

max

Figure2 3 Graph between normalized voltage and normalized pressure

SWITCHED CAPACITOR CIRCUIT:

We use a switched capacitor circuit to interface with the CPS, as shown in the figure the capacitor of the CPS. The purpose of the SCC (switched capacitor circuit) is to provide an equivalent voltage signal which is proportional to the capacitance change in the CPS because of the applied pressure. The operation of the can be explained as it is controlled by the reset signal

,if the reset signal

 

v

, value

reset signal

 

1 , the total charge

 

R

voltage which is

V

0

 

,where

K

 

V

R

C

S

.with change in ambient temperature the output of the CPS changes as the applied pressure changes. Then to adjust the normalized output of the SCC in such a way that

V

N

C

N

, we choose proper values of the

Development of an intelligent model of the CPS:

In this section direct modelling and inverse modelling of the CPS by using ANN structure is proposed. The purpose of the direct modelling is to calibrate the inputs and to estimate the internal parameters of the CPS, whereas that of the inverse modelling is to estimate the applied input pressure.

Direct modelling:

The direct modelling of the CPS is similar to system identification problem in control system. The motive of the direct model is to get an ANN model of the CPS so that output of the CPS matches closely to that of the CPS. The output of the model of the CPS which is interfaced with SCC provides a voltage signal proportional to the change in capacitance due to applied pressure. By connecting the switched capacitor interface circuit with the CPS we can get an equivalent voltage signal which is proportional to change in capacitance. As shown in figure drawn below the normalized pressure ( P ) and normalized temperature (

N

T

N

)are given as inputs (since temperature also affects the output voltage of the CPS). The output voltage of the CPS ( V ) and that of the

N

network model (

V

'

N

) are compared to get the error signal (

e ). The error signal is used to update the model.

Figure2 4 A scheme of direct modeling of a CPS and SCC using ANN based model

Inverse modeling:

Figure2 5 Development of an inverse ANN model of CPS

The inverse modelling scheme of the CPS by using different ANN techniques to estimate the applied input pressure is shown as above, which is analogous to a scheme used in digital communication receiver to cancel the adverse effects of the channel called as channel equalization.

To get the direct digital readout of the applied input pressure and to compensate for the unwanted effects on the sensor due to nonlinear response characteristics of the sensor this can be cascaded with the sensor model. The generation of the training data and testing data patterns is same as that of the direct model of the CPS ,the difference is here normalized temperature (

T

N

) and the CPS

output ( V ) are taken as inputs and normalized pressure (

N

P ) is taken as desired output of the

N

model.

Simulation studies:

The MLP based direct and inverse modeling of the CPS is presented in this section which have been carried out in MATLAB environment. The output voltage from SCC at reference temperature i.e. at

0

25 C

is obtained for by taking different values of normalized pressure. The values of the normalized pressure is chosen in between 0.1 to 0.7 by taking an interval of 0.05. In this way 13 pairs of the input-output pattern forms a set of pattern at reference temperature. Then the values of the

1

and

2 are taken as

2.0 10

3

and

g t and

1

 

g

2

 

3

respectively to get values of the functions

 is selected to be 0.64 remaining details are as below.

The MLP based direct modeling:

To get direct model of the CPS simulation studies are carried out. For this purpose a two layer

MLP with following specifications is chosen

Structure is chosen to be 3-5-1 i.e. number of input layers are 3

Number of hidden layers are 5

And number of output layers are 1

The activation function used for hidden layer and for output layer is tanh(. ).

We are using back propagation algorithm where learning rate parameter is selected to be 0.5 and the momentum rate parameter is selected to be 1 to adapt the weights of the MLP. The input patterns to the MLP are normalized temperature (

T

N

) and normalized pressure ( P ), while the

N

desired pattern of the MLP is the output from the SCC (

V

N

C

N

). The weights of the ANN model are updated by using BP algorithm after application of each pattern, we get one iteration of training after completion of all patterns of all training sets. After some 10,000 iterations to train the ANN the weights of the MLP are frozen and stored and we’ll load these frozen weights into the MLP during testing phase. Now after feeding the inputs

T

N

to the model, the output of the model is compared with the real output. The response characteristics of the CPS at different temperature values is as follows

Figure2 6 Plots of true and estimated forward characteristics of the CPS at and by MLP

The MLP based inverse modelling:

In case of inverse modeling we choose same MLP with same number on input output and hidden layers. Also the number of input patterns is again kept 13 during training phase. Here also the learning rate parameter and momentum parameter are kept as 0.5 and 1 respectively. After 10,000 iterations by using BP algorithm the obtained patterns are frozen and stored in memory. Now in

testing phase, the output of the CPS i.e.

V is given as input to the MLP network with normalized

N

temperature

T

N

. Now we get the estimated pressure

P

'

N

from the MLP network. The response characteristics of the inverse model at different temperature is as follows

Figure2 7 Plot of forward, inverse and overall characteristics of the CPS by MLP at

Figure2 8 Plot of forward, inverse and overall characteristics of the CPS by MLP at

Figure2 9 Plot of forward, inverse and overall characteristics of the CPS by MLP at

0

70 C

Figure2 10 The resulting error

Figure2 11 Normalized CPS response characteristics

Figure2 12 Noisy SCC output

Conclusion:

The conclusion from this thesis which can be drawn is as follows

1. The problem of nonlinearity can arise due to any of the following factors i) It can be because of the aging of the sensor. ii) The nonlinearity in the sensors may be introduced because of the constructional limitations of the sensor. iii) Environmental parameters such as change in temperature, change in humidity level or change in atmospheric pressure is also one of the major factors which introduces nonlinearity into the system or the sensor.

2. The problem of nonlinearity if creped into the system that may lead to difficulties in utilizing full range of the sensor or it may lead to some other problems which are as i ) it may lead to inaccuracy in the result of the measurement ii ) it may limit the dynamic range of the sensor i.e. the linear region of the sensor iii ) if nonlinearity is introduced into the system it may lead to difficulties in utilizing full potential of the sensor.

3. Here in this thesis adaptive methods to compensate the nonlinearity of the sensor is suggested.

4. The sensor of interest here is a capacitive pressure sensor (CPS).

5. The intelligent methods can be based on any of the following structures

a. MLP b. FLANN c. CFLANN d. RBFNN

The learning algorithm which can be employed may be a. LMS algorithm b. BP algorithm c. RBF learning algorithm

In this thesis multilayer perceptron (MLP) based adaptive method by using BP algorithm is employed to compensate the nonlinearity of the sensor, and the nonlinear compensation is achieved by using i. Direct modelling of the sensor ii. Inverse modelling of the sensor

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