An artificial neural network-based smart capacitive pressure sensor

E L S E V I E R Measurement 22 (1997) 113-121

Measurement

An artificial neural network-based smart capacitive pressure sensor

Jagdish C. Patra Department of Applied Electronics and Instrumentation Engineering, Regional Engineering College, Rourkela,

Orissa 769008, India

Abstract

A smart capacitive pressure sensor (CPS) using a multi-layer artificial neural network is proposed in this paper. A switched capacitor circuit (SCC) converts change in capacitance of the CPS due to applied pressure into a proportional voltage. The nonlinear characteristics of the CPS make the SCC output nonlinear. Further, due to dependence of the CPS characteristics on ambient temperature, the SCC output becomes quite complex for obtaining correct digital output of the applied pressure, especially when the ambient temperature varies with time and/or place.

To circumvent this difficulty, an ANN is employed to model the sensor. By training the ANN model suitably, the digital readout of the applied pressure can be obtained which is independent of ambient temperature. A new idea for collecting temperature information from the sensor characteristics themselves, and automatic feeding of this information into the ANN-based CPS model is proposed. From the simulation results it is verified that the ANN model can give correct readout of the applied pressure within +__ 1% error (FS) over a wide range of temperature variation starting from -20°C to 70°C. This modeling technique of the CPS provides greater flexibility and accuracy in a changing environment. © 1998 Elsevier Science Ltd.

Keywords: Smart sensor; Pressure sensor modeling; Artificial neural networks; Multilayer perceptron; Automatic temperature compensation

1. Introduction

Recently, the terms smart, intelligent and knowledge-based instrumentation have been used for many systems due to the application of advanced information techniques in instrumentation and measurement. The information processing techniques enable the smart instruments to correct or compensate for inadequacies and errors such as linearization and automatic calibration etc. of the sensors [ 1 ].

In modern sophisticated and complex systems such as process control, robotics, bio-medical etc., pressure sensors have been used very extensively.

0263-2241/97/$17.00 © 1998 Elsevier Science Ltd. All rights reserved. Pll S0263-2241 (97)00074-2

The capacitive pressure sensor (CPS) possesses many advantages with respect to other varieties of such sensors in terms of low power dissipation, high sensitivity and low temperature dependence, however, its response characteristics are highly nonlinear in nature. In the event of any change in ambient temperature, the CPS characteristics becomes quite complex and complex signal processing techniques may be required to obtain correct digital readout of the applied pressure. As the change in capacitance is a function of two vari- ables, i.e. applied pressure and ambient temperature, the problem becomes two-dimensional (2-D).

114 J. C Patra / Measurement 22 (1997) 113 121

For obtaining a solution to this 2-D sensor problem, several approaches have been reported with limited success. A scheme of a microproces- sor-based 2-D lookup table in which the coefficients of the interpolation polynomials are stored has been reported [2]. Another approach to this problem using a switched capacitor bridge has been reported [3]. Here, by using an over-sampling A-E demodulator and complex signal processing techniques the sensor model is stored in ROM from which digital readout of the applied pressure can be obtained.

A promising approach to such 2-D sensor problems is a model-based technique which can provide versatility, flexibility and ease of implementation. Models of measurement systems in schemes of representation are the basis of description, analysis and design of such systems. Measurement may be considered as a modeling process and the results of measurement is a model of the manifestation of a variable, or of a complete system. Identification is a method of empirical establishment of the model of the system which may determine both its structure and parameters [4].

Artificial neural network (ANN) techniques have emerged to become highly successful in solv- ing numerous complex and intractable problems in science and engineering. These networks are endowed with some unique attributes: the universal approximation (input-output mapping), the ability to learn from and to adapt to their environment, and the ability to invoke weak assumptions about the underlying physical phenomena responsible for generation of the input data. Some of the advantages of using ANNs for modeling of nonlinear systems are: (i) the ANN is capable of learning complex input output patterns from a set of training patterns; (ii) when implemented in hardware form, it has potential to be inherently fault tolerant in the sense that its performance degrades grace- fully under adverse operating conditions; and (iii) the ANNs have a built-in capability to adapt to their synaptic weights to changes in surroundings [5].

In the direction of smart sensors, an ANN- based CPS model for estimation of its nonlinearity and for obtaining direct digital readout of applied pressure with quite satisfactory results was first

reported in Refs. [6, 7]. In this technique, a simple functional-link ANN was used to model the CPS in which the power series coefficients required for estimation of nonlinearity (direct modeling) and for estimation of applied pressure (inverse modeling) were obtained by applying a simple learning algorithm.

To tackle the 2-D sensor problem a multi-layer ANN has been proposed [8]. Here, two modeling techniques, i.e. direct modeling for estimation of sensor capacitance, and inverse modeling for estimation of applied pressure have been proposed under a changing temperature environment with quite satisfactory results. In the present paper, a novel technique based on multi-layer ANNs is proposed for estimation of applied pressure which is independent of ambient temperature. The major difference between the present paper and Ref. [8] is the method of collecting and feeding the temperature information to the ANN model. In the present paper, a new idea for generation of temperature information from the sensor characteristics themselves, and automatic feeding of this information to the ANN model is proposed. Whereas, in the latter paper the temperature information is collected from some other source, maybe by measuring the room temperature, and is to fed manually to the ANN model to obtain the correct digital readout of the applied pressure.

The structure of the rest of the paper is as follows. Section 2 describes a mathematical model of the CPS, and in Section 3 the switched capacitor circuit is described. In Section 4, the multi-layer perceptron network has been explained concisely. The proposed ANN-based modeling scheme for obtaining correct readout of the applied pressure under a changing temperature environment has been explained in Section 5. In Section 6 the results obtained from extensive simulation studies have been reported, and finally, the conclusions are drawn in Section 7.

2. Model of a capacitive pressure sensor

A CPS senses the applied pressure due to the elastic deflection of its diaphragm. In the case of a simple structure, this deflection is proportional

J. C Patra / Measurement 22 (1997) 113-121 115

to the applied pressure P and the sensor capacitance C(P) and varies hyperbolically. Neglecting higher order terms, C(P) may be approximated by

1-c~ C(P)= Co + AC(P) = Co + Co - - -- Co(1 +7),

1 --PN

(l)

where Co is the sensor capacitance when P= O; is the sensitivity parameter which depends upon the geometrical structure of the sensor; PN is the normalized pressure given by

PN = PIP . . . . (2)

where Pm~x is the maximum permissible input pressure to the sensor; and 7 = (1 - a)/( 1 - PN).

In the 2-D problem discussed in this paper, the sensor capacitance is a function of the applied pressure and the room temperature T. Assuming that the change in capacitance due to change in temperature is linear and independent of the applied pressure, the CPS model may be expressed as

C(P,T) = C O + AC(P,T) = Cof l (T)

+ AC(P, To)f2(T ), (3)

where AC(P, To) represents the change in capacitance due to the applied pressure at the reference temperature To as given in Eq. (1). The functions f l (T) and fz(T) are given by

f , ( T ) = 1 + i l l (T- To); fz(T) = 1 +fl2(T- To),

(4)

where the coefficients fll and f12 may have different values depending on the CPS chosen. The normalized capacitance of the CPS, CN, is obtained by dividing Eq. (3) by Co and may be expressed as

C N = C(P, r)/Co =]'1 (r) + Yf2 (T). (5)

3. Switched capacitor interface circuit

A switched capacitor circuit (SCC) for interfac- ing the CPS is shown in Fig. 1, where the CPS is represented by C(P). The purpose of the SCC is to obtain a voltage signal proportional to capaci-

VR

] i r - - - - I

C(P)

-----~ ] Cs

m

..___._J t t vo

Fig. 1. A switched capacitor interface circuit.

tance change in the sensor due to applied pressure to the CPS. The circuit operation can be controlled by a reset signal q~. When qS=l (logic 1), C(P) charges to the reference voltage, VR, while the capacitor Cs is discharged to ground. Whereas, when q) = 1, the total charge C(P) VR stored in the C(P) is transferred to Cs producing an output voltage given by

Vo = K. C(P), (6)

where K= VR/C s. It may be noted that if the room temperature changes then the SCC output also changes although the applied pressure remains the same. By choosing proper values of Cs and V R the output of the SCC is adjusted in such a way that

vo=cN. (7)

4. The multi-layer perceptron network

An artificial neural network based on multi- layer perceptron (MLP) is a feed forward network with one or more layer of nodes between its input and output layers. The popular baekpropagation (BP) algorithm, which is a generalization of the LMS algorithm, is used to train the MLP. The BP algorithm is an iterative gradient search algorithm designed to minimize the mean square error (MSE) between the output of the MLP and its corresponding desired output.

Consider an L-layer MLP [5,9] as shown in Fig. 2. This network has No inputs, Nt hidden layer

116 J.C. Patra / Measurement 22 (1997) 113 121

W(1) W (2) W(3)

Layer 0 Layer 1 3

Input Output Layer Layer

(o) An L- layer networ/~ ( L = 3 1 .

( t ) ,

J 1 tayerlt ' / ~ , . ~ tN " °de J !

• (t) / " / I \ ( t ) , Wio~!ti / ] ~OJni . i t

eL-, 1 x~ ~-1) x~ L-T) x (i-o x 0 .= n t . I

{b} Processing in a single node.

Fig. 2. A multi-layer perceptron.

nodes in layer /, l= 1,2 ..... L - l , and NL output nodes. After application of the nth training sample to the MLP, the input and output relationship of the ith node in layer l+ 1 is characterized by a nonlinear recursive difference equation which may be given by

xp+, =g[~,+ iq, (8)

where Nz

S!'+') = ~ w!Orto +01z), (9) t "'tJ "'3 j = l

x~ z+~) is the ith node output of the (l+ 1)th layer, w!~ is the connecting weight between the ith node of the (l+ 1)th layer and the flh node of the /th layer, and 0~ ° is the weight between a fixed bias of +1 and the ith node of the ( l+ l ) th layer. The nonlinear function g(.) is a hyperbolic tangent function given by

1 - e x p ( - 2 z ) g(z) = tanh(z) = (10)

1 + e x p ( - 2 z )

The error signal ¢s(n) at the nth training time which is required for weight adaptation is given by

ej(n) = E(n) -- yj(n), j = 1,2 ..... NL, ( 11 )

where di(n ) and ys(n) are the desired response and

the output at the jth node of the output layer, respectively. Thus, the sum of error squares pro- duced by the network is given by

NL E(n) = ~ [ej(n)] z. (12)

j = l

The BP algorithm minimizes the cost functional E(n) recursively altering the coefficients {wl~, O~ t) } based on a gradient search technique. The MSE is defined as E(n)/NL. The BP algorithm for weight adaptation of the entire network is given by [5,9]

wl~)(n -~ 1 ) = w!~(n) + o~" A i j (n ) + ~ " A i j (n -- 1 ),

(13)

where

Aij(n) ~p'~

= 6! l+ 1)x~9, 1= L - 1,L - 2,..,0,

=¢i(n)g~S~/)] for output layer (p=L),

= [ N~ l S~+ l'w~)(n) a for other layers

• g'[S~ ) ] (p= L--1,L-- 2,. . .,1).

The partial derivative of the hyperbolic tangent function (Eq. (10)) with respect to S is given by g'(S). The learning rate and momentum rate are denoted by a and r, respectively, and their values should lie between 0 and 1.

Norm.

Pressure (PN)

J. C Patra / Measurement 22 (1997) 113 121

1 CPS ~ Scale. T ~ / Estimated + factor Pressure (~N)

SCC

/ Err°r (F)

Desired + Pressure (PN)

Fig. 3. The scheme of ANN-based modeling of a capacitive pressure sensor.

>

117

5. ANN modeling of the CPS

A scheme of inverse modeling of a CPS using an MLP for estimation of applied pressure is shown in Fig. 3. This is analogous to the channel equalization scheme used in a digital communica- tion receiver to cancel the adverse effects of the channel on the data being transmitted. For obtaining a direct digital readout of the applied pressure, an inverse model of the CPS may be used in cascade with it to compensate for the adverse effects of the nonlinear characteristics and its varia- tions due to change in room temperature on the CPS output.

To obtain a correct readout of the applied pressure, first, the ANN is required to be trained with an appropriately chosen data-set. These training data-sets are chosen in such a way that they will cover the entire dynamic response characteristics of the sensor and also will cover the range of temperature within which the sensor is expected to operate. The procedure of generation of data- sets is explained below. One data-set contains input-output patterns of the sensor characteristics at a particular temperature.

In this sensor modeling, input to the ANN consists of a normalized SCC output (VN) and normalized temperature (TN), and the desired output for the network is the normalized applied pressure (PN). By noting the SCC output for different values of applied pressure covering the dynamic range of the sensor at a particular temperature one can generate one data-set for that temperature. At different temperature values covering

the full operating range of temperature, its corresponding data-set is generated. Then the entire number of data-sets are segregated into two parts; one the training-set and the other the test-set.

Next, the ANN architecture is chosen by specify- ing the number of layers and number of nodes in each layer. In this application, the number of input nodes and output nodes are 2 and 1, respectively, and the number of nodes in the hidden layers are determined experimentally. It is seen that a two- layer MLP is capable of universal approximation, and hence, a single hidden layer is used in this application and the number of its nodes are determined from experiments to obtain the optimum solution in the MSE sense.

Next, the data patterns (V~ and TN) from the training set are fed to the ANN for learning and the weights of the ANN are updated using some learning algorithm. In the proposed scheme, the resulting error obtained from the comparison between the desired output (PN) and the ANN output (fiN) is used to update the ANN weights using the back-propagation (BP) algorithm as described in Section 4. This training procedure continues considering all patterns of the training- set until the error reduces to a pre-set minimum value. Next, the weights of the ANN are frozen and stored in a ROM for testing of the model.

Once the training of the ANN model is over, the weights of the ANN are stored in a ROM. During the testing phase, these stored weights are loaded into the ANN model, the input patterns from the test-set are applied, and the model output is computed. If the model output matches quite

118 J. C Patra / Measurement 22 (1997) 113 121

closely with the actual applied pressure, then it may be said that the ANN has learned the CPS system satisfactorily.

The method for obtaining the temperature information from the sensor characteristics is as follows. From a close inspection of Eq. (5), one can observe that when the applied pressure is zero, then the normalized capacitance is given by

CNo=C(P,T)/Co=fl(T)+ f2(T)=f~(T) 1 - -PN

+ (1 -- a)fz(T) = 1 + f l , (T- To)

+(1 -~)[1 + fl2(r-- To)]=f(T). (14)

Since ~, ill, fie and T O are constants for a sensor, CNO is directly proportional to the ambient temperature and hence, contains temperature information. Therefore, instead of collecting the temperature information, TN, from some other source, maybe by measuring the room temperature by a thermometer, the same information can be obtained from the knowledge of CN0, and it may be fed to the ANN model automatically during its learning phase and testing phase.

During mathematical modeling of the CPS in Section 2, it was assumed that the change in capacitance due to change in temperature is linear and independent of applied pressure, and from Eq. (14), it is seen that the temperature and CNO bear a linear relationship. The variation of CN0 with temperature is shown in Fig. 4 with the chosen values of fla and f12 as --2.0xlO -3 and 7.0 x 1 0 - 3 , respectively.

For proper learning of the ANN, it is required that the normalized temperature TN be within ___ 1.0. The normalized temperature T N can be obtained from CN0 by multiplying it by a suitable scale-factor. From Fig. 4 it is seen that a linear relationship exists between CN0 and TN, and hence TN may be computed as

T N = I T o + ( 1 - CNo)m]/10.0, (15)

where m is the slope of the graph of ( 1 - CN0) VS temperature and its value is equal to 500 for the chosen values of fll and f12- As the output of the SCC represents the change in capacitance of the CPS, if Voo denotes the SCC output when

(D

~D " 0

c

F a)

5 0 - - - -

J i \

1 0 ~ - ~s~ . . . . . . i i

i

i

0.90 0.95 1.00 1.05 1.10 Norm. Capacitance (at P:O)

Fig. 4. R e l a t i o n s h i p be tween CNO a n d t e m p e r a t u r e .

the applied pressure is zero, then 11oo = CNO, and TN may be directly obtained from Eq.(15). However, if a linear relationship does not exist between CNo and the temperature, then another ANN may be utilized to estimate the normalized temperature. After obtaining the temperature information it may be automatically fed to the ANN model of the sensor.

6. Simulation of the A N N model

A two-layer MLP was utilized for modeling of the CPS to estimate the applied pressure in a changing temperature environment. The SCC output voltage VN was obtained experimentally at a reference temperature of 25°C for different values of normalized pressure chosen between 0.0 and 0.6 with an interval of 0.05. Thus, these 13 number of input-output data constitute a set of patterns at the reference temperature.

From the available CPS pattern-set at the reference temperature, i.e. PN ~ CN, and with the knowledge of functions fx(T) and f2(T), eight sets of patterns (each containing 13 number of input-- output data) were obtained at an interval of 10°C starting from -10°C to 60°C. The CPS response characteristics for the chosen values of fll and r2 at T = - 10°C, 25°C and 60°C are plotted in Fig. 5. From this figure, wide variation of capaci-

J. C. Patra / Measurement 22 (1997) 113-121 119

0 . 6 ~ , ~ , L , / ~ , J ° J 4 ~ ~GO000 2 5 I ' ' j ~ " " ~ / ]

0.5 - 1 , ~ , ~ 60: ; ~ , , I

0 . 4 - - " -i - - i - - . . . . ' ( ] . ) ~ i i / f ' ~ ~ i i /

1:2_ 0 . 3 Jr : -, ~ ++,- c~ ,- - - - ~ - - , - - • ( . ( ' ' i i i i i

• ~ z , ~ ~ . . . .

0 ~• i , , / ~ / i i i q

'~ ' ' ' 2 ? Z 0 . 1 .I" i ¢ 7 + ¢ -~,' . . . . . . . . . . ' ' ' ' lJ

0 . 0

0 . 9 1 . 0 1 , 1 1 . 2 1 . 3 1 . 4 1 . 5 1 . 6

Norm. Capacitance

Fig. 5. CPS response characteristics at different temperatures.

tance change due to change in temperature can be observed.

A two-layer MLP with 3-5-1 structure (denot- ing 3, 5 and 1 number of nodes including the bias units in the input layer, the first layer, i.e. the hidden layer, and the output layer of the ANN, respectively) was chosen for direct modeling of a CPS as shown in Fig. 3. Four sets of patterns corresponding to -10°C, 10°C, 30°C and 50°C were chosen for training of the ANN. The BP algorithm in which the learning rate and the momentum rate were chosen as 0.5 and 0.7, respectively, was used to adapt the weights of the ANN.

During training, the above four sets were chosen randomly and further, the individual patterns in the set were also chosen randomly. The temperature input was obtained from the knowledge of Voo and was normalized by a suitable scale-factor to keep the normalized temperature TN within -t-1.0. Initially, all the weights of the ANN were fixed to some random values between +0.5. The normalized temperature (TN), and the output of the SCC (Vy) were used as the input pattern, and the normalized applied pressure (PN) was used as the desired pattern to the MLP. After application of each pattern, the ANN weights were updated using the BP algorithm. Completion of all the 13 patterns in one set constitutes one iteration of training. To make the learning complete and effec- tive, 10,000 iterations were made to train the ANN. Then, the weights of the MLP were frozen and

Table 1 Final weight values of the A N N model

Node First No. layer

0 1 2

1 0.6934 0.0026 -1 .1467 2 2.7696 - 1.0424 -7 .0300 3 1.4187 0.2697 -2 .0573 4 0.1405 0.0229 -0 .2506

Second layer

0 1 2 3 4

1 -0 .8835 -0 .2683 -1 .4867 -0.5091 -0 .0590

stored in a ROM for testing the effectiveness of learning. These weight values are tabulated in Table 1.

During the testing phase of the model, the frozen weights are loaded into the ANN. Then the inputs, i.e. T N and VN from the test-set were fed to this model. Next, its output was computed and com- pared with the actual applied pressure (if known) to verify the effectiveness of the model. The SCC output i.e. VN was applied as input to the MLP with an increment of 0.001 in the range from 0.9 to 1.9 along with the normalized temperature TN. Then, the estimated pressure PN was obtained from the output of the ANN. The estimated pressure along with the true pressure at - 10°C (training-set) are plotted in Fig. 6. The same parameters at 60°C (test-set) are plotted in Fig. 7. From these figures it may be observed that the resemblance between the estimated pressure and true pressure is quite close. This is true for the full range of temperature values ranging from -20°C to 70°C.

The estimated pressure values for 44°C and 4°C (actual values not available) and true pressure values available for the nearest temperature i.e. 40°C and 0°C are plotted in Fig. 8. Although the ANN was trained by taking training patterns corresponding to four values of temperature such as -10°C, 10°C, 30°C and 50°C, the ANN is capable of estimating the pressure for any given temperature.

The plots between normalized actual pressure and estimated pressure (by the ANN model) at

120 J.C. Patra / Measurement 22 (1997) 113 121

0 .7 o o o o o ' , T - 2 5 i : ~*~<

, ~ . ~ ¢ , _ _ , t - -- - - r . . . . . . . . .

- ,E 10 ,

~ 0 .5 ' ' '

i i i

~ 0 . 4 . . . . . . . . ~ . . . . . . . 13_. '

• 0 .3

E ~- 0.2 . . . . . 0

Zo.1

0 . 0 I "r i- , I ~ I ~ , ] , r ~

0 . 9 1.1 1 .3 1 .5 1 .7 1.9

N o r m • Ca p a c i l o n c e

Fig. 6. True and estimated pressure at - 10°C (training-set).

0 .7

(D 0 . 6 k -

0 . 5 O9

~ 0.4- Q_

0 .3

E O . 2 0

Z O . 1

o o o o o : T - 2 5 i I ' ~ ~ "~ ~ - 6 0 ' , . ~ 4

i i i

~ - i i i

- r i

: . . . . F . . . . . . . . . . ,~- - - - i p

i ,

0 .0

0 . 9 1.1 1 .3 1 .5 1 .7 1 .9

Norm. Capaci fance

Fig. 7. True and estimated pressure at 60°C (test-set).

0°C and 60°C are shown in Fig. 9. Form these plots a high accuracy of the estimation of pressure for a wide range of temperature is quite evident. Further, it may be noted that a nearly linear relationship exist between the actual and estimated pressure. The variation of error in estimation of pressure by the A N N model ( 3 - 5 - 1 structure) at 0°C, 20°C, 40°C and 60°C is plotted in Fig. 10. From this plot it may be seen that the error between the actual and estimated pressure remains within + 1% (FS).

The simulation studies were carried out extensively with different MLP structures over a wide temperature range and tested for different temper-

0

0 . 5 ( 1 9

~ 0 . 4 13_

0 . 5

L 0 .2 0

Z 0.1

0 .0

0 . 7 ~ , > o o o o 1 T - 2 5 i +'}~ i o u c ~ ' T - 4 0 , * ' ^ ~

0.6 ~ - ~ - ~ E - ~ . 4 - - - ,~__~¢~- ~-

~ +++~< E-4 f i - J I

I

r

o . e .1 1 .3 1 . 5 1 . 7 1 .9

N o r m . C a p o c i f o n c e

Fig. 8. True and estimated pressure at 4°C and 44°C (unknown-set).

0 .6 o o o o d 5 - 0 ' ' ' - - - - . ~

n i i i

* * * ~ , 5 - s 0 , , , / I "2".0. 5 ....... , ' /

i i i , i

r t t t

" - " 0 . 4 _ _ L _ L_ __, ,:~¢f;~ , I p I - . . . . . . t . . . .

~ i , i p

' ' / - ' r ' r ( D I ' I / " t t

L . P ~ / I t ; t h t t I F t

0 . 2 ~ i - - -'~ - - - '- - - ' - - - ~ - - ; t i i

d ~

i . " t ~ i t

x . _ i - J i i O 0.1 . . . . . ~ - - -,~ - - -~- - J-. _

Z ~ i t , i

i i i

o . 0 ' , , , I , , , , I , , , , b , , , , ! , , , , I , , ,

0 . 0 0.1 0 . 2 0 . 3 0 . 4 0 .5 0 . 6

N o r m . P ressu re ( f r ue )

Fig. 9. Plot between true and estimated pressure at 0°C and 60°C.

ature values. Although the MLP was trained with patterns corresponding to only four temperature values, the A N N model is found to be capable of estimating the applied pressure at any given temperature within the specified range. From the results of these studies it may be concluded that the MLP-based model of the CPS performs quite effectively over a wide range of temperature starting from - 2 0 ° C to 70°C.

J. C. Patra / Measurement 22 (1997) 113-121 121

0 L -

@ 0 . 5

f -

~) - 0 . 0 O k...

(1) 13__

1 .5 j , oc -~ ,d~ 0 , uE~-mae 20 L ~6~- 'b6 40

1 .0 - - 60-

i

L _ - /

- 0 . 5 ~ - - ~ \ . - . . / J /

T ~

- 1 . 0 -I 1 1 1 1

0 . 0

i i .

L \ i

0.1 0 . 2 0 . 5 0 . 4 0 . 5 0 . 6

Norm. Pressure (frue)

A new idea for collection of temperature information required during training and testing of the ANN model is explained. The temperature information is obtained from the sensor characteristics themselves and is fed to the ANN automatically. Thus, the model automatically makes necessary corrections needed due to the change in ambient temperature while computing the applied pressure. Further, this technique provides flexibility and simplicity of operation. The proposed ANN-based modeling technique can very well be extended to other types of sensors to compensate for adverse effects due to the change in environmental parameters on the performance of the sensor.

Fig. 10. Percentage of error (FS) between the true and estimated pressure at different temperatures.

7. Conclusions

A novel ANN-based model of a smart pressure sensor for the purpose of direct digital readout of the applied pressure is proposed in this paper. This ANN-based model is insensitive to the variation of sensor characteristics due to change in ambient temperature. The proposed model works quite satisfactorily over a wide range temperature starting from - 2 0 ° C to 70°C. Even this temperature range can be further extended by training the MLP with a sufficient number of pattern-sets covering the temperature range.

As the training of the A N N involves a substan- tial amount of computation, it is carried out off- line and its weights are stored in a ROM for later use during testing of the model. These weights are entered into a plug-in-module which may be attached with the sensor to compute the applied pressure required for a direct digital readout. It is revealed from the simulation studies that the estimation error remains within _ 1% (FS) through- out the dynamic range of the sensor over a wide range of temperature.

References

[ 1 ] L. Finkelstein, Intelligent and knowledge based instrumentation - an examination of basic concepts, Measurement 14 (1994) 23-29.

[2] P. N. Mahana, F. N, Trofimenkoff, Transducer output signal processing using eight-bit microcomputer. IEEE Trans. Instrum. Meas., June 1986, 35, pp. 182 186.

[3] M. Yamada, K. Watanabe, A capacitive pressure sensor interface using oversampling A-E demodulation techniques. IEEE Trans. lnstrum. Meas., Feb. 1997, 46, pp. 3-7.

[4] F. Abdullah, L. Finkelstein, S. H. Khan, W. J. Hill, Model- ing in measurement and instrumentation an overview, Measurement 14 (1994) 41 53.

[5] S. Haykin, Neural Networks, Maxwell Macmillan, Ont., Canada, 1994.

[6] J. C. Patra, G. Panda, R. Baliarsingh, Artificial neural network-based nonlinearity estimation of pressure sensors. IEEE Trans. Instrum. Meas., Dec. 1994, 43, pp. 874-881.

[7] J. C. Patra, Some studies on artificial neural networks for signal processing applications. Ph.D. thesis, Indian Institute of Technology, Kharagpur, India, 1996.

[8] J. C. Patra, G. Panda, An intelligent capacitive pressure using artificial neural networks. IEEE Trans. lnstrum. Meas., 1997, under revision.

[9] Y. H. Pao, Adaptive Pattern Recognition and Neural Net- works, Addison-Wesley, Reading, MA, 1989.

Documents

An artificial neural network-based smart capacitive pressure sensor