A Piezoresistive Pressure Sensor Modeling by Artificial Neural Networks

Subject Areas : Journal of Optoelectronical Nanostructures

Behzad Hadi ¹ , Farzin Shama ² , Hamid Sherafat Vaziri ³ , Mohsen Eghbalkhah ⁴

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Received: 2023-12-28 Accepted : 2024-04-30 Published : 2024-11-15

Keywords: ANN, Modelling, Piezoresistive sensor,

Abstract :

An efficient artificial neural network (ANN) model for a pressure sensor is presented in this paper. This pressure sensor has a piezoresistive structure and its experimental data is used in this work to train and test the proposed ANN model. The selected network is a multi-layer perceptions ANN type, which has one hidden layer with five neurons inside. The proposed MLP modelled system has been trained to recognize the output of the pressure sensor, which is a generated voltage in millivolts, according to the temperature and pressure levels. The obtained mean square relative error (MSRE) error of this method is only 0.137 for test data set.

References:

[1] B. Stephen, MEMS mechanical sensors, Artech House, 2004.
[2] G. Cao, et al. A micromachined piezoresistive pressure sensor with a shield layer. Sensors. 16 (8) (2016) 1286. Available: https://doi.org/10.3390/s16081286
[3] J. G. Taylor, Neural Networks and Their Applications, John Wiley & Sons, West Sussex, UK, 1996.
[4] A. R. Gallant and H. White. On learning the derivatives of an unknown mapping with multilayer feedforward networks. Neural Networks. 5(1) (1992) 129-138.‏ Available: https://doi.org/10.1016/S0893-6080(05)80011-5
[5] G. H Roshani, et al. Prediction of materials density according to number of scattered gamma photons using optimum artificial neural network. Journal of Computational Methods in Physics. 2014 (2014).‏ Available : https://doi.org/10.1155/2014/305345
[6] M. Hayati, et al. Linearization design method in class-F power amplifier using artificial neural network. Journal of Computational Electronics, 13(2014) 943-949.‏ Available: https://doi.org/10.1007/s10825-014-0612-x
[7] G. Sadeghi, et al. Energy and exergy evaluation of the evacuated tube solar collector using Cu2O/water nanofluid utilizing ANN methods. Sustainable Energy Technologies and Assessments, 37 (2020), 100578.‏ Available: https://doi.org/10.1016/j.seta.2019.100578
[8] G. H. Roshani, et al. Designing a simple radiometric system to predict void fraction percentage independent of flow pattern using radial basis function. Metrology and Measurement Systems, 25(2) (2018) 347-358.‏ Available: https://doi.org/10.24425/119560
[9] G. Sadeghi, et al. Empirical data-driven multi-layer perceptron and radial basis function techniques in predicting the performance of nanofluid-based modified tubular solar collectors. Journal of Cleaner Production, 295 (2021) 126409.‏ Available: https://doi.org/10.1016/j.jclepro.2021.126409
[10] G. H. Roshani, et al. Volume fraction determination of the annular three-phase flow of gas-oil-water using adaptive neuro-fuzzy inference system. Computational and Applied Mathematics, 37 (2018) 4321-4341.‏ Available: https://doi.org/10.1007/s40314-018-0578-6
[11] G. H. Roshani, et al. Utilizing features extracted from registered 60Co gamma-ray spectrum in one detector as inputs of artificial neural network for independent flow regime void fraction prediction. MAPAN, 34(2) (2019), 189-196.‏ Available: https://doi.org/10.1007/s12647-018-0298-9
[12] S. Hosseini, et al. Increasing efficiency of two-phase flowmeters using frequency-domain feature extraction and neural network in the detector output spectrum. Journal of Modeling in Engineering, 19(67) (2021), 47-57.‏ Available: https://doi.org/10.22075/JME.2021.19817.1860
[13] A. Abdykian and Z. Safi. Finding electrostatics modes in metal thin films by using of quantum hydrodynamic model. Journal of Optoelectronical Nanostructures, 1(3) (2016), 43-50. Available: https://jopn.marvdasht.iau.ir/article_2193.html
[14] A. Abdikian, et al. Electrostatics Modes in Mono-Layered Graphene. Journal of Optoelectronical Nanostructures, 1(2) (2016), 1-8.‏ Available: https://jopn.marvdasht.iau.ir/article_2044.html
[15] P. Ripka and A. Tipek. Modern sensors handbook. John Wiley & Sons; (2007).
[16] O. N. Tufte, et al. Silicon diffused-element piezoresistive diaphragms. Journal of Applied Physics, 33(11) (1962), 3322-3327.‏ Available: https://doi.org/10.1063/1.1931164
[17] N. Bhalla, et al. Finite element analysis of MEMS square piezoresistive accelerometer designs with low crosstalk. Semiconductor Conference (CAS), 2011 International (2011 Oct 17), Vol. 2, pp. 353-356
[18] A.Farmani, et al. Numerical modeling of a metamaterial biosensor for cancer tissues detection. Journal of Optoelectronical Nanostructures, 5(1) (2020), 1-18.‏ Available: https://jopn.marvdasht.iau.ir/article_4030_526.html
[19] H. Bahramiyan and S. Bagheri. Linear and nonlinear optical properties of a modified Gaussian quantum dot: pressure, temperature and impurity effect. journal of optoelectronical nanostructures, 3(3) (2018), 79-100.‏ Available: https://jopn.marvdasht.iau.ir/article_3047_0a2d460925ad6686daf5ac62c9082227.pdf
[20] A. Moftakharzadeh, et al. Noise Equivalent Power Optimization of Graphene-Superconductor Optical Sensors in the Current Bias Mode. Journal of Optoelectronical Nanostructures, 3(3) (2018), 1-12.‏ Available: https://jopn.marvdasht.iau.ir/article_3040_c11f2d8d2fa24f1f5bb3d07f5a0660f1.pdf
[21] G. H. Roshani, et al. Combined application of neutron activation analysis using IECF device and neural network for prediction of cement elements. Radiation detection technology and methods, 1 (2017), 1-7. Available: https://doi.org/10.1007/s41605-017-0025-z
[22] G. H. Roshani, et al. Some applications of artificial neural network in nuclear engineering. (2013) LAP LAMBERT Academic Publishing.
[23] M. A. Sattari, et al. A miniaturized filter design approach using GMDH neural networks. Microwave and Optical Technology Letters, 65(9) (2023), 2507-2516. Available: https://doi.org/10.1002/mop.33741
[24] A. Sadighzadeh, et al. Prediction of Neutron Yield of IR‐IECF Facility in High Voltages Using Artificial Neural Network. Journal of Engineering, 2014(1) (2014), 798160. Available: https://doi.org/10.1155/2014/798160
[25] F. Fouladinia, et al. A novel metering system consists of capacitance-based sensor, gamma-ray sensor and ANN for measuring volume fractions of three-phase homogeneous flows. Nondestructive Testing and Evaluation, (2024) 1-27. Available: https://doi.org/10.1080/10589759.2024.2375575
[26] S. Amiri and G. H. Roshani. Investigating the Impact of Gamification on the Consumer Buying Behavior using Artificial Neural Network. Journal of Business Management, 14(4) (2022), 647-674. Available: https://doi.org/10.22059/JIBM.2022.334038.4249
[27] S. Amiri and G. H. Roshani. Modeling the impact of Covid-19’s stress and resilience on job burnout using Radial Basis Functions-Artificial Neural Network The case of knowledge-based companies. Research in Production and Operations Management, 13(2) (2022), 23-43. Available: https://doi.org/10.22108/JPOM.2022.131194.1407
[28] A. R. Shahani, et al. Prediction of influence parameters on the hot rolling process using finite element method and neural network. Journal of materials processing technology, 209(4) (2009), 1920-1935. Available: https://doi.org/10.1016/j.jmatprotec.2008.04.055
[29] N. Ghaemi, et al. Application of ANN and ANFIS to predict the effect of fatty acids on the performance of CA composite membranes in removal of pesticides from water. Desalination and Water Treatment, 78 (2017) 132-140. Available: https://doi.org/10.5004/dwt.2017.20730
[30] E. K. Vahidi, et al. Application of ANN and RBF to Optimize the Properties of the RCC Pavement Containing RHA. American Journal of Civil and Environmental Engineering, 2(5) (2017), 57-66.

Full-Text:



Islamic Azad University

Journal of Optoelectronical Nanostructures     Winter 2024 / Vol. 9, No. 4

 

Research Paper
A Piezoresistive Pressure Sensor Modeling by Artificial Neural Networks
Behzad Hadi1, Farzin Shama2*, Hamid Sherafat Vaziri2, Mohsen Eghbalkhah3   1Mechanical Engineering Department, Faculty of Engineering, Razi University, Kermanshah, Iran 2Electrical Engineering Department, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran E-mail: [e-mail] 3Electrical Engineering Department, Faculty of Engineering, Razi University, Kermanshah, Iran
Received: 28 Aug. 2024 Revised: 25 Oct. 2024 Accepted: 30 Oct. 2024 Published: 15 Nov. 2024	Abstract An efficient artificial neural network (ANN) model for a pressure sensor is presented in this paper. This pressure sensor has a piezoresistive structure and its experimental data is used in this work to train and test the proposed ANN model. The selected network is a multi-layer perceptions ANN type, which has one hidden layer with five neurons inside. The proposed MLP modelled system has been trained to recognize the output of the pressure sensor, which is a generated voltage in millivolts, according to the temperature and pressure levels. The obtained mean square relative error (MSRE) error of this method is only 0.137 for test data set.
Keywords: ANN; Modelling; Piezoresistive sensor

 

1.       INTRODUCTION 

There is a lot of electronic-based sensors for various purposes [1-20]. MEMS (micro-electromechanical system) pressure sensors are one the most important devices because of their wide application in industry, and so many studies have been done in order to improve their performance. Also, many structures such as piezoresistive, capacitive and optical pressure sensor have been proposed [1]. Modeling the MEMS structures is an efficient method to study their behavior which can be useful in optimization of their performance and also predicting their responses. Piezorsistive pressure sensors are the most common pressure sensors because of their desirable performance and ease of fabrication. In [2], a novel piezoresistive pressure sensor is presented. In the proposed paper, a shield layer is used to help improving the stability of the sensor. Fig.1 shows the pressure sensor presented in [2].   There are a lot of modeling methods including artificial neural network modeling [3-12] and other mathematical or physical modeling methods [13-14].

Artificial neural network (ANN) modeling is one of the popular tools to recognize and investigate the nonlinear and complex systems and devices. In fact, an ANN is a big-data/information processor, which inspires from human cognition and neural biology as a mathematical abstraction form. There are two common architectures for ANNs, the feedforward ones and feedback ones. There are also many learning algorithms types for each ANN [3-4]. A multi-layer perceptron (MLP) is a feedforward ANN, which is widely used in modeling and prediction [5-7] problems.

Pressure sensors (transducers) are fundamental components in control systems due to their extensive utility in detecting mechanical parameters like pressure and flow. As a result, various configurations have been explored and suggested over the years to create a pressure transducer with optimal characteristics including high sensitivity, excellent linearity, cost-effectiveness, and simplicity in manufacturing. Piezoresistive pressure sensors are the predominant structures among MEMS pressure transducers, having been pioneered in 1962. The fundamental concept involves converting mechanical stress into an electrical signal through a Wheatstone bridge integrated onto a thin square diaphragm that bends under applied pressure. This principle can also be extended to other MEMS devices such as accelerometers. The benefits of Piezoresistive pressure transducers include compact dimensions, straightforward and economical fabrication processes typically utilizing bulk micromachining methods, superior sensitivity, and a direct current output [15-17].

In this paper, using the experimental results in [2], an efficient MLP type ANN model is proposed, which is a predictable model for output voltage of the sensor in some temperatures and any variable pressures. The applied learning algorithm is Levenberg Marquaret (LM) that is a good learning method using in MLP networks, due to fast and stable convergence [7]. The Levenberg-Marquardt algorithm is an estimation of the Hessian matrix commonly encountered in Newton's optimization method. This feature enables the algorithm to significantly decrease complexity, presenting a substantial advantage [7]. 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

Fig.1 the pressure sensor presented in [2]

 

 

Fig.2 shows the output signal of the sensor (in mV) for different value of input pressure and the temperature. 

Fig2. characteristics of the pressure sensor

 

 

 

2. ANN Model

Multi-layer perceptions (MLPs) are the most frequently used ANN network architectures in modeling and prediction issues. MLPs include calculation systems including simple processing components called neuron which, has been ran in parallel at multiple layers [3]. The feed forward network has been used just with minimum three layers. Processing units of Each layer are independent and each unit has been completely interconnected with weighted connections to units in the next layer [4]. The offered model in this work has been shown in Figure 3. The used input variables in this network are sensor temperature (in ℃) and input pressure of the sensor (in MPa); the output is sensor output as a DC voltage (in mV). The input to the node l at the only hidden layer is obtained as below [5]:

l=1, 2, …, 10                                                        (1)

 

        Where variables are defined as: x as the input, b as the bias parameter, w as the weighting parameter and ŋ as the neuron activation function, which are applied at the hidden layer. The jth output neuron will be:

 

j=1, 2, …, 2                                                    (2)

 

 

Fig. 3. The designed MLP model

 

 

The acquired values for training the obtained ANN is achieved using the validated actual data in [2]. To obtain an accurate model and validate the results, there are two set experimental data: 70% as training data-set and 30% as testing data-set. MATLAB 7.0.4 program has been employed for training the MLP modeled system. The details of the designed network have been shown in Table 1.

 

Table 1. Specifications of the network

 

Neural network type	MultiLayer Perceptron
Neurons deposed at the input layer	2
Neurons deposed at the first hidden layer	5
Neurons deposed at the output layer	1
Epochs repetition	300
Neuron activation function	Tangent sigmoid

 

 

 

3.Results

 

The calculated errors for the designed MLP modeled system have been illustrated in Table 2. In this table, mean absolute error percentage (MAE %), the mean relative error percentage (MRE %) and the roots mean square error (RMSE), of the model are defined as [6-12]:

 

                                                                                 (3)

                                                                                 (4)

                                                                                 (5)

 

Where N is the number of features and ‘X (Exp)’ and ‘X (Pred)’ consider as real and predicted (ANN) values, respectively.

The ANN design and learning process flowchart in MATLAB software has been illustrated in Fig.4.

 

 

Fig. 4. The ANN design and learning process flowchart in MATLAB

 

As seen in Table. 2, the MAE%, MRE% and RMSE of the MLP modeled system for train and test data have very dispensable values. The RMSE is only 0.13700 for test data and can validate the efficiency of this model.

 

Table 2. Calculated Errors

Error type	For train	For test
MAE %	0.11231	0.11110
MRE %	0.00065	0.02910
RMSE	0.14410	0.13700

The regression diagram of the MLP modeled network are illustrated in Figs. 5 for trained and tested results. As can be seen from Table 2 and Fig.5, it is obviously the predicted voltage by the proposed network is near to the experiential results, which proves the strength of the MLP ANN as a precise and accurate model for the prediction of sensor output voltage as a function of other temperatures and any input pressures.

   Some predicted output voltage in new temperatures at the previous pressures has been indicted in Table 3.

 

Fig 5.  Regression diagrams of real and predicted results (a) trained data (b) tested

 

Table 3. Predicted Sensor output (mV) using ANN model.

Sensor output (mV)	Variable Temperatures (C)	Desired Pressure (MPa)
166.0733	125	2
150.7200	125	1.8
125.9944	125	1.5
100.5504	125	1.2
218.9349	-40	2
206.2966	-40	1.8
181.1562	-40	1.5
149.4540	-40	1.2
187.5937	-55	2
169.0529	-55	1.8
138.8035	-55	1.5
124.2340	-55	1.2

 

 

4 Conclusion

The output of a pressure sensor in voltage depends on pressure (in Pa) and temperature. This tomography system only measures the output voltage of the sensors at 3 temperature points. The measurement accuracy one of the main challenge in the industry. In this work, easy and powerful method of artificial intelligence has been used to prediction problems, the sensor has been modeled. In this study, we select pressure and temperature as the input of the MLP modeled system. Then, the output voltage is used as the output of the MLP modeled system. The outcomes of proposed ANNs proof that the presented MLP modeled system would be used to predict the unknown desired points.

 

References 

[1]       B. Stephen, MEMS mechanical sensors, Artech House, 2004.

[2]       G. Cao, et al. A micromachined piezoresistive pressure sensor with a shield layer. Sensors. 16 (8) (2016) 1286. Available: https://doi.org/10.3390/s16081286

[3]       J. G. Taylor, Neural Networks and Their Applications, John Wiley & Sons, West Sussex, UK, 1996.

[4]       A. R. Gallant and H. White. On learning the derivatives of an unknown mapping with multilayer feedforward networks. Neural Networks. 5(1) (1992) 129-138.‏ Available: https://doi.org/10.1016/S0893-6080(05)80011-5

[5]       G. H Roshani, et al. Prediction of materials density according to number of scattered gamma photons using optimum artificial neural network. Journal of Computational Methods in Physics. 2014 (2014).‏  Available : https://doi.org/10.1155/2014/305345

[6]       M. Hayati, et al. Linearization design method in class-F power amplifier using artificial neural network. Journal of Computational Electronics, 13(2014) 943-949.‏ Available: https://doi.org/10.1007/s10825-014-0612-x

[7]       G. Sadeghi, et al. Energy and exergy evaluation of the evacuated tube solar collector using Cu2O/water nanofluid utilizing ANN methods. Sustainable Energy Technologies and Assessments, 37 (2020), 100578.‏ Available: https://doi.org/10.1016/j.seta.2019.100578

[8]       G. H. Roshani, et al. Designing a simple radiometric system to predict void fraction percentage independent of flow pattern using radial basis function. Metrology and Measurement Systems, 25(2) (2018) 347-358.‏ Available: https://doi.org/10.24425/119560

[9]       G. Sadeghi, et al. Empirical data-driven multi-layer perceptron and radial basis function techniques in predicting the performance of nanofluid-based modified tubular solar collectors. Journal of Cleaner Production, 295 (2021) 126409.‏ Available: https://doi.org/10.1016/j.jclepro.2021.126409

[10]       G. H. Roshani, et al. Volume fraction determination of the annular three-phase flow of gas-oil-water using adaptive neuro-fuzzy inference system. Computational and Applied Mathematics, 37 (2018) 4321-4341.‏ Available: https://doi.org/10.1007/s40314-018-0578-6

[11]       G. H. Roshani, et al. Utilizing features extracted from registered 60Co gamma-ray spectrum in one detector as inputs of artificial neural network for independent flow regime void fraction prediction. MAPAN, 34(2) (2019), 189-196.‏ Available: https://doi.org/10.1007/s12647-018-0298-9

[12]       S. Hosseini, et al. Increasing efficiency of two-phase flowmeters using frequency-domain feature extraction and neural network in the detector output spectrum. Journal of Modeling in Engineering, 19(67) (2021), 47-57.‏ Available: https://doi.org/10.22075/JME.2021.19817.1860

[13]       A. Abdykian and Z. Safi. Finding electrostatics modes in metal thin films by using of quantum hydrodynamic model. Journal of Optoelectronical Nanostructures, 1(3) (2016), 43-50. Available: https://jopn.marvdasht.iau.ir/article_2193.html

[14]       A. Abdikian, et al. Electrostatics Modes in Mono-Layered Graphene. Journal of Optoelectronical Nanostructures, 1(2) (2016), 1-8.‏ Available: https://jopn.marvdasht.iau.ir/article_2044.html

[15]       P. Ripka and A. Tipek. Modern sensors handbook. John Wiley & Sons; (2007).

[16]       O. N. Tufte, et al. Silicon diffused-element piezoresistive diaphragms. Journal of Applied Physics, 33(11) (1962), 3322-3327.‏ Available: https://doi.org/10.1063/1.1931164

[17]       N. Bhalla, et al. Finite element analysis of MEMS square piezoresistive accelerometer designs with low crosstalk. Semiconductor Conference (CAS), 2011 International (2011 Oct 17), Vol. 2, pp. 353-356

[18]       A.Farmani, et al. Numerical modeling of a metamaterial biosensor for cancer tissues detection. Journal of Optoelectronical Nanostructures, 5(1) (2020), 1-18.‏ Available: https://jopn.marvdasht.iau.ir/article_4030_526.html

[19]       H. Bahramiyan and S. Bagheri. Linear and nonlinear optical properties of a modified Gaussian quantum dot: pressure, temperature and impurity effect. journal of optoelectronical nanostructures, 3(3) (2018), 79-100.‏ Available: https://jopn.marvdasht.iau.ir/article_3047_0a2d460925ad6686daf5ac62c9082227.pdf

[20]       A. Moftakharzadeh, et al. Noise Equivalent Power Optimization of Graphene-Superconductor Optical Sensors in the Current Bias Mode. Journal of Optoelectronical Nanostructures, 3(3) (2018), 1-12.‏ Available: https://jopn.marvdasht.iau.ir/article_3040_c11f2d8d2fa24f1f5bb3d07f5a0660f1.pdf

[21]       G. H. Roshani, et al. Combined application of neutron activation analysis using IECF device and neural network for prediction of cement elements. Radiation detection technology and methods, 1 (2017), 1-7. Available: https://doi.org/10.1007/s41605-017-0025-z

[22]       G. H. Roshani, et al. Some applications of artificial neural network in nuclear engineering. (2013) LAP LAMBERT Academic Publishing.

[23]       M. A. Sattari, et al. A miniaturized filter design approach using GMDH neural networks. Microwave and Optical Technology Letters, 65(9) (2023), 2507-2516. Available: https://doi.org/10.1002/mop.33741

[24]       A. Sadighzadeh, et al. Prediction of Neutron Yield of IR‐IECF Facility in High Voltages Using Artificial Neural Network. Journal of Engineering, 2014(1) (2014), 798160. Available: https://doi.org/10.1155/2014/798160

[25]       F. Fouladinia, et al. A novel metering system consists of capacitance-based sensor, gamma-ray sensor and ANN for measuring volume fractions of three-phase homogeneous flows. Nondestructive Testing and Evaluation, (2024) 1-27. Available: https://doi.org/10.1080/10589759.2024.2375575

[26]       S. Amiri and G. H. Roshani. Investigating the Impact of Gamification on the Consumer Buying Behavior using Artificial Neural Network. Journal of Business Management, 14(4) (2022), 647-674. Available: https://doi.org/10.22059/JIBM.2022.334038.4249

[27]       S. Amiri and G. H. Roshani. Modeling the impact of Covid-19’s stress and resilience on job burnout using Radial Basis Functions-Artificial Neural Network The case of knowledge-based companies. Research in Production and Operations Management, 13(2) (2022), 23-43. Available: https://doi.org/10.22108/JPOM.2022.131194.1407

[28]       A. R. Shahani, et al. Prediction of influence parameters on the hot rolling process using finite element method and neural network. Journal of materials processing technology, 209(4) (2009), 1920-1935. Available: https://doi.org/10.1016/j.jmatprotec.2008.04.055

[29]       N. Ghaemi, et al. Application of ANN and ANFIS to predict the effect of fatty acids on the performance of CA composite membranes in removal of pesticides from water. Desalination and Water Treatment, 78 (2017) 132-140. Available: https://doi.org/10.5004/dwt.2017.20730

[30]       E. K. Vahidi, et al. Application of ANN and RBF to Optimize the Properties of the RCC Pavement Containing RHA. American Journal of Civil and Environmental Engineering, 2(5) (2017), 57-66.

 

Citation: Behzad Hadi, Farzin Shama, Hamid Sherafat Vaziri, Mohsen Eghbalkhah. A Piezoresistive Pressure Sensor Modeling by Artificial Neural Networks. Journal of Optoelectronical Nanostructures. 2024; 9 (4): 69- 81 DOI: 10.30495/JOPN.2024.32877.1308

*Corresponding author: Farzin Shama Address: Electrical Engineering Department, Kermanshah Branch, Islamic Azad University, Kermanshah, Iran E-mail: [e-mail] Tell: 00989183363650   Email: [e-mail]

*Corresponding author: Abdossaleh Zar Address: Department of Sport Science, School of Literature and Humanities, Persian Gulf University, Boushehr, Iran.   Tell: 00989173027100 Email: [e-mail]