A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling
Abstract
:1. Introduction
2. Working Principle and Structural Design of MEMS Accelerometer
3. Design and Analysis of Computer Experiments (DACE) Based Multi-Response Optimization
3.1. Gaussian Process Modelling
3.2. Design Parameters and Their Levels
3.3. Latin Hypercube Sampling (LHS) Based Space Filling Design
3.4. FEM Modelling of 2-DoF MEMS Accelerometer
4. Development of GP Based Metamodels for the Output Responses
4.1. Significant Design Parameters and Interaction Analysis for Natural Frequency ()
4.2. Significant Design Parameters and Interaction Analysis for Proof Mass Displacement ()
4.3. Significant Design Parameters and Interaction Analysis for Pull-In Voltage ()
4.4. Significant Design Parameters and Interaction Analysis for Capacitance Change ()
4.5. Significant Design Parameters and Interaction Analysis for BNEA ()
4.6. Prediction Accuracy of the Fitted GP Metamodels
5. Multi-Response Optimization
5.1. Optimization Objective Function
5.2. Desirability Function Based Simultaneous Multi-Response Optimization
5.3. Verification of Predicted Values for the Output Responses
5.3.1. Natural Frequency Analysis
5.3.2. Frequency Response Analysis
5.3.3. Pull-In Voltage Analysis
5.3.4. Capacitance Change Analysis
5.3.5. Estimation of Brownian Noise Equivalent Acceleration (BNEA)
6. Discussion
7. Conclusions
Supplementary Materials
Author Contributions
Funding
Institutional Review Board Statement
Conflicts of Interest
References
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Code | Design Parameters | Low Level | High Level |
---|---|---|---|
X1 | Overlap length of comb | 150 µm | 250 µm |
X2 | Length of suspension beam 1 | 400 µm | 500 µm |
X3 | Length of suspension beam 2 | 400 µm | 500 µm |
X4 | Width of suspension beam | 6 µm | 8 µm |
X5 | Input acceleration | 1 g | 25 g |
X6 | Operating temperature | 233.15 K | 373.15 K |
X7 | Operating pressure | 100 Torr | 760 Torr |
X8 | Frequency ratio | 0.1 | 0.5 |
Output Responses | Design Parameters | |||||||
---|---|---|---|---|---|---|---|---|
X1 | X2 | X3 | X4 | X5 | X6 | X7 | X8 | |
Natural frequency (Y1) | 4.23 × 10−6 | 5.52 × 10−6 | 9.74 × 10−5 | 0.36 | 0 | 0 | 0 | 0 |
Proof mass displacement (Y2) | 0 | 0 | 8.26 × 10−5 | 0.34 | 0.01 | 0 | 0 | 1.24 |
Pull-in voltage (Y3) | 6.29 × 10−5 | 1.23 × 10−5 | 5.49 × 10−5 | 0.14 | 1.49 × 10−5 | 4.29 × 10−6 | 6.18 × 10−9 | 2.19 |
Capacitance change (Y4) | 2.19 × 10−5 | 1.01 × 10−6 | 0.000026 | 0.1235 | 0.0018 | 7.66 × 10−7 | 3.82 × 10−8 | 0.88 |
BNEA (Y5) | 0.000142 | 0 | 0 | 0 | 0 | 5.26 × 10−5 | 6.03 × 10−6 | 0 |
Output Responses | Significant Design Parameters Interaction | |
---|---|---|
Design Parameters | Interaction Value | |
Natural frequency (Y1) | 0.005 | |
Proof mass displacement (Y2) | 0.031 | |
Pull-in voltage (Y3) | 0.004 | |
Capacitance change (Y4) | 0.038 | |
BNEA (Y5) | , | 0.007, 0.007 |
Output Responses | MAE | RMSE | R |
---|---|---|---|
Natural frequency (Y1) | 29.64 Hz | 41.19 Hz | 0.998 |
Proof mass displacement (Y2) | 0.024 μm | 0.034 μm | 0.981 |
Pull-in voltage (Y3) | 0.085 V | 0.134 V | 0.997 |
Capacitance change (Y4) | 10.178 fF | 14.05 fF | 0.996 |
BNEA (Y5) | 0.973 |
Reference | Optimization Approach | Design Factor(s) | Output Response(s) | Simultaneous Optimization of Output Responses |
---|---|---|---|---|
Mohammed et al. [13] | One design factor | Geometric parameters | Differential capacitance | No |
Keshavarzi and Hasani [20] | Two design factors | Geometric parameters | Capacitance sensitivity | No |
Ramakrishnan et al. [21] | Traditional DOE | Geometric parameters | Mechanical displacement, stress, bandwidth | No |
Li et al. [22] | One design factor | Geometric parameters | Capacitance sensitivity | No |
Shi et al. [51] | Two design factors | Geometric parameters | Mechanical sensitivity, stress, natural frequency | No |
Martha et al. [52] | Two design factors | Geometric parameters | Pull-in voltage, capacitance sensitivity | No |
This work | Combined DACE and GP Modelling | Geometric parameters, Operating conditions | Natural frequency, mechanical displacement, capacitance sensitivity, BNEA, pull-in voltage | Yes |
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Saghir, S.; Saleem, M.M.; Hamza, A.; Riaz, K.; Iqbal, S.; Shakoor, R.I. A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling. Sensors 2021, 21, 7242. https://doi.org/10.3390/s21217242
Saghir S, Saleem MM, Hamza A, Riaz K, Iqbal S, Shakoor RI. A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling. Sensors. 2021; 21(21):7242. https://doi.org/10.3390/s21217242
Chicago/Turabian StyleSaghir, Shayaan, Muhammad Mubasher Saleem, Amir Hamza, Kashif Riaz, Sohail Iqbal, and Rana Iqtidar Shakoor. 2021. "A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling" Sensors 21, no. 21: 7242. https://doi.org/10.3390/s21217242
APA StyleSaghir, S., Saleem, M. M., Hamza, A., Riaz, K., Iqbal, S., & Shakoor, R. I. (2021). A Systematic Design Optimization Approach for Multiphysics MEMS Devices Based on Combined Computer Experiments and Gaussian Process Modelling. Sensors, 21(21), 7242. https://doi.org/10.3390/s21217242