THERMAL SCIENCE

International Scientific Journal

Juan Du

,

Haibin Li

,

Yun He

A METHOD FOR CALCULATING STRUCTURAL RELIABILITY OF MEMS SYSTEMS BY THE IMPLICIT FUNCTIONAL FUNCTION

ABSTRACT
In this paper, a novel approach to calculate the structural reliability of micro-electro-mechanical systems systems is proposed. This approach utilizes the implicit functional function, which involves the acquisition of multiple sets of inputs and responses of the structure through numerical simulation or experimentation. Concurrently, the exponential function is employed as the activation function of the hidden layer of the neural network. A multi-layer neural network possesses the capacity to approximate the properties of arbitrary non-linear functions with arbitrary precision and construct a customized neural network structure. The training of this customized neural network enables the visualization and expression of the structural function. This approach has been demonstrated to enhance the precision of functional fitting. The proposed method for modeling complex structural systems reliability is substantiated by numerical examples. Micro-electro-mechanical systems play a pivotal role in modern engineering, and their integration has the potential to further enhance structural analysis and reliability assessment.
KEYWORDS
implicit function, custom neural network, response surface method, structural reliability, complex structure, micro-electro-mechanical systems
PAPER SUBMITTED: 2024-10-29
PAPER REVISED: 2025-08-12
PAPER ACCEPTED: 2025-08-12
PUBLISHED ONLINE: 2026-04-12
DOI REFERENCE: https://doi.org/10.2298/TSCI2602961D
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2026, VOLUME 30, ISSUE No. 2, PAGES [961 - 971]
REFERENCES
[1] Nadeem, M., et al., Analysis of Nanobeam-Based Microstructure in N/MEMS System Using van der Waals Forces, Facta Universitatis, Series: Mechanical Engineering, 22 (2024), 4, pp. 673-688
[2] He, J.-H., et al., Piezoelectric Biosensor Based on Ultrasensitive MEMS System, Sensors and Actuators A: Physical, 376 ( 2024), 115664
[3] Ozdemir, K., Mutlu, A. K., Cost-Effective Data Acquisition Systems for Advanced Structural Health Monitoring, Sensors, 24 (2024), 4269
[4] He, J.-H., Periodic Solution of a Micro-Electromechanical System, Facta Universitatis, Series: Mechanical Engineering, 22 (2024), 2, pp. 187-198
[5] Babaeimorad, S., et al., An Integrated Optimization of Production and Preventive Maintenance Scheduling in Industry 4.0, Facta Universitatis, Series: Mechanical Engineering, 22 (2024), 4, pp. 711-720
[6] Mudasir, S., et al., A Dual Approach to Parameter Estimation: Classical vs. Bayesian Methods in Power Rayleigh Modelling, Thermal Science, 28 (2024), 6B, pp. 4877-4894
[7] Darwish, J. A., Statistical Properties and Applications for Exponentiated Exponential Rayleigh Distribution, Thermal Science, 28 (2024), 6B, pp. 4855-4006
[8] Deng, J., et al., Structural Reliability Analysis for Implicit Performance Functions Using Artificial Neural Network, Structural Safety, 27 (2025), 1, pp. 25-48
[9] Li, H. S., et al., Support Vector Machine for Structural Reliability Analysis, Applied Mathematics and Mechanics, 27 (2006), 10, pp. 1295-1303
[10] Cheng, J., Li, Q. S., Application of the Response Surface Methods to Solve Inverse Reliability Problems with Implicit Response Functions, Computational Mechanics, 43 (2009), 4, pp. 451-459
[11] Zhang, L. G., et al., Efficient Structural Reliability Analysis Method Based on Advanced Kriging Model, Applied Mathematical Modelling, 39 (2015), 2, pp. 781-793
[12] Wen, Z. X., et al., A Sequential Kriging Reliability Analysis Method with Characteristics of Adaptive Sampling Regions and Parallelizability, Reliability Engineering & System Safety, 153 (2016), Sept., pp. 170-179
[13] Su, G. S., et al., A Gaussian Process-Based Response Surface Method for Structural Reliability Analysis, Structural Engineering and Mechanics, 56 (2015), 4, pp. 549-567
[14] He, Y., Li, H. B., A Novel Numerical Method for Heat Equation, Thermal Science, 20 (2016), 3, pp. 1018-1021
[15] He, Y., et al., Fitting Methods Based on Custom Neural Network for Relaxation Modulus of Viscoelastic Materials, International Journal of Performability Engineering, 15 (2019), 1, pp. 107-115
[16] Li, H. B., et al., Structural Reliability Calculation Method Based on the Dual Neural Network and Direct Integration Method, Neural Computing and Applications, 29 (2018), 7, pp. 425-443
[17] Li, H. B., et al., Dual Neural Network Method for Solving Multiple Definite Integrals, Neural Computation, 31 (2019), 1, pp. 208-232
[18] Echard, B., et al., Ak-Mcs: An Active Learning Reliability Method Combining Kriging and Monte Carlo Simulation, Structural Safety, 33 (2011), 2, pp. 145-154
[19] Dai, H., et al., Wavelet Density-Based Adaptive Importance Sampling Method, Structural Safety, 52 (2015), Part B, pp. 161-169
[20] Huang, X., et al., Assessing Small Failure Probabilities by Ak-Ss: An Active Learning Method Combining Kriging and Subset Simulation, Structural Safety, 59 (2016), Mar., pp. 86-95
[21] Feng, G. Q., A Circular Sector Vibration System in a Porous Medium: a Fractal-Fractional Model and He's Frequency Formulation, Facta Universitatis Series: Mechanical Engineering, 23 (2025), 2 pp. 377-385
[22] He, J.-H., et al., Frequency-Amplitude Relationship in Damped and Forced Nonlinear Oscillators with Irrational Nonlinearities, Journal of Computational Applied Mechanics, 56 (2025), 2, pp. 307-317
[23] He, J.-H. Frequency Formulation for Nonlinear Oscillators (Part 1), Sound & Vibration, 59 (2025), 1, 1687
[24] He, J.-H., et al., Modeling and Numerical Analysis for an MEMS Graphene Resonator, Front. Phys. 13 (2025), 1551969
[25] He, J.-H., et al., Variational Approach to Micro-Electro-Mechanical Systems, Facta Universitatis Series: Mechanical Engineering, 23 (2025), 4, pp. 649-665
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A method for calculating structural reliability of MEMS systems by the implicit functional function

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence