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Uncertain Fractional-Order Multi-Objective Optimization Based on Reliability Analysis and Application to Fractional-Order Circuit with Caputo Type

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Abstract

Reliability analysis is critical to the study of uncertain dynamic systems under noise excitation. This paper focuses on the uncertain fractional-order multi-objective optimization model and its application. Firstly, based on the infinite time-based expected utility criterion, we propose two innovative first-hitting criteria, namely the reliability index criterion and the reliability lifetime criterion. Secondly, by replacing the ordinary derivative with the Caputo fractional-order derivative and introducing uncertain variables to the system, we develop an uncertain fractional-order differential equations to better model the actual electronic system. Subsequently, combining two proposed first-hitting criteria, we present a novel uncertain fractional-order multi-objective optimization problem, which is then transformed into the corresponding single-objective crisp optimization model. Lastly, the proposed model is applied to a fractional-order resistor–capacitance circuit model, where the analytic expression of the uncertainty distribution for the first-hitting time and the sufficient condition for the optimal solution are derived for the order of 1. Also, we give numerical examples to illustrate how our optimal solution fluctuates under various constraints.

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Data sharing is not applicable to this article as no datasets were generated or analyzed during the current study.

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Acknowledgements

This work is supported by the National Natural Science Foundation of China (No.61771087 and No.12071219), a project funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD), and Jiangsu Province Student Innovation Training Program (202110298040Z).

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Authors and Affiliations

  1. School of Science, Nanjing Forestry University, Nanjing, 210037, Jiangsu, China

    Ting Jin

  2. College of International Education, Nanjing Forestry University, Nanjing, 210037, Jiangsu, China

    Hongxuan Xia

  3. College of Electronic Information and Automation, Civil Aviation University of China, Tianjin, 300300, China

    Wu Deng

  4. Business School, Dalian University of Foreign Languages, Dalian, 116044, China

    Yuangang Li

  5. State Grid Jiangsu Electric Power Maintenance Branch Company, Nanjing, 211102, Jiangsu, China

    Hao Chen

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  1. Ting Jin
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  2. Hongxuan Xia
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  3. Wu Deng
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Correspondence to Yuangang Li.

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Jin, T., Xia, H., Deng, W. et al. Uncertain Fractional-Order Multi-Objective Optimization Based on Reliability Analysis and Application to Fractional-Order Circuit with Caputo Type. Circuits Syst Signal Process 40, 5955–5982 (2021). https://doi.org/10.1007/s00034-021-01761-2

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  • DOI: https://doi.org/10.1007/s00034-021-01761-2

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