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The nonlinear output frequency response functions (NOFRFs) are extensions of the frequency response function (FRF) in linear systems to weakly nonlinear systems, have been applied in nonlinear system analysis and structural damage detection. The calculation of NOFRFs of the system is accomplished by solving a series of linear difference or linear differential equations, known as generalized associated linear equations (GALEs). In the present study, taking a beam structure with initial breathing crack damage as an example, the nonlinear differential equation (NDE) model of a beam structure unit represented by a bilinear oscillator is investigated. Meanwhile, the approximate polynomial model of the bilinear oscillator is studied based on the function approximation theory of Weierstrass and the theory of the expansion of the basic function (Legendre polynomial), and then the first four orders of the NOFRFs of the beam structural units in different damage states are obtained by using the theory of the GALEs of the NDE model. Finally, the first four orders of the NOFRFs of the beam structural units in different damage states are obtained by means of the support vector machine (SVM) algorithm to train the classification model of the beam structure and its structural damage detection and assessment.

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Structural Damage Detection of Cracked Beams Based on Nonlinear Output Frequency Response Functions and Support Vector Machine

  • 会议论文

  • 发表日期：

    2025年

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  • Wenbo Zhang,
  • Xiaoyue Guo,
  • Yunhe Zhang,
  • Yunpeng Zhu,
  • Bo Zhang,
  • Zhike Peng

摘要

The nonlinear output frequency response functions (NOFRFs) are extensions of the frequency response function (FRF) in linear systems to weakly nonlinear systems, have been applied in nonlinear system analysis and structural damage detection. The calculation of NOFRFs of the system is accomplished by solving a series of linear difference or linear differential equations, known as generalized associated linear equations (GALEs). In the present study, taking a beam structure with initial breathing crack damage as an example, the nonlinear differential equation (NDE) model of a beam structure unit represented by a bilinear oscillator is investigated. Meanwhile, the approximate polynomial model of the bilinear oscillator is studied based on the function approximation theory of Weierstrass and the theory of the expansion of the basic function (Legendre polynomial), and then the first four orders of the NOFRFs of the beam structural units in different damage states are obtained by using the theory of the GALEs of the NDE model. Finally, the first four orders of the NOFRFs of the beam structural units in different damage states are obtained by means of the support vector machine (SVM) algorithm to train the classification model of the beam structure and its structural damage detection and assessment.