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Spectrum analysis of interval process model and its application in uncertain vibration analysis

Science China(Technological Sciences) 2024年第8期67卷 2549-2564页

作者： LI JinWu JIANG Chao NI BingYu State Key Laboratory of Advanced Design and Manufacturing Technology for Vehicle College of Mechanical and Vehicle EngineeringHunan UniversityChangsha 410082China

In recent years, the authors have extended the traditional interval method into the time dimension to develop a new mathematical tool called the “interval process model” for quantifying time-varying or dynamic uncertainties. This model employs upper and lower bounds instead of precise probability distributions to quantify uncertainty in a parameter at any given time point. It is anticipated to complement the conventional stochastic process model in the coming years owing to its relatively low dependence on experimental samples and ease of understanding for engineers. Building on our previous work, this paper proposes a spectrum analysis method to describe the frequency domain characteristics of an interval process, further strengthening the theoretical foundation of the interval process model and enhancing its applicability for complex engineering problems. In this approach, we first define the zero midpoint function interval process and its auto/cross-power spectral density(PSD) functions. We also deduce the relationship between the auto-PSD function and the auto-covariance function of the stationary zero midpoint function interval process. Next, the auto/cross-PSD function matrices of a general interval process are defined, followed by the introduction of the concepts of PSD function matrix and cross-PSD function matrix for interval process vectors. The spectrum analysis method is then applied to random vibration problems, leading to the creation of a spectrum-analysis-based interval vibration analysis method that determines the PSD function for the system displacement response under stationary interval process excitations. Finally, the effectiveness of the formulated spectrum-analysis-based interval vibration analysis approach is verified through two numerical examples.

关键词： interval process spectrum analysis power spectral density(PSD) time-varying uncertainty uncertain vibration analysis

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