Abstract
To predict the multi-point vibration response in the frequency domain when the uncorrelated multi-source loads are unknown, a data-driven and multi-input multi-output least squares support vector regression (MIMO LS-SVR)-based method in the frequency domain is proposed. Firstly, the relationship between the measured multi-point vibration response and unmeasured multi-point vibration response is formulated using the transfer function in the frequency domain. Secondly, the data-driven multiple regression analysis problem of multi-point vibration response prediction in the frequency domain is described formally, and its mathematical model is established. With the measured multi-point vibration response as the input and the unmeasured multi-point vibration response as the output, the vibration response history data are assembled as a MIMO training dataset at each frequency. Thirdly, using the MIMO LS-SVR algorithm and MIMO history training dataset, the multi-point vibration response prediction model is built at each frequency point. By comparing the transmissibility matrix method, multiple linear regression model-based method, and MIMO neural network method, the application scope of the proposed method and its advantages are analyzed. The experimental results for acoustic and vibration experiment on a cylindrical shell verified that the MIMO LS-SVR-based method predicts the multi-point vibration response effectively when the loads are unknown, and has higher precision than the transfer function method, multiple linear regression method, MIMO neural network method, and transmissibility matrix method.
Highlights
Excessive vibration is one of the main reasons for the structural damage of a mechanism
Vibration response prediction methods can be divided into the time domain and frequency domain, which was the first to be studied and is the most mature [3]
Traditional methods of multi-point vibration response prediction in the frequency domain for structures are all based on multiple loads excitation and structural characteristics
Summary
Excessive vibration is one of the main reasons for the structural damage of a mechanism. When the transmissibility matrix or transfer function of the LTI structure is unknown, Zhan [38] used the measured vibration response based multiple linear regression model to predict the unmeasured vibration response in the frequency domain without the information of loads. This method can achieve good prediction results, the prediction accuracy is often affected by ill-posed problems at resonance frequencies. Using the measured multi-point vibration response in Equation (3) as the input directly and the unmeasured multi-point vibration response as the output, a multi-input and multi-output multi-point vibration response prediction model for an LTI dynamics structure under unknown uncorrelated multi-source loads can be established using the history training dataset and multiple linear regression model.
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