Mathematical systems often have nonlinear, time-varying, time-lagged, and uncertain factors, which affect the experimental prediction accuracy. In order to improve the experimental prediction accuracy, this paper inputs the independent and dependent variable data sets as the original samples into a multiple linear regression function performs fitting calculations to obtain the nonlinear factors, and constructs a mathematical model of nonlinear systems based on a multiple linear regression model. In this model, the expected output value is calculated, and the input vector and output vector are continuously controlled for rolling operations to obtain the prediction results. A mathematical experiment of nonlinear system dynamics of vibration of deep water trap-test pipe system is set up to test the prediction ability of the model. The results show that the nonlinear system mathematical model based on the multiple linear regression model has a very high prediction accuracy. In the mathematical experiments of vibration nonlinear system dynamics of deep water trap-test pipe system, the error of the nonlinear system mathematical model based on multiple linear regression model in the transverse flow vibration frequency of the trap pipe column is 2%, which is lower than the single trap pipe calculation model by 4%. The prediction accuracy of the nonlinear system mathematical model based on the multiple linear regression model is higher than that of the single test tube model calculation by 78%. This shows that the nonlinear system mathematical model based on the multiple linear regression model can improve the experimental prediction accuracy.
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