Research On Data-Driven Modeling And Feature Analysis Of Nonlinear Systems

With the rapid development of data acquisition technology,the cost of acquiring data has decreased,providing an opportunity for developing data-driven mechanics research.Compared with traditional mechanics research methods,the data-driven approach will use data-driven models to portray the underlying mechanics mechanism instead of the mechanical equations to describe the problem,which has significant advantages in analyzing and predicting more complex systems.However,the limitations of the data-driven approach itself are obvious,such as whether the quality of the acquired data meets the research conditions,whether the combination of the datadriven approach and physical laws is reasonable,how to select effective data features and the scalability,interpretability,and generality of the data approach.This paper focuses on the dynamics analysis of data-driven nonlinear systems from two perspectives in response to the current situation and problems.Data-driven modeling analysis generally extracts feature information from data to construct system models for estimation and identification.It can be used for system response prediction and system health management.However,most data-driven models are still uninterpretable black-box models.Therefore,this paper uses neural ordinary differential equations to approximate the governing equations,especially by incorporating the inherent mathematical relationships in calculating the loss function.The method is also improved to focus on the system modeling of the forced vibration problem.A new strategy to identify the local parameters of the system is proposed,which can be used for system parameter identification and damage detection.Numerical and experimental results show that the method has high identification accuracy and good local parameter identification capability.At the same time,the way proposed in this paper is interpretable.It can directly approximate the potential dynamical evolution law instead,so it is a system parameter identification strategy worth to be considered.Data-driven feature analysis is mainly due to the difficulty of modeling or the unavailability of modeling conditions.Therefore,the empirical mode decomposition method is used for non-smooth signals in bearing fault detection,and the signals are decomposed into intrinsic mode functions from high to low frequencies.In addition,an improved method based on the empirical mode decomposition method is used to overcome the mode mixing problem.This paper uses the sliding time window method to detect abnormal bearing vibration signals.It uses the ensemble mode decomposition method and the complementary ensemble mode decomposition method for bearing fault detection’s signal decomposition and reconstruction process.Then,the relevant intrinsic mode functions containing defect information are selected based on statistical indicators for signal reconstruction.Finally,based on the frequency-weighted energy operator,the amplitudes and frequencies in the signal are extracted.The two sets of experimental results show that the evaluation of the integrated multiple statistical indicators can reconstruct the appropriate signal.The method is easier to obtain the spectral lines corresponding to specific faults in the case of strong noise and with other vibration disturbances,as well as better feature extraction for weak signals and direct signal detection for any signal without pre-processing.Intelligent monitoring of anesthesia procedures based on heart rate variability signals can only be performed with data-driven feature analysis because the signals themselves are not modeled.It would greatly benefit both doctors and patients if the patients’ states could be accurately monitored based on medical signals.This paper uses the empirical mode decomposition method to decompose and recombine the heart rate variability signals.Next,the sliding time window method extracts the noxious stimulation signal features.Finally,a neural network is proposed to classify the patients’ states using the extracted signal features to monitor noxious stimulation effectively.Based on this,the decomposition method for heart rate variability signals is simplified.Then the effect of the sliding time window size when extracting noxious stimulation features is quantified,the impact of the time window size on the extracted features is determined,and the relationship between the effectiveness and efficiency of the extracted features is balanced.When the data are in good condition,and the underlying mechanics mechanism is precise,data-driven modeling analysis is performed,and data-driven feature analysis is performed when modeling is complex or unavailable.For these two aspects of research of interest,we use the problem as traction to combine data-driven and mechanics research methods to form interdisciplinary research methods to drive research progress on specific issues.