Incipient Faults Identification,Detection And Prediction Of Nonlinear Systems Via Deterministic Learning

With the increasing automation level of the practical system,the key equipments of the system are developing towards precision and complexity.The safe and reliable operation of these equipments is an important issue,and the safety monitoring of these equipments has an important social and economic significance.As the actual industrial production system can be considered as a complex nonlinear dynamical system,no mat-ter how high the quality of the system design,the unexpected fault will be occurring in different operating conditions during some times.Especially,when the system has incip-ient faults,it is very important to monitor the running state of the system accurately and timely?extracting effective and stable features from the system which reflect the degradation trend of the system?,fault diagnosis and health management.This paper mainly studies the following three aspects:Firstly,considering a class of nonlinear uncertain systems with incipient faults,the dynamic trajectory of the system is identified accurately based on deterministic learning theory along the system state tra-jectory.Then,the more sensitive dynamical features are extracted based on the dynamic trajectory.Secondly,the dynamic pattern recognition technology is used to detect the incipient fault of the nonlinear system quickly.Finally,the system failure time is accu-rately predicted based on the change of system residual to achieve the real-time health evaluation of the system.The details are as follows:1.This chapter presents a new dynamic feature extraction method for nonlinear dynamical systems based on deterministic learning theory and spatio-temporal Lempel-Ziv complexity?LZC?.The new method extracts features from the dynamics trajectory which is different from the state trajectory of nonlinear systems.Through deterministic learning theory,the unknown system dynamics can be accurately modeled in a local region along the recurrent trajectories of nonlinear dynamical systems,and the dynamics trajectory is obtained by bringing the state trajectory into the dynamics model.Firstly,the obtained dynamics trajectory is characterized with a temporal-LZC index and a spatio-LZC index.Secondly,sensitivity analysis of the dynamic feature characterization is investigated to evaluate the sensitivity of the system dynamic indices.Finally,numerical experiment based on the Rossler system is used to demonstrate the effectiveness of the proposed method.Furthermore,the proposed method is applied to the actual dynamical characteristics of ECG signals.The extracted dynamic complexity indices of ECG signals can reflect the condition of myocardial ischemia more sensitively,and can improve the accuracy,specificity and sensitivity of detection of myocardial ischemia significantly.2.This chapter presents a new incipient fault detection approach for nonlinear dynamical systems via deterministic learning.Through defining and establishing the banks of health,sub-health and incipient fault modes,the incipient fault detectability condition is derived with the fault mismatch function.The system dynamics underlying three kinds of system modes are accurately approximated via deterministic learning firstly.Secondly,a bank of estimators is constructed using the learned modes.A set of residuals is achieved by comparing the bank of estimators with the monitored system.According to the smallest residual principle and the fault mismatch function,if the average L₁norm of the residual,which is associated with one of the incipient fault modes,is smaller than the others at a time instant t_d,the system incipient fault is detected.Finally,the incipient fault detectability is analyzed rigorously.Numerical simulation is investigated to demonstrate the effectiveness of the approach.Different from the existing online approximation incipient fault detection methods,the most distinct feature of the proposed detection scheme lies in that the design of detection threshold is eliminated,and it also can detect different stages of system incipient fault and provide a more accurate and rapid fault detection.3.In this chapter,a new model-based TTF prediction scheme is proposed.Based on deterministic learning theory,a system dynamical pattern bank consisting of health,sub-health and fault patterns is established,and a set of estimators associated with the learned system patterns is used to generate average L₁norms of system residuals.Then,a TTF prediction model is derived based on the system residual generator with a predefined failure pattern.Once the first predicting time is obtained according to the incipient fault detection scheme,the system TTF can be predicted by projecting the learned fault dynamics at the current time against the failure threshold.Finally,an incipient fault detection and TTF prediction?IFDTP?algorithm is implemented by combining the established bank,the first predicting time and the TTF model.The novelty of this paper lies in that the new TTF prediction scheme can provide a more accurate system failure time for nonlinear dynamical systems,and the effectiveness of the proposed IFDTP algorithm is illustrated by simulation studies.Since the detection and prediction processes are executed in parallel,the comprehensive IFDTP algorithm can be implemented on practical systems easily.