Fault Diagnosis For Nonlinear Systems Research Articles

Integrating reinforcement learning with deterministic learning for fault diagnosis of nonlinear systems

Reliable fault diagnosis (FD) is important to ensure safety in nonlinear engineering systems. Modern engineering systems are often subject to unknown complex nonlinearities and varying operation conditions, therefore, one of the main challenges for FD of nonlinear systems is the robustness against these uncertainties. In this paper, a novel robust FD approach combining the reinforcement learning (RL) and the deterministic learning theory (DLT) is developed for a class of discrete-time nonlinear systems. The DLT is employed to pre-train the neural network (NN) aiming at approximating the unknown nonlinear complexity and obtaining dynamical fault models, then RL techniques are employed to adapt the NN parameters to improve the robustness of fault models. The stability of the learning process is rigorously analyzed using Lyapunov-based methods, and the effectiveness of the presented method is validated by a rotating stall warning experiment based on the data from Beihang University compressor test rig. Experiment results demonstrate that compared with other methods, the proposed method can achieve better performance in lead warning time and robustness.

Adaptive fast smooth super-twisting observer–based robust fault diagnosis for nonlinear systems

This study investigates the problem of robust fault diagnosis for nonlinear systems subjected to actuator faults and unknown input disturbances. A novel adaptive fast smooth super-twisting observer based on the super-twisting and adaptive dual-layer algorithms is presented, and a robust fault-diagnosis scheme based on an adaptive threshold is proposed to take the estimation error generated by the observer as the residual. In the adaptive fast smooth super-twisting observer, additional fractional powers less than 1 and linear terms are added to improve the smoothness and rapidity of the observer. The finite-time stability of the adaptive fast smooth super-twisting observer is then analyzed based on the Moreno–Lyapunov function algorithm, and rigorous proof confirms that the estimation-error dynamic is robust to unknown input disturbances and can converge to a region of zero in finite time. Finally, simulations of the rigid spacecraft attitude kinematics and dynamics are used to validate the effectiveness of the developed adaptive fast smooth super-twisting observer and the designed robust fault-diagnosis scheme.

Virtual Sensors Design for Nonlinear Dynamic Systems

The objective of the paper is virtual sensors design, estimating prescribed components of the systems state vector to solve the tasks of fault diagnosis in nonlinear systems. To solve the problem, the method called logic-dynamic approach is used, which allows to solve the problem for systems with non-smooth nonlinearities subjected to external disturbance by methods of linear algebra. According to this method, the problem is solved in three steps: at the first step, the nonlinear term is removed from the system, and the linear model invariant with respect to the disturbance is designed; at the second step, a possibility to take into account the nonlinear term and to estimate the given variable is checked; finally, the transformed nonlinear term is added to the linear model. The relations allowing to design virtual sensor of minimal dimension estimating prescribed component of the state vector of the system are obtained. The main contribution of the present paper is that a procedure to design virtual sensors of minimal dimension for nonlinear systems estimating prescribed components of the state vector is developed. This allows to reduce complexity of the virtual sensors in comparison with known papers where such sensors of full dimension are constructed. Besides, the limitations imposed on the initial system are relaxed that allow to extend a class of systems for which the virtual sensors can be constructed.

Application of Generalized Frequency Response Functions and Improved Convolutional Neural Network to Fault Diagnosis of Heavy-duty Industrial Robot

The combination of nonlinear spectrum and convolutional neural network (CNN) is efficient for fault diagnosis of nonlinear system . However, in traditional method, the nonlinear spectrum calculation was accomplished by identification algorithm outside the CNN, which reduced the diagnosis efficiency. To solve this problem, a novel CNN with the function of spectrum calculation and fault diagnosis is designed, in which the spectrum calculation network and the fault diagnosis network are connected in series. By extracting the optimized parameters of network, the nonlinear spectrum based on generalized frequency response function (GFRF) is obtained in the former network. Then, the GFRF spectrum is automatically put into the latter network for feature extraction and diagnosis. Hence, after determining the structure of the CNN, only by system input and output, the fault diagnosis can be realized, which avoids the complex process in traditional method. What's more, a new error cost function model is designed to guide the network parameters optimization in the direction of feature classification , which is conductive to improve the diagnosis accuracy. The proposed network model is applied to the heavy-duty industrial robot system, and the best performance is demonstrated by several experiments.

Design of functional observers for fault detection and isolation in nonlinear systems in the presence of noises

This work deals with the problem of designing functional observers for fault diagnosis in nonlinear systems in the presence of noises. It follows up previous work of the authors on design of functional observers (residual generators) for deterministic systems from the point of view of observer error linearization. Here, we consider the effect of noises on residual generation. The effect of sensor noises on the residuals is studied analytically and the associated probability distributions are derived. Following this, a well-known statistical hypothesis testing approach, Generalized Likelihood Ratio, is used to track changes in the mean of the residual to enable robust fault detection. The approach is also extended to process noises (plant-model mismatch) numerically. Throughout the study the methods presented are tested on a non-isothermal CSTR case study. The results show that the fault diagnosis scheme is able to quickly and accurately detect faults in the presence of both sensor and process noises.

Fault detection and isolation of gas turbine using series–parallel NARX model

This paper describes the design and implementation of intelligent dynamic models for fault detection and isolation of V94.2(5)/MGT-70(2) single-axis heavy-duty gas turbine system. The series–parallel structure of nonlinear autoregressive exogenous (NARX) models are used for fault detection, which initiate greater robustness and stability against uncertainties and perturbations. Moreover, to improve the fault detection robustness against uncertainties, the Monte Carlo technique is used in the proposed fault detection structure to select the best threshold. The analysis of fault detectability and fault detection sensitivity are accomplished to analyze the performance of the suggested technique. The fault isolation process is also achieved by using the residual classification approach. The results show the feasibly, robustness, and performance of the presented approach for fault diagnosis of nonlinear systems in the presence of uncertainties.

A sensor fault diagnosis method based on KPCA and contribution graph

In this paper, a sensor fault diagnosis method based on KPCA and contribution graph are proposed to adapt to the nonlinear and non-Gaussian characteristics of the system. Based on the kernel function theory, this method uses SPE and T2 statistics for fault detection and contribution graph for fault location, thus completing fault diagnosis. The numerical simulation results verify that the proposed method is more effective than the traditional PCA method in detecting nonlinear faults. At the same time, the KPCA contribution map can be used to accurately locate the fault sensor, which can provide a reference value for the sensor fault diagnosis of nonlinear systems in the future.

Optimal state estimation and fault diagnosis for a class of nonlinear systems

This study proposes a scheme for state estimation and, consequently, fault diagnosis in nonlinear systems. Initially, an optimal nonlinear observer is designed for nonlinear systems subject to an actuator or plant fault. By utilizing Lyapunov &#x02BC s direct method, the observer is proved to be optimal with respect to a performance function, including the magnitude of the observer gain and the convergence time. The observer gain is obtained by using approximation of Hamilton-Jacobi-Bellman &#x0028 HJB &#x0029 equation. The approximation is determined via an online trained neural network &#x0028 NN &#x0029 . Next a class of affine nonlinear systems is considered which is subject to unknown disturbances in addition to fault signals. In this case, for each fault the original system is transformed to a new form in which the proposed optimal observer can be applied for state estimation and fault detection and isolation &#x0028 FDI &#x0029 . Simulation results of a singlelink flexible joint robot &#x0028 SLFJR &#x0029 electric drive system show the effectiveness of the proposed methodology.

Information Dynamic Correlation of Vibration in Nonlinear Systems.

In previous studies, information dynamics methods such as Von Neumann entropy and Rényi entropy played an important role in many fields, covering both macroscopic and microscopic studies. They have a solid theoretical foundation, but there are few reports in the field of mechanical nonlinear systems. So, can we apply Von Neumann entropy and Rényi entropy to study and analyze the dynamic behavior of macroscopic nonlinear systems? In view of the current lack of suitable methods to characterize the dynamics behavior of mechanical systems from the perspective of nonlinear system correlation, we propose a new method to describe the nonlinear features and coupling relationship of mechanical systems. This manuscript verifies the above hypothesis by using a typical chaotic system and a real macroscopic physical nonlinear system through theory and practical methods. The nonlinear vibration correlation in multi-body mechanical systems is very complex. We propose a full-vector multi-scale Rényi entropy for exploring the chaos and correlation between the dynamic behaviors of mechanical nonlinear systems. The research results prove the effectiveness of the proposed method in modal identification, system dynamics evolution and fault diagnosis of nonlinear systems. It is of great significance to extend these studies to the field of mechanical nonlinear system dynamics.

Fault estimation based on observer for chaotic Lorenz system with bifurcation problem

In this paper, the simultaneous estimation of the process and sensor fault of a chaotic Lorenz system in a noisy environment is investigated. The problem of the process fault leads to the occurrence of a bifurcation in the Lorenz system. The purpose of this article is to combine the concept of fault and bifurcation. Fault diagnosis of nonlinear systems becomes more practicable when it is managed over Takagi-Sugeno (TS) approximated fuzzy models. TS fuzzy model unknown input observer can estimate faults and states. In this respect, a TS fuzzy model augmented by a proportional plus integral, for fault modeling observer (FO) is lined up for the estimation of the unmeasured signal. The simulation conclusions hint that the observer runs well in estimating process fault, states, and sensor fault. Using these estimates, the deviation value of a parameter is determined from its actual value, which is the same as the low amount of deviation in this article because the bifurcation occurs in the system. In the first part of the simulation, the process fault occurs and drives system behavior into chaos, and the bifurcation diagram uses to explain it. In the second part, the system is influenced by actuator fault. The conclusion is validated through extensive simulations.

Fault diagnosis of nonlinear systems using recurrent neural networks

In this work, we propose a fault detection and isolation (FDI) methodology that enables diagnose of single, multiple and simultaneous actuator and sensor faults regardless of the utilized model structure. The basis of the proposed methodology is modelling and inversion of nonlinear systems using recurrent neural network (RNN)s. To this end, a bank of RNNs is used to estimate system inputs and/or outputs and build predictive models using the obtained estimates and an RNN as the plant model. Then a bank of residuals is generated in a way each residual is sensitive to a subset of faults and insensitive to the rest and as a result of this, a unique fault signature is obtained for each fault scenario. RNNs can be replaced by other machine learning techniques such as partial least square (PLS)s, random forest, etc. One of the advantages of the proposed methodology is that it does not require the existence of plant fault history or first principles models unlike other existing results in the literature. Also, it enables isolation of actuator and simultaneous actuator and sensor faults in highly interconnected systems. The effectiveness of the proposed FDI scheme is shown via simulation examples.

A quadratic boundedness approach to a neural network-based simultaneous estimation of actuator and sensor faults

The paper is devoted to the problem of a neural network-based robust simultaneous actuator and sensor faults estimator design for the purpose of the fault diagnosis of nonlinear systems. In particular, the methodology of designing a neural network-based fault estimator is developed. The main novelty of the approach is associated with possibly simultaneous sensor and actuator faults under imprecise measurements. For this purpose, a linear parameter-varying description of a recurrent neural network is exploited. The proposed approach guaranties a predefined disturbance attenuation level and convergence of the estimator. In particular, it uses the quadratic boundedness approach to provide uncertainty intervals of the achieved estimates. The final part of the paper presents an illustrative example concerning the application of the proposed approach to the multitank system fault diagnosis.

Active Fault Diagnosis for Stochastic Nonlinear Systems: Online Probabilistic Model Discrimination

Reliable and timely diagnosis of system faults under uncertainties is imperative for safe, reliable, and profitable operation of technical systems. This paper presents an input design method for active fault diagnosis for nonlinear systems that are subject to probabilistic model uncertainty and stochastic disturbances, and are under operational constraints. A computationally efficient sample-based method is presented for joint propagation of model uncertainty and stochastic disturbances using non-intrusive generalized polynomial chaos and unscented transformation. A tractable sample-based distance measure, inspired by the k-nearest neighbors algorithm, is used for fault diagnosis, which seeks to discriminate between probabilistic predictions of the model hypotheses for normal and faulty operation. Simulation results on a benchmark bioreactor case study demonstrate the effectiveness of the proposed input design method for reliable fault diagnosis under uncertainty through online model discrimination.

A new reconstruction-based auto-associative neural network for fault diagnosis in nonlinear systems

Auto-associative neural network (AANN) is a typical nonlinear principal component analysis method, which is widely used in industry for fault diagnosis purposes, especially in nonlinear systems. However, the basic AANN often suffers from “smearing effects” problems that may lead to misdiagnosis, particularly with regards to the complex faults involving multiple variables. In this work, a new reconstruction-based AANN (RBAANN) method is proposed to enhance the capacity of fault diagnosis. In RBAANN, a generic derivative equation is developed to investigate the effects of AANN model inputs on the prediction error between model inputs and outputs. Based on the derivative equation, the reconstruction-based index for single or multiple variables, which is defined as the minimum prediction error, is obtained by tuning the corresponding model inputs iteratively. However, without the prior knowledge of the real faulty variables, all the possible variable sets need to be evaluated by the reconstruction-based index, and this may result in an exhaustive search and cause a huge computational burden. Thus, a branch and bound algorithm is introduced into RBAANN to solve the variable selection problem. Finally, an efficient fault diagnosis strategy by integrating RBAANN and branch and bound algorithm (BAB-RBAANN) is implemented to further pinpoint the source of the detected faults. This BAB-RBAANN method can handle both single and multiple variable(s) faults for nonlinear systems without prior knowledge efficiently. The effectiveness of the proposed methods is evaluated on a validation example and an industrial example. Comparisons with other methods, including principal component analysis techniques, are also presented.

An improved LLE-based cluster security approach for nonlinear system fault diagnosis

This paper proposes a novel improved LLE-based (local linear embedding) approach (TLLE) for solving the fault diagnosis problem of the nonlinear system. Firstly, tangent space distance is introduced to LLE approach, which can satisfy the local linearity of LLE and better preserve the local manifold features of the original data simultaneously. Then, to solve the problem of inner dimension in LLE approach is hard to estimate, the method of intrinsic dimension estimation based on fractal dimension is employed in the approach by means of linear fitting. Furthermore, a fault diagnosis scheme is presented based on the TLLE approach. We combine fault state with special distribution to complete the fault diagnosis, which can simplify the computation obviously and improve the real-time capability of the approach. Finally, numerical simulations of the TE process data are performed to illustrate the effectiveness of the proposed fault diagnosis scheme.

Input Design for Online Fault Diagnosis of Nonlinear Systems with Stochastic Uncertainty

Fault diagnosis is crucial for ensuring stable and reliable operation of high-performance systems in the presence of abnormal events. System uncertainties often make discrimination between normal and faulty behavior a challenging task. This paper presents an active fault diagnosis (AFD) method for nonlinear systems with stochastic uncertainty. AFD involves the optimal design of system inputs for discriminating between multiple model hypotheses that correspond to various operational scenarios. The proposed AFD method relies on minimizing the probability of error in hypothesis selection subject to hard input and state chance constraints. Moment-based approximations for a bound on the probability of error in hypothesis selection as well as for chance constraint evaluation are introduced in order to derive a tractable surrogate AFD problem that is amenable to online implementations. The performance of the AFD method for offline and online fault diagnosis is demonstrated on a continuous bioreactor with multipl...

Observer-Based Fault Diagnosis of Nonlinear Systems via an Improved Homogeneous Polynomial Technique

The problem of observer-based fault diagnosis is investigated for a class of nonlinear systems via an improved homogeneous polynomial technique (HPT). In the design of the estimator, some adjustable parameters are introduced that can lead to less conservatism. By developing an improved HPT, the employment of multi-instant and multi-index can achieve desired $$H_{\infty }$$ system performance. A tunnel diode circuit example is shown to demonstrate that (1) less conservative results are expected in comparison with existing ones; and (2) faults can be distinguished in only a few steps after their occurrence.

Component fault diagnosis for nonlinear systems

Component fault diagnosis for nonlinear systems

Nonlinear sensor fault diagnosis using mixture of probabilistic PCA models

This paper presents a methodology for sensor fault diagnosis in nonlinear systems using a Mixture of Probabilistic Principal Component Analysis (MPPCA) models. This methodology separates the measurement space into several locally linear regions, each of which is associated with a Probabilistic PCA (PPCA) model. Using the transformation associated with each PPCA model, a parity relation scheme is used to construct a residual vector. Bayesian analysis of the residuals forms the basis for detection and isolation of sensor faults across the entire range of operation of the system. The resulting method is demonstrated in its application to sensor fault diagnosis of a fully instrumented HVAC system. The results show accurate detection of sensor faults under the assumption that a single sensor is faulty.

The Design and Implementation of Automatic Fire Extinguishing and Explosion Suppression System's Testing Equipment

According to the automatic fire extinguishing equipment requirements for explosion suppression platform system, this paper using the flexible neural tree and the clonal selection principle, describes the creation method of flexible neural tree model, embedded virtual instrument technology, to solve the nonlinear system fault diagnosis problem, realize the fire (explosion) detection system control components, improves the diagnostic sensitivity and accuracy. After the trial, the equipment illustrates high integrity, good versatility and high stability.