A Fault Detection and Isolation Method Based on Supervised Nonnegative Matrix Factorizations

ABSTRACTQuick and timely fault detection is of great importance in control systems reliability. Undetected faulty sensors could result in irreparable damages. Although fault detection and isolation (FDI) methods in control systems have received much attention in the last decade, these techniques have not been applied for some classes of nonlinear systems yet. This paper deals with the issues of sensor fault detection and isolation for a class of Lipschitz uncertain nonlinear system. By introducing a coordinate transformation matrix for states and output, the original system is first divided into two subsystems. The first subsystem is affected by uncertainty and disturbance. The second subsystem just has sensor faults. The nonlinear term is separated to linear and pure nonlinear parts. For fault detection, two sliding mode observers (SMO) are designed for the two subsystems. The stability condition is obtained based on the Lyapunov approach. The necessary matrices and parameters are obtained by solving the linear matrix inequality (LMI) problem. Furthermore, two sliding mode observers are designed for fault isolation. Finally, the effectiveness of the proposed approach is illustrated by simulation examples.

SummaryThis paper proposes an integrated actuator and sensor active fault‐tolerant model predictive control scheme. In this scheme, fault detection is implemented by using a set‐valued observer, fault isolation (FI) is performed by set manipulations, and fault‐tolerant control is carried out through the design of a robust model predictive control law. In this paper, a set‐valued observer is used to passively complete the fault detection task, while FI is actively performed by making use of the constraint‐handling capability of robust model predictive control. The set‐valued observer is chosen to implement fault detection and isolation (FDI) because of its simple mathematical structure that is not affected by the type of faults such as sensor, actuator, and system‐structural faults. This means that only one set‐valued observer is needed to monitor all considered actuator and sensor statuses (health and fault) and to carry out the fault detection and isolation task instead of using a bank of observers (each observer matching a health/fault status). Furthermore, in the proposed scheme, the advantage of robust model predictive control is that it can effectively deal with system constraints, disturbances, and noises and allow to implement an active FI strategy, which can improve FI sensitivity when compared with the passive FI methods. Finally, a case study based on the well‐known two‐tank system is used to illustrate the effectiveness of the proposed fault‐tolerant model predictive control scheme. Copyright © 2016 John Wiley & Sons, Ltd.

In this work, we will consider the dimension reduction of the set of time series, such as economic data, to find the meaningful basis vector for the set of data, and indicate which data use which basis vector. Usually each of the time series is analyzed independently in economics but here we will analyze the set of time series simultaneously. Since some of the economic data are measured as positive values and we want to decompose them as a mixture of the parts, we will apply non-negative matrix factorization to the economic data. Non-negative matrix factorization can compress dimensions by approximating a non-negative matrix with the product of two non-negative matrices. The two non-negative matrices are called the coefficient matrix and the basis matrix, and the basis matrix can be considered as a dimensionally compressed matrix. If the standard non-negative matrix factorization is used for economic data, the basis matrix may not be smooth. We think that the basis vectors should be smooth except a few special economical incidents. In the proposed method, a Graph-based non-negative matrix factorization is introduced to regularize the basis matrix of the time series. A path graph for representing the time series of economic data is incorporated into the non-negative matrix factorization as regularization. As a result, basis vectors that maintains the time series of economic data are decomposed. Furthermore, we propose to introduce a sparsity in the non-negative matrix factorization. Traditionally, the sparsity incorporated into non-negative matrix factorization has been used for basis vectors. However, the proposed method introduces the sparsity for coefficient vectors. Thus the proposed method, which simultaneously incorporates the sparsity for the coefficient vectors and the smoothness for the basis vectors, can extract the smooth basis vectors and the original economical data are approximated as the weighted sum of the few bases vectors. This allows us to discover economic trends and the best-fit trends for each data at the same time.

This paper deals with the fault detection, diagnosis and control problems of time delay systems by designing a disturbance observer (DOB). In proposed method, the DOB estimates the changes occurred as an input disturbance. In fact, the DOB is implemented as a residual generator for the system. Subsequently, the estimated changes can be used to compensate the effect of faults and plant alterations directly. In this method, the estimated disturbances can be used for the FDI purpose and the final system would be fault tolerant, without the need to have all other faults isolable and identifiable. It provides a simple, low cost and effective fault detection and isolation method which can be applied to more practical systems. The applicability and effectiveness of the proposed method is illustrated by the simulations provided for an industrial water pressure control system which is supposed to be subject to faults.

The day-by-day increase in digital loads draws attention towards the need for an efficient and compatible distribution network. An LVDC distribution network has the capability to fulfill such digital load demands. However, the major challenge of an LVDC distribution network is its vulnerability during a fault. The need for a high-speed fault detection method is inevitable before it can be widely adopted. This paper proposes a new fault detection method which extracts the features of the current during a fault. The proposed fault detection method uses the merits of overcurrent, the first and second derivative of current, and signal processing techniques. Three different features are extracted from a time domain current signal through a sliding window. The extracted features are based upon the root squared zero, second, and fourth order moments. The features are then set with individual thresholds to discriminate low-, high-, and very high-resistance faults. Furthermore, a fault is located through the superimposed power flow. Moreover, this study proposes a new method based on the vector sum of positive and negative pole currents to identify the faulty pole. The proposed scheme is verified by using a modified IEEE 13 node distribution network, which is implemented in Matlab/Simulink. The simulation results confirm the effectiveness of the proposed fault detection and identification method. The simulation results also confirm that a fault having a resistance of 1 m Ω is detected and interrupted within 250 μ s for the test system used in this study.

This paper covers model-based fault detection and isolation for linear and nonlinear distributed parameter systems (DPS). The first part mainly deals with actuator, sensor and state fault detection and isolation for a class of DPS represented by a set of coupled linear partial differential equations (PDE). A filter based observer is designed based on the linear PDE representation using which a detection residual is generated. A fault is detected when the magnitude of the detection residual exceeds a detection threshold. Upon detection, several isolation estimators are designed using filters whose output residuals are compared with predefined isolation thresholds. A fault on a linear DPS is declared to be of certain type if the corresponding isolation estimator output residual is below its isolation threshold while the other fault isolation estimator output residual is above its threshold. Next, the fault location is determined when a state fault is identified. The second part of this paper focuses on fault detection and isolation of nonlinear DPS by using a Luenberger type observer. Here fault isolation framework is introduced to isolate actuator, sensor and state faults with isolability condition by using additional boundary measurements and without filters. Finally, the effectiveness of the proposed fault detection and isolation schemes for both linear and nonlinear DPS are demonstrated through simulation.

Non-negative matrix factorization for speech/music separation using source dependent decomposition rank, temporal continuity term and filtering

In this paper, a diagnosis method for time-delay fractional systems is developed. The fault detection and isolation are ensured by the use of a bank of unknown input fractional observers. Theoretical development leads to the obtention of the observer parameters in order to engender structured residuals. A numerical example illustrating the validity of the method in fault detection and isolation is given.

This paper proposes a novel scheme combining support vector machines (SVM) and a residual-based method for wind turbine fault detection and isolation (FDI). SVMs with radius basis function kernels are used for detecting and identifying sensor stuck and offset faults, where binary codes of fault types are used as the outputs of the SVMs to minimize the number of SVMs being used. The same output of a SVM may correspond to different types of faults and the final decision is made by all SVMs instead of one SVM. Moreover, a residual-based fault detection method using a time-variant threshold is developed to identify the abrupt change and scaling faults. Monte Carlo simulations are carried out in MATLAB to test the effectiveness and robustness of the proposed FDI methods using a wind turbine FDI benchmark model. Results show that the proposed methods can always detect the faults successfully within the required time limits.

This chapter discusses the definition of a detection observer, its structural conditions and the solution of their solution. A method of designing a bank of detection observers to give maximise the fault isolation capability, is described. The design approach is guided by a fault isolation logic which is not necessarily associated with a particular fault detection method, but can be also be used with other fault detection methods. It is thought that this fault isolation logic may serve as a general guide for the design of fault detection schemes based upon quantitative models and not solely for the design of the type of fault detection observers under discussion.

Automaton-based fault detection and isolation

In this paper, it is shown that the high automation level of the object-oriented modeling paradigm for physical systems can significantly rationalize the design procedure of fault detection and isolation (FDI) systems. Consequently, an object-oriented FDI method for complex engineering systems consisting of subsystems from different physical domains like mechatronic systems, commercial vehicles, and chemical process plants is developed. The mathematical composition of the objects corresponding to the subsystems results in a differential algebraic equation (DAE) that describes the overall system. This DAE is automatically analyzed and transferred into a set of residual generators that enable a two-stage FDI procedure for multiple fault modes.

Fault Detection and Isolation (FDI) methods have been developed over the past thirty years but only in the last several years they have been applied to complex real applications. This paper presents a synthesis of H∞ FDI filters for the longitudinal motion of the Boeing 747-100/200 aircraft. The filters are synthesized to detect and isolate faults in the elevator actuator and pitch rate sensor while attenuating disturbances and noise on the fault signals. They are synthesized for open-loop LTI models of the aircraft. Closed-loop simulations with a highfidelity nonlinear model in the presence of gust and noise are performed to validate the disturbance rejection and robust properties of the H∞ LTI FDI filters.

Comparison Between Statistical and Observer-Based Approaches for Fault Detection and Isolation in a Chemical Process

Accurate and timely fault detection and isolation (FDI) improve the availability, safety, and reliability of target systems and enable cost-effective operations. In this study, a shared nearest neighbor (SNN)-based method is proposed to identify the fault variables of a circulating fluidized bed boiler. SNN is a derivative method of the k-nearest neighbor (kNN), which utilizes shared neighbor information. The distance information between these neighbors can be applied to FDI. In particular, the proposed method can effectively detect faults by weighing the distance values based on the number of neighbors they share, thereby readjusting the distance values based on the shared neighbors. Moreover, the data distribution is not constrained; therefore, it can be applied to various processes. Unlike principal component analysis and independent component analysis, which are widely used to identify fault variables, the main advantage of SNN is that it does not suffer from smearing effects, because it calculates the contributions from the original input space. The proposed method is applied to two case studies and to the failure case of a real circulating fluidized bed boiler to confirm its effectiveness. The results show that the proposed method can detect faults earlier (1 h 39 min 46 s) and identify fault variables more effectively than conventional methods.