Stable Kernel Representation Research Articles

A data-driven configurability evaluation method for spacecraft control systems

<p style='text-indent:20px;'>To release severe constraints of spacecraft on orbit resources (in-cluding computing resources, hardware resources and energy resources), the data-driven reconfigurability evaluation of spacecraft attitude control system is studied in this paper. Firstly, the reconfiguration capability is quantitatively described based on the data forms of stable kernel representation and stable image representation of spacecraft control system subject to noise. Then, based on the obtained reconfigurability index, the maximum boundary of system re-configurability is given, which provides theoretical guidance for the design of autonomous reconfiguration strategy. Finally, an example is employed to verify the effectiveness and correctness of the proposed method.</p>

Subspace-Aided Sensor Fault Diagnosis and Compensation for Industrial Systems

Sensors are ubiquitous in automatized industrial systems. To ensure the safety of the process control, the fault diagnosis and fault-tolerant control of sensors are necessary. This paper proposes subspace-aided sensor fault diagnosis and compensation control approaches based on the data-driven stable kernel representation (SKR) and stable image representation (SIR) identified by the process data decompositions. First, this paper obtains data-driven SKR and SIR through the mapping relationship of the subspaces of signals and proposes a series of fault diagnosis and compensation approaches. Furthermore, considering the accuracy and timeliness, the paper presents an accurate online fault diagnosis and compensation approach by the online updating LQ decomposition. These approaches can perform fault diagnosis, fault estimation, and fault compensation for the multiple and different types of additive sensor faults. The effectiveness of the strategies has been verified by the numerical study and the three-tank experimental system, which has a specific engineering significance.

Data-driven designs of observers and controllers via solving model matching problems

This paper targets the development of a data-driven framework for designing observers and controllers of close-loop systems with consideration of disturbances. Under this framework, both the design of the observer and optimization of the controller can be achieved by only using data. After parameterizing the feedback control systems subject to disturbances, the first step is to identify data-driven stable kernel and image representations (SKR and SIR) with the aid of time-series data. Then, SKR constructs a data-driven realization of a diagnostic observer. Through disturbance elimination and reference tracking, online optimization using SIR provides a data-driven solution to the model matching problem (MMP) whilst the controller is re-configured and optimized in real time. An example is used to demonstrate the effectiveness of the proposed data-driven designs.

A Novel Data-Driven Fault Detection Method Based on Stable Kernel Representation for Dynamic Systems.

With the steady improvement of advanced manufacturing processes and big data technologies, modern industrial systems have become large-scale. To enhance the sensitivity of fault detection (FD) and overcome the drawbacks of the centralized FD framework in dynamic systems, a new data-driven FD method based on Hellinger distance and subspace techniques is proposed for dynamic systems. Specifically, the proposed approach uses only system input/output data collected via sensor networks, and the distributed residual signals can be generated directly through the stable kernel representation of the process. Based on this, each sensor node can obtain the identical residual signal and test statistic through the average consensus algorithms. In addition, this paper integrates the Hellinger distance into the residual signal analysis for improving the FD performance. Finally, the effectiveness and accuracy of the proposed method have been verified in a real multiphase flow facility.

Sparse Actuator Attack Detection and Identification: A Data-Driven Approach.

This article aims to investigate the data-driven attack detection and identification problem for cyber-physical systems under sparse actuator attacks, by developing tools from subspace identification and compressive sensing theories. First, two sparse actuator attack models (additive and multiplicative) are formulated and the definitions of I/O sequence and data models are presented. Then, the attack detector is designed by identifying the stable kernel representation of cyber-physical systems, followed by the security analysis of data-driven attack detection. Moreover, two sparse recovery-based attack identification policies are proposed, with respect to sparse additive and multiplicative actuator attack models. These attack identification policies are realized by the convex optimization methods. Furthermore, the identifiability conditions of the presented identification algorithms are analyzed to evaluate the vulnerability of cyber-physical systems. Finally, the proposed methods are verified by the simulations on a flight vehicle system.

A New Residual Generation-Based Fault Estimation Approach for Cyber-Physical Systems

This article investigates the problem of data-driven actuator fault estimation for cyber-physical systems (CPSs). First, a stable kernel representation (SKR)-based residual generator is constructed to achieve online detection for actuator fault using the system inputs–outputs (I/O) data. Then an iterative learning fault estimation (ILFE) algorithm is designed to reconstruct the actuator fault in real time. The proposed method realizes the actuator fault estimation when the model parameters are unknown, which avoids much time spent in the modeling process. Moreover, compared with the existing model-based approaches, the presented method still has better transient performance, steady-state performance, and computational efficiency, which is more suitable for the fault identification of practical control systems. Finally, the application to a servo motor demonstrates the superiority of the designed fault estimation method.

An Integrated Design Scheme for SKR-Based Data-Driven Dynamic Fault Detection Systems

In this article, an integrated design diagram for a stable kernel representation (SKR)-based data-driven fault detection (FD) system and performance criteria is proposed for stochastic dynamic systems in the probabilistic sense. A new distributionally robust FD system is developed using input and output data in the absence of a system model and perfect probability distributions for noises and random faults. To be specific, an SKR-based data-driven primary residual generator is first constructed. By introducing the so-called mean-covariance based ambiguity sets, families of probability distributions of the primary residual in fault-free and the concerned multiple faulty cases are characterized. The FD system design is then formulated as a distributionally robust optimization problem in the sense of minimizing the missed detection rate (MDR) with a predefined upper bound of false alarm rate (FAR). With the aid of worst-case conditional value-at-risk, a matrix-valued distribution independent solution to the targeting FD problem is derived without posing specific distribution assumptions. The developed FD system is, thus, robust against the distributional uncertainties of noises and random faults. Simultaneously, a tighter upper bound of MDR for an identical FAR criterion is achieved in comparison with the vector-valued distributionally robust FD method. An experimental study on a laboratory setup of a three-tank system shows the applicability of the proposed method.

Takagi–Sugeno Fuzzy Realization of Stability Performance-Based Fault-Tolerant Control for Nonlinear Systems

This article is dedicated to studying realization issues of the stability performance-based nonlinear fault-tolerant control framework via Takagi–Sugeno (T–S)fuzzy models. To this end, the nonlinear fault-tolerant control strategy with an online fault detection system monitoring the system stability performance degradation induced by faults is first introduced by means of the stable image and kernel representations. On this basis, the T–S fuzzy models are applied to approximate the nonlinear system, and a design approach of the fuzzy observer-based controller is proposed for the system stabilization via the iterative linear matrix inequality method. With the controller gains, the fuzzy-model-based nominal stable image representation of the system is formulated, which leads to the generation of the input and output error signals. Then, with the reference signal and system input and output error signal data, a data-driven algorithm is given to online estimate the evaluation function defined in terms of system uncertainties and faults. By virtue of the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$L_{2}$</tex-math></inline-formula> input–output stability of the controller stable kernel representation, a threshold calculation method is presented and, thus, the stability performance-based fault detection system based on fuzzy models is realized. Furthermore, for fault-tolerant purpose, the fault-tolerant controller design is discussed, which aims to retain the system stability. Two examples are provided in the end to illustrate the proposed results.

Detection of Malicious Attacks in Autonomous Cyber-Physical Inverter-Based Microgrids

The distributed generation capabilities of microgrids (MGs) arise as essential assets in enhancing grid resilience. The integration of distributed energy sources, controllable loads, and prosumers necessitates the deployment of potent control and communication synergies. While those synergies transform MGs into cyber-physical systems through information technologies able to sense, control, and actuate local resources and loads, they inadvertently expose MGs to cyber-attack threats. Increasing the security of critical communication and control systems against “black swan” events, i.e., high-impact low-probability cyber-physical incidents, is a major priority for MG operations. Such incidents, if left unabated, can intensify and elicit system dynamics instability, eventually causing outages and system failures. In this article, we develop an integrated approach for multiagent MG systems able to perform the detection of malicious cyber-physical attacks based on subspace methods. We employ the small-signal model of an autonomous/islanded MG and consider different attack models targeting the MG’s secondary frequency control. The attack detector is constructed via identifying the stable kernel representation of the autonomous cyber-physical MG in the attack-free case. We illustrate the impact of the attack models as well as the feasibility of the developed detection method in simulation models of the Canadian urban benchmark distribution system.

Fault Detection Approach for Nonlinear Systems via Nonlinear Factorization and Fuzzy Models

This brief aims to propose an effective fault detection method for general class of nonlinear systems in the context of the closed-loop system stability. To this end, the nonlinear factorization technique is first used to model the faulty nonlinear systems, which can be represented by the so-called stable kernel representation with a stable parameterization of the system changes triggered by faults. Then, the closed-loop system stability is discussed according to the internal stability definition and the small gain theorem, respectively, to present the design framework of the fault detection system. Different from the traditional fault detection schemes, the proposed fault detection approach focuses on detecting whether the system closed-loop stability is damaged by faults utilizing the online measurable system and controller residual signals. Furthermore, for the implementation of the proposed fault detection framework, Takagi-Sugeno fuzzy models are applied to approximate the nonlinear systems and thus the fault detection system design methods can be provided by taking advantage of the linear matrix inequality technique. Finally, a case study is used to verify the achieved results.

A Novel Subspace-Aided Fault Detection Approach for the Drive Systems of Rolling Mills

This brief proposes a subspace-aided fault detection approach for the drive systems of strip rolling mills. Considering the impact of the unknown periodic load generated by the strip rolling process, the primary contributions are concluded as follows. First, this brief presents an approach to describe the subspace of the unknown/unmeasurable periodic load. Second, a fundamental frequency identification approach for the drive systems is proposed and then the subspace of the unknown periodic load can be constructed by the fundamental frequency. Third, this brief presents a subspace-aided fault detection approach to identify the data-driven stable kernel representation (SKR) of the closed-loop system by projecting the input–output (I/O) process data, so as to obtain a robust residual against the unknown periodic load. In addition, the effectiveness and performance of the approaches are verified by numerical examples and experimental data of the test rig for the drive systems of strip rolling mills. The results show that a robust residual generation against the unknown periodic load in the drive systems can be obtained and the robust subspace-aided fault detection can be achieved. Compared with the traditional method, the proposed approaches can improve the fault detection rate more effectively and be applied to the drive systems of strip rolling mills reliably.

A Probabilistic Projection Approach to Data-Driven Dynamic Fault Detection⋆

In this work, a probabilistic projection approach is proposed to data-driven fault detection (FD) for stochastic dynamic systems. To this end, a stable kernel representation based residual generator is first constructed with main attention to the design of a projection matrix based on system input and output data in kernel space. Concerning the practically inaccessible probability distribution for stochastic disturbance and limited priori knowledge of fault, a distributionally robust optimal FD problem is formulated in the sense of maximizing the fault detectability for an acceptable upper bound of false alarm rate, wherein the distributional profile of stochastic disturbance is characterized by a mean-covariance based ambiguity set. By means of worst-case conditional value-at-risk and singular value decomposition, an analytical solution to the targeting FD problem is derived in the probabilistic context, that achieves the best fault detectability in worst-case setting. Simultaneously, the robustness of the designed FD system against distributional uncertainties can be guaranteed. A simulation study is finally illustrated to show the applicability of the proposed method.

Multiplicative Fault Detection and Isolation in Dynamic Systems Using Data-Driven K-Gap Metric based kNN Algorithm

In this paper, a fault detection and isolation scheme for multiplicative faults in dynamic systems based on data-driven K-Gap metric and k-nearest neighbour (kNN) classification is proposed. To detect multiplicative faults, the standard classification task of kNN is studied from the viewpoint of system analysis. To this end, the data-driven stable kernel representation based on input/output data is presented for feature extraction capturing the dynamic of linear time-invariant (LTI) systems. Data-driven K-Gap metric is used as an alternative tool for distance measure between two kernel subspaces in the kNN algorithm. A simulation example on the three-tank system (DTS200) demonstrates the successful detection and isolation of various multiplicative faults

Real-Time Implementation of Plug-and-Play Process Monitoring and Control on an Experimental Three-Tank System

Three-tank system is an important benchmark in industrial process. However, so far, the research on the three-tank system is mainly limited to simulation studies, and the use of virtual simulators. In this article, a real-time three-tank system setup is used for practical investigations. Differing with the virtual simulator of a three-tank system, the setup can enable the setting of different types of faults (such as cloggings and leaks in the system, sensor faults, and actuator faults) through manual manipulation, users can choose the combinations of different valves and knobs in the setup, which is helpful to evaluate and compare methods for process monitoring and control. The relevant codes or modules can be applied directly that are developed in the MATLAB/Simulink environment. On this setup, two methods are used to verify the effectiveness in this study. One method is to solve the problem of process monitoring and fault detection; due to the fluctuation of the liquid level caused by flow, the input/output (I/O) data are preferred to be decomposed to different subspaces, which aims to identify the data-driven stable kernel representation. Moreover, the original controller of the three-tank system cannot match the system accurately, and therefore, needs to be modified. To solve the problem, a plug-and-play process control method (the other method used in this article) is applied, which adds a stable Youla parameterization matrix on the basis of the original controller. All controllers that internally stabilize the control loop improves the performance of the system without changing the original controller of the three-tank system. The experimental results of the two methods indicate that the proposed approach has strong practicality.

Component-Level Fault Detection for Suspension System of Maglev Trains Based on Autocorrelation Length and Stable Kernel Representation

At present, in the suspension system of maglev train, the self-diagnosis of most of the components can be realized employing direct sensor measurement, however, there are still some components that cannot be directly measured by sensors or model-based methods, such as the power components in the suspension control box, electromagnetics and related connectors. And although the detection method based on Stable Kernel Representation (SKR) can detect the fault, the length of the data used for SKR affects the speed and results of the detection. To obtain better detection results with the shortest possible data, this paper studies a component-level fault detection method based on autocorrelation length and SKR. This method uses the autocorrelation length to determine the length of the data used to identify the SKR, and then applies the SKR to build a residual generator and set the residual threshold. The experimental results show that the studied method can detect faults of the suspension control box in real-time and effectively, and the simulation results show that the studied method can detect faults of the electromagnet in real-time and effectively. In addition, compared with the traditional method, the method in this paper can obtain better results with less data.

Data-driven design of fault detection and isolation method for distributed homogeneous systems

Driven by the increasing needs in large-scale industrial processes for maintaining stable operation using process data, a data-driven fault detection and isolation (FDI) method for distributed homogeneous systems is proposed in this paper. To this end, the original distributed homogeneous system is first decomposed into several separate subsystems using invertible transformations of the state, input, and output variables. On this basis, the fault detection method according to the one-step identification of the stable kernel representation (SKR) is developed for the transformed subsystems. It is followed by the fault estimation for the transformed subsystems along with implementation on fault isolation for the original distributed system. Experiments comparing the proposed FDI method and the centralized FD method are performed using a numerical example. In this specific example, the proposed FDI method has a computational complexity of 2.32×107, while the centralized FD method has a computational complexity of 9.31×107. This shows the effectiveness and advantages of the proposed method.

Data-driven design of fault-tolerant control systems based on recursive stable image representation

Driven by the increasing needs in the process industry for designing fault-tolerant control systems based on process data and maintaining its performance during online operation, data-driven realization and design of feed-forward fault-tolerant control systems with embedded residual generation are studied. To this end, a parameterized and data-driven realization form of stable image representation in a feedback control loop is derived first. On this basis, a feed-forward controller design scheme is proposed for fault-tolerant purpose. It is followed by a recursive approach for online tuning the feed-forward controller in case of malfunctions, which is triggered by a fault detection scheme based on the so-called stable kernel representation. The effectiveness of the proposed fault-tolerant method is demonstrated by a case study on the laboratory three-tank system.

Data-driven fault identifiability analysis for discrete-time dynamic systems

Fault identifiability plays a key role in the fault diagnosability performance analysis of a system. However, considering the need for an accurate model, the design of control systems and fault diagnosis systems based on fault identifiability performance suffers from a limited application range because accurate models are rarely available for complex processes or plants, whereas substantial quantities of offline and online data can be obtained from systems with ease. This situation constitutes the motivation to develop a data-driven analysis method for determining the identifiability of faults in dynamic systems. The fault identifiability analysis problem is reformulated as the quantification of the difficulty associated with estimating an unknown value from a regression analysis perspective. Moreover, the proposed identification scheme for a stable kernel representation provides a direct way to identify the matrices required to compute the proposed measure, the estimability, which effectively reduces engineering costs in practical applications. Finally, the proposed method is applied to a vehicle lateral dynamic system to exemplify how to analyse the fault identifiability performance of a dynamic system.

Control performance‐based fault detection and fault‐tolerant control schemes for a class of nonlinear systems

SummaryThe objective of this paper is to develop performance‐based fault detection (FD) and fault‐tolerant control (FTC) schemes for a class of nonlinear systems. To this end, the representation forms of nonlinear systems with faults and the controller parameterization forms are studied first with the aid of the nonlinear factorization technique. Then, based on the stable kernel representation and the stable image representation of the faulty nonlinear system, the stability performance of the closed‐loop system is addressed, respectively. The so‐called fault‐tolerant margin is defined to evaluate the system fault‐tolerant ability. On this basis, two performance‐based FD schemes are developed aiming at detecting the system performance degradation caused by system faults. Furthermore, to recover the system stability performance, two performance‐based FTC strategies are proposed based on the information provided by the FD unit. In the end, a numerical example and a case study on the three‐tank system are given to demonstrate the proposed results.

A Robust Data-Driven Fault Detection Approach for Rolling Mills With Unknown Roll Eccentricity

This brief proposes a robust subspace-aided fault detection approach for rolling mill processes with roll eccentricity. The novelty of this brief relies on the closed-loop identification of the so-called data-driven realization of the stable kernel representation (SKR) of the rolling mill process. In order to ensure an accurate and robust closed-loop identification, the mappings among the closed-loop process data and the unknown disturbance are analyzed analytically based on the process model, which play essential roles in the data-driven realizations and designs. By determining the kernel subspace of the rolling mill process, a robust data-driven fault detection approach is derived and a disturbance-decoupled residual signal can be obtained. The effectiveness of the proposed approach in comparison to conventional data-driven designs is demonstrated through case studies on a rolling mill benchmark process.