Data-driven realizations of kernel and image representations and their application to fault detection and control system design

This paper deals with the data-driven design of observer-based fault detection and control systems. We first introduce the definitions of the data-driven forms of kernel and image representations. It is followed by the study of their identification. In the context of a fault-tolerant architecture, the design of observer-based fault detection, feed-forward and feedback control systems are addressed based on the data-driven realization of the kernel and image representations. Finally, the main results are demonstrated on the laboratory continuous stirred tank heater (CSTH) system.     

Subspace identification of continuous time models for process fault detection and isolation

This paper proposes a novel subspace approach towards identification of optimal residual models for process fault detection and isolation (PFDI) in a multivariate continuous-time system. We formulate the problem in terms of the state space model of the continuous-time system. The motivation for such a formulation is that the fault gain matrix, which links the process faults to the state variables of the system under consideration, is always available no matter how the faults vary with time. However, in the discrete-time state space model, the fault gain matrix is only available when the faults follow some known function of time within each sampling interval. To isolate faults, the fault gain matrix is essential. We develop subspace algorithms in the continuous-time domain to directly identify the residual models from sampled noisy data without separate identification of the system matrices. Furthermore, the proposed approach can also be extended towards the identification of the system matrices if they are needed. The newly proposed approach is applied to a simulated four-tank system, where a small leak from any tank is successfully detected and isolated. To make a comparison, we also apply the discrete time residual models to the tank system for detection and isolation of leaks. It is demonstrated that the continuous-time PFDI approach is practical and has better performance than the discrete-time PFDI approach.     

Closed-loop subspace identification using the parity space

It is known that many subspace algorithms give biased estimates for closed-loop data due to the existence of feedback. In this paper we present a new subspace identification method using the parity space employed in fault detection in the past. The basic algorithm, known as subspace identification method via principal component analysis (SIMPCA), gives consistent estimation of the deterministic part and stochastic part of the system under closed loop. Column weighting for SIMPCA is introduced which shows improved efficiency/accuracy. A simulation example is given to illustrate the performance of the proposed algorithm in closed-loop identification and the effect of column weighting.     

Subspace method aided data-driven design of fault detection and isolation systems

This paper deals with data-driven design of fault detection and isolation (FDI) systems. The basic idea is to identify a primary form of residual generators, instead of the process model, directly from test data and, based on it, to design advanced FDI systems. The proposed method can be applied for the parity space and observer based detection and isolation of sensor and actuator faults as well as the construction of soft-sensors. The application of the proposed method is illustrated by a simulation study on the Tennessee Eastman process.     

Subspace-based prediction of linear time-varying stochastic systems

In this paper, a new subspace method for predicting time-varying stochastic systems is proposed. Using the concept of angle between past and present subspaces spanned by the extended observability matrices, the future signal subspace is predicted by rotating the present subspace in the geometrical sense, and time-varying system matrices are derived from the resultant signal subspace. Proposed algorithm is improved for fast-varying systems. Furthermore, recursive implementation of both algorithms is developed.     

Subspace aided data-driven design of robust fault detection and isolation systems

This paper deals with subspace method aided data-driven design of robust fault detection and isolation systems. The basic idea is to identify a primary form of residual generators directly from test data and then make use of performance indices to make uniform the design of different type robust residuals. Four algorithms are proposed to design fault detection, isolation and identification residual generators. Each of them can achieve robustness to unknown inputs and sensitivity to sensor or actuator faults. Their existence conditions and multi-fault identification problem are briefly analyzed as well and the application of the method proposed is illustrated by a simulation study on the vehicle lateral dynamic system.     

Data-driven diagnosis of sensor precision degradation in the presence of control

This paper considers the precision degradation type of sensor faults within control loops. In a closed loop, sensor faults propagate through controller to manipulated variables and disturb the other process variables, which obscures the source of sensor faults but receives less attention in existing methods of data-driven sensor fault diagnosis. With the assumption that only closed-loop data in normal condition are available, difficulty arises due to the facts that little a priori knowledge is known about closed-loop sensor fault propagation and the open-loop process model may not be identifiable. The proposed method in this paper constructs residual that is regarded as including two parts: the first part is the current sensor faults whose fault direction is known to be the identity matrix; and for the purpose of diagnosing the first part, the second part is considered as the disturbance which is affected by noises and past sensor faults due to unknown fault propagation. The disturbance variance is minimized in residual generator design to improve fault sensitivity. And the corresponding disturbance covariance is estimated and then utilized in residual evaluation. The proposed method in this paper is motivated by a pioneer work on closed-loop sensor fault diagnosis which performs principal component analysis in the feedback-invariant subspace of the closed-loop process outputs. But it is revealed by the proposed method that the feedback-invariant signal is affected by past sensor faults, leading to performance degradation of the pioneer work. The improvement of the proposed approach is due to analysis of residual dynamics and explicit handling of the disturbance in residual evaluation, which is not considered in the pioneer work. A simulated 4 × 4 dynamic process and a simulated two-product distillation column are studied to verify the effectiveness of the proposed approach compared to the existing principal component analysis method in feedback-invariant subspace.     

基于数据驱动的故障诊断技术研究现状及展望

对基于数据驱动的过程故障诊断方法进行了总结和划分,其中包含多元统计方法、机器学习方法、流形学习方法等。将各类基于数据驱动的故障诊断方法的原理、研究进展及其在工业过程中的应用进行了描述和分析,最后指出这一领域中需要进一步解决的问题以及近期的研究热点。     

Subspace like identification incorporating prior information

The subspace identification methods have proved to be a powerful tool, which can further benefit from the prior information incorporation algorithm proposed in this note. In the industrial environment, there is often some knowledge about the identified system (known static gains, dominant time constants, low frequency character, etc.), which can be used to improve model quality and its compliance with first principles. The proposed algorithm has two stages. The first one is similar to the subspace methods as it uses their interpretation as an optimization problem of finding parameters of an optimal multi-step linear predictor for the experimental data. This problem is reformulated in the Bayesian framework allowing prior information incorporation in the form of the mean value and the covariance of the impulse response, which is shown to be useful for the incorporation of several prior information types. The second stage with state space model realization from the posterior impulse response estimate is different from the standard subspace methods as it is based on the structured weighted lower rank approximation, which is necessary to preserve the prior information incorporated in the first stage.     

Subspace identification for FDI in systems with non-uniformly sampled multirate data

This paper proposes a novel subspace approach towards direct identification of a residual model for fault detection and isolation (FDI) in a system with non-uniformly sampled multirate (NUSM) data without any knowledge of the system. From the identified residual model, an optimal primary residual vector (PRV) is generated for fault detection. Furthermore, by transforming the PRV into a set of structured residual vectors, fault isolation is performed. The proposed algorithms have been applied to an experimental pilot plant with NUSM data for sensor FDI, where different types of faults are successfully detected and isolated, fully validating the practicality and utility of the developed theory.     

递推子空间模型辨识算法的研究与仿真

为了很好的解决在线辨识系统模型问题,在对子空间模型辨识研究的基础上,结合递推最小二乘算法和子空问状态辨识方法。推导了子空间状态辨识的递推算法。该算法不仅解决了在线辨识问题,而且算法简单,计算方便,很好地克服了在线辨识时子空间矩阵维数的变化问题。经仿真研究表明,该递推算法克服了一次完成算法在大批量数据运算时,耗时大,专用内存多的缺点,而且对于测量和过程均有噪声干扰的多输入多输出系统,有很好的辨识效果,有较为广阔的应用前景。     

Experimental evaluation of fault diagnosis in a skew-configured UAV sensor system

This paper presents an experimental evaluation of a hybrid fault detection and isolation scheme against three successive faults in skew-configured inertial sensors of an unmanned aerial vehicle (UAV). An additional small and low-cost inertial measurement unit is installed with a skewed angle to a primary inertial measurement unit. A parity space method and an in-lane monitoring method are combined to increase system tolerance to the occurrence of multiple successive faults during flight. The first and second faults are detected and isolated by the parity space method. The third fault is detected by the parity space method and isolated by the in-lane monitoring method based on the discrete wavelet transform. Hardware in-the-loop tests and flight experiments with a fixed-wing UAV are performed to verify the performance of the proposed fault diagnosis scheme.     

Subspace identification using instrumental variable techniques

Subspace-based algorithms for system identification have lately been suggested as alternatives to more traditional techniques. Variants of the MOESP type of subspace algorithms are in addition to open-loop identification applicable to closed-loop and errors-in-variables identification. In this paper, a new instrumental variable approach to subspace identification is presented. It is shown how existing MOESP-algorithms can be derived within the proposed framework, simply by changing instruments and weighting matrices. A noteworthy outcome of the analysis is that an improvement of an existing MOESP method for errors-in-variables identification can be proposed.     

Subspace identification of multivariable linear parameter-varying systems

A subspace identification method is discussed that deals with multivariable linear parameter-varying state-space systems with affine parameter dependence. It is shown that a major problem with subspace methods for this kind of system is the enormous dimension of the data matrices involved. To overcome the curse of dimensionality, we suggest using only the most dominant rows of the data matrices in estimating the model. An efficient selection algorithm is discussed that does not require the formation of the complete data matrices, but processes them row by row.     

Comprehensive subspace decomposition and isolation of principal reconstruction directions for online fault diagnosis

Reconstruction based fault diagnosis isolates the fault cause by finding fault subspace to bring the faulty data back to normal. However, the conventional reconstruction model was often defined using principal component analysis (PCA) to extract the general distribution information of fault data and may not well discriminate fault from normal status. It thus may fail to recover the fault-free data efficiently. To overcome the above problem, a relative principal component of fault reconstruction (RPCFR) modeling algorithm is proposed in the present work for fault subspace extraction and online fault diagnosis. Instead of directly modeling fault data to extract the reconstruction directions, the algorithm gives the original fault space a comprehensive decomposition according to its relationship with the normal process information. Those fault directions that can more efficiently characterize the effects of fault deviations relative to normal data are separated from the others and used for fault reconstruction. Its performance on online fault diagnosis is illustrated by the data from the Tennessee Eastman process.     

Integrated design of feedback controllers and fault detectors

This paper addresses the integrated design of controllers and fault detectors embedded in the feedback control loops. The state of the art of the integrated design technique is first reviewed. The focus of the review study is on the comparison between different design schemes and on the evaluation of the diagnostic performance. The second part of this paper consists of a study on controller configurations, observer-based residual generation and residual signals embedded in the feedback control loops. Based on the observer and residual generator realization forms of the Youla controller parameterization, integrated design schemes for some practical control configurations are proposed and studied.     

Kernel methods for subspace identification of multivariable LPV and bilinear systems

Subspace identification methods for multivariable linear parameter-varying (LPV) and bilinear state-space systems perform computations with data matrices of which the number of rows grows exponentially with the order of the system. Even for relatively low-order systems with only a few inputs and outputs, the amount of memory required to store these data matrices exceeds the limits of what is currently available on the average desktop computer. This severely limits the applicability of the methods. In this paper, we present kernel methods for subspace identification performing computations with kernel matrices that have much smaller dimensions than the data matrices used in the original LPV and bilinear subspace identification methods. We also describe the integration of regularization in these kernel methods and show the relation with least-squares support vector machines. Regularization is an important tool to balance the bias and variance errors. We compare different regularization strategies in a simulation study.     

A novel fault-tolerant sensor system for sensor drift compensation

The conventional fault-tolerant sensor systems would fail when outputs from incorporated sensors are either noisy or drifting. This paper presents a novel real-time fault compensation method, which uses state estimation and compensation techniques, that the sensor system can perform robust measurements even when outputs from every incorporated sensor are noisy and drifting. In a simulation example, the proposed design can detect and correct the sensor errors (dc bias and drift) in real time. For the dc bias, the minimum detectable offset value is 0.1, which is the same as the standard deviation of the sensor noise. The compensated sensor output is biased at values smaller than 0.02. For the sensor drifts, the proposed method can compensate drifts for the change rate of drifts up to four times faster than that of the signal to be measured. The highest change rate of drifts, that can be compensated by this method, is determined by the standard deviation of the sensor noise.