An optimal scheme for fast rate fault detection based on multirate sampled data

Multirate systems are abundant in industry. In this paper, the problem studied is designing a residual generator for fault detection based on multirate sampled data. The key new feature of such a residual generator is that it operates at a fast rate for prompt fault detection. The design is based on optimizing a performance index to obtain an optimal parity space based residual generator. The lifting technique is used to convert the time-varying multirate design problem into a time-invariant one with a causality constraint for implementability. A procedure for computing an explicit optimal, causal solution is proposed. The advantages of this design are shown through an example.     

Optimal tracking control of nonlinear partially-unknown constrained-input systems using integral reinforcement learning

In this paper, a new formulation for the optimal tracking control problem (OTCP) of continuous-time nonlinear systems is presented. This formulation extends the integral reinforcement learning (IRL) technique, a method for solving optimal regulation problems, to learn the solution to the OTCP. Unlike existing solutions to the OTCP, the proposed method does not need to have or to identify knowledge of the system drift dynamics, and it also takes into account the input constraints a priori. An augmented system composed of the error system dynamics and the command generator dynamics is used to introduce a new nonquadratic discounted performance function for the OTCP. This encodes the input constrains into the optimization problem. A tracking Hamilton–Jacobi–Bellman (HJB) equation associated with this nonquadratic performance function is derived which gives the optimal control solution. An online IRL algorithm is presented to learn the solution to the tracking HJB equation without knowing the system drift dynamics. Convergence to a near-optimal control solution and stability of the whole system are shown under a persistence of excitation condition. Simulation examples are provided to show the effectiveness of the proposed method.     

An LMI approach to design robust fault detection filter for uncertain LTI systems

In this paper, the robust fault detection filter design problem for uncertain linear time-invariant (LTI) systems with both unknown inputs and modelling errors is studied. The basic idea of our study is to use an optimal residual generator (assuming no modelling errors) as the reference residual model of the robust fault detection filter design for uncertain LTI systems with modelling errors and, based on it, to formulate the robust fault detection filter design as an H_∞ model-matching problem. By using some recent results of H_∞ optimization, a solution of the optimization problem is then presented via a linear matrix inequality (LMI) formulation. The main results include the development of an optimal reference residual model, the formulation of robust fault detection filter design problem, the derivation of a sufficient condition for the existence of a robust fault detection filter and a construction of it based on the LMI solution parameters, the determination of adaptive threshold for fault detection. An illustrative design example is employed to demonstrate the effectiveness of the proposed approach.     

Data-driven output-feedback fault-tolerant control for unknown dynamic systems with faults changing system dynamics

This paper studies the data-driven output-feedback fault-tolerant control (FTC) problem for unknown dynamic systems with faults changing system dynamics. In a framework of active FTC, two basic issues are addressed: the fault detection employing only the measured input–output information; the controller reconfiguration to achieve optimal output-feedback control in the presence of multiple faults. To detect faults and write the system state via the input–output data, an approach to data-driven design of a residual generator with a full-rank transformation matrix is presented. An output-feedback approximate dynamic programming method is developed to solve the optimal control problem under the condition that the unknown linear time-invariant discrete-time plant has multiple outputs. According to the above results and the proposed input–output data-based value function approximation structure of time-varying plants, a model-free output-feedback FTC scheme considering optimal performance is given. Finally, two numerical examples and a practical example of a DC motor control system are used to demonstrate the effectiveness of the proposed methods.     

Thruster fault diagnosis and accommodation for open-frame underwater vehicles

This paper introduces a novel thruster fault diagnosis and accommodation system (FDAS) for open-frame underwater vehicles. Basically, the FDAS is a control allocator, but this primary function is enhanced with the ability of automatic thruster fault detection and accommodation. The proposed FDAS consists of two subsystems: a fault diagnosis subsystem (FDS) and a fault accommodation subsystem (FAS). The FDS uses fault detector units (FDUs), associated with each thruster, to monitor their state. Robust and reliable FDUs are based on integration of self-organising maps and fuzzy logic clustering methods. These units are able to detect internal and external faulty states of thrusters. The FAS uses information provided by the FDS to accommodate faults and perform an appropriate control reallocation. A control energy cost function is used as the optimisation criteria. The FAS uses weighted pseudo-inverse to find the solution of the control allocation problem, which minimise this criteria. Two approximations (truncation or scaling) can be used to ensure feasibility of the solution. The proposed FDS is evaluated with data obtained during test trials. The feasible region concept, related with the problem of thruster velocity saturation, is developed in order to provide geometrical interpretation of the control allocation problem. The proposed FDAS is implemented as a Simulink model (ROV simulator), in order to evaluate its performance in different faulty situations.     

线性离散马尔科夫跳跃系统最优故障检测

本文研究线性离散马尔科夫跳跃系统的最优故障检测问题。通过设计基于观测器的故障检测滤波器作为残差产生器,将滤波器的设计问题归结为随机意义下H_/H或H/H性能指标优化问题。基于算子优化方法,通过解耦合Riccati方程得到上述问题的统一解。算例验证所提方法的有效性。     

Active fault detection for open loop stable LTI SISO systems

Active fault detection for a stable open-loop LTI SISO system is considered. The optimal active fault detection setup is developed around an estimator based architecture. The auxiliary signal and estimator are then designed in order to maximize detection performance. Equations are derived which relate the estimator design to the nominal residual signal covariance. The relationship between the auxiliary input and the system performance degradation constraint is considered. The effect of estimator gain and excitation signal frequency on the dual Youla-Jabr-Bongiorno-Kucera parameter is investigated. Finally, the effect of the excitation signal frequency on detector performance is investigated, and a minimum targeted detection time parameter is introduced. This set of equations are then used to minimise the fault detection time for fixed performance constraints and minimum targeted detection time.     

Fault detection for linear discrete-time systems with output quantisation

This paper is concerned with the problem of fault detection for a class of linear discrete-time quantised feedback systems, and system outputs are, respectively, quantised by a uniform quantiser and a non-uniform quantiser. A novel unified method is proposed to deal with the two different types of quantisation errors, i.e. the quantisation errors are considered as unknown inputs of the residual generator. Then, an optimal residual generator is constructed to guarantee a suitable trade-off between the sensitivity to faults and the robustness against disturbances as well as quantisation errors. In order to detect the occurrence of faults, the generated residual signal is evaluated, and then two different thresholds based on the stochastic properties of quantisation errors are designed for these two quantisers. In addition, the false alarm rate is introduced to evaluate the fault detection performance. Finally, two examples are given to illustrate the feasibility of the proposed approach.     

Preview control for a class of linear stochastic systems with multiplicative noise

ABSTRACT

In this paper, the preview control problem for a class of linear continuous time stochastic systems with multiplicative noise is studied based on the augmented error system method. First, a deterministic assistant system is introduced, and the original system is translated to the assistant system. Then, the integrator is employed to ensure the output of the closed-loop system tracking the reference signal accurately. Second, the augmented error system, which includes integrator vector, control vector and reference signal, is constructed based on the system after translation. As a result, the tracking problem is transformed into the optimal control problem of the augmented error system, and the optimal control input is obtained by the dynamic programming method. This control input is regarded as the preview controller of the original system. For a linear stochastic system with multiplicative noise, the difficulty being unable to construct an augmented error system by the derivation method is solved in this paper. And, the existence and uniqueness solution of the Riccati equation corresponding to the stochastic augmented error system is discussed. The numerical simulations show that the preview controller designed in this paper is very effective.     

Fuzzy-model-based robust fault detection with stochastic mixed time delays and successive packet dropouts

This paper is concerned with the network-based robust fault detection problem for a class of uncertain discrete-time Takagi-Sugeno fuzzy systems with stochastic mixed time delays and successive packet dropouts. The mixed time delays comprise both the multiple discrete time delays and the infinite distributed delays. A sequence of stochastic variables is introduced to govern the random occurrences of the discrete time delays, distributed time delays, and successive packet dropouts, where all the stochastic variables are mutually independent but obey the Bernoulli distribution. The main purpose of this paper is to design a fuzzy fault detection filter such that the overall fault detection dynamics is exponentially stable in the mean square and, at the same time, the error between the residual signal and the fault signal is made as small as possible. Sufficient conditions are first established via intensive stochastic analysis for the existence of the desired fuzzy fault detection filters, and then, the corresponding solvability conditions for the desired filter gains are established. In addition, the optimal performance index for the addressed robust fuzzy fault detection problem is obtained by solving an auxiliary convex optimization problem. An illustrative example is provided to show the usefulness and effectiveness of the proposed design method.     

Towards the optimal control of Markov chains with constraints

An optimal control problem with constraints is considered on a finite interval for a non-stationary Markov chain with a finite state space. The constraints are given as a set of inequalities. The optimal solution existence is proved under a natural assumption that the set of admissible controls is non-empty. The stochastic control problem is reduced to a deterministic one and it is shown that the optimal solution satisfies the maximum principle, moreover it can be chosen within a class of Markov controls. On the basis of this result an approach to the numerical solution is proposed and its implementation is illustrated by examples.     

基于辅助输入信号和冗余执行器的主动故障诊断

针对具有模型不确定项的系统,提出一种辅助信号结合冗余执行器的主动故障检测方法来检测微小故障.首先,以提升故障灵敏度和抗干扰鲁棒性为指标,构建最优观测器得到残差信号;其次,引入辅助输入信号来增大故障系统的残差,同时构建冗余执行器来避免辅助输入信号对无故障系统的影响;然后,给出随模型不确定项变化的自适应阈值构建方法降低故障检测的保守性.所提出的主动故障检测方法对无故障系统不造成影响,当故障发生时残差迅速变化且高于阈值以实现快速检测.最后通过仿真对比验证了所提出方法的有效性.     

Input design for active fault diagnosis

Reliably diagnosing faults and malfunctions has become increasingly challenging in modern technical systems because of their growing complexity as well as increasingly stringent requirements on safety, availability, and high-performance operation. Traditional methods for fault detection and diagnosis rely on nominal input–output data, which can contain insufficient information to support reliable conclusions. Recent years have witnessed a growing interest in active fault diagnosis, which addresses this issue by injecting input signals specifically designed to reveal the fault status of the system. This paper provides an overview of state-of-the-art methods for input design for active fault diagnosis and discusses the primary considerations in the formulation and solution of the input-design problem. We also discuss the primary challenges and suggest avenues for future research in this rapidly evolving field.     

Integrated design of fault detection systems in time-frequencydomain

Problems related to the integrated design of robust fault detection (FD) systems are studied. First, it is revealed that due to the time window introduced to realize the 2-norm based evaluation function, an optimal design of a FD system with the 2-norm based evaluation function may not ensure the expected optimal performance when the system is realized in real applications. To solve this problem, an integrated design method of FD systems using the absolute value of residual signal as evaluation function is then proposed. It leads to a residual generator which is much easier to be realized. Different from the usual 2-norm based approaches whose mathematical basis is the relationship between the energy of the output and input signals of a dynamic system, a relationship between the instant power of the output signal and the energy of the past input signal of a dynamic system is established and further used for FD system design. Another new kind of evaluation function based on the absolute value of wavelet transform of residual signal and the corresponding integrated design approach for FD systems are further proposed     

采样数据系统的故障检测

研究了采样数据系统的故障检测问题.关键在于通过引入算子来分别描述连续时间的 未知输入信号和故障信号对离散时间的残差信号的影响,从而把鲁棒性和灵敏度问题定义为一 个优化问题,并给出了相应的解.仿真例子验证了该方法的有效性.     

Auxiliary signal design for robust active fault detection of linear discrete-time systems

In this paper, algorithms are proposed to design auxiliary signals for active fault detection based on a multi-model formulation of discrete-time systems. Two different scenarios are considered for this problem; the first one assumes there is no a priori information on initial conditions and no exogenous input signal, while the second allows for having a priori information and the possibility of having a known input in addition to the test signal. Approaches are proposed for solving these two types of problems which are capable of solving the problems efficiently. This is achieved by using a recursive approach based on the use of special Riccati equations. These algorithms can be used for systems of higher dimension and on longer time horizons than the existing methods.     

Robust detection of intermittent multiplicative sensor fault

In this paper, the detection problem of intermittent multiplicative sensor fault is investigated for stochastic uncertain systems. A robust optimal filter is designed according to the criterion of minimum estimation error covariance. Then, based on this, a residual generator is constructed, and the quantitative effect of the fault on it is discussed in detail. After that we design the evaluation function and detection threshold to achieve intermittent fault detection. Our proposed strategy has a recursive form and only includes simple arithmetic operations, thus it is suitable for real‐time online applications. Finally, a simulation example is given to demonstrate the effectiveness of the proposed strategy.     

Robust fault detection for networked systems with communication delay and data missing

In this paper, the robust fault detection problem is investigated for a class of discrete-time networked systems with unknown input and multiple state delays. A novel measurement model is utilized to represent both the random measurement delays and the stochastic data missing phenomenon, which typically result from the limited capacity of the communication networks. The network status is assumed to vary in a Markovian fashion and its transition probability matrix is uncertain but resides in a known convex set of a polytopic type. The main purpose of this paper is to design a robust fault detection filter such that, for all unknown inputs, possible parameter uncertainties and incomplete measurements, the error between the residual signal and the fault signal is made as small as possible. By casting the addressed robust fault detection problem into an auxiliary robust H_∞ filtering problem of a certain Markovian jumping system, a sufficient condition for the existence of the desired robust fault detection filter is established in terms of linear matrix inequalities. A numerical example is provided to illustrate the effectiveness and applicability of the proposed technique.     

网络化切换控制系统故障检测与优化设计

研究存在未知短时延、丢包和系统不确定性的网络化切换控制系统故障检测与时域优化问题. 首先基 于观测器构建残差发生器, 结合Lyapunov 函数方法和平均驻留时间方法分析系统的稳定性, 并以线性矩阵不等式(LMI) 形式给出故障检测滤波器的求解方法; 然后为了改善故障检测系统的性能, 采用后置滤波器对残差信号进行时域优化, 并利用奇偶空间方法给出其最优解; 最后设计并推导出自适应阈值. 仿真结果验证了所提出方法的有效性.

     

奇异Markov跳跃系统的鲁棒故障检测

研究受L2有界未知输入影响的一类奇异Markov跳跃系统的鲁棒故障检测问题。采用基于观测器的故障检测滤波器（FDF）作为残差产生器,将故障检测滤波器的设计归结为随机意义下的H∞滤波问题。推导并证明了问题可解的充分条件,并通过求解线性矩阵不等式得到了故障检测滤波器参数矩阵的解。算例验证了所给算法的有效性。