Fault detection and isolation using viability theory and interval observers

This paper proposes the use of interval observers and viability theory in fault detection and isolation (FDI). Viability theory develops mathematical and algorithmic methods for investigating the viability constraints characterisation of dynamic evolutions of complex systems under uncertainty. These methods can be used for checking the consistency between observed and predicted behaviour by using simple sets that approximate the exact set of possible behaviour (in the parameter or state space). In this paper, FDI is based on checking for an inconsistency between the measured and predicted behaviours using viability theory concepts and sets. Finally, an example is provided in order to show the usefulness of the proposed approach.     

Robust identification and fault diagnosis based on uncertain multiple input–multiple output linear parameter varying parity equations and zonotopes

We present a robust fault diagnosis method for uncertain multiple input–multiple output (MIMO) linear parameter varying (LPV) parity equations. The fault detection methodology is based on checking whether measurements are inside the prediction bounds provided by the uncertain MIMO LPV parity equations. The proposed approach takes into account existing couplings between the different measured outputs. Modelling and prediction uncertainty bounds are computed using zonotopes. Also proposed is an identification algorithm that estimates model parameters and their uncertainty such that all measured data free of faults will be inside the predicted bounds. The fault isolation and estimation algorithm is based on the use of residual fault sensitivity. Finally, two case studies (one based on a water distribution network and the other on a four-tank system) illustrate the effectiveness of the proposed approach.     

Observer gain effect in linear interval observer-based fault detection

An interval observer has been shown to be a suitable passive robust strategy to generate an adaptive threshold to be used in residual evaluation when model uncertainty is located in parameters (interval model). In such an approach, the observer gain plays an important role since it determines the minimum detectable fault for a given type of fault and allows enhancing the observer fault detection properties. The aim of this paper is to analyze the influence of the observer gain on the time evolution of the residual sensitivity to a fault. Thereby, as a result of this sensitivity study, the minimum detectable fault time evolution for a given type of fault and the interval observer fault detection performance could be determined. In particular, three types of faults according to their detectability time evolution are introduced: permanently (strongly) detected, non-permanently (weakly) detected or just non-detected. An example based on a mineral grinding-classification process is used to illustrate the results derived.     

Limnimeter and rain gauge FDI in sewer networks using an interval parity equations based detection approach and an enhanced isolation scheme

In this paper, a methodology for limnimeter and rain-gauge fault detection and isolation (FDI) in sewer networks is presented. The proposed model based FDI approach uses interval parity equations for fault detection in order to enhance robustness against modelling errors and noise. They both are assumed unknown but bounded, following the so-called interval (or set-membership) approach. On the other hand, fault isolation relies on an algorithm that reasons using several fault signature matrices that store additional information to the typical binary one used in standard FDI approaches. More precisely, the considered fault signature matrices contain information about residual fault sign/sensitivity and time/order of activation. The paper also proposes an identification procedure to obtain the interval models used in fault detection that delivers the nominal model plus parameter uncertainty is proposed. To exemplify the proposed FDI methodology, a case study based on the Barcelona sewer network is used.     

Fault detection using interval LPV models in an open-flow canal

This paper proposes a new method of fault detection using Linear Parameter Varying (LPV) interval models and its application to an open-flow canal. The use of such models is motivated because the parameters and transport delay in the canal transfer function model vary with the operating point. LPV models allow to consider these variations by characterizing the parameters/delay variation law with the operating point while intervals are used to bound the parameter/delay uncertainty. Additionally, a LPV parameter estimation algorithm that allows to estimate parameter/delay uncertainty intervals is also proposed. As an application case study, an open-flow canal system based on the Lunax dam-gallery system located in France is used to show the effectiveness of the proposed method to detect faults. The satisfactory results obtained allow to assess the effectiveness of the proposed approach.     

Robust fault isolation for a class of non-linear input?output systems

The design and analysis of fault diagnosis methodologies for non-linear systems has received significant attention recently. This paper presents a robust fault isolation scheme for a class of non-linear systems with unstructured modelling uncertainty and partial state measurement. The proposed fault diagnosis architecture consists of a fault detection and approximation estimator and a bank of isolation estimators. Each isolation estimator corresponds to a particular type of fault in the fault class. A fault isolation decision scheme is presented with guaranteed performance. If at least one component of the output estimation error of a particular fault isolation estimator exceeds the corresponding adaptive threshold at some finite time, then the occurrence of that type of fault can be excluded. Fault isolation is achieved if this is valid for all but one isolation estimator. Based on the class of non-linear systems under consideration, fault isolability conditions are rigorously investigated, characterizing the class of non-linear faults that are isolable by the proposed scheme. Moreover, the non-conservativeness of the fault isolability conditions is illustrated by deriving a subclass of nonlinear systems and faults for which this condition is also necessary for fault isolability. A simulation example of a simple robotic system is used to show the effectiveness of the robust fault isolation methodology.     

Robust decentralized actuator fault detection and estimation for large-scale systems using a sliding mode observer

In this paper, robust decentralized actuator fault detection and estimation is considered for a class of non-linear large-scale systems. A sliding mode observer is proposed together with an appropriate coordinate transformation to find the sliding mode dynamics. Then, based on the features of the observer, a decentralized fault estimation strategy is proposed using an equivalent output error injection, and a decentralized reconstruction scheme follows by further exploiting the structure of the uncertainty which is allowed to have non-linear bounds. The estimation and reconstruction signals only depend on the available measured information and thus the proposed strategy can work on-line. The theoretical results which have been obtained are applied to an automated highway system. Simulation shows the feasibility and effectiveness of the proposed scheme.     

基于正多胞体线性规划的滤波故障诊断方法

针对含有未知但有界噪声的线性系统故障诊断问题,提出一种基于正多胞体的滤波故障诊断方法,利用线性规划方程表示递归运算过程中的约束条件,同时在递归过程中更新正多胞体的空间表达式,求取每个参数的不确定区间,并以正多胞体的空间形态描述参数可行集,通过检测滤波器参数正多胞体可行集是否为空,判断系统有无故障.针对不同故障类型设计集员滤波器,当参数正多胞体可行集为空,即系统发生故障时,采用模型匹配的方式实现故障诊断,如果出现故障样本中未包含的故障类型,则将该故障类型添加到故障样本库中.分别给出低维和高维空间的仿真实例,描述正多胞体空间的结构变化情况,给出不同故障状态下的正多胞体空间分析结果.最后通过仿真结果和分析验证了所提出的故障诊断方法的有效性和实用性.     

Passive robust fault detection using interval observers: Application to the DAMADICS benchmark problem

In this paper, the “passive approach” to robust fault detection and isolation (FDI) is presented in the context of observer methodology, when a model with parameters bounded in intervals (“interval model”) is used, deriving the interval version corresponding to the classical use of observers. The passive approach is based on allowing the effect of the uncertainties to propagate into the residuals and then the principle of adaptive thresholds is used to achieve robustness. Finally, the approach proposed is applied to detect some of the faults proposed in an industrial actuator used as an FDI benchmark in the European RTN DAMADICS.     

不确定奇异时滞系统的鲁棒H∞故障诊断滤波器设计

研究一类受参数不确定性和干扰影响的奇异时滞系统鲁棒故障诊断滤波器设计问题. 把基于观测器的故障诊断滤波器作为残差产生器, 将故障诊断滤波器设计归结为H∞滤波问题, 使产生的残差信号即为故障的H∞估计, 给出了鲁棒H∞故障诊断滤波器存在的充分条件, 并利用锥面互补线性化迭代算法得到了故障诊断滤波器设计的线性矩阵不等式求解方法. 算例验证了算法的有效性.     

Robust stability of the systems with mixed uncertainties under the IQC descriptions

This paper studies the problem of robust stability checking for a single-input single-output uncertain feedback system which consists of a linear uncertain plant in the forward loop and a non-linear dynamic uncertain unit in the feedback loop. It is supposed that the linear part of the system is of parametric uncertainties described by a polytopic perturbation mode, and that the non-linear part of the system is of dynamic uncertainties characterized by an integral quadratic constraint (IQC). The problem of stability checking is discussed for different structures of the IQC multiplier based on the concepts of biconvex and convex-concave functions and their properties. For different uncertainty structures of the system, a finite vertex checking result and an edge checking result are presented. As an application of the above results, the problem of robust H performance checking is discussed for the case that the uncertain plant of a feedback system is parameterized by a polytopic perturbation mode, and an edge checking result is given under a fairly mild assumption. Also, the absolute stability of an interval system is investigated, and the vertex results of circle criterion and Popov criterion are obtained. Finally, a demonstrating example is included.     

Robust fault detection of non-linear systems using set-membership state estimation based on constraint satisfaction

In this paper, the robust fault detection problem for non-linear systems considering both bounded parametric modelling errors and measurement noises is addressed. The non-linear system is monitored by using a state estimator with bounded modelling uncertainty and bounded process and measurement noises. Additionally, time-variant and time-invariant system models are taken into account. Fault detection is formulated as a set-membership state estimation problem, which is implemented by means of constraint satisfaction techniques. Two solutions are presented: the first one solves the general case while the second solves the time-variant case, being this latter a relaxed solution of the first one. The performance of the time-variant approach is tested in two applications: the well-known quadruple-tank benchmark and the dynamic model of a representative portion of the Barcelona's sewer network. In both applications, different scenarios are presented: a faultless situation and some faulty situations. All considered scenarios are intended to show the effectiveness of the presented approach.     

Design of hybrid differential evolution and group method of data handling networks for modeling and prediction

This paper proposes a hybrid modeling approach based on two familiar non-linear methods of mathematical modeling; the group method of data handling (GMDH) and differential evolution (DE) population-based algorithm. The proposed method constructs a GMDH self-organizing network model of a population of promising DE solutions. The new hybrid implementation is then applied to modeling tool wear in milling operations and also applied to two representative time series prediction problems of exchange rates of three international currencies and the well-studied Box-Jenkins gas furnace process data. The results of the proposed DE–GMDH approach are compared with the results obtained by the standard GMDH algorithm and its variants. Results presented show that the proposed DE–GMDH algorithm appears to perform better than the standard GMDH algorithm and the polynomial neural network (PNN) model for the tool wear problem. For the exchange rate problem, the results of the proposed DE–GMDH algorithm are competitive with all other approaches except in one case. For the Box-Jenkins gas furnace data, the experimental results clearly demonstrates that the proposed DE–GMDH-type network outperforms the existing models both in terms of better approximation capabilities as well as generalization abilities. Consequently, this self-organizing modeling approach may be useful in modeling advanced manufacturing systems where it is necessary to model tool wear during machining operations, and in time series applications such as in prediction of time series exchange rate and industrial gas furnace problems.     

Robust l1 estimation using the Popov-Tsypkin multiplier with application to robust fault detection

This paper considers the design of robust l₁ estimators based on multiplier theory (which is intimately related to mixed structured singular value theory) and the application of robust l₁ estimators to robust fault detection. The key to estimator-based, robust fault detection is to generate residuals which are robust against plant uncertainties and external disturbance inputs, which in turn requires the design of robust estimators. Specifically, the Popov-Tsypkin multiplier is used to develop an upper bound on an l₁ cost function over an uncertainty set. The robust l₁ estimation problem is formulated as a parameter optimization problem in which the upper bound is minimized subject to a Riccati equation constraint. A continuation algorithm that uses quasi-Newton BFGS (the algorithm of Broyden, Fletcher, Goldfab and Shanno) corrections is developed to solve the minimization problem. The estimation algorithm has two stages. The first stage solves a mixed-norm H₂/l₁ estimation problem. In particular, it is initialized with a steady-state Kalman filter and, by varying a design parameter from 0 to 1, the Kalman filter is deformed to an l₁ estimator. In the second stage the l₁ estimator is made robust. The robust l₁ estimation framework is then applied to the robust fault detection of dynamic systems. The results are applied to a simplified longitudinal flight control system. It is shown that the robust fault detection procedure based on the robust l₁ estimation methodology proposed in this paper can reduce false alarm rates.     

Heuristics free group method of data handling algorithm of generating optimal partial polynomials with application to air pollution prediction†

In this paper a revised GMDH (Group Method of Data Handling) algorithm is developed in which heuristicsare not required such as dividing the available date. into training data and checking data, predetermining the structure of the partial polynomials, or predetermining the number of intermediate variables. In this algorithm the prediction error criterion, such as PSS (Prediction Sum of Squares) or AIC (Akaike's Information Criterion) evaluated from all the available data, in used as a criterion for generating optimal partial polynomials, for selecting intermediate variables and for stopping the multilayered iterative computation. This heuristics freeGMDH algorithm is applied to non-linear modelling for short-term prediction of air pollution concentration. By using the time series data of SO₂, concentration, the wind velocity and the wind direction in Tokushima; Japan, a suitable model for predicting SO₂concentration at a few hours in advance is developed. The predicted results obtained by the revised GMDH model are compared with the results obtained by a linear regression model, a linear autoregressive model and a. basic GMDH model.