Fault diagnosis based on set membership identification using output‐error models

Reppa, Vasso; Tzes, Anthony

doi:10.1002/acs.2537

Cited by 13 publications

(19 citation statements)

References 68 publications

(134 reference statements)

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“…11 Theorem 1 shows that (9), with the quantities defined in (11), (12), and (13), is a bounding ellipsoid. 11 Theorem 1 shows that (9), with the quantities defined in (11), (12), and (13), is a bounding ellipsoid.…”

Section: Bounding Ellipsoid Adaptive Constrained Least Squaresmentioning

confidence: 99%

A new kernel RLS algorithm for systems with bounded noise

Constantin

Bigand

2017

Adaptive Control & Signal

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In this paper, we propose a new nonlinear set-membership recursive least-squares algorithm. The algorithm draws on a linear set-membership filter in conjunction with kernels for nonlinear processing. Set-membership algorithms exploit a priori model information that directly, or indirectly, prescribes dynamic constraints on the solution space. Such information is disregarded by conventional approaches. Kernel methods provide an implicit mapping of the data in a high-dimensional feature space where linear techniques are applied.Computations are done in the initial space by means of kernel functions. In this work, we develop a kernel-based version of a set-membership filter that belongs to a class of optimal bounding ellipsoid algorithms. Optimal bounding ellipsoid algorithms compute ellipsoidal approximations to regions in the parameter space that are consistent with the observed data and the model assumptions.Experiments involving stationary and nonstationary data are presented. Compared with existing kernel adaptive algorithms, the proposed algorithm offers an enhanced performance and sparsity, conjugated with better tracking capabilities.

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Section: Bounding Ellipsoid Adaptive Constrained Least Squaresmentioning

confidence: 99%

A new kernel RLS algorithm for systems with bounded noise

Constantin

Bigand

2017

Adaptive Control & Signal

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“…Note that both SSDF in (24) and SFDR in (25) are independent of disturbances, thus the solution to Problem 2 does not depend on disturbances.…”

Section: Remarkmentioning

confidence: 99%

“…In these works, a deterministic bounded set, such as ellipsoids, polytopes and zonotopes, is adopted to describe uncertainties. The basic idea of set-membership-based FD is to check the consistency between the monitored behavior and the predicted behavior using the a priori knowledge of the bounded uncertainty sets [21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

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A set‐membership approach to integrated trade‐off design of robust fault detection system

Zhai

Wan

Hao

2016

Adaptive Control & Signal

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In order to improve fault detection (FD) performance, integrated design of residual generation and evaluation is investigated in this paper for trade-offs between fault detection rate and false alarm rate (FAR). A setmembership approach is proposed in residual evaluation by adopting a threshold ellipsoid, which enables more design freedom than a conventional threshold value. With the set-based definitions of fault detection rate and FAR, the integrated design problem is formulated by maximizing the FD performance under a predefined FAR. The joint optimal selection of a residual generator and a threshold ellipsoid is equivalently transformed into a simplified optimization problem of determining an optimal threshold ellipsoid for any given residual generator. A suboptimal solution for the set-membership-based integrated FD system design is obtained based on approximated computation of the FD performance. Monte Carlo simulations show the performance improvement of the proposed method compared with an existing integrated design method.

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“…A passive FDI mechanism only monitors the input and output data of the system, and obtains a decision based on the processed information. Assuming bounded uncertainties, several researchers have developed passive FDI methods, where sets in the parameter or residual space are generated on-line [33,34,30,7,31]. A fault is detected when either the parameter set is empty, or the inclusion of the residual within the corresponding set does not hold.…”

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confidence: 99%

Active Fault Isolation: A Duality-Based Approach via Convex Programming

Blanchini¹,

Casagrande²,

Giordano³

et al. 2017

SIAM J. Control Optim.

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Abstract. This paper presents the mathematical conditions and the associated design methodology of an active fault diagnosis technique for continuous-time linear systems. Given a set of faults known a priori, the system is modeled by a finite family of linear time-invariant systems, accounting for one healthy and several faulty configurations. By assuming bounded disturbances and using a residual generator, an invariant set and its projection in the residual space (i.e., its limit set) are computed for each system configuration. Each limit set, related to a single system configuration, is parameterized with respect to the system input. Thanks to this design, active fault isolation can be guaranteed by the computation of a test input, either constant or periodic, such that the limit sets associated with different system configurations are separated, and the residual converges towards one limit set only. In order to alleviate the complexity of the explicit computation of the limit set, an implicit dual representation is adopted, leading to efficient procedures, based on quadratic programming, for computing the test input. The developed methodology offers a competent continuous-time solution to the optimization-based computation of the test input via Hahn-Banach duality. Simulation examples illustrate the application of the proposed active fault diagnosis methods and its efficiency in providing a solution, even in relatively large state-dimensional problems.

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Fault diagnosis based on set membership identification using output‐error models

Cited by 13 publications

References 68 publications

A new kernel RLS algorithm for systems with bounded noise

A new kernel RLS algorithm for systems with bounded noise

A set‐membership approach to integrated trade‐off design of robust fault detection system

Active Fault Isolation: A Duality-Based Approach via Convex Programming

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