Complete Fault Diagnosis Of Uncertain Polynomial Systems

The problem of designing an input to improve the detectability of faults has been addressed previously using both stochastic and deterministic formulations. This article presents a hybrid approach that provides a worst-case guarantee of diagnosis within a time interval [0, N], while maximizing the probability of diagnosis at some earlier time M < N. Compared to purely deterministic methods, this strategy reduces the average time required for diagnosis. Moreover, a high probability of diagnosis at M enables N to be chosen large, thus reducing the conservatism of the required input.

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“…Conversely, suppose that (19) holds. Then, for every ω ∈ Ω(γ, σ ), ∄ξ such that ξ ∞ ≤ 1 and ψ (20) has no feasible point with δ ≤ 0.…”

Section: A Bounding the Probability Of Diagnosismentioning

confidence: 95%

“…Many methods have been proposed to address this challenge [8], [24], [11], [9], [19], [18], [23]. The vast majority of these methods are passive, meaning that the fault status is decided on the basis of measurements accrued during normal operation, compared with model predictions or historical data.…”

Section: Introductionmentioning

confidence: 99%

A hybrid stochastic-deterministic input design method for active fault diagnosis

Scott

Marseglia

Magni

et al. 2013

52nd IEEE Conference on Decision and Control

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“…Examples are model invalidation and parameter estimation [2], [3], model analysis [4], fault diagnosis [5], [6], robust model predictive control [7]- [10], the analysis of batch and semibatch processes [11], [12], and the safety analysis of plant operations [13]. The computation of tight outer bounds on the state is challenging in general.…”

Section: Introductionmentioning

confidence: 99%

Efficient Polynomial-Time Outer Bounds on State Trajectories for Uncertain Polynomial Systems Using Skewed Structured Singular Values

Kishida

Rumschinski

Findeisen

et al. 2014

IEEE Trans. Automat. Contr.

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Outer bounds for the evolution of state trajectories of uncertain systems are useful for many purposes such as robust control, state and parameter estimation, model invalidation, safety evaluation, fault diagnosis, and experimental design. Obtaining tight outer bounds is, however, a challenging task. This technical note proposes a new approach to obtaining such bounds for discrete-time polynomial systems with uncertain initial state, uncertain parameters, and bounded disturbances. To obtain outer bounds, the nonlinear map describing the uncertain dynamical system is represented via linear fractional transformation. The bounds on the trajectories are obtained by computing polynomial-time upper and lower bounds for the skewed structured singular value of the linear fractional transformation. Algorithms with different tradeoffs between computational complexity and conservatism are outlined. The tradeoffs as well as efficiency of the approach are illustrated in a numerical example, which shows small conservatism of the obtained bounds.Index Terms-Discrete-time polynomial systems.

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“…In response, either an active or a passive approach can be taken. Passive fault detection methods rely solely on the measurements accrued during normal operation, compared with model predictions or historical data, and are now quite mature; e.g., residual and observer-based methods [1], [4], set-based approaches [5], [6], [7], [8], [9], [10], and many more [11], [12], [13]. In contrast, the active approach involves injecting a signal into the system to improve detectability of the fault [14], [15], [16], [17].…”

Section: Introductionmentioning

confidence: 99%

Design of active inputs for set-based fault diagnosis

Scott

Findeisen

Braatz

et al. 2013

2013 American Control Conference

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Effective fault diagnosis depends on the detectability of the faults in the measurements, which can be improved by a suitable input signal. This article presents a deterministic method for computing the set of inputs that guarantee fault diagnosis, referred to as separating inputs. The process of interest is described, under nominal and various faulty conditions, by linear discrete-time models subject to bounded process and measurement noise. It is shown that the set of separating inputs can be efficiently computed in terms of the complement of one or several zonotopes, depending on the number of fault models. In practice, it is essential to choose elements from this set that are minimally harmful with respect to other control objectives. It is shown that this can be done efficiently through the solution of a mixed-integer quadratic program. The method is demonstrated for a numerical example.

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Complete Fault Diagnosis Of Uncertain Polynomial Systems

Cited by 14 publications

References 15 publications

A hybrid stochastic-deterministic input design method for active fault diagnosis

A hybrid stochastic-deterministic input design method for active fault diagnosis

Efficient Polynomial-Time Outer Bounds on State Trajectories for Uncertain Polynomial Systems Using Skewed Structured Singular Values

Design of active inputs for set-based fault diagnosis

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