Model based fault detection for two-dimensional systems

Fault detection and isolation (FDI) are essential in ensuring safe and reliable operations in industrial systems. Extensive research has been carried out on FDI for one dimensional (1-D) systems, where variables vary only with time. The existing FDI strategies are mainly focussed on 1-D systems and can generally be classified as model based and process history data based methods. In many industrial systems, the state variables change with space and time (e.g., sheet forming, fixed bed reactors, and furnaces). These systems are termed as distributed parameter systems (DPS) or two dimensional (2-D) systems. 2-D systems have been commonly represented by the Roesser Model and the F-M model. Fault detection and isolation for 2-D systems represent a great challenge in both theoretical development and applications and only limited research results are available. In this thesis, model based fault detection strategies for 2-D systems have been investigated based on the F-M and the Roesser models. A dead-beat observer based fault detection has been available for the F-M model. In this work, an observer based fault detection strategy is investigated for systems modelled by the Roesser model. Using the 2-D polynomial matrix technique, a dead-beat observer is developed and the state estimate from the observer is then input to a residual generator to monitor occurrence of faults. An enhanced realization technique is combined to achieve efficient fault detection with reduced computations. Simulation results indicate that the proposed method is effective in detecting faults for systems without disturbances as well as those affected by unknown disturbances.The dead-beat observer based fault detection has been shown to be effective for 2-D systems but strict conditions are required in order for an observer and a residual generator to exist. These strict conditions may not be satisfied for some systems. The effect of process noises are also not considered in the observer based fault detection approaches for 2-D systems. To overcome the disadvantages, 2-D Kalman filter based fault detection algorithms are proposed in the thesis. A recursive 2-D Kalman filter is applied to obtain state estimate minimizing the estimation error variances. Based on the state estimate from the Kalman filter, a residual is generated reflecting fault information. A model is formulated for the relation of the residual with faults over a moving evaluation window. Simulations are performed on two F-M models and results indicate that faults can be detected effectively and efficiently using the Kalman filter based fault detection. In the observer based and Kalman filter based fault detection approaches, the residual signals are used to determine whether a fault occurs. For systems with complicated fault information and/or noises, it is necessary to evaluate the residual signals using statistical techniques. Fault detection of 2-D systems is proposed with the residuals evaluated using dynamic principal component analysis (DPCA). Based on historical data, the reference residuals are first generated using either the observer or the Kalman filter based approach. Based on the residual time-lagged data matrices for the reference data, the principal components are calculated and the threshold value obtained. In online applications, the T2 value of the residual signals are compared with the threshold value to determine fault occurrence. Simulation results show that applying DPCA to evaluation of 2-D residuals is effective.Doctoral These

Integration Techniques of Fault Detection and Isolation Using Interval Observers

An interval observer has been illustrated to be a suitable approach to detect and isolate faults affecting complex dynamical industrial systems. Concerning fault detection, interval observation is an appropriate 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 approach, the observer gain is a key parameter since it determines the time evolution of the residual sensitivity to a fault and the minimum detectable fault. This thesis illustrates that the whole fault detection process is ruled by the dynamics of the fault residual sensitivity functions and by the time evolution of the adaptive threshold related to the interval observer. Besides, it must be taken into account that these two observer fault detection properties depend on the used observer gain. As a consequence, the observer gain becomes a tuning parameter which allows enhancing the observer fault detection performance while avoiding some drawbacks related to the analytical models, as the wrapping effect. In this thesis, the effect of the observer gain on fault detection and how this parameter can avoid some observer drawbacks (i.e. wrapping effect) are deeply analyzed. One of the results of this analysis is the determination of the minimum detectable fault function related to a given fault type. This function allows introducing a fault classification according to the fault detectability time evolution: permanently (strongly) detected, non-permanently (weakly) detected or just non-detected. In this fault detection part of this thesis, two examples have been used to illustrate the derived results: a mineral grinding-classification process and an industrial servo actuator. Concerning the interface between fault detection and fault isolation, this thesis shows that both modules can not be considered separately since the fault detection process has an important influence on the fault isolation result. This influence is not only due to the time evolution of the fault signals generated by the fault detection module but also to the fact that the fault residual sensitivity functions determines the faults which are affecting a given fault signal and the dynamics of this fault signal for each fault. This thesis illustrates this point suggesting that the interface between fault detection and fault isolation must consider a set of fault signals properties: binary property, sign property, fault residual sensitivity property, occurrence order property and occurrence time instant property. Moreover, as a result of the influence of the observer gain on the fault detection stage and on the fault residual sensitivity functions, this thesis demonstrates that the observer gain has also a key role in the fault isolation module which might allow enhancing its performance when this parameter is tuned properly (i.e. fault distinguishability may be increased). As a last point, this thesis analyzes the timed discrete-event nature of the fault signals generated by the fault detection module. As a consequence, it suggests using timed discrete-event models to model the fault isolation module. This thesis illustrates that this kind of models allow enhancing the fault isolation result. Moreover, as the monitored system is modelled using an interval observer, this thesis shows as this qualitative fault isolation model can be built up on the grounds of this system analytical model. Finally, the proposed fault isolation method is applied to detect and isolate faults of the Barcelona’s urban sewer system limnimeters. Keywords: Fault Detection, Fault Diagnosis, Robustness, Observers, Intervals, Discrete-event Systems.En la presente tesis se demuestra que el uso de observadores intervalares para detectar y aislar fallos en sistemas dinámicos complejos constituye una estrategia apropiada. En la etapa de detección del fallo, dicha estrategia permite determinar el umbral adaptativo usado en la evaluación del residuo (robustez pasiva). Dicha metodología, responde a la consideración de modelos con parámetros inciertos (modelos intervalares). En dicho enfoque, la ganancia del observador es un parámetro clave que permite determinar la evolución temporal de la sensibilidad del residuo a un fallo y el mínimo fallo detectable para un tipo de fallo determinado. Esta tesis establece que todo el proceso de detección de fallos viene determinado por la dinámica de las funciones sensibilidad del residuo a los diferentes fallos considerados y por la evolución temporal del umbral adaptativo asociado al observador intervalar. Además, se debe tener en cuenta que estas dos propiedades del observador respecto la detección de fallos dependen de la ganancia del observador. En consecuencia, la ganancia del observador se convierte en el parámetro de diseño que permite mejorar las prestaciones de dicho modelo respecto la detección de fallos mientras que permite evitar algunos defectos asociados al uso de modelos intervalares, como el efecto wrapping. Uno de los resultados obtenidos es la determinación de la función fallo mínimo detectable para un tipo de fallo dado. Esta función permite introducir una clasificación de los fallos en función de la evolución temporal de su detectabilidad: fallos permanentemente detectados, fallos no permanentemente detectados y fallos no detectados. En la primera parte de la tesis centrada en la detección de fallos se utilizan dos ejemplos para ilustrar los resultados obtenidos: un proceso de trituración y separación de minerales y un servoactuador industrial. Respecto a la interfaz entre la etapa de detección de fallos y el proceso de aislamiento, esta tesis muestra que ambos módulos no pueden considerarse separadamente dado que el proceso de detección tiene una importante influencia en el resultado de la etapa de aislamiento. Esta influencia no es debida sólo a la evolución temporal de las señales de fallo generados por el módulo de detección sino también porque las funciones sensibilidad del residuo a los diferentes posibles fallos determinan los fallos que afectan a un determinado señal de fallo y la dinámica de éste para cada uno de los fallos. Esta tesis ilustra este punto sugiriendo que el interfaz entre detección y aislamiento del fallo debe considerar un conjunto de propiedades de dichos señales: propiedad binaria, propiedad del signo, propiedad de la sensibilidad del residuo a un fallo dado, propiedad del orden de aparición de las señales causados por los fallos y la propiedad del tiempo de aparición de estos. Además, como resultado de la influencia de la ganancia del observador en la etapa de detección y en las funciones sensibilidad asociadas a los residuos, esta tesis ilustra que la ganancia del observador tiene también un papel crucial en el módulo de aislamiento, el cual podría permitir mejorar el comportamiento de dicho módulo diseñando éste parámetro del observador de forma adecuada (Ej. Incrementar la distinción de los fallos para su mejor aislamiento). Como último punto, esta tesis analiza la naturaleza temporal de eventos discretos asociada a las señales de fallo generados por el módulo de detección. A consecuencia, se sugiere usar modelos de eventos discretos temporales para modelizar el módulo de aislamiento del fallo. Esta tesis muestra que este tipo de modelos permite mejorar el resultado de aislamiento del fallo. Además, dado que el sistema monitorizado es modelado usando un observador intervalar, esta tesis muestra como este modelo cualitativo de aislamiento puede ser construido usando dicho modelo analítico del sistema. Finalmente, el método propuesto de aislamiento del fallo es aplicado para detectar y aislar fallos en los limnimetros del sistema de alcantarillado de Barcelona. Palabras clave: Detección de Fallos, Diagnosis de Fallos, Robusteza, Observadores, Intervalos, Sistemas de Eventos Discretos

Contemporary Natural Philosophy and Philosophies - Part 1

This book is a printed edition of the Special Issue titled "Contemporary Natural Philosophy and Philosophies" - Part 1 that was published in the journal Philosophies