Diagnosis and Fault-tolerant Control 1. Группа авторов

some concluding remarks and open research directions.

      In particular, Chapter 7 of Volume 2 summarizes the main achievements of the book by highlighting the key features of the proposed diagnosis and fault-tolerant solutions when applied to safety critical systems.

      Finally, Chapter 8 of Volume 2 analyzes some perspectives in the field of diagnosis and FTC by exploring open problems and future issues that could require further investigation. Future possible research directions are also outlined.

      Therefore, the book reviews the state of the art of the data-driven and model-based FDI and FTC. The FDI and FTC problems are formalized in an uniform framework by presenting the mathematical description and definitions. The fundamental issue of model-based methods is the generation of residuals using the mathematical model of the monitored system. By analyzing residuals, fault diagnosis and FTC can be performed. Some structures of the residual generator are recalled to give ideas as to how to implement the residual generation. A residual generator can be designed for achieving the required diagnosis performances, for example, fault isolation and disturbance decoupling.

      In order to design the residual generator, some assumptions about the modeling uncertainties need to be made. The most frequently used hypothesis is that the modeling uncertainty is expressed as a disturbance term in the system dynamic equation. The disturbance vector is unknown, while its distribution matrix can be estimated by using identification procedures. On the basis of this assumption, the disturbance decoupling residual generator can be designed by using UIO methods Chen and Patton (1999); Liu and Patton (1998).

      The book also demonstrates how to apply dynamic system identification methods and more general data-driven approaches in order to estimate an accurate model of the monitored system.

      The FDI and FTC methods presented can, in fact, require a mathematical model of the process under investigation, either in a state–space or an input–output form.

      In particular, since state–space descriptions provide general and mathematically rigorous tools for system modeling, they may be used in the residual generator design, both for the deterministic case (generalized observers, such as UIOs and output dynamic observers) (Chen and Patton (1999); Frank (1990); Luenberger (1979); Watanabe and Himmelblau (1982)) and the stochastic case (such as Kalman filters and unknown input Kalman filters) (Jazwinski (1970); Xie et al. (1994); Xie and Soh (1994)).

In such a manner, the suggested FDI and FTC tools may not require any physical knowledge of the process under observation since the linear models are obtained by means of an identification scheme, which can, for example, exploit equation error (EE) and errors-in-variables (EIV) models. In this situation, the identification technique is based on the rules of the Frisch scheme (Frisch 1934), traditionally exploited to analyze economic systems. This approach, modified to be applied to dynamic system identification (Kalman 1982b, 1990; Beghelli et al. 1990), gives a reliable model of the plant under investigation, as well as the variances of the input–output noises affecting the data.

      For the nonlinear case, fuzzy models and neural networks can be used as prototypes for the identification. In particular, the multiple-model approach, using several local affine submodels each describing a different operating condition of the process, is exploited.

      Under these considerations, this book aims to define a comprehensive methodology for actuator, process component and sensor fault detection. It is based on an output estimation approach, in conjunction with residual processing schemes, which include simple threshold detection, in a deterministic case, as well as statistical analysis when data are affected by noise. The final result consists of a strategy based on fault diagnosis methods well known in the literature for generating redundant residuals.

      In particular, this work studies different approaches to residual generation and fault compensation with the aid of several methodologies. In general, the residual is defined as the output estimation error, obtained by the difference between the measurement of one output and the relative estimate. This work also presents the design of such estimators both in the deterministic and stochastic environment.

      The diagnosis procedure may be further specialized for actuators, input or output sensors and process components. In fact, the fault diagnosis of input sensors and actuators uses banks of estimators in high signal-to-noise ratio conditions, or filters, otherwise. The general principle designs the ith reconstructor to be insensitive to the ith signal of the system. On the other hand, output sensor and process component faults affecting a single residual can be detected by means of output observer or filters, driven by a single output and all the inputs of the system.

      The book shows how the proposed algorithms can be applied to the FDI and FTC of actuators, process components and input–output sensors of industrial plants.

      In particular, the different techniques presented in this book have been tested on time series of data acquired from different simulated and realistic industrial processes, energy conversion systems, power plants, and more general safety critical systems, whose linear mathematical description is obtained by using data-driven and model-based procedures.

Results from simulation show that minimum detectable faults are perfectly compatible with the industrial target of this application.

      Finally, the book concludes the proposed research and application topics by summarizing its contributions and achievements, providing some suggestions for possible further research topics as an extension of this work.

      I.12. Summary

      This Introduction has provided a common terminology in the fault diagnosis framework in order to comment on some developments in the field of fault detection and diagnosis based on papers selected from the last 30 years. The structure of the 14 chapters and their main contributions have also been outlined briefly.

      I.13. References

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      Frank, P.M. (1990). Fault diagnosis in dynamic systems using analytical and knowledge based redundancy: A survey of some new results. Automatica, 26(3), 459–474.