research studies on the residual generation of nonlinear dynamic systems, for example using nonlinear observers (Chen and Patton 1999; De Persis and Isidori 2001). There have been some attempts to use nonlinear observers to solve nonlinear system FDI problems, (Chen and Patton 1999; De Persis and Isidori 2001), for example, nonlinear UIOs, including adaptive observers and sliding mode observers. If the class of nonlinearities can be restricted, observers for bilinear systems were also proposed (Chen and Patton 1999).
On the other hand, the analytical models that the nonlinear observer approaches are based on are not easy to obtain in practice. Sometimes, it is impossible to model the system using an explicit mathematical model. To overcome this problem, it is desirable to find a universal approximate model that can be used to represent the real system with an arbitrary degree of accuracy. Different approaches were proposed and they are currently under investigation: neural networks, fuzzy models and hybrid models.
As shown in Simani et al. (2003) and Simani and Farsoni (2018), fuzzy systems and neural networks are a powerful tool for handling nonlinear problems. One of the most important advantages of neural networks is their ability to implement nonlinear transformations for functional approximation problems. Therefore, neural networks can be used in a number of ways to tackle fault diagnosis problems for nonlinear dynamic systems. In existing publications, they were mainly exploited as fault classifier with steady-state processes, whereas neural networks have been used as residual generators and for modeling nonlinear dynamic systems for FDI purposes (Chen and Patton 1999).
Fuzzy models can be used both as a residual classifier and as a nonlinear system parametric model (Chen and Patton 1999). In the second case, the main idea is to build an FDI scheme based on fuzzy observers. Estimated outputs and residuals are computed as fuzzy fusion of local observer output and residuals. The main problem of this approach concerns the stability of the global observer. A linear matrix inequality method was proposed in Chen and Patton (1999) using Lyapunov theorem, but this solution can be quite conservative.
Hybrid models can describe the behavior of any nonlinear dynamic process if they are described as a composition of several local affine models, selected according to the process operating conditions (Chen and Patton 1999; Simani et al. 2003). Instead of exploiting complicated nonlinear models obtained by modeling techniques, it is possible to describe the plant by a collection of affine models. Such a compound system requires the identification of the local models from data. Several works (Chen and Patton 1999; Simani et al. 2003) addressed a method for the identification and the optimal selection of the local affine models from a sequence of noisy measurements acquired from the process. Application of these results to model-based fault diagnosis for safety critical systems is another research area worthy of mention.
I.11. Structure of the book
To detect and isolate faults in a dynamic system, based on the use of an analytical model, a residual signal has to be used. It is derived from a comparison between real measurements and the relative estimates (generated by the model). The modeling uncertainty problem can be tackled by designing FDI and FTC schemes, whose residuals are insensitive to uncertainties while sensitive to faults. On the other hand, a model with satisfactory accuracy can be estimated using identification procedures (Norton 1986; Söderström and Stoica 1987; Ljung 1999).
The aim of the design of FDI and FTC schemes is to reduce the effects of uncertainties on the residuals and to enhance the effects of faults acting on the residuals. The main aim of this book is to develop a residual generator for model-based fault diagnosis and to design an effective FTC strategy for a dynamic process by means of input and output signals. An accurate model of the process under investigation will be estimated using identification procedures from data affected by noises and acquired from simulated and/or actual plants. The book consists of an Introduction and six chapters in Volume 1 and eight chapters in Volume 2 and the main contributions are summarized in the following.
The Introduction, provides a brief overview and critical discussion of the state of the art of the most recent literature from 2015 to 2020, thereby introducing the field of fault detection, fault diagnosis and fault-tolerant systems with methods, which have proven their significance in practical applications.
Chapter 1 addresses the mathematical modeling and description of the faults most commonly exploited for providing a proper description of the process under diagnosis, in connection with the strategy proposed for the diagnosis and FTC designs.
By taking into account these aspects, Chapter 2 is focused on structural analysis issues. In particular, this chapter addresses the standard tool used to identify submodels that can be used to design model-based and data-driven diagnostic modules. Structural approaches typically operate on models described by a set of equations, which can also be obtained from model-free approaches.
With reference to FDI, Chapter 3 considers set-based methods. The set-membership and interval observer approaches are introduced to deal with the robustness problem in fault detection. The design conditions to guarantee robustness, and at the same time fault sensitivity, are presented. Next, the extension to fault isolation using unknown-input observer schemes is described.
Chapter 4 describes stochastic methods for FDI. In particular, the chapter revises the existing methods for FDI using stochastic modeling of uncertainty, using both models and data.
As an alternative to analytical approaches, Chapter 5 proposes data-driven schemes. It is therefore devoted to the problem of fault detection in technical systems described by nonlinear dynamical models containing non-smooth nonlinearities. The so-called “model-free” or “data-driven” solutions can be exploited to solve the considered FTD and FTC problems. The feature of this method is that parameters of the system under consideration may be unknown.
Among data-driven solutions, Chapter 6 considers the artificial intelligence (AI) approach to fault diagnosis. After revising the evolution of fault diagnosis methods in the AI domain, the chapter focuses on the model-based approach rooted in the logic theory of diagnosis.
When considering analytical approaches, Chapter 1 of Volume 2 proposes the development of nonlinear methods. This chapter gives a review of the principal model-based fault diagnosis and fault-tolerant approaches for nonlinear systems. Some schemes extending the well-known diagnosis methods for linear systems to the nonlinear case are considered. The robustness of these schemes in the presence of uncertainty is discussed. Similarities between the approaches considered are also pointed out.
With reference to Volume 2, the problem of the FTC is addressed. In particular, Chapter 2 of Volume 2 considers the use of linear parameter varying (LPV) methods. In particular, this chapter considers FDI and FTC for descriptor LPV systems with unmeasurable decision variables under actuator faults and perturbations.
A different approach is considered in Chapter 3 of Volume 2, where fuzzy Takagi–Sugeno and neural network methods for FDI and FTC are revised. After introducing the different types of models, their application to fault diagnosis and estimation is presented. The extension to FTC is then described.
Chapter 4 of Volume 2 presents the model predictive control (MPC) techniques to deal with robustness and nonlinearity. To this aim, the use of neural networks is considered.
Chapter 5 of Volume 2 considers nonlinear methods for FTC. This chapter presents a methodology for detecting, isolating and accommodating faults
