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are as follows (Basseville and Nikiforov 1993; Chen and Patton 1999):

      1 1) probabilistic reasoning;

      2 2) possibilistic reasoning with fuzzy logic;

      3 3) reasoning with artificial neural networks.

      This very short consideration shows that many different methods have been developed over the last 30 years. It is also clear that many combinations of them are possible.

      On the basis of different contributions during the last 30 years, it can be stated that parameter estimation and observer-based methods are the most frequently applied techniques for fault detection, especially for the detection of sensor and process faults. Nevertheless, the importance of neural network-based and combined methods for fault detection is steadily growing. In most applications, fault detection is supported by simple threshold logic or hypothesis testing. Fault isolation is often carried out using classification methods. For this task, neural networks are being more and more widely used.

      The number of applications using nonlinear models is growing, while the trend of using linearized models is diminishing. It seems that analytical redundancy-based methods have their best application areas in mechanical systems where the models of the processes are relatively precise. Most nonlinear processes under investigation belong to the group of thermal and fluid dynamic processes. The field of applications to chemical processes has few developments, but the number of applications is growing. The favorite linear process under investigation is the DC motor. In general, the trend is changing from applications to safety-related processes with many measurements, as in nuclear reactors or aerospace systems, to applications in common technical processes with only a few sensors. For diagnosis, classification and rule-based reasoning methods are the most important, and the use of neural network classification as well as fuzzy logic-based reasoning is growing.

      I.9. FDI application report

Because of the many publications and increasing number of applications (IFAC Congress and IFAC Symposia SAFEPROCESS) between 1991 and 2018, it is of interest to show some trends (Patton et al. 1989; Basseville and Nikiforov 1993; Gertler 1998; Chen and Patton 1999; Frank et al. 2000). Therefore, a literature study is briefly presented as follows. Contributions taking into account the applications reported in Table I.1 were considered. The type of faults considered is distinguished according to Table I.2. Among all contributions, the fault detection methods were classified as in Table I.3. The change detection and fault classification methods are indicated in Table I.4. The reasoning strategies for fault diagnosis are reported in Table I.5. The contributions considered are summarized in Table I.6. The evaluation has been limited to the fault detection and diagnosis (FDD) of laboratory, pilot and industrial processes.

Table I.1. FDI applications and number of contributions

Application	Number of contributions
Simulation of real processes	105
Large-scale pilot processes	94
Small-scale laboratory processes	68
Full-scale industrial processes	98

Table I.2. Fault type and number of contributions

Fault type	Number of contributions
Sensor faults	129
Actuator faults	111
Process faults	123
Control loop or controller faults	48

Table I.3. FDI methods and number of contributions

Method type	Number of contributions
Observer	123
Parity space	74
Parameter estimation	101
Frequency spectral analysis	57
Neural networks	79

Table I.4. Residual evaluation methods and number of contributions

Evaluation method	Number of contributions
Neural networks	89
Fuzzy logic	65
Bayes classification	54
Hypothesis testing	48

Table I.5. Reasoning strategies and number of contributions

Reasoning strategy	Number of contributions
Rule based	40
Sign directed graph	33
Fault symptom tree	32
Fuzzy logic	66

Table I.6. Applications of model-based fault detection

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