Marco Münchhof

Neural Networks and Lookup Tables for Identification

Many processes show a non-linear static and dynamic behavior, especially if wide areas of operation are considered. Therefore, the identification of non-linear processes is of increasing interest. Examples are vehicles, aircraft, combustion engines, and thermal plants. In the following, models of such non-linear systems will be derived based on artificial neural networks, that had first been introduced as universal approximators of non-linear static functions.

Operation Point Dependent Diagnosis - WAI

Abstract As fault detection is becoming increasingly relevant for modern passenger car Diesel engines, it is now time to take a closer look at the engine specific fault diagnosis problems. Many of the applied fault detection algorithms can only be computed in certain operation ranges of the engine. Whenever the engine is operated outside these ranges, the corresponding symptoms are usually not actualized. As a matter of course this has to be considered in the design of a diagnosis system. However, since there are many well-developed diagnosis system structures, a method for the consideration of operation ranges should not impact on them. Hence, the diagnosis system structures are kept interchangeable and can be chosen from the available systems independently. The paper at hand focuses on the prevention of false alarms by considering operation ranges in a certain class of well-known diagnosis algorithms. For this purpose special symptoms and artificial fault measures are introduced. It can be shown that operation range dependent false alarms will no longer occur, if the diagnosis system is constructed using the new symptoms and fault measures. Since only new symptoms and fault measures are introduced, the choice of the diagnosis system structure can remain independent from the consideration of the operation ranges.

Practical Aspects of Parameter Estimation

Going back to Fig. 1.7, one sees at once that the preceding chapters mainly described the block Application of Identification Method and the resulting Process Model that was either non-parametric or parametric. The other blocks will now be discussed in more detail. Also, some special issues, such as low frequent and high frequent disturbances, which are typically not accounted for by the identification method itself, disturbances at the system input, as well as a special treatment of integral acting systems shall be discussed.

Bayes and Maximum Likelihood Methods

While the parameter estimation methods presented so far assumed that the parameters θ and the observations of the output y are deterministic values, the parameters themselves and/or the output will now be seen in a stochastic view as a series of random variables.

State and Parameter Estimation by Kalman Filtering

While the classical approach for filtering, smoothing and prediction, which was developed by Wiener and Kolmogorov (e.g. Hansler, 2001; Papoulis and Pillai, 2002), was based on a design in the frequency domain, the Kalman filter can completely be designed in the time domain. In Sect. 21.1, first the original Kalman filter for linear, time-invariant discrete-time systems will be developed.

Parameter Estimation for Frequency Responses

This chapter presents parameter estimation methods which use the non-parametric frequency response function as an intermediatemodel. Using this intermediatemodel can provide many advantages: One can use methods such as the orthogonal correlation to record the frequency response function even under very adverse (noise) conditions. Furthermore, the experimental data are in most cases condensed by smoothing the frequency response function before the parameter estimation method is applied. Also, the non-parametric frequency response function can give hints on the model order to choose, the presence of a dead-time, resonances, and so forth.

Mathematical Models of Linear Dynamic Systems and Stochastic Signals

The main task of identification methods is to derive mathematical models of processes and their signals. Therefore, the most important mathematical models of linear, time-invariant SISO processes as well as stochastic signals shall shortly be presented in the following. It is assumed that the reader is already familiar with timeand frequency domain based models and methods.

Frequency Response Measurement for Periodic Test Signals

The frequency response measurement with periodic test signals allows the determination of the relevant frequency range for linear systems for certain, discrete points in the frequency spectrum. Typically, one uses sinusoidal signals at fixed frequencies, see Sect. 5.1. However, one can also use other periodic signals such as e.g. rectangular, trapezoidal, or triangular signals as shown in Sect. 5.2. The analysis can be carried out manually or with the aid of digital computers, where the Fourier analysis or special correlation methods come into play.

Correlation Analysis with Continuous Time Models

The correlation methods for single periodic test signals, which have been described in Chap. 5 provide only one discrete point of the frequency response at each measurement with one measurement frequency. At the start of each experiment, one must wait for the decay of the transients. Due to these circumstances, the methods are not suitable for online identification in real time. Thus, it is interesting to employ test signals which have a broad frequency spectrum and thus excite more frequencies at once as did the non-periodic deterministic test signals.

Parameter Estimation for MIMO Systems

The choice of an appropriate model structure plays an important role in the identification of MIMO systems as it determines the number of parameters, the convergence and the computational effort. Hence, in this chapter, different model structures for MIMO systems will be presented.