Tobias Münker

Local model network with regularized MISO finite impulse response models

The problem of learning nonlinear multiple input single output (MISO) systems is considered. The usually applied procedure for the identification of these systems is analysed and the shortcomings of the commonly used structures are described. Based on that a novel approach for the estimation of local model networks or Takagi-Sugeno fuzzy systems is presented, which incorporates recent results of regularized identification of linear finite impulse response (FIR) models for the rules consequent. With the assumption that the impulse response of the local model is a realization of a Gaussian process two properties of impulse responses can be considered. These are exponential decay and smoothness. This approach is extended to the identification of nonlinear multiple input single output systems using the LOLIMOT construction algorithm and incorporating the regularized approach for the local model identification. The results are demonstrated at a test example and the results are compared to a local model network with local ARX models and unregularized FIR models. The comparison reveals the advantages of the novel method.

Nonlinear system identification with regularized local FIR model networks

Abstract An algorithm for the identification of nonlinear black-box systems is introduced utilizing recently proposed techniques for the regularized estimation of impulse responses for linear systems. Based on a comparison of the fundamental advantages and disadvantages of (N)FIR and (N)ARX model structures for the linear and nonlinear case it is outlined that the novel regularized FIR model estimation removes the major drawback of high parameter variances from the FIR model and makes it thus feasible and even advantageous as a local model structure in local model networks. The estimation of the local FIR models is performed with a special regularization matrix, which is derived from the concept of reproducing Kernel Hilbert spaces incorporating the knowledge of the exponential decay of the impulse response of a stable system. The algorithm is applied to a test system and is, in contrast to local ARX models, always able to achieve stability and a fairly good prediction accuracy. The proposed procedure is also applied for the identification of a Diesel engine. A validated simulation model is used to generate identification data and the described approach is used to construct a model that is able to represent the influence of the variable turbine geometry and the injected fuel mass on the predicted motor torque.

Gray-box identification with regularized FIR models

Abstract The problem of modeling a linear dynamic system is discussed and a novel approach to automatically combine black-box and white-box models is introduced. The solution proposed in this contribution is based on the usage of regularized finite-impulse-response (FIR) models. In contrast to classical gray-box modelling, which often only optimizes the parameters of a given model structure, our approach is able to handle the problem of undermodeling as well. Therefore, the amount of trust in the white-box or gray-box model is optimized based on a generalized cross-validation criterion. The feasibility of the approach is demonstrated with a pendulum example. It is furthermore investigated, which level of prior knowledge is best suited for the identification of the process.

Hierarchical model predictive control for Local Model Networks

Nonlinear model structures based on multiple linear models, which are overblended by validity functions (Local Model Networks) have proven to be successful for many examples in nonlinear system identification. Here a novel method for computing a suboptimal solution of the model predictive control (MPC) problem for local model networks with a hierarchical structure is developed. Therefore a representation of the local model networks as a binary directed tree is introduced. The novel method does not try to solve the nonlinear program of the model predictive control algorithm directly for the local model network, but provides a suboptimal solution by a hierarchical scheme. In the first step the optimal control problem is solved for a global linear model and in the next step the trajectory of this model is used to compute the linearization of a local model network with two local models. For this linearized model the predictive control problem is solved. Afterwards the number of used models is increased again and the procedure is iterated until the maximum number of local models is reached. Thus the method subsequently improves the quality and accurancy of the suboptimal predictive control solution. The feasibility of the approach is demonstrated for a highly nonlinear pH process.

A Probabilistic Approach for Fault Detection of Railway Suspensions

Vehicle dynamics and safety against derailment are directly influenced by the primary and secondary suspension of a railway vehicle. During the operation faults of components like broken springs or dampers can occur. To prevent a complete system failure, the early detection of faults in the suspension of trains is thus of high importance. For the application of a vibration-based fault detection system several acceleration sensors can be mounted on the frame of the bogie. The signals of these sensors are collected during operation and are available for the application of online monitoring methods. In this publication, we present a probabilistic method to distinguish the faulty and the fault-free cases. The utilization of multiple sensor signals from one bogie for the fault detection and diagnosis yields a performance increase. This is conducted by the application of a subspace-based system identification algorithm. Afterwards, identified mode-shapes, damping factors and eigenfrequencies are considered in a probabilistic approach to distinguish the different failure causes. In this methodically new approach probability density plots are used to describe the most likely values of the eigenfrequencies and other characteristic parameters in the faultfree and faulty case. Comparing new data to the density plots determined in a previous training phase allows to assess if a failure has occurred or is likely to occur and what type of fault is the most likely one.