-This article presents two techniques to improve the calculation of the fuzzy covariance matrix in the GustafsonKessel (GK) clustering algorithm. The first one overcomes problems that occur in the standard GK clustering when the number of data samples is small or when the data within a cluster are linearly correlated. The improvement is achieved by k i n g the ratio between the maximal and minimal eigenvalue of the covariance matrix. The second technique is useful when the GK algorithm is employed in the extraction of Takagi-Sugeno fuzzy model from data. It reduces the risk of overfitting when the number of training samples is low in comparison to the number of clusters. This is achieved by adding a scaled unity matrix to the calculated covariance matrix. Numerical examples are presented to demonstrate the benefits of the proposed techniques.

Interdependencies among system components and the existence of multiple operating modes present a challenge for fault diagnosis of Heating, Ventilation, and Air Conditioning (HVAC) systems. Reliable and timely diagnosis can only be ensured when it is performed in all operating modes, and at the system level, rather than at the level of the individual components. Nevertheless, almost no HVAC fault diagnosis methods that satisfy these requirements are described in literature. In this paper, we propose a multiple-model approach to system-level HVAC fault diagnosis that takes component interdependencies and multiple operating modes into account. For each operating mode, a distinct Bayesian network (diagnostic model) is defined at the system level. The models are constructed based on knowledge regarding component interdependencies and conservation laws, and based on historical data through the use of virtual sensors. We show that component interdependencies provide useful features for fault diagnosis. Incorporating these features results in better diagnosis results, especially when only a few monitoring signals are available. Simulations demonstrate the performance of the proposed method: faults are timely and correctly diagnosed, provided that the faults result in observable behavior.

Even though various frameworks exist for reasoning under uncertainty, a realistic fault diagnosis task does not fit into any of them in a straightforward way. For each framework, only part of the available data and knowledge is in the desired format. Moreover, additional criteria, like clarity of inference and computational efficiency, require trade-offs to be made. Finally, fault diagnosis is usually just a subpart of a larger process, e.g. condition-based maintenance. Consequently, the final goal of fault diagnosis is not (just) decision making, and the outcome of the diagnosis process should be a suitable input for the subsequent reasoning process. In this chapter, we analyze how a knowledge-based diagnosis task is influenced by uncertainty, investigate which additional objectives are of relevance, and compare how these characteristics and objectives are handled in two well-known frameworks, namely the Bayesian and the Dempster-Shafer reasoning framework. In contrast to previous works, which take the reasoning method as the starting point, we start from the application, knowledge-based fault diagnosis, and examine the effectiveness of different reasoning methods for this specific application. It is concluded that the suitability of each reasoning method highly depends on the problem under consideration and on the requirements of the user. The best framework can only be assigned given that the problem (including uncertainty characteristics) and the user requirements are completely known.

Model-free reinforcement learning and nonlinear model predictive control are two different approaches for controlling a dynamic system in an optimal way according to a prescribed cost function. Reinforcement learning acquires a control policy through exploratory interaction with the system, while nonlinear model predictive control exploits an explicitly given mathematical model of the system. In this article, we provide a comprehensive comparison of the performance of reinforcement learning and nonlinear model predictive control for an ideal system as well as for a system with parametric and structural uncertainties. The comparison is based on two different criteria, namely the similarity of trajectories and the resulting rewards. The evaluation of both methods is performed on a standard benchmark problem: a cart-pendulum swing-up and balance task. We first find suitable mathematical formulations and discuss the effect of the differences in the problem formulations. Then, we investigate the robustness of reinforcement learning and nonlinear model predictive control against uncertainties. The results demonstrate that nonlinear model predictive control has advantages over reinforcement learning if uncertainties can be eliminated through identification of the system parameters. Otherwise, there exists a break-even point after which model-free reinforcement learning performs better than nonlinear model predictive control with an inaccurate model. These findings suggest that benefits can be obtained by combining these methods for real systems being subject to such uncertainties. In the future, we plan to develop a hybrid controller and evaluate its performance on a real seven-degree-of-freedom walking robot.

Adequate fault diagnosis requires actual system data to discriminate between healthy behavior and various types of faulty behavior. Especially in large networks, it is often impracticable to monitor a large number of variables for each subsystem. This results in a need for fault diagnosis methods that can work with a limited set of monitoring signals. In this paper, we propose such an approach for fault diagnosis in networks. This approach is knowledge based and uses the temporal, spatial, and spatio-temporal network dependencies as diagnostic features. These features can be derived from the existing monitoring signals; so no additional sensors are required. Besides that the proposed approach requires only a few monitoring devices, it is, thanks to the use of the spatial dependencies, robust with respect to environmental disturbances. For a railway track circuit example, we show that, without the temporal, spatial, and spatio-temporal features, it is not possible to identify the cause of a detected fault. Including the additional features allows potential causes to be identified. For the track circuit case, based on one signal, we can distinguish between six fault classes.