Dynamical systems identification using Gaussian process models with incorporated local models

Gaussian process (GP) models form an emerging methodology for modelling nonlinear dynamic systems which tries to overcome certain limitations inherent to traditional methods such as e.g. neural networks (ANN) or local model networks (LMN).The GP model seems promising for three reasons. First, less training parameters are needed to parameterize the model. Second, the variance of the model's output depending on data positioning is obtained. Third, prior knowledge, e.g. in the form of linear local models can be included into the model. In this paper the focus is on GP with incorporated local models as the approach which could replace local models network.Much of the effort up to now has been spent on the development of the methodology of the GP model with included local models, while no application and practical validation has yet been carried out. The aim of this paper is therefore twofold. The first aim is to present the methodology of the GP model identification with emphasis on the inclusion of the prior knowledge in the form of linear local models. The second aim is to demonstrate practically the use of the method on two higher order dynamical systems, one based on simulation and one based on measurement data.     

Simulations, models, and testbeds: A mutual catalysis

Recent developments in the area of decentralized and infrastructureless systems opened avenues for novel applications. Along with these new technologies, new questions regarding their operational bounds in terms of e.g. scalability and security arose. Due to the sparse presence of real-world decentralized and infrastructureless systems, new protocols and applications have to be scrutinized by means of simulation, in (small-scale) testbeds, and by analytical models. In this paper, we discuss challenges of evaluating security mechanisms for mobile ad hoc networks and peer-to-peer systems. We focus on harmonizing predictions of analytical models and results obtained from simulation studies and testbed experiments.     

Iterative analysis of Markov regenerative models

Conventional algorithms for the steady-state analysis of Markov regenerative models suffer from high computational costs which are caused by densely populated matrices. In this paper, a new algorithm is suggested which avoids computing these matrices explicitly. Instead, a two-stage iteration scheme is used. An extended version of uniformization is applied as a subalgorithm to compute the required transient quantities “on-the fly”. The algorithm is formulated in terms of stochastic Petri nets. A detailed example illustrates the proposed concepts.     

Model-based cognitive diagnosis

This paper considers the problem of cognitive diagnosis as an instance of general diagnosis, as studied in artificial intelligence. Cognitive diagnosis is the process of inferring a cognitive state from observations of performance. It is thus a key component of any system which attempts to build a dynamic model of the user of that system. Many issues in cognitive diagnosis, previously discussed informally, are mapped onto formal techniques, with consequent increased clarity and rigour. But it is concluded that the general theories for diagnosis must be broadened to fully encompass the problems of cognitive diagnosis.     

On the probability theory on MV algebras

 The paper contains a review of some results concerning probability theory on MV algebras (laws of large numbers, central limit theorem, martingale convergence theorem). Also some algebraic and methodical aspects are discussed.     

ON THE PARTIAL SUMS OF RESIDUALS IN AUTOREGRESSIVE AND MOVING AVERAGE MODELS

Abstract. The limiting process of partial sums of residuals in stationary and invertible autoregressive moving-average models is studied. It is shown that the partial sums converge to a standard Brownian motion under the assumptions that estimators of unknown parameters are root- n consistent and that innovations are independent and identically distributed random variables with zero mean and finite variance or, more generally, are martingale differences with moment restrictions specified in Theorem 1. Applications for goodness-of-fit and change-point problems are considered. The use of residuals for constructing nonparametric density estimation is discussed.     

Robust joint modeling of mean and dispersion through trimming

The Maximum Likelihood Estimator (MLE) and Extended Quasi-Likelihood (EQL) estimator have commonly been used to estimate the unknown parameters within the joint modeling of mean and dispersion framework. However, these estimators can be very sensitive to outliers in the data. In order to overcome this disadvantage, the usage of the maximum Trimmed Likelihood Estimator (TLE) and the maximum Extended Trimmed Quasi-Likelihood (ETQL) estimator is recommended to estimate the unknown parameters in a robust way. The superiority of these approaches in comparison with the MLE and EQL estimator is illustrated by an example and a simulation study. As a prominent measure of robustness, the finite sample Breakdown Point (BDP) of these estimators is characterized in this setting.     

Stochastic Models for Pad Structure and Pad Conditioning Used in Chemical-Mechanical Polishing

Stochastic models are presented for the structure and conditioning of pads used in chemical-mechanical polishing of wafers. First the one-dimensional distribution function of surface depth in the case of a conditioned solid pad is described. Then, for characterizing the structure of a foamed pad, the theory of random closed sets is applied. An important distributional characteristic of a random closed set, the linear contact distribution function, yields the contribution to surface depth resulting from pores. As a special example the Boolean model is considered. This leads to a formula that describes the variability of the surface of a conditioned foamed pad after a certain time. Simulations and experimental data show a good agreement between theory and reality.