Identification of nonlinear time-varying systems using an online sliding-window and common model structure selection (CMSS) approach with applications to EEG

The identification of nonlinear time-varying systems using linear-in-the-parameter models is investigated. A new efficient Common Model Structure Selection (CMSS) algorithm is proposed to select a common model structure. The main idea and key procedure is: First, generate K 1 data sets (the first K data sets are used for training, and theK 1 th one is used for testing) using an online sliding window method; then detect significant model terms to form a common model structure which fits over all the K training data sets using the new proposed CMSS approach. Finally, estimate and refine the time-varying parameters for the identified common-structured model using a Recursive Least Squares (RLS) parameter estimation method. The new method can effectively detect and adaptively track the transient variation of nonstationary signals. Two examples are presented to illustrate the effectiveness of the new approach including an application to an EEG data set

Implicit Copulas from Bayesian Regularized Regression Smoothers

We show how to extract the implicit copula of a response vector from a Bayesian regularized regression smoother with Gaussian disturbances. The copula can be used to compare smoothers that employ different shrinkage priors and function bases. We illustrate with three popular choices of shrinkage priors --- a pairwise prior, the horseshoe prior and a g prior augmented with a point mass as employed for Bayesian variable selection --- and both univariate and multivariate function bases. The implicit copulas are high-dimensional, have flexible dependence structures that are far from that of a Gaussian copula, and are unavailable in closed form. However, we show how they can be evaluated by first constructing a Gaussian copula conditional on the regularization parameters, and then integrating over these. Combined with non-parametric margins the regularized smoothers can be used to model the distribution of non-Gaussian univariate responses conditional on the covariates. Efficient Markov chain Monte Carlo schemes for evaluating the copula are given for this case. Using both simulated and real data, we show how such copula smoothing models can improve the quality of resulting function estimates and predictive distributions

Parallel Computing and Neural Networks in Behavioral Modeling

Tato disertační práce se zabývá metodami modelování elektronického zařízení letadel. První část je stručným přehledem klasických metod modelování systémů a adaptivních, fuzzy a hybridních metod používaných převážně k black-box modelování. Cílem práce je vytvořit algoritmus pro identifikaci a modelování obecného systému, který může být nelineární, dynamický a velmi složitý, například co do množství rozměrů. Předpokládá se, že model má několik vstupů a výstupů. V hlavní části práce je rozebrána metoda, která patří mezi hybridní systémy, protože kombinuje fuzzy systém s parametricky definovanými pravidly a regresní neuronovou síť. Nejprve je zmíněn základní princip regresní sítě a způsob určení jejího parametru strmosti, dále se kapitola zabývá zavedením fuzzy pravidel do této sítě. Třetí část se zabývá jedním z hlavních bodů práce, paralelními výpočty. Výsledný algoritmus je navržen pro paralelní zpracování, protože výpočetní čas může být v případě složitějších modelů příliš vysoký, případně nelze výsledky získané ze sítě vyhodnotit pomocí výpočtu v jednom vlákně. V závěru práce je metoda ověřena na datech získaných z měření zmenšeného modelu letadla. Ověření je provedeno pomocí střední kvadratické odchylky a srovnáním s odpovídajícím modelem vytvořeným pomocí vícevrstvé neuronové sítě trénované zpětným šířením chyby s algoritmem Levenberg-Marquardt.This thesis is focused on methods for the aircraft equipment modeling. The first part provides a brief overview of classical system modeling approaches used for system description, identification, and modeling. Then adaptive, fuzzy and hybrid methods used mainly for black-box system modeling are introduced. Aim of the thesis is to develop an algorithm for identification and modeling of a general system, which can be nonlinear, dynamic and complex. Multiple inputs and multiple outputs of model are assumed. The main part of the thesis introduces a new method which falls into the hybrid systems. It combines fuzzy approach with parametrically defined rules and general regression neural network. Firstly, the fundamentals of simple general regression neural network and its smoothness parameter determination are presented. Secondly, the general regression neural network with the fuzzy rules is introduced. Third part of the thesis is focused on the parallel computing, one of the main objectives. The final algorithm is designed for the parallel machine, because the computational time can be significantly high and for the larger datasets, the model is not achievable when evaluated in single thread. Block diagram for parallel computing in Matlab and CUDA is provided, as well as the basic structure of CUDA source code. Finally, the method is verified on data obtained from the measurement of a miniaturized aircraft model using the antenna outside the aircraft and the probe inside the fuselage of the aircraft model. The validation of the method is done using mean squared error and compared to mean squared error of corresponding model performed using the multilayer neural network with backpropagation learning and Levenberg-Marquardt algorithm.

Evolutionary Computation in System Identification: Review and Recommendations

Two of the steps in system identification are model structure selection and parameter estimation. In model structure selection, several model structures are evaluated and selected. Because the evaluation of all possible model structures during selection and estimation of the parameters requires a lot of time, a rigorous method in which these tasks can be simplified is usually preferred. This paper reviews cumulatively some of the methods that have been tried since the past 40 years. Among the methods, evolutionary computation is known to be the most recent one and hereby being reviewed in more detail, including what advantages the method contains and how it is specifically implemented. At the end of the paper, some recommendations are provided on how evolutionary computation can be utilized in a more effective way. In short, these are by modifying the search strategy and simplifying the procedure based on problem a priori knowledge