Implementation and Application of Statistical Methods in Research, Manufacturing Technology and Quality Control

Práce se zabývá možnostmi použití moderních statistických postupů se zaměřením na robustní metody. Vybrané postupy jsou analyzovány a aplikovány na častých problémech z praxe v českém průmyslu a technologii. Studovaná témata, metody a algoritmy jsou voleny tak, aby byla přínosem v reálných aplikacích ve srovnání s používanými klasickými metodami. Použitelnost a účinnost algoritmů je ověřena a demonstrována na reálných studiích a problémech z výzkumného prostředí českých průmyslových subjektů. V práci je poukázáno na nevyužitý potenciál současné teoreticko-matematické a výpočetní kapacity a nových přístupů k chápání statistických modelů a metod. Výsledkem práce je rovněž původní vývojové prostředí s programovacím jazykem DARWin (Data Analysis Robot for Windows) pro intenzivní využití efektivních numerických postupů pro získávání informací z dat. Práce je impulsem pro širší využití robustních a numericky, nebo výpočetně náročnějších metod, jako jsou neuronové sítě, pro modelování procesů a kontrolu kvality.This thesis deals with modern statistical approaches and their application aimed at robust methods and neural network modelling. Selected methods are analyzed and applied on frequent practical problems in czech industry and technology. Topics and methods are to be benificial in real applications compared to currently used classical methods. Applicability and effectivity of the algorithms is verified and demonstrated on real studies and problems in czech industrial and research bodies. The great and unexploited potential of modern theoretical and computational capacity and the potential of new approaces to statistical modelling and methods. A significant result of this thesis is also an environment for software application development for data analysis with own programming language DARWin (Data Analysis Robot for Windows) for implemenation of effective numerical algorithms for extaction information from data. The thesis should be an incentive for boarder use of robust and computationally intensive methods as neural networks for modelling processes, quality control and generally better understanding of nature.

Efficient training of neural networks with interval uncertainty

In this paper we attempt to build upon past work on Interval Neural Networks, and provide a robust way to train and quantify the uncertainty of Deep Neural Networks. Specifically, we propose a back propagation algorithm for Neural Networks with constant width predictions. In order to maintain numerical stability we propose minimising the maximum of the batch of errors at each step. Our approach can accommodate incertitude in the training data, and therefore adversarial examples from a commonly used attack model can be trivially accounted for. We present preliminary results on a test function example. The reliability of the predictions of these networks are guaranteed by the non-convex Scenario approach to chance constrained optimisation. A key result is that, by using minibatches of size M, the complexity of our approach scales as O(MNiter), and does not depend upon the number of training data points as with other Interval Predictor Model methods

Efficient training of neural networks with interval uncertainty

In this paper we attempt to build upon past work on Interval Neural Networks, and provide a robust way to train and quantify the uncertainty of Deep Neural Networks. Specifically, we propose a back propagation algorithm for Neural Networks with constant width predictions. In order to maintain numerical stability we propose minimising the maximum of the batch of errors at each step. Our approach can accommodate incertitude in the training data, and therefore adversarial examples from a commonly used attack model can be trivially accounted for. We present preliminary results on a test function example. The reliability of the predictions of these networks are guaranteed by the non-convex Scenario approach to chance constrained optimisation. A key result is that, by using minibatches of size M, the complexity of our approach scales as O(MNiter), and does not depend upon the number of training data points as with other Interval Predictor Model methods

On Applications of New Soft and Evolutionary Computing Techniques to Direct and Inverse Modeling Problems

Adaptive direct modeling or system identification and adaptive inverse modeling or channel equalization find extensive applications in telecommunication, control system, instrumentation, power system engineering and geophysics. If the plants or systems are nonlinear, dynamic, Hammerstein and multiple-input and multiple-output (MIMO) types, the identification task becomes very difficult. Further, the existing conventional methods like the least mean square (LMS) and recursive least square (RLS) algorithms do not provide satisfactory training to develop accurate direct and inverse models. Very often these (LMS and RLS) derivative based algorithms do not lead to optimal solutions in pole-zero and Hammerstein type system identification problem as they have tendency to be trapped by local minima. In many practical situations the output data are contaminated with impulsive type outliers in addition to measurement noise. The density of the outliers may be up to 50%, which means that about 50% of the available data are affected by outliers. The strength of these outliers may be two to five times the maximum amplitude of the signal. Under such adverse conditions the available learning algorithms are not effective in imparting satisfactory training to update the weights of the adaptive models. As a result the resultant direct and inverse models become inaccurate and improper. Hence there are three important issues which need attention to be resolved. These are : (i) Development of accurate direct and inverse models of complex plants using some novel architecture and new learning techniques. (ii) Development of new training rules which alleviates local minima problem during training and thus help in generating improved adaptive models. (iii) Development of robust training strategy which is less sensitive to outliers in training and thus to create identification and equalization models which are robust against outliers. These issues are addressed in this thesis and corresponding contribution are outlined in seven Chapters. In addition, one Chapter on introduction, another on required architectures and algorithms and last Chapter on conclusion and scope for further research work are embodied in the thesis. A new cascaded low complexity functional link artificial neural network (FLANN) structure is proposed and the corresponding learning algorithm is derived and used to identify nonlinear dynamic plants. In terms of identification performance this model is shown to outperform the multilayer perceptron and FLANN model. A novel method of identification of IIR plants is proposed using comprehensive learning particle swarm optimization (CLPSO) algorithm. It is shown that the new approach is more accurate in identification and takes less CPU time compared to those obtained by existing recursive LMS (RLMS), genetic algorithm (GA) and PSO based approaches. The bacterial foraging optimization (BFO) and PSO are used to develop efficient learning algorithms to train models to identify nonlinear dynamic and MIMO plants. The new scheme takes less computational effort, more accurate and consumes less input samples for training. Robust identification and equalization of complex plants have been carried out using outliers in training sets through minimization of robust norms using PSO and BFO based methods. This method yields robust performance both in equalization and identification tasks. Identification of Hammerstein plants has been achieved successfully using PSO, new clonal PSO (CPSO) and immunized PSO (IPSO) algorithms. Finally the thesis proposes a distributed approach to identification of plants by developing two distributed learning algorithms : incremental PSO and diffusion PSO. It is shown that the new approach is more efficient in terms of accuracy and training time compared to centralized PSO based approach. In addition a robust distributed approach for identification is proposed and its performance has been evaluated. In essence the thesis proposed many new and efficient algorithms and structure for identification and equalization task such as distributed algorithms, robust algorithms, algorithms for ploe-zero identification and Hammerstein models. All these new methods are shown to be better in terms of performance, speed of computation or accuracy of results

Estimación Borrosa del Riesgo Beta. Análisis Comparativo

Aquesta tesi representa una aportació a la literatura empírica sobre el risc sistemàtic a nivell sectorial en mercats emergents llatinoamericans, en calcular betes borroses, sectorials i individuals, de Xile, Brasil i Mèxic, i comparar el seu comportament amb el de les betes d’alguns països desenvolupats com Estats Units, Regne Unit i Japó. Proposem una representació borrosa del model de mercat que incorpora el càlcul del rendiment d’un actiu expressat a través d’un interval de confiança. D’aquesta manera incorporem en el càlcul de la beta tota la informació disponible de les cotitzacions d’un actiu durant el dia. Com a resultat de l’estimació amb aquest model obtenim un coeficient beta borrós. Comencem l’estudi comparant i avaluant els resultats obtinguts segons s’expressi la rendibilitat dels actius i segons els diferents mètodes d’estimació de la beta, MCO i regressió borrosa lineal de Tanaka i Ishibuchi (1992) millorada amb el mètode de detecció d’outliers de Hung i Yang (2006). Finalment, avancem en l’estudi de la beta borrosa com a indicador del risc sistemàtic. Proposem una classificació dels actius basada en la beta borrosa i verifiquem si dues de les hipòtesis tradicionals de la teoria de carteres es compleixen en un entorn d’incertesa: i) la beta sectorial presenta major estabilitat que la beta individual; ii) com més gran és el període d’estimació, major és l’estabilitat de la beta.Esta tesis representa un aporte a la literatura empírica sobre el riesgo sistemático a nivel sectorial en mercados emergentes latinoamericanos, al calcular betas borrosas, sectoriales e individuales, en Chile, Brasil y Méjico y comparar su comportamiento con él de las betas de algunos países desarrollados como Estados Unidos, Reino Unido y Japón. Proponemos una representación borrosa del modelo de mercado que incorpora el cálculo del rendimiento de un activo expresado a través de un intervalo de confianza. Con ello incorporamos en el cálculo de la beta toda la información disponible de las cotizaciones de un activo durante el día. Como resultado de la estimación con dicho modelo obtenemos un coeficiente beta borroso. Comenzamos el estudio comparando y evaluando los resultados obtenidos según se exprese la rentabilidad de los activos y según los diferentes métodos de estimación de la beta, MCO y regresión borrosa lineal de Tanaka e Ishibuchi (1992) mejorada con el método de detección de outliers de Hung y Yang (2006). Por último, avanzamos en el estudio de la beta borrosa como indicador del riesgo sistemático. Proponemos una nueva clasificación de los activos basada en la beta borrosa y verificamos si dos de las hipótesis tradicionales de la teoría de carteras se cumplen en un entorno de incertidumbre: i) la beta sectorial presenta mayor estabilidad que la beta individual; ii) Cuánto mayor es el período de estimación, mayor es la estabilidad de la beta.This thesis represents a contribution to empirical literature on systematic risk at the sectoral level in Latin American emerging markets, by calculating fuzzy betas, sectoral and individual, in Chile, Brazil and Mexico, and to compare its behavior with that of betas in some developed countries as the United States, the United Kingdom and Japan. We propose a fuzzy representation of the model of market that incorporates the calculation of the return of an asset expressed through a confidence interval. With it we incorporate in the calculation of the beta all the information available of the quotation of an asset during the day. As a result of the estimation with that model we obtain a fuzzy beta coefficient. We begin the study by comparing and evaluating the results obtained according to assets return and to the different beta methods of estimation, MCO and lineal fuzzy regression of Tanaka e Ishibuchi (1992) improved with the detection of outliers model of the Hung and Yung (2006). Finally, we advance in the study of fuzzy beta as an indicator of systematic risk. We propose a classification of assets based on fuzzy beta and we verify if two of the traditional hypotheses of the portfolio theory are met in an uncertainty environment: i) sectoral beta shows greater stability than individual beta; ii) the longer the estimation period is, the greater the stability of the bet