Experimental-statistical methods constructing of mathematical models

Description: This course provides the basics knowledge about experimental and statistical methods for obtaining mathematical models. Automation of technological processes is the most important production task, which can be solved using models and modeling. The course allows students to gain knowledge and ideas about the basics and methodology of modeling, about obtaining and applying models to control of technological processes. The result of studying the course should be the assimilation by doctoral students of the basic concepts and definitions of the theory of modeling, classifications of models and types of modeling and the acquisition of skills in statistical processing of experimental results and the establishment of functional dependencies of measured values, as well as analysis of the reliability and optimality of the applied models.

Amount of credits: 5

Пререквизиты:

• Adaptive methods of prediction of technological process parameters

Course Workload:

Component: Component by selection

Cycle: Base disciplines

Goal

• The formation basic ideas and knowledge about experimental-statistical methods for the development of mathematical models and the skills of statistical processing of the experimental results and the establishment of functional dependencies of the measured quantities, as well as the analysis of the reliability and optimality of the models used

Objective

• obtaining knowledge about the fundamentals and methodology of modeling, the use of experimental and statistical methods for constructing mathematical models for controlling technological processes;
• acquiring the ability to statistically process experimental results and establish functional dependencies of measured quantities, as well as analyze the reliability and optimality of the models used;
• acquiring the ability to work with technical documentation and necessary software.

Learning outcome: knowledge and understanding

• extract the basic concepts and principles of constructing mathematical models of stochastic processes using experimental and statistical methods;

Learning outcome: applying knowledge and understanding

• apply knowledge, understanding and ability to solve problems in new or unfamiliar situations in contexts and within the wider (or interdisciplinary) areas related to the field of automation and control

Learning outcome: formation of judgments

• independently apply methods and means of cognition, training and self-control, realize the prospects of intellectual, cultural, moral, physical and professional self-development and self-improvement, be able to critically evaluate one’s strengths and weaknesses.

Learning outcome: communicative abilities

• demonstrate readiness to change social, economic, professional roles, geographic and social mobility in the context of the dynamics of change, continue learning independently;

Learning outcome: learning skills or learning abilities

• demonstrate communication skills in the professional sphere and in society as a whole, including in a foreign language, analyze existing and independently develop technical documentation, clearly present and defend the results of complex engineering activities in the field of automation and control
• demonstrate skills in statistical processing of experimental results and establishing functional dependencies of measured quantities, as well as analyzing the reliability and optimality of the models used.

Teaching methods

Technology of scientific research activities

Technology of educational and research activities

Topics of lectures

• Modeling: basic concepts and definitions
• Types of models and simulation
• Mathematical modeling: basic concepts and definitions
• Classification of mathematical models
• Modeling technologies
• Algorithm for constructing an empirical model
• Construction of empirical regression models: basic concepts, planning an experiment, choosing factor levels, full factorial experiment, conducting an experiment
• Regression models with one input variable: basic concepts
• Regression models with multiple input variables
• Assessing the adequacy and accuracy of a multivariate linear model
• Nonlinear regression models with multiple input variables
• Interpretation and optimization of regression models
• Statistical modeling and its techniques
• Statistical modeling software
• Mathematical models of stochastic processes obtained by experimental and statistical methods

Key reading

• Montgomeri D. K., Ranger G. K., Hubele N. R. Inzhenernaya statistika, 2-e izd., John Wiley and Sons Inc., Hoboken, SShA, 2001, 342 str.
• Ayupov, V.V. Matematicheskoe modelirovanie tekhnicheskih sistem: uchebnoe posobie/V.V.Ayupov; M-vo s.-h. RF, federal'noe gos. byudzhetnoe obrazov.uchrezhdenie vysshego obrazovaniya «Permskaya gos. s.-h. akad. im. akad. D.N. Pryanishnikova». – Perm' : IPC «Prokrost"», 2017. – 242 s.
• Shterenzon V. A. Modelirovanie tekhnologicheskih processov: konspekt lekcij / V.A. Shterenzon. Ekaterinburg: Izd-vo Ros. gos. prof.-ped. un-ta, 2010. 66 s.
• Alonceva D. L. Research organization and planning. Lecture course (Organizaciya i planirovanie nauchnyh issledovanij. Kurs lekcij na angl. .yaz). Uchebnoe posobie. VKTU im D. Serikbaeva, Ust'-Kamenogorsk, 2022 g., 118 str. (6,89 p.l.) ISBN 978-601-208-723-9.

Further reading

• Alontseva D.L. Theory of linear systems of automatic control: textbook / D.L. Alontseva, A.L. Krasavin, A.T. Kussayin-Murat. Ust-Kamenogorsk: D. Serikbayev EKTU, 2020.-136 p. (In Russian)
• Alontseva D.L. Automatic control theory. Linear automatic control systems: a tutorial / D.L. Alontseva, A.L. Krasavin, A.T. Kussayin-Murat. Ust-Kamenogorsk: D. Serikbayev EKTU, 2021.-112 р. (In Russian)
• Bellomo N., De Angelis E.,. Delitala M Lecture Notes on Mathematical Modelling from Applied Sciences to Complex Systems. Vol. 8 – 2010, Published by: SIMAI Politecnico Torino, Roma, Italy,171 p. l