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Probability and Optimization for Engineers covers the fundamentals of probabilistic design and optimum design and methods for high performance design. It presents the principle of finite element method in probabilistic and optimum design with solved specific interactive problems of finite element analysis using Ansys. This is the first book to use the principles of Artificial Intelligence (AI) to optimum design, offering a general introduction to the optimum design using AI algorithms such as Machine Learning, Deep Learning, artificial neural networks, Bayesian optimum design, Bayesian machine learning optimization, and genetic algorithms. The visual appeal of the book is enhanced by numerous new full-color graphic illustrations.
Probability method is an effective means for probabilistic design as it is an analysis technique for assessing the effect of uncertain input parameters and assumptions on your model. A probabilistic analysis allows you to determine the extent to which uncertainties in the model affect the results of a finite element analysis. An uncertainty (or random quantity) is a parameter whose value is impossible to determine at a given point in time (if it is time-dependent) or at a given location (if it is location-dependent). An example is ambient temperature; you cannot know precisely what the temperature will be 1 week from now in a given city. In a probabilistic analysis, statistical distribution functions (such as the Gaussian or normal distribution, the uniform distribution, etc.) describe uncertain parameters.
Computer models are expressed and described with specific numerical and deterministic values; material properties are entered using certain values; the geometry of the component is assigned a certain length or width; and so on. An analysis based on a given set of specific numbers and values is called a deterministic analysis. Naturally, the results of a deterministic analysis are only as good as the assumptions and input values used for the analysis. The validity of those results depends on how correct the values were for the component under real-life conditions.
The objectives of this book are:
• To incorporate knowledge learned in the probability and optimization courses and to understand the difference between them
• To reinforce competence in using the fundamentals of probabilistic methods and optimization in design and to understand the importance of using them to determine high-performance design.
• To obtain a working knowledge of the proper probabilistic theories under steady and variable loadings.
• To master the design by using the probability and optimization theories.
• To use the principle of the finite element method in probabilistic and optimum design, with solved examples by the analytical method and Ansys software.
• To use the principle of AI algorithms in optimal design.
• To use the principle of the optimal design methods with solved examples using graphical, analytical, and numerical methods, and MatLAB built-in algorithms.
Preface
The probability methods
Probability distributions
Choosing a distribution for a random variable
Probabilistic design techniques
Tutorial: probabilistic design analysis of circular plate bending
Tutorial: probabilistic design analysis of a laminate composite plate under distributed pressure
The optimization methods
Tutorial: optimization of heat transfer rate from the rod of a cylindrical pin fin
The optimum design using artificial intelligence
