Computational Intelligence for Efficient Numerical Design of Structures with Uncertain Parameters

An important task in engineering is the numerical design of structures. The current state of technology is characterized by deterministic thinking and practices. Fact is that all available data and information are characterized by uncertainty. An adequate consideration is necessary. The contribution gives an overview about approaches and methods for the numerical structural design, which consider the uncertainty of the data (a priori and design parameters). As the basis of the uncertainty modeling, the definition of polymorphic uncertainty models is proposed, to take real-world scenarios into account. Polymorphic uncertainty models allow the incorporation of the uncertainty characteristics variability (randomness), imprecision and incompleteness simultaneously. The direct consideration of data uncertainty in design tasks is for the optimization and the solution of the inverse problem not possible, due to the missing of rules for comparing uncertain quantities. An efficient approach is the formulation of surrogate models, differing in the order of evaluation uncertainty and solving the optimization task. This contribution presents the well known passive ("wait-and-see") and active ("here-and-now") approach for numerical design tasks analyzed with optimization or solving the inverse problem. The advantages and disadvantages of each concept are pointed out and the applicability, especially in early stages of design is demonstrated. Furthermore, numerical structural analysis, assessments, replacement models and reduction methods with uncertain data are outlined, leading to an efficient numerical design and to practical engineering solutions. This contribution demonstrates algorithms and methods for the numerical design concepts under consideration of polymorphic uncertainty models, by applying different surrogate models. Surrogate models allow the application of an appropriate uncertainty model. Suitable approaches for increasing numerical efficiency are reduction methods and replacement models among others. Reduction methods include model reduction, reducing the number of function calls and the complexity (e.g., The dimensionality with sensitivities). Replacement models are, e.g., Physically motivated and analytical metamodels. Analytical metamodel can be distinguished into approximation and classification methods. Numerically efficient classification algorithms are, e.g., Support Vector Machines or Self-Organizing Maps. Efficient approximate metamodels are, e.g., Artificial Neural Networks, Radial Basis Function Networks, and Extreme Learning Machines. The applicability of approach are demonstrated by means of engineering examples.