Design Optimization Utilizing Dynamic Substructuring and Artificial Intelligence Techniques

In mechanical and structural systems, resonance may cause large strains and stresses which can lead to the failure of the system. Since it is often not possible to change the frequency content of the external load excitation, the phenomenon can only be avoided by updating the design of the structure. In this paper, a design optimization strategy based on the integration of the Component Mode Synthesis (CMS) method with numerical optimization techniques is presented. For reasons of numerical efficiency, a Finite Element (FE) model is represented by a surrogate model which is a function of the design parameters. The surrogate model is obtained in four steps: First, the reduced FE models of the components are derived using the CMS method. Then the components are aassembled to obtain the entire structural response. Afterwards the dynamic behavior is determined for a number of design parameter settings. Finally, the surrogate model representing the dynamic behavior is obtained. In this research, the surrogate model is determined using the Backpropagation Neural Networks which is then optimized using the Genetic Algorithms and Sequential Quadratic Programming method. The application of the introduced techniques is demonstrated on a simple test problem

Design optimization applied in structural dynamics

This paper introduces the design optimization strategies, especially for structures which have dynamic constraints. Design optimization involves first the modeling and then the optimization of the problem. Utilizing the Finite Element (FE) model of a structure directly in an optimization process requires a long computation time. Therefore the Backpropagation Neural Networks (NNs) are introduced as a so called surrogate model for the FE model. Optimization techniques mentioned in this study cover the Genetic Algorithm (GA) and the Sequential Quadratic Programming (SQP) methods. For the applications of the introduced techniques, a multisegment cantilever beam problem under the constraints of its first and second natural frequency has been selected and solved using four different approaches

An optimization method for dynamics of structures with repetitive component patterns

The occurrence of dynamic problems during the operation of machinery may have devastating effects on a product. Therefore, design optimization of these products becomes essential in order to meet safety criteria. In this research, a hybrid design optimization method is proposed where attention is focused on structures having repeating patterns in their geometries. In the proposed method, the analysis is decomposed but the optimization problem itself is treated as a whole. The model of an entire structure is obtained without modeling all the repetitive components using the merits of the Component Mode Synthesis method. Backpropagation Neural Networks are used for surrogate modeling. The optimization is performed using two techniques: Genetic Algorithms (GAs) and Sequential Quadratic Programming (SQP). GAs are utilized to increase the chance of finding the location of the global optimum and since this optimum may not be exact, SQP is employed afterwards to improve the solution. A theoretical test problem is used to demonstrate the method

Automatic surrogate model type selection during the optimization of expensive black-box problems

The use of Surrogate Based Optimization (SBO) has become commonplace for optimizing expensive black-box simulation codes. A popular SBO method is the Efficient Global Optimization (EGO) approach. However, the performance of SBO methods critically depends on the quality of the guiding surrogate. In EGO the surrogate type is usually fixed to Kriging even though this may not be optimal for all problems. In this paper the authors propose to extend the well-known EGO method with an automatic surrogate model type selection framework that is able to dynamically select the best model type (including hybrid ensembles) depending on the data available so far. Hence, the expected improvement criterion will always be based on the best approximation available at each step of the optimization process. The approach is demonstrated on a structural optimization problem, i.e., reducing the stress on a truss-like structure. Results show that the proposed algorithm consequently finds better optimums than traditional kriging-based infill optimization

Stochastic Training of Neural Networks via Successive Convex Approximations

This paper proposes a new family of algorithms for training neural networks (NNs). These are based on recent developments in the field of non-convex optimization, going under the general name of successive convex approximation (SCA) techniques. The basic idea is to iteratively replace the original (non-convex, highly dimensional) learning problem with a sequence of (strongly convex) approximations, which are both accurate and simple to optimize. Differently from similar ideas (e.g., quasi-Newton algorithms), the approximations can be constructed using only first-order information of the neural network function, in a stochastic fashion, while exploiting the overall structure of the learning problem for a faster convergence. We discuss several use cases, based on different choices for the loss function (e.g., squared loss and cross-entropy loss), and for the regularization of the NN's weights. We experiment on several medium-sized benchmark problems, and on a large-scale dataset involving simulated physical data. The results show how the algorithm outperforms state-of-the-art techniques, providing faster convergence to a better minimum. Additionally, we show how the algorithm can be easily parallelized over multiple computational units without hindering its performance. In particular, each computational unit can optimize a tailored surrogate function defined on a randomly assigned subset of the input variables, whose dimension can be selected depending entirely on the available computational power.Comment: Preprint submitted to IEEE Transactions on Neural Networks and Learning System