Adaptiver Suchansatz zur multidisziplinären Optimierung von Leichtbaustrukturen unter Verwendung hybrider Metaheuristik

Within the last few years environmental regulations, safety requirements and market competitions forced the automotive industry to open up a wide range of new technologies. Lightweight design is considered as one of the most innovative concepts to fulfil environmental, safety and many other objectives at competitive prices. Choosing the best design and production process in the development period is the most significant link in the automobile production chain. A wide range of design and process parameters needs to be evaluated to achieve numerous goals of production. These goals often stand in conflict with each other. In addition to the variation of the concepts and following the objectives, some limitations such as manufacturing restrictions, financial limits, and deadlines influence the choice of the best combination of variables. This study introduces a structural optimization tool for assemblies made of sheet metal, e.g. the automobile body, based on parametrization and evaluation of concepts in CAD and CAE. This methodology focuses on those concepts, which leads to the use of the right amount of light and strong material in the right place, instead of substituting the whole structure with the new material. An adaptive hybrid metaheuristic algorithm is designed to eliminate all factors that would lead to a local minimum instead of global optimum. Finding the global optimum is granted by using some explorative and exploitative search heuristics, which are intelligently organized by a central controller. Reliability, accuracy and the speed of the proposed algorithm are validated via a comparative study with similar algorithms for an academic optimization problem, which shows valuable results. Since structures might be subject to a wide range of load cases, e.g. static, cyclic, dynamic, temperature-dependent etc., these requirements need to be addressed by a multidisciplinary optimization algorithm. To handle the nonlinear response of objectives and to tackle the time-consuming FEM analyses in crash situations, a surrogate model is implemented in the optimization tool. The ability of such tool to present the optimum results in multi-objective problems is improved by using some user-selected fitness functions. Finally, an exemplary sub-assembly made of sheet metal parts from a car body is optimized to enhance both, static load case and crashworthiness.Die Automobilindustrie hat in den letzten Jahren unter dem Druck von Umweltvorschriften, Sicherheitsanforderungen und wettbewerbsfähigem Markt neue Wege auf dem Gebiet der Technologien eröffnet. Leichtbau gilt als eine der innovativsten und offenkundigsten Lösungen, um Umwelt- und Sicherheitsziele zu wettbewerbsfähigen Preisen zu erreichen. Die Wahl des besten Designs und Verfahrens für Produktionen in der Entwicklungsphase ist der wichtigste Ring der Automobilproduktionskette. Um unzählige Produktionsziele zu erreichen, müssen zahlreiche Design- und Prozessparameter bewertet werden. Die Anzahl und Variation der Lösungen und Ziele sowie einige Einschränkungen wie Fertigungsbeschränkungen, finanzielle Grenzen und Fristen beeinflussen die Auswahl einer guten Kombination von Variablen. In dieser Studie werden strukturelle Optimierungswerkzeuge für aus Blech gefertigte Baugruppen, z. Karosserie, basierend auf Parametrisierung und Bewertung von Lösungen in CAD bzw. CAE. Diese Methodik konzentriert sich auf die Lösungen, die dazu führen, dass die richtige Menge an leichtem / festem Material an der richtigen Stelle der Struktur verwendet wird, anstatt vollständig ersetzt zu werden. Eine adaptive Hybrid-Metaheuristik soll verhindern, dass alle Faktoren, die Bedrohungsoptimierungstools in einem lokalen Minimum konvergieren, anstelle eines globalen Optimums. Das Auffinden des globalen Optimums wird durch einige explorative und ausbeuterische Such Heuristiken gewährleistet. Die Zuverlässigkeit, Genauigkeit und Geschwindigkeit des vorgeschlagenen Algorithmus wird mit ähnlichen Algorithmen in akademischen Optimierungsproblemen validiert und führt zu respektablen Ergebnissen. Da Strukturen möglicherweise einem weiten Bereich von Lastfällen unterliegen, z. statische, zyklische, dynamische, Temperatur usw. Möglichkeit der multidisziplinären Optimierung wurde in Optimierungswerkzeugen bereitgestellt. Um die nichtlineare Reaktion von Zielen zu überwinden und um den hohen Zeitverbrauch von FEM-Analysen in Absturzereignissen zu bewältigen, könnte ein Ersatzmodell vom Benutzer verwendet werden. Die Fähigkeit von Optimierungswerkzeugen, optimale Ergebnisse bei Problemen mit mehreren Zielsetzungen zu präsentieren, wird durch die Verwendung einiger vom Benutzer ausgewählten Fitnessfunktionen verbessert. Eine Unterbaugruppe aus Blechteilen, die zur Automobilkarosserie gehören, ist optimiert, um beide zu verbessern; statischer Lastfall und Crashsicherheit

State-of-the-art in aerodynamic shape optimisation methods

Aerodynamic optimisation has become an indispensable component for any aerodynamic design over the past 60 years, with applications to aircraft, cars, trains, bridges, wind turbines, internal pipe flows, and cavities, among others, and is thus relevant in many facets of technology. With advancements in computational power, automated design optimisation procedures have become more competent, however, there is an ambiguity and bias throughout the literature with regards to relative performance of optimisation architectures and employed algorithms. This paper provides a well-balanced critical review of the dominant optimisation approaches that have been integrated with aerodynamic theory for the purpose of shape optimisation. A total of 229 papers, published in more than 120 journals and conference proceedings, have been classified into 6 different optimisation algorithm approaches. The material cited includes some of the most well-established authors and publications in the field of aerodynamic optimisation. This paper aims to eliminate bias toward certain algorithms by analysing the limitations, drawbacks, and the benefits of the most utilised optimisation approaches. This review provides comprehensive but straightforward insight for non-specialists and reference detailing the current state for specialist practitioners

Approximation methodologies for explicit model predictive control of complex systems

This thesis concerns the development of complexity reduction methodologies for the application of multi-parametric/explicit model predictive (mp-MPC) control to complex high fidelity models. The main advantage of mp-MPC is the offline relocation of the optimization task and the associated computational expense through the use of multi-parametric programming. This allows for the application of MPC to fast sampling systems or systems for which it is not possible to perform online optimization due to cycle time requirements. The application of mp-MPC to complex nonlinear systems is of critical importance and is the subject of the thesis. The first part is concerned with the adaptation and development of model order reduction (MOR) techniques for application in combination to mp-MPC algorithms. This first part includes the mp-MPC oriented use of existing MOR techniques as well as the development of new ones. The use of MOR for multi-parametric moving horizon estimation is also investigated. The second part of the thesis introduces a framework for the ‘equation free’ surrogate-model based design of explicit controllers as a possible alternative to multi-parametric based methods. The methodology relies upon the use of advanced data-classification approaches and surrogate modelling techniques, and is illustrated with different numerical examples.Open Acces

Contribution to the definition of non deterministic robust optimization in aeronautics accounting with variable uncertainties

Shape optimization is a largely studied problem in aeronautics. It can be applied to many disciplines in this field, namely efficiency improvement of engine blades, noise reduction of engine nozzles, or reduction of the fuel consumption of aircraft. Optimization for general purposes is also of increasing interest in many other fields. Traditionally, optimization procedures were based on deterministic methodologies as in Hamalainen et al (2000), where the optimum working point was fixed. However, not considering what happens in the vicinity of the defined working conditions can produce problems like loose of efficiency and performance. That is, in many cases, if the real working point differs from the original, even a little distance, efficiency is reduced considerably as pointed out in Huyse and Lewis (2001). Non deterministic methodologies have been applied to many fields (Papadrakakis, Lagaros and Tsompanakis, 1998; Plevris, Lagaros and Papadrakakis, 2005). One of the most extended nondeterministic methodologies is the stochastic analysis. The time consuming calculations required on Computational Fluid Dynamics (CFD) has prevented an extensive application of the stochastic analysis to shape optimization. Stochastic analysis was firstly developed in structural mechanics, several years ago. Uncertainty quantification and variability studies can help to deal with intrinsic errors of the processes or methods. The result to consider for design optimization is no longer a point, but a range of values that defines the area where, in average, optimal output values are obtained. The optimal value could be worse than other optima, but considering its vicinity, it is clearly the most robust regarding input variability. Uncertainty quantification is a topic of increasing interest from the last few years. It provides several techniques to evaluate uncertainty input parameters and their effects on the outcomes. This research presents a methodology to integrate evolutionary algorithms and stochastic analysis, in order to deal with uncertainty and to obtain robust solutions

Contribution to the Definition of Non Deterministic Robust Optimization in Aeronautics Accounting with Variable Uncertainties

Shape optimization is a largely studied problem in aeronautics. It can be applied to many disciplines in this field, namely efficiency improvement of engine blades, noise reduction of engine nozzles, or reduction of the fuel consumption of aircraft. Optimization for general purposes is also of increasing interest in many other fields. Traditionally, optimization procedures were based on deterministic methodologies as in Hamalainen et al (2000), where the optimum working point was fixed. However, not considering what happens in the vicinity of the defined working conditions can produce problems like loose of efficiency and performance. That is, in many cases, if the real working point differs from the original, even a little distance, efficiency is reduced considerably as pointed out in Huyse and Lewis (2001) Non deterministic methodologies have been applied to many fields (Papadrakakis, Lagaros and Tsompanakis, 1998; Plevris, Lagaros and Papadrakakis, 2005). One of the most extended nondeterministic methodologies is the stochastic analysis. The time consuming calculations required on Computational Fluid Dynamics (CFD) has prevented an extensive application of the stochastic analysis to shape optimization. Stochastic analysis was firstly developed in structural mechanics, several years ago. Uncertainty quantification and variability studies can help to deal with intrinsic errors of the processes or methods. The result to consider for design optimization is no longer a point, but a range of values that defines the area where, in average, optimal output values are obtained. The optimal value could be worse than other optima, but considering its vicinity, it is clearly the most robust regarding input variability. Uncertainty quantification is a topic of increasing interest from the last few years. It provides several techniques to evaluate uncertainty input parameters and their effects on the outcomes. This research presents a methodology to integrate evolutionary algorithms and stochastic analysis, in order to deal with uncertainty and to obtain robust solutions

Development of an optimization framework for solving engineering design problems.

The integration of optimization methodologies with computational simulations plays a profound role in the product design. Such integration, however, faces multiple challenges arising from computation-intensive simulations, unknown function properties (i.e., black-box functions), complex constraints, and high-dimensionality of problems. To address these challenges, metamodel-based methods which apply metamodels as a cheaper alternative to costly analysis tools prove to be a practical way in design optimization and have gained continuous development. In this thesis, an intrinsically linear function (ILF) assisted and trust region based optimization method (IATRO) is proposed first for solving low-dimensional constrained black-box problems. Then, the economical sampling strategy (ESS), modified trust region strategy and self-adaptive normalization strategy (SANS) are developed to enhance the overall optimization capability. Moreover, as the radial basis function (RBF) interpolation is found to better approximate both objective and constraint functions than ILF, a RBF-assisted optimization framework is established by the combination of the balanced trust region strategy (BTRS), global intelligence selection strategy (GIS) and early termination strategy (ETS). Following that, the fast computation strategy (FCS) and successive refinement strategy (SRS) are proposed for solving large-scale constrained black-box problems and the final optimization framework is called as RATRLO (radial basis function assisted and trust region based large-scale optimization framework). By testing a set of well-known benchmark problems including 22 G-problems, 4 engineering design problems and 1 high-dimensional automotive problem, RATRLO shows remarkable advantages in achieving high-quality results with very few function evaluations and slight parameter tuning. Compared with various state-of-the-art algorithms, RATRLO can be considered one of the best global optimizers for solving constrained optimization problems. Further more, RATRLO provides a valuable insight into the development of algorithms for efficient large-scale optimization

Global and local surrogate-assisted differential evolution for expensive constrained optimization

The file attached to this record is the author's final peer reviewed version.For expensive constrained optimization problems, the computation of objective function and constraints is very time-consuming. This paper proposes a novel global and local surrogate-assisted differential evolution for solving expensive constrained optimization problems with inequality constraints. The proposed method consists of two main phases: global surrogate-assisted phase and local surrogate-assisted phase. In the global surrogate-assisted phase, differential evolution serves as the search engine to produce multiple trial vectors. Afterward, the generalized regression neural network is used to evaluate these trial vectors. In order to select the best candidate from these trial vectors, two rules are combined. The first is the feasibility rule, which at first guides the population toward the feasible region, and then toward the optimal solution. In addition, the second rule puts more emphasis on the solution with the highest predicted uncertainty, and thus alleviates the inaccuracy of the surrogates. In the local surrogate-assisted phase, the interior point method coupled with radial basis function is utilized to refine each individual in the population. During the evolution, the global surrogate-assisted phase has the capability to promptly locate the promising region and the local surrogate-assisted phase is able to speed up the convergence. Therefore, by combining these two important elements, the number of fitness evaluations can be reduced remarkably. The proposed method has been tested on numerous benchmark test functions from three test suites and two real-world cases. The experimental results demonstrate that the performance of the proposed method is better than that of other state-of-the-art methods

On Parametric Optimal Execution and Machine Learning Surrogates

We investigate optimal order execution problems in discrete time with instantaneous price impact and stochastic resilience. First, in the setting of linear transient price impact we derive a closed-form recursion for the optimal strategy, extending the deterministic results from Obizhaeva and Wang (J Financial Markets, 2013). Second, we develop a numerical algorithm based on dynamic programming and deep learning for the case of nonlinear transient price impact as proposed by Bouchaud et al. (Quant. Finance, 2004). Specifically, we utilize an actor-critic framework that constructs two neural-network (NN) surrogates for the value function and the feedback control. The flexible scalability of NN functional approximators enables parametric learning, i.e., incorporating several model or market parameters as part of the input space. Precise calibration of price impact, resilience, etc., is known to be extremely challenging and hence it is critical to understand sensitivity of the execution policy to these parameters. Our NN learner organically scales across multiple input dimensions and is shown to accurately approximate optimal strategies across a wide range of parameter configurations. We provide a fully reproducible Jupyter Notebook with our NN implementation, which is of independent pedagogical interest, demonstrating the ease of use of NN surrogates in (parametric) stochastic control problems.Comment: 33 pages, 8 figures. Github repo at https://github.com/moritz-voss/Parametric_Optimal_Execution_M

Machine Learning-Based Data and Model Driven Bayesian Uncertanity Quantification of Inverse Problems for Suspended Non-structural System

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and control strategies based on simulation or prediction results. However, in the surrogate model, preventing overfitting and incorporating reasonable prior knowledge of embedded physics and models is a challenge. Suspended Nonstructural Systems (SNS) pose a significant challenge in the inverse problem. Research on their seismic performance and mechanical models, particularly in the inverse problem and uncertainty quantification, is still lacking. To address this, the author conducts full-scale shaking table dynamic experiments and monotonic & cyclic tests, and simulations of different types of SNS to investigate mechanical behaviors. To quantify the uncertainty of the inverse problem, the author proposes a new framework that adopts machine learning-based data and model driven stochastic Gaussian process model calibration to quantify the uncertainty via a new black box variational inference that accounts for geometric complexity measure, Minimum Description length (MDL), through Bayesian inference. It is validated in the SNS and yields optimal generalizability and computational scalability

Computer Science Research Institute 2004 annual report of activities.

This report summarizes the activities of the Computer Science Research Institute (CSRI) at Sandia National Laboratories during the period January 1, 2004 to December 31, 2004. During this period the CSRI hosted 166 visitors representing 81 universities, companies and laboratories. Of these 65 were summer students or faculty. The CSRI partially sponsored 2 workshops and also organized and was the primary host for 4 workshops. These 4 CSRI sponsored workshops had 140 participants--74 from universities, companies and laboratories, and 66 from Sandia. Finally, the CSRI sponsored 14 long-term collaborative research projects and 5 Sabbaticals