Design optimization using Statistical Confidence Boundaries of response surfaces: Application to robust design of a biomedical implant (original) (raw)
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An algorithm for engineering design optimization
International Journal for Numerical Methods in Engineering, 1983
In this paper a new concept for development of algorithms for optimal design of engineering systems is presented. The basic idea is to use upper and lower bounds on optimum cost to develop iterative search strategies. The main feature of the concept is that it does not rely on one-dimensional search to compute a step size at any design iteration. Implication of the feature is that the algorithms based on this concept require evaluation of constraint functions only once at any design iteration. This is highly desirable for optimal design of engineering systems because evaluation of functions for such systems is very expensive due to their implicit dependence on design variables. An algorithm based on the new concept is derived in the paper. Several new step sizes are introduced and their relation to proper reduced optimal design problems are presented. A new step size based on the constant cost requirement at some design iterations is introduced. Numerical aspects for the algorithm are also presented. Based on the new algorithm, a general-purpose computer code GRP2 is developed. The code is used to solve several problems to gain experience and insight for the algorithm. Numerical experience with examples is discussed. It is concluded that algorithms based on bounding optimum cost have substantial potential for applications in optimal design of engineering systems.
Optimization approach under uncertainty in preliminary design for mechanical engineering
This work is a contribution to the integration of the concepts of reliability and robustness in the design phase of a product optimization, However, the lack of information and the high degree of uncertainty during the early design phases hinder the use of these tools. To overcome this problem, we have proposed a structured approach based on the evaluation under uncertainty of two main phases of the design process (conceptual design and embodiment design).
Mathematical Optimization for Engineering Design Problems
2013
Applications in engineering design and the material sciences motivate the development of optimization theory in a manner that additionally draws from other branches of mathematics including the functional, complex, and numerical analyses. The first contribution, motivated by an automotive design application, extends multiobjective optimization theory under the assumption that the problem information is not available in its entirety to a single decision maker as traditionally assumed in the multiobjective optimization literature. Rather, the problem information and the design control are distributed among different decision makers. This requirement appears in the design of an automotive system whose subsystem components themselves correspond to highly involved design subproblems each of whose performance is measured by multiple criteria. This leads to a system/subsystem interaction requiring a coordination whose algorithmic foundation is developed and rigorously examined mathematical...
Mathematical programming models and algorithms for engineering design optimization
Computer Methods in Applied Mechanics and Engineering, 2005
Mathematical Programming provides general tools for Engineering Design Optimization. We present numerical models for Simultaneous Analysis and Design Optimization (SAND) and Multidisciplinary Design Optimization (MDO) represented by Mathematical Programs and numerical techniques to solve these models. These techniques are based on the Feasible Arc Interior Point Algorithm (FAIPA) for Nonlinear Constrained Optimization. Even if MDO is a very large optimization problem, our approach reduces considerably the computer effort. Several tools for very large problems are also presented. The present approach is very strong and efficient for real industrial applications and can easily interact with existing simulation engineering codes.
Design optimization application in accordance with product and process requirements
Advances in Engineering Software, 2010
Structural optimization techniques are a well-known approach for improving product performances. Often, optimization procedures do not include manufacturing constraints arising from corporate technologies. This aspect becomes a disadvantage in the design review phase when the final product release is a trade-off between optimization results and manufacturing constraints. This paper describes a specific new approach, which considers product/process guidelines an input/output data in the optimization phase. The study case is represented by a high performance aeronautic seat structure having as mission profiles the SAE-AS Standard, in order to demonstrate occupant protection when a seat/occupant/restraint system is subjected to statically applied ultimate loads and to dynamic impact test conditions. The authors' aim, in accordance with standards' requirements, is to achieve a final design based on an optimized structural solution for the chosen process technologies, taking into account the low volume production and typical attitude of the aeronautical industry. The presented study case offers the proper reference in order to extend this methodology to more complex structural applications.
Precision Engineering Design Process for Optimal Design based on Engineering Sciences
Journal of Mechanical Engineering Research, 2021
Concepts of precision engineering design process for optimal design where engineering sciences contribute in the successful good design are elaborated in this paper. Scientific theory, numerical methods and practicality are discussed in this paper. Factors necessary for a complete product or systems design are detailed and application of mathematical design optimization in producing a good design are shown. Many applicable engineering design examples are itemized to show relevancy of the optimal design theory to engineering design. Future trends of optimal design with respect to the 4th industrial revolution of digitization is presented. Paper sets to elaborate that most of the engineering and scientific design problems can be optimized to a good design based on many new/advanced optimization techniques.
Analysis of uncertainty in engineering design optimization problems
2016
In this paper, we analyze popular benchmark instances in the field of engineering design optimization regarding the robustness of published solutions. First, we implement selected benchmark problems with HeuristicLab and show the advantages of having a framework that enables rapid prototyping for optimization and analysis. Then, we show that many solutions quickly become infeasible when considering uncertainty like production inaccuracies. Based on these findings, we motivate why robust solutions for engineering design are important and present methods for measuring, identifying and visualizing robustness. Finally, we present how solutions can be compared and selected using a novel robustness measure.
Within the design development phases the Design for Six Sigma concept optimizes a design such that the products conform to Six Sigma quality. Which means that robustness and reliability are explicit optimization goals even with variations e.g. in manufacturing, design configuration and environment. The application of the reliability-and variance-based robust design optimization results in optimized designs such that they are insensitive to uncertainties up to a six sigma safety level. In this paper an efficient iterative decoupled loop approach is provided for reducing the necessary number of design evaluations. This is exemplary applied to a CAD and CAE parameter-based robust design optimization of an axial turbine, including manufacturing tolerances based on random field modeling. The probabilistic and optimization tasks are performed with the optiSLang, SoS and SL ang software packages. Whereby, the CAE integration is realized by the ANSYS Workbench environment and optiPLug. In addition, the ANSYS Mechanical and CFD software offers a comprehensive solution for structural, thermal and fluid analysis. The software package also includes solutions for both direct and sequentially coupled physics problems including direct coupled-field elements and the ANSYS multi-field solver for supported physics, which is very efficient for tolerance interpolation of measurement data to different finite element meshes.