Preferences and Correlated Uncertainties in Engineering Design

Y-stiffened panel multi-objective optimization using genetic algorithm

Preliminary design information is characteristically imprecise or fuzzy: specifications and requirements are subject to change, and the design description is vague and incomplete. The Method of Imprecision uses the mathematics of fuzzy sets to explicitly represent and manipulate imprecise preliminary design information, enabling the designer to better understand the full range of designs and performances that satisfy an imprecise set of specifications and requirements. This paper discusses the foundations of this methodology, and introduces pragmatic extensions that provide computationally tractable methods to map design imprecision from multiple design variables onto multiple performance variables. These methods attempt to minimize the number of function evaluations required while retaining an appropriate level of accuracy. This is achieved by using optimization to obtain extremal points for each performance variable and selectively applying a linear approximation for the mapping from the design variable space (DVS) to the performance variable space (PVS) to interpolate between extremal points. This linear approximation is constructed using regression techniques adapted from experiment design.

Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Methods for incorporating imprecision in engineering design decision-making are briefly reviewed and compared. A tutorial is presented on the Method of Imprecision (MoI), a formal method, based on the mathematics of fuzzy sets, for representing and manipulating imprecision in engineering design. The results of a design cost estimation example, utilizing a new informal cost specification, are presented. The MoI can provide formal information upon which to base decisions during preliminary engineering design and can facilitate set-based concurrent design.

Various optimization problems have been studied for the purpose of structural morphogenesis by many researchers. Structural optimization problems can be classified into three different sub-problems, namely size, shape and topology optimization problem. Size optimization problem is consisted of small sets of design variables. The shape and topology of a structure are defined by a set of design variables, and these design variables are adjusted to achieve given objectives, such as minimum volume. Such optimization problems can be solved iteratively, using gradient-based techniques. Introducing more design variables increases the complexity of the optimization problem. Therefore, it becomes difficult to solve the optimization problem by using MP techniques with large sets of design variables. Heuristics can be improved the difficulty. There are many studies using heuristics like genetic algorithm and simulated annealing. An effective method for structural morphogenesis inspired by self-organization phenomena is presented in this paper. Self-organization is a phenomenon that an entire structure gradually emerges by interaction between elements of the structure, and the elements are affected by the entire structure. Since the self-organization algorithm consists of simple calculation iteration, it can be applied to problems with large number of design variables. Proposed method is applied to problems of uniform member length, minimization of strain energy and cross-section design for frame structures, and the effectiveness is demonstrated through some examples. On the other hand, the number of projects incorporating computational design has increased in recent year, and designs with complicated forms composed of free surfaces are also increasing. In order to design such a shape, the designer needs to consider the rationality of the structure from the initial stage. So, it seems necessary to develop simple software for the structural morphogenesis. Therefore, we developed components of Grasshopper that works within Rhinoceros, so that it will be possible to reassemble algorithms in an intuitive way for designers who have never experienced programming. Grasshopper is one of Graphical Algorithm Editor (GAE), and can be visually constructed an algorithm by connecting components that is a function of modeling. Analysis by gradient-based MP techniques often involves jumping of solutions and analytical instability peculiar to non-linear problems, and it is difficult to apply to the computer aided systems as described above. Analysis algorithms based on self-organizing algorithms are considered to be suitable for the above system due to their high robustness.

Engineering design is usually a daunting optimization task which often involving time-consuming, even computation-prohibitive process. Variable fidelity metamodeling has been developed as an efficient approach to alleviate this issue, owing to its capacity of achieving accurate metamodels within limited sample size. An output mapping modeling method is proposed in this paper as an alternative variable fidelity metamodeling method in which the low fidelity outputs is directly mapped to the high fidelity outputs through least square support vector regression. Furthermore, a nested Latin hypercube design method is developed for the output mapping modeling, in which a simple sampling design is treated as a building block or DOE seed to be translated and propagated through the design space, resulting in a final sampling configuration. Effectiveness of the proposed method are demonstrated by several numerical functions and two engineering design problem, in which different sample sizes, predictive accuracies and robustness are considered.

Designing a drive train for an industrial robot is a demanding task where a set of design variables need to be determined so that optimal performance is obtained for a wide range of different duty cycles. The paper presents a method where singular value decomposition (SVD) is used to reduce the design variable set. The application is a six degree of freedom serial manipulator, with nine drive train parameters for each axis and the objective is to minimize the cycle time on 122 representative design cycles without decreasing the expected lifetime of the robot. The optimization is based on a simulation model of the robot and conducted on a reduced set of the initial duty cycles and with the design variables suggested by the SVD analysis. The obtained design reduces the cycle time with 1.6% on the original design cycles without decreasing the life time of the robot.

Size optimization of MEMS gyroscopes using substructuring

This paper deals with joint penalization and material selection in frame topology optimization. The models used in this study are frame structures with flexible joints. The problem considered is to find the frame design which fulfills a stiffness requirement at the lowest structural weight. To support topological change of joints, each joint is modelled as a set of subelements. A set of design variables are applied to each beam and joint subelement. Two kinds of design variables are used. One of these variables is an area-type design variable used to control the global element size and support a topology change. The other variables are length ratio variables controlling the cross section of beams and internal stiffness properties of the joints. This paper presents two extensions to classical frame topology optimization. Firstly, penalization of structural joints is presented. This introduces the possibility of finding a topology with less complexity in terms of the number of beam connections. Secondly, a material interpolation scheme is introduced to support mixed material design.

In this paper we develop an as-yet-missing theoretical framework as well as a general methodology for model-based robust design. At the outset, a distinction is made between three sets: the set of design variables, grouped in the n-dimensional vector x, which are to be assigned values as an outcome of the design job; the set of design-environment parameters (DEP), grouped in the v-dimensional vector p, over which the designer has no control; and the set of performance functions, arrayed in the m-dimensional vector f, representing the functional relations among performance, design variables and DEP. Resorting to the mathematical model available for the object under design, an m × v design performance matrix F, mapping the space of relative variations of p into that of relative variations of f, is derived. Moreover, two pertinent concepts are introduced: the design sensitivity matrix, which plays a major role in the transmission of the variations of p into variations off, and its associated bandwidth, defined as the logarithm of the square root of the ratio between the maximum to the minimum singular values of the design performance matrix, measured in decades. A result stating the relation between the bandwidth of a matrix and its inverse is shown. Consequently, the aforementioned bandwidth represents an index for evaluating the robustness of a design. To demonstrate our approach, case studies are included

Discussion of this paper is invited. Three copies of any discussion should be sent to the Society of Petroleum Engineers office. Such discussion may be presented at the above meeting and, with the paper, may be considered for publication in one of the two SPE magazines. Abstract This paper explains how 9 5/8" turbine diamond bit designs for the North Sea were optimized through the combined results of practical field developments and analytical practical field developments and analytical design studies. Various mechanical characteristics such as bit face contour, diamond size, and diamond pattern were analyzed with the aid of the diamond drilling theory, taking into account the particular conditions encountered in North Sea drilling. The mathematical model for rotary and turbine diamond drilling as used in this study was developed during recent years, and is now considered an effective aid to design optimization. The drilling theory is based on previously reported studies on the cutting actions of single diamonds in rocks, now expanded to encompass the total effect of all diamonds on the cutting surfaces of the bit. Using specific drilling conditions and rock properties, expressions for bit torque, properties, expressions for bit torque, penetration rate, rotary power and other penetration rate, rotary power and other performance characteristics are obtained in performance characteristics are obtained in terms of bit weight, rotary speed and the design parameters, like diamond size, fluid handling characteristics and geometric factors. The evolution of the bit designs leads to a bit style which, within the known limitations on diamonds, has best theoretical performance and best field performance. Introduction In view of the expanding use and importance of turbo diamond drilling techniques, particularly in modern offshore development, particularly in modern offshore development, it is important to study the way in which diamond bits work under the specific conditions imposed by turbines, and to use this knowledge to improve the performance of the diamond tools. In this study, several practical turbo diamond bit design approaches are practical turbo diamond bit design approaches are studied analytically in an effort to isolate the best performing or "optimum" combination of bit design variables. The goal of optimization is to find the particular set of design variables which yields the highest penetration rate under the selected operating conditions, without violating any of the assumed practical limitations on loading and application of the diamonds, the diamond bits and the turbines.

Aircraft manufacturing companies have to consider multiple derivatives to satisfy various market requirements. They modify or extend an existing aircraft to meet new market demands while keeping the development time and cost to a minimum. Many researchers have studied the derivative design process, but these research efforts consider baseline and derivative designs together, while using the whole set of design variables. Therefore, an efficient process that can reduce cost and time for aircraft derivative design is needed. In this research, a more efficient design process is proposed which obtains global changes from local changes in aircraft design in order to develop aircraft derivatives efficiently. Sensitivity analysis was introduced to remove unnecessary design variables that have a low impact on the objective function. This prevented wasting computational effort and time on low priority variables for design requirements and objectives. Additionally, uncertainty from the fidelity of analysis tools was considered in design optimization to increase the probability of optimization results. The Reliability Based Design Optimization (RBDO) and Possibility Based Design Optimization (PBDO) methods were proposed to handle the uncertainty in aircraft conceptual design optimization. In this paper, Collaborative Optimization (CO) based framework with RBDO and PBDO was implemented to consider uncertainty. The proposed method was applied for civil jet aircraft derivative design that increases cruise range and the number of passengers. The proposed process provided deterministic design optimization, RBDO, and PBDO results for given requirements.

This study proposes a decision-making support method for designers by evaluating the characteristics of design spaces narrowed down through set-based design (SBD) in the early design stages, where uncertainty in design information is high. Specifically, diverse subspaces (i.e., solution ranges) are extracted from the initial broad design space using the SBD approach. Each subspace is evaluated using four metrics: region size, constraint satisfaction rate, independence among design variables, and designer preference with respect to performance variables. By presenting these evaluation results, the proposed method supports designers in identifying and configuring subspaces that reflect their design intent.

This paper introduces an Enhanced Seasons Optimization (ESO) algorithm that significantly enhances the search performance and solution quality of the standard Seasons Optimization (SO) algorithm. The SO shows promising results for numerical and engineering optimization tasks, but has weaknesses in balancing exploitation and exploration, resulting in suboptimal solutions and premature convergence. To address these limitations, the ESO incorporates four key innovations: (i) a root spreading operator which enhances local exploitation, (ii) a wildfire operator that enhances the diversity of population, (iii) refined competition and resistance operators that strengthen solution quality and convergence performance, and (iv) opposition-based learning to avoid local optimums. The effectiveness of the ESO algorithm is examined through a comparative analysis against a diverse set of counterpart optimizers, including foundational and highly cited algorithms (PSO, DE), top-performing algorithms (CMAES, LSHES, RRTO, ALA, THRO), and novel nature-inspired algorithms (SO, HO, CBKA). The set of benchmarks comprises 25 numerical optimization functions and 4 engineering design problems. Statistical results demonstrate that the ESO significantly outperforms the original SO algorithm and exhibits competitive or superior performance compared to the counterpart optimizers regarding convergence performance and solution quality. Our key findings include: (i) ESO is the top-performing algorithm in 16 out of 25 of the numerical functions and 3 out of 4 engineering design problems; (ii) it achieved an average ranking of 3.68 in the Friedman test on all numerical benchmarks, outperforming all counterpart algorithms in solving numerical benchmarks; Meanwhile, the second-ranked THRO algorithm attains the average ranking of 4.5 on all functions; (iii) ESO generated the best results in shifted and composite numerical functions, and (iv) it obtained the best performance in the scalability analysis test on 1000-dimensional numerical problems.

Our goal in this work is to develop analytical tools to support the definition of balanced and compatible sets of vehicle specifications in the early stages of vehicle development. In this paper, we discuss the development and application of a Technical Feasibility Model (TFM) that may be used in preliminary design to assess the technical feasibility and optimality of specified combinations of vehicle performance targets. For this paper, we have exercised the TFM specifically to explore the relationships between vehicle mass, vehicle performance measures, (such as acceleration, fuel efficiency, and interior roominess), and high-level vehicle design parameters (such as overall exterior dimensions, occupant positions, and selection of a powertrain). The TFM is developed by first applying a MultiObjective Genetic Algorithm to a multidisciplinary design framework to generate a set of Pareto-optimal design solutions, then applying response surface methods to generate a smooth mathematical representation of the Pareto set, and finally using geometric construction to analyze the position of a test point relative to the representation of the Pareto set. Results of this analysis include an assessment of the feasibility and optimality of the test point as well as a variety of projections from the test point to the representation of the Pareto set that may be used to identify opportunities for refining, relaxing, improving, or prioritizing performance specifications. The mapping between performance space and design space has been preserved, allowing for investigation of relationships between performance specifications and design variable settings.