An evolutionary approach for worst-case tolerance design

A sliding-level orthogonal differential evolution algorithm with a two-level orthogonal array (SLODEA2OA) is proposed for solving worst-case tolerance design problems. Tolerance affects system performance and leads to violate design constraints. By including a two-level orthogonal array, the proposed SLODEA2OA obtains robust optimal solutions that minimize the impact of parameter variations and that maintain compliance with a comprehensive constraint set. Two design examples are used for performance evaluation of the SLODEA2OA. The first is a 10-variable function, which includes linear, non-linear, quadratic, and polynomial forms to illustrate its general robustness and computational efficiency. The second example is a speed reducer design that involves seven variables and multiple non-linear engineering constraints. The SLODEA2OA is also compared with sliding-level orthogonal differential evolution algorithms with either three-level orthogonal array or two-level full-factorial design. Additionally, performance comparisons confirm that the proposed SLODEA2OA outperforms nature-inspired methods presented in the literature.     

A random set approach to the optimization of uncertain structures

The single-objective optimization of structures, whose parameters are assigned as fuzzy numbers or fuzzy relations, is presented in this paper as a particular case of the random set theory and evidence theory approach to uncertainty. Some basic concepts concerning these theories are reviewed and the relationships among interval analysis, convex modeling, possibility theory and probability theory are pointed out. In this context a frequentistic view of fuzzy sets makes sense and it is possible to calculate bounds on the probability that the solution satisfies the constraints. Some special but useful cases illustrate in detail the meaning of the approach proposed and its links with a recent formulation conceived within the context of convex modeling. Some theorems allow a very efficient computational procedure to be set up in many real design situations. Two numerical examples illustrate the model presented.     

A modern approach to sampling plan design and evaluation

This paper describes an interactively programmed computer tool with wide ranging capability for sampling plan design and evaluation. Developed under sponsorship of the National Science Foundation, this tool is useful in sampling plan optimization, evaluation, and simulation of inspection activities. It has both a statistical and an economic base, and can also consider perfect or imperfect inspection. It is meant to be used for actual sampling plan design and evaluation and/or training of industrial quality control engineers, as well as for classroom use in an academic setting.     

A new approach to optimal design of elastic structures

A new approach to the optimization of elastic trusses under stress constraints is discussed. The stress constraints are transformed into compliance constraints, which makes possible the derivation of a simple optimality condition. The condition provides a simple test to check whether a fully stressed design is optimal, for single as well as multiple loading conditions. It is readily extended to optimization problems, in which both stress and displacement constraints are imposed. An iterative routine, that is both simple and efficient, is derived from the optimality condition. Numerical examples of the application of the routine are presented.     

Optimum design of structures with random parameters

A general formulation of the minimum-weight optimization problem for indeterminate structures with random parameters is presented. The formulation enables the designer to specify maximum allowable probability of system failure and maximum allowable probabilities of occurrence of individual failure modes. All random parameters are characterized by their mean values and coefficients of variation, with the latter assumed to be amenable to realistic estimation at the outset. The standard deviations of response quantities are then obtained in a straightforward manner for use in the constraint equations, which generally resemble those for deterministic optimization problems. Several examples of truss and frame designs illustrate applications of the formulation.     

Reliability-based design optimization applied to structures submitted to random fatigue loads

Structural and Multidisciplinary Optimization - The reliability-based design optimization (RBDO) aims to find the most balanced design through a compromise between cost and safety when...     

A fuzzy compromise approach for solving multi-objective stratified sampling design

Neural Computing and Applications - In this paper, we established a framework for finding out the optimal allocation in the multivariate stratified sample using the fuzzy compromise method. The...     

Minimum weight design of structures with random parameters

A general formulation of the minimum-weight optimization problem is presented in the paper. Formulation of the problem is based on the concept of the expected value. Solution of the corresponding mathematical programming problem has been obtained by means of indirect method. To evaluate the magnitude of the influence of random character of the structure parameters two numerical examples concerning plane truss and free vibrating plane strain structure are presented.     

Efficient worst-case data structures for range searching

In this paper we investigate the worst-case complexity of range searching: preprocess N points in k-space such that range queries can be answered quickly. A range query asks for all points with each coordinate in some range of values, and arises in many problems in statistics and data bases. We develop three different structures for range searching in this paper. The first structure has absolutely optimal query time (which we prove), but has very high preprocessing and storage costs. The second structure we present has logarithmic query time and O(N ¹⁺²) preprocessing and storage costs, for any fixed >0. Finally we give a structure with linear storage, O(N ln N) preprocessing and O(N ) query time.Research in this paper has been supported partially under Office of Naval Research contract N000014-76-C-0373, USA, and by the Austrian Federal Ministry for Science and Research     

Automated optimum design of wing structures: A probabilistic approach

The optimization of aircraft wing structures is presented by considering the dynamic stresses developed during landing impact and gust load conditions. The random nature of the sinking speed and the forward velocity at the instant of contact is considered in the calculation of landing stresses. The vertical velocity due to gust is treated as a stochastic process for the computation of gust-induced stresses. The optimum designs of a symmetric double wedge airfoil, based on beam type of analysis, and a supersonic airplane wing, based on finite element analysis, are considered to illustrate the procedure. A graphical procedure is used in the case of the double wedge airfoil, and nonlinear programming techniques are used in the case of the supersonic wing, for finding the optimum solutions.     

A variational inequality approach to optimal plastic design of structures via the Prager-Rozvany theory

The theory of optimal plastic design of structures via optimality criteria (W. Prager approach) transforms the optimal design problem into a certain nonlinear elastic structural analysis problem with appropriate stress-strain laws, which are derived by the adopted specific cost function for the members of the structure and which generally have complete vertical branches. Moreover, the concept of structural universe (introduced by G.I.N. Rozvany) permits us to tackle complicated optimal layout problems.On the other hand, a significant effort in the field of nonsmooth mechanics has recently been devoted to the solution of structural analysis problems with complete material and boundary laws, e.g. stress-strain laws or reaction-displacement laws with vertical branches.In this paper, the problem of optimal plastic design and layout of structures following the approach of Prager-Rozvany is revised within the framework of recent progress in the area of nonsmooth structural analysis and it is treated by means of techniques primarily developed for the solution of inequality mechanics problems. The problem of the optimal layout of trusses is used here as a model problem. The introduction of general convex, continuous and piecewise linear specific cost functions for the structural members leads to the formulation of linear variational inequalities or equivalent piecewise linear, convex but nonsmooth optimization problems. An algorithm exploiting the particular structure of the minimization problem is then described for the numerical solution. Thus, practical structural optimization problems of large size can be treated. Finally, numerical examples illustrate the applicability and the advantages of the method.On leave from the Institute of Applied Mechanics, Department of Engineering Sciences, Technical University of Crete, GR-73100 Chania, Greece     

A graph mining approach for detecting identical design structures in object-oriented design models

The object-oriented approach has been the most popular software design methodology for the past twenty-five years. Several design patterns and principles are defined to improve the design quality of object-oriented software systems. In addition, designers can use unique design motifs that are designed for the specific application domains. Another commonly used technique is cloning and modifying some parts of the software while creating new modules. Therefore, object-oriented programs can include many identical design structures. This work proposes a sub-graph mining-based approach for detecting identical design structures in object-oriented systems. By identifying and analyzing these structures, we can obtain useful information about the design, such as commonly-used design patterns, most frequent design defects, domain-specific patterns, and reused design clones, which could help developers to improve their knowledge about the software architecture. Furthermore, problematic parts of frequent identical design structures are appropriate refactoring opportunities because they affect multiple areas of the architecture. Experiments with several open-source and industrial projects show that we can successfully find many identical design structures within a project (intra-project) and between different projects (inter-project). We observe that usually most of the detected identical structures are an implementation of common design patterns; however, we also detect various anti-patterns, domain-specific patterns, reused design parts and design-level clones.     

A fuzzy set approach to Retinex spray sampling

The color sensation at a point, for the Human Visual System (HVS), derives not only from the color stimulus at that point, but also from the relative spatial arrangement of the stimuli in the image. Based on this observation, the Retinex algorithm, an early and widely studied model of the HVS, determines the output – for each chromatic channel – by rescaling the input intensity of a pixel w.r.t. a reference white level, computed by sampling the brightest points in the neighborhood of the target pixel. In this work, we argue that several elements, inherent to the above observation, can benefit from a fuzzy formalization. We show that the adoption of the fuzzy formalism allows to better encode the mutual influence of pixels. Overall, the fuzzy formalization can provide a general framework for designing and tuning image enhancement algorithms inspired by the HVS. We demonstrate its use by the construction of a fuzzy version of the point-sampling algorithm Random Spray Retinex (RSR). Using RSR as a guide, we build a more efficient algorithm, based on the fact that each spray (a set of sampled points used in RSR to determine the reference white of a specific target) can be assumed to belong to some degree to all the target pixels of the image, provided that a suitable membership function is defined. The features of this alternative formalization of RSR are discussed here, using synthetic and natural test images.     

A self-training approach to cost sensitive uncertainty sampling

Uncertainty sampling is an effective method for performing active learning that is computationally efficient compared to other active learning methods such as loss-reduction methods. However, unlike loss-reduction methods, uncertainty sampling cannot minimize total misclassification costs when errors incur different costs. This paper introduces a method for performing cost-sensitive uncertainty sampling that makes use of self-training. We show that, even when misclassification costs are equal, this self-training approach results in faster reduction of loss as a function of number of points labeled and more reliable posterior probability estimates as compared to standard uncertainty sampling. We also show why other more naive methods of modifying uncertainty sampling to minimize total misclassification costs will not always work well.     

A knowledge-based approach to design

A framework is presented for constructing knowledge-based aids for design problems. In particular, we describe the organization of an interactive knowledge-based consultant for VLSI design (called VEXED?an acronym for VLSI expert editor), and a prototype implementation of VEXED. The paper focuses on the principles underlying the design of VEXED, and on several lessons and research issues that have arisen from implementing and experimenting with this prototype.     

A unified approach to the definition of random sequences

Using the concept of test functions, we develop a general framework within which many recent approaches to the definition of random sequences can be described. Using this concept we give some definitions of random sequences that are narrower than those proposed in the literature. We formulate an objection to some of these concepts of randomness. Using the notion of effective test function, we formulate a thesis on the true concept of randomness.     

A new approach to design safe-supported HDD against random excitation by using optimization of rubbers spatial parameters

Hard disk drives (HDDs) of laptop personal computers (LPCs) are devices vulnerable in harsh mechanical environments. Hence, they need to be protected against damages due to vibration in order to have better read/write performance. In the present study, a LPC and its HDD are modeled as a system with two degrees of freedom and the nonlinear optimization method is employed to perform a passive control through minimizing the root mean square of HDD absolute acceleration due to a base random excitation. The presented random excitation is considered as a stationary, zero mean process with Gaussian distribution. In addition, eleven inequality constraints are defined based on geometrical limitations and allowable intervals of lumped modal parameters. The target of the optimization is to obtain optimum modal parameters of rubber mounts and rubber feet as design variables and subsequently propose new characteristics of rubber mounts and rubber feet to be manufactured for HDD protection against random excitation. In this paper, a nonlinear optimization problem is separately solved for three widely-used cases of HDD by using modified constrained steepest descent algorithm (PLBA) which was extended based on sequential quadratic programming. Finally, the genetic algorithm is used to verify results of the PLBA algorithm.

     

Data-driven design approach to hierarchical hybrid structures with multiple lattice configurations

This work presents a data-driven design approach to hierarchical hybrid structures with multiple lattice configurations. Two design variables are considere     

Decoupled approach to integrated optimum design of structures and robust control systems

Integrated optimum design of structures and control systems is studied by using H ₂ and robust control formulations. It is derived that conventional simultaneous optimization approach by using these robust control laws can be approximated by a decoupled optimization approach in which the structures are optimized by shaping the structural singular values and then the controllers can be designed, namely, decoupled, sequential or successive design approach. It is shown that the proposed decoupled optimization approach can be used to design optimum robust structures and has certain advantages over the conventional simultaneous optimization procedures such as it avoids the drawbacks of pure robust control laws and faster, especially if the number of degrees of freedom (DOF) of the associated structure is large. The bounds for achievable robustness measures are also obtained. Following, simultaneous and decoupled optimization approaches are applied to active control of two structures. The optimization results are presented, and it is concluded that the proposed decoupled optimization approach yields the achieved global minimum much faster than the simultaneous optimization approach.