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In this work, four orthogonal composite designs (orthogonal-array composite designs (OACDs), orthogonal-array composite minimax-loss (OACM) designs, orthogonal uniform composite designs (OUCDs) and orthogonal uniform composite minimax-loss (OUCM) designs) for second-order models were evaluated in the presence of errors for 3 ≤ k ≤ 7 factors with 1 ≤ nc ≤ 3 center points. The design efficiency (in terms of D- and G-efficiency values) and fraction of design space (FDS) plots were used to evaluate the performance of these designs in the presence of errors. The results showed that in terms of D-efficiency values, OACDs and OUCDs performed poorly for k = 6 and 7 factors in the presence of errors while OACM designs were the best-performing designs. The OUCM designs outperformed all the other designs for G-efficiency values with OACM designs as the next best performing designs. The FDS plots showed that OACM and OUCM designs maintained high G-efficiency values in the presence of errors. [ABSTRACT FROM AUTHOR]

In this paper, the prediction variance capabilities of two new second-order designs orthogonal uniform composite designs and orthogonal array composite designs are examined using the variance dispersion graph and the fraction of design space plot in the spherical region. Also, the D- and G-optimality criteria are evaluated for these two response surface designs. The orthogonal array composite designs were shown to have a better prediction variance in terms of the fraction of design space plot and the variance dispersion graphs over the orthogonal uniform composite designs. [ABSTRACT FROM AUTHOR]

Most of the scientific and industrial experiments usually involve small number of factors, especially biomedical experiments and computer based experiments. We construct some highly useful designs for small number of factors. Designs are constructed using subsets of regular structure and the subsets based on irregular fractions. We compare the various designs on the basis of their robustness to missing design point under minimax loss criterion. To explore some other useful properties designs are also compared on the basis of common alphabetic optimalities. For the investigation of prediction capability of competing designs, we have constructed fraction of design space plots for the variance of difference of response. We observe that some uncommon designs reveal nicer qualities of a good design. It was interesting to see various choices of designs under different optimality criteria. Suggested designs can be highly useful for the experimenters to choose a plan possessing desirable qualities. [ABSTRACT FROM AUTHOR]

The possibility of constructing a multi-position direction finding system for the case of a priori uncertainty, based on the application of the principles of multiplication of single marks of the location of the emitting target (multistructure principle) and their subsequent partition into classes (clustering principle) is considered. The criteria and algorithms for detecting the resulting cluster and for constructing the optimal estimation of target location stable to anomalous measurement errors are presented, taking into account the time costs of their computer realization. Practical recommendations and results of comparative analysis of different algorithms are given. [ABSTRACT FROM AUTHOR]

Predator-prey models are often used in ecology to represent realistic encounters between species. Lotka-Volterra differential equations are famously used by ecologists to model the relationship between a predator and prey. Given ecological data collection is known to be time consuming and difficult, the purpose of this paper is to optimize the process and improve sampling efficiency. The method of sequential optimality is applied to a more complex population model with multiple basins of attraction, the Lotka-Volterra differential equations. In this application, various theoretical scenarios are simulated using varying sample sizes and timeframes to determine optimal designs. The first scenario uses a standard sample size and design window to represent a realistic budget for ecological data collection. The second scenario decreases the budget and extends the design window as a representation of a limited budget. The third scenario represents ample resources available for sampling. The three scenarios are used to then compare the optimal designs and help ecologists evaluate the method of sequential optimality. I, A and D optimal designs are compared in the simulation results. The I-optimality criterion tends to outperform the A and D criteria and is recommended as a primary selection when using the sequential optimality algorithm. This simulation study has further developed sequential optimality by predicting optimal sampling regimes according to the dynamics associated with the Lotka-Volterra differential equations. [ABSTRACT FROM AUTHOR]

Optimal designs provide the best experimental conditions, where the researcher should observe or measure a variable of interest. To find these designs, the assumption of uncorrelation in the model's error term is generally required, this allows to easily obtain the Fisher information matrix used in the optimization process for the search for the designs of interest. This article proposes a methodology to compare exact D-optimal designs when the assumption of uncorrelation of the error term in the model is not fulfilled and four covariance structures are taken into consideration to model it. A simplified expression of the Fisher’s information matrix is found for the general case of correlated observations and is used in the four considered covariance structures. With each covariance structure, the respective optimal design is found, known as the nominal design, and the robustness of the other optimal designs is evaluated by finding their efficiency in relation to the nominal design. It is concluded that the four optimal designs are competitive with respect to the other considered covariance structures, by observing a minimal loss of efficiency of each of these designs and showing that the optimal designs, at least with the considered covariance structures, are robust to the choice of the covariance structure. Additionally, it is shown, via simulation, that, with the optimal designs, under each covariance structure, good estimators are obtained for the model parameters when evaluating the magnitude of the coefficient of variation and the relative mean square error. [ABSTRACT FROM AUTHOR]

Variational inequalities provide us with a unified, natural, novel and simple framework to study a wide class of problems arising in pure and applied sciences. In this paper, we introduce and consider a new class of exponentially general variational inequalities. Some new iterative methods are proposed and analyzed using the auxiliary principle technique. Our results present a significant improvement of previously known results for solving variational inequalities and related optimization problems. Several open problems have been suggested for further research in these areas. [ABSTRACT FROM AUTHOR]

Sigmund's 2001 educational paper with a self-contained 99-line MATLAB code had far-reaching impact to teaching and research of topology optimization. This brief note aims to close the gaps on self-contained content desirable for classroom teaching. The goal is to add clarity to the theoretical foundation, and to enable students' learning of the complete iterative optimization solution with minimum additional effort. [ABSTRACT FROM AUTHOR]

In this paper, we study the quantum-state estimation problem in the framework of optimal design of experiments. We first find the optimal designs about arbitrary qubit models for popular optimality criteria such as A -, D -, and E -optimal designs. We also give the one-parameter family of optimality criteria which includes these criteria. We then extend a classical result in the design problem, the Kiefer–Wolfowitz theorem, to a qubit system showing the D -optimal design which is equivalent to a certain type of the A -optimal design. We next compare and analyze several optimal designs based on the efficiency. We explicitly demonstrate that an optimal design for a certain criterion can be highly inefficient for other optimality criteria. [ABSTRACT FROM AUTHOR]

In structural optimization, one of the most fascinating fields is Topological Optimization (TO). In this article, the evolutionary topological optimization methods Smoothing Evolutionary Structural Optimization (SESO) and Sequential Element Rejection and Admission (SERA) are used to minimize the growth of compliance using the Method of Moving Asymptotes (MMA). The effect of changing asymptotes is to control the generation of subproblems, which can both stabilize and accelerate the convergence of the overall process. The three-dimensional topological optimization of two large-scale problems: a) a cantilever beam with distributed load, b) an MBB beam and c) a cantilever with concentrated load is performed. Therefore, to solve computational problems such as cost and excess memory, which occur in these types of problems, the Preconditioned Conjugated Gradient Method (PCG) is used as an iterative solver. The results obtained are compared with the Solid Isotropic Material with Penalization (SIMP) that uses for convergence the Optimality Criteria (OC). [ABSTRACT FROM AUTHOR]

The problem of subsample selection among an enormous number of combinations arises when some covariates are available for all units, but the response can be measured only for a subset of them. When estimating a Bayesian prediction model, optimized selections can be more efficient than random sampling. The work is motivated by environmental management of aquatic systems. We consider data on 4360 Finnish lakes and aim to find an approximately optimal subsample of lakes in the sense of Bayesian D-optimality. We study Bayesian two-stage selection where the choice of lakes to be measured at the second stage depends on the measurements carried out at the first stage. The results indicate that the two-stage approach has a modest advantage compared to the single-stage approach. [ABSTRACT FROM AUTHOR]

In this study, the method of inscribed hyperspheres (IHS) is presented and applied for the optimal design of 2-D steel moment frame structures. The weight of the structures, which is a function of the design variables (cross-sectional areas), is optimized subject to stress, displacement, size limits, and the variables' linkage constraints. The IHS approach is employed to find the acceptable centers. The basic idea of this method is to inscribe the largest possible sphere in a closed space that has been created by the objective function and linearized constraints in each step. The obtained results were presented in discrete and continuous variables and compared to the results reported in the literature. This comparison showed the efficiency of this method. Also, a new mixed method of combining the optimality criteria (OC) method and the IHS method is presented in this study. It was observed that the number of iterations needed to reach the optimal solution using this new method is less than that of the above two methods when used individually, and the problem is converged to the optimal answer with extremely low iterations. [ABSTRACT FROM AUTHOR]

We present a 250-line Matlab code for topology optimization for linearized buckling criteria. The code is conceived to handle stiffness, volume and buckling load factors (BLFs) either as the objective function or as constraints. We use the Kreisselmeier-Steinhauser aggregation function in order to reduce multiple objectives (viz. constraints) to a single, differentiable one. Then, the problem is sequentially approximated by using MMA-like expansions and an OC-like scheme is tailored to update the variables. The inspection of the stress stiffness matrix leads to a vectorized implementation for its efficient construction and for the sensitivity analysis of the BLFs. This, coupled with the efficiency improvements already presented by Ferrari and Sigmund (Struct Multidiscip Optim 62:2211–2228, 2020a), cuts all the computational bottlenecks associated with setting up the buckling analysis and allows buckling topology optimization problems of an interesting size to be solved on a laptop. The efficiency and flexibility of the code are demonstrated over a few structural design examples and some ideas are given for possible extensions. [ABSTRACT FROM AUTHOR]

In this work, interval programming problems are considered for financial investment and optimality criteria. An order relation, defined by Ishibuchi and Tanaka for maximization problems, is used to obtain the solution of the problems. A real-life example, related to investment, and its solution are given. Necessary and sufficient optimality criteria including weak and strongly solution for interval programming problems are introduced via basic calculus rule, scalarization, and vectorization. [ABSTRACT FROM AUTHOR]

Measures of the prediction variance performances of three variations of central composite designs when the region is hypercube were examined and compared using the G-efficiency and I-optimality criterion so as to determine the economical design(s) that perform(s) better than the other. The hypercube is the multidimensional cuboidal region with the axial distance, α = 1.0 . The designs are the standard central composite designs (CCD), the small composite design (SCD) and minimum run resolution V (minResV) design. Two prediction variance based optimality criteria, I-optimality and G-efficiency were determined, a plot of variance dispersion graph and fraction of design space are used to give a comprehensive picture of the behavior of the prediction variance throughout the region of interest. Comparing the three designs mentioned above for 3, 4, and 5 factors on cuboidal region, the result showed that CCD performed better than SCD and MinResVdesign considering 2, 3, and 5 center points. [ABSTRACT FROM AUTHOR]

In topology optimization, the bisection method is typically used for computing the Lagrange multiplier associated with a constraint. While this method is simple to implement, it leads to oscillations in the objective and could possibly result in constraint failure if proper scaling is not applied. In this paper, we revisit an alternate and direct method to overcome these limitations. The direct method of Lagrange multiplier computation was popular in the 1970s and 1980s but was later replaced by the simpler bisection method. In this paper, we show that the direct method can be generalized to a variety of linear and nonlinear constraints. Then, through a series of benchmark problems, we demonstrate several advantages of the direct method over the bisection method including (1) fewer and faster update iterations, (2) smoother and robust convergence, and (3) insensitivity to material and force parameters. Finally, to illustrate the implementation of the direct method, drop-in replacements to the bisection method are provided for popular Matlab-based topology optimization codes. [ABSTRACT FROM AUTHOR]

Considerable academic research has been conducted on truss design optimization by standard metaheuristic methods; however, the generic nature of these methods becomes inefficient for problems with many decision variables. This may explain the simplicity of the relevant test problems in the academic literature in comparison with real structures. To address this challenge, this study advocates a customized optimization methodology which utilizes problem-specific knowledge. It improves upon a new bilevel truss optimization method to allow for an arbitrary trade-off between the stochastic upper level and the deterministic lower level search. Numerical simulations demonstrate that for large-scale truss design problems, the proposed method can find significantly lighter structures up to 300 times more quickly than the best existing metaheuristic methods. The remarkable findings of this study demonstrate the importance of using engineering knowledge and discourage future research on the development of purely metaheuristic methods for truss optimization. [ABSTRACT FROM AUTHOR]

Technological assurance and improvement of the economic efficiency of production are the first-priority issues for the modern manufacturing engineering area. It is possible to achieve a higher value of economic efficiency in multiproduct manufacturing by multicriteria optimization. A set of optimality criteria based on technological and economic indicators was defined with the aim of selecting the optimal manufacturing process. Competitive variants and a system of optimization were developed and investigated. A comparative analysis of the optimality criteria and their influence on the choice of optimal machining processes was carried out. It was determined that the batch of parts made an impact on the selection of the manufacturing process. [ABSTRACT FROM AUTHOR]

In this work, set-valued optimization problems are considered according to an order relation, which is a partial order on the family such that contains nonempty bounded sets of the space. A generalized convexity is defined for set-valued mapping by using the partial order relation. Nonsmooth variational inequality problems are introduced with the aid of M-directionally derivative. Some optimality criteria including the necessary and sufficient optimality conditions are obtained for mentioned optimization problems. [ABSTRACT FROM AUTHOR]

• An Optimality Criteria method was proposed for the wind resistant structural optimization of a portal steel frame. • The GLF based, single objective LRC-based and multiple objective universal-based ESWLs were derived for the large-span portal frame. • The effect of different forms of ESWLs, the stiffness of support restraint and semi-rigid connection on the optimized results were analyzed. • The optimized section heights of rafters and columns for minimum structural weight were obtained under wind-induced drift constraint. Large span portal-rigid frames with tapered sections in low-rise metal building system are often used in industrial and commercial buildings. The drift of such portal-rigid frames induced by the wind load needs to be smaller than a prescribed limit, and at the same time the frames should be as light as possible for cost-effectiveness. To this end, structural optimization of such portal-rigid frames subjected to the wind-induced drift constraint is required. However, little research for optimization of the large span portal-rigid frame with tapered sections has been reported. This paper proposed a procedure for structural optimization of such portal-rigid frames by adopting the Optimality Criteria (OC) method. Based on an aerodynamic database of the measured wind pressure from a wind tunnel test, several forms of the Equivalent Static Wind Load (ESWL) acting on a large-span portal-rigid frame were evaluated by the Gust Loading Factor (GLF), Load Response Correlation (LRC) and Proper Orthogonal Decomposition (POD) method. The method of virtual-work was utilized to construct the wind-induced drift or displacement. An effective iteration algorithm was derived for the minimum weight optimization of the frame while all wind-induced drift constraints were satisfied. The wind resistant structural optimization for the large-span rigid frame with taped section were conducted when it was bore by different forms of ESWL (GLF based, single objective and multiple objective ESWLs), and their optimized results were multi-compared in the form of the optimized total weight and the height of the optimized structural members. The effects of the connection stiffness at semi-rigid joints and the stiffness of support restraints on the optimized results are also investigated. Finally the global optimality property of the proposed OC method adopted for the optimized case in this paper was also discussed and verified. Optimized results show that the OC optimization procedure proposed in this paper is very effective for the optimization design of large-span portal-rigid steel frames with tapered sections under wind-induced drift constraints. [ABSTRACT FROM AUTHOR]

In probabilistic robust optimization problems we generally take as objective function the weighted sum of the expected value and the standard deviation of the performance. Unfortunately, it has been observed that if the weight given to the standard deviation is too high, then the designs obtained may have no physical meaning at all. If this occurs we say that the design obtained is not consistent from the physical point of view. In this work we present a probabilistic robust optimization approach aimed to preserve physical consistency of the problem being addressed. The objective function is written as the p -norm of a vector composed of the expected value and the weighted standard deviation. We then demonstrate that the standard approach is a particular case of this p -norm approach with p = 1. In the proposed approach we take p = 2 and prove that physical consistency is ensured provided the standard deviation is not given more weight than the expected value. A similar proof is not available for the standard approach. This makes statement of the robust optimization problem much easier with the proposed approach. The proposed approach can be adapted into existing computational routines, since the same statistical moments and sensitivities are required. The theoretical results are illustrated in the context of compliance-based topology optimization. In the numerical examples we show that the concept of physical consistency may have a significant impact on the designs obtained. • A discussion on physical consistency of robust optimization is presented. • An approach that is always consistent is proposed. • Theoretical results are illustrated in the context of compliance-based topology optimization. [ABSTRACT FROM AUTHOR]

This study developed a new framework by correlating the clinical measurements in vivo with numerical modeling in silico at different time points for quantifying the magnitudes and directions of oral muscle forces. The human masticatory system has received significant attention in the areas of biomechanics due to its sophisticated co-activation of a group of masticatory muscles which contribute to the fundamental oral functions. However, determination of each muscular force remains fairly challenging in vivo ; the conventional data available may be inapplicable to patients who experience major oral interventions such as maxillofacial reconstruction, in which the resultant unsymmetrical anatomical structure invokes a more complex stomatognathic functioning system. Therefore, this study aimed to (1) establish an inverse identification procedure by incorporating the sequential Kriging optimization (SKO) algorithm, coupled with the patient-specific finite element analysis (FEA) in silico and occlusal force measurements at different time points over a course of rehabilitation in vivo ; and (2) evaluate muscular functionality for a patient with mandibular reconstruction using a fibula free flap (FFF) procedure. The results from this study proved the hypothesis that the proposed method is of certain statistical advantage of utilizing occlusal force measurements, compared to the traditionally adopted optimality criteria approaches that are basically driven by minimizing the energy consumption of muscle systems engaged. Therefore, it is speculated that mastication may not be optimally controlled, in particular for maxillofacially reconstructed patients. For the abnormal muscular system in the patient with orofacial reconstruction, the study shows that in general, the magnitude of muscle forces fluctuates over the 28-month rehabilitation period regardless of the decreasing trend of the maximum muscular capacity. Such finding implies that the reduction of the masticatory muscle activities on the resection side might lead to non-physiological oral biomechanical responses, which can change the muscular activities for stabilizing the reconstructed mandible. [ABSTRACT FROM AUTHOR]

Inferential sensing is a cost-effective and reliable approach to replace expensive and impractical hardware sensing, while yielding robust fault detection and isolation (FDI) during system maintenance or operation. Yet, their high computational footprint necessitates the employment of advanced and efficient estimation techniques, along with symbolic mathematics and automatic differentiation. Herein, we attempt to combine model-driven sensor selection methods with inferential sensing to accurately identify faults in the presence of system noise and uncertainty. During sensor selection, we employ criteria from information theory to maximize the estimability of system faults from available system measurements. The most informative sensor set stems from a comparison of all possible sensor suites via information theoretic criteria expressed as functions of the Fisher Information Matrix. Optimal inferential sensors are calculated through a novel fusion of symbolic regression and information theory. For built-in test deployment, we utilize k -Nearest Neighbors classification to assess the capability of each sensor suite for all plausible instantiations of uncertainty and system noise, and evaluate FDI performance benefits from the inclusion of inferential sensor(s). The proposed computational framework is deployed with steady-state and dynamic models of a cross-flow plate-fin heat exchanger, at varying levels of measurement noise and uncertainty. As shown, the augmented system of composite sensors (i.e., inferential and hardware) provides accurate information on system fault(s) and reduces the evidence of uncertainty. Compared to traditional sensor approaches, the proposed techniques are shown to be more precise while simultaneously granting increased insight into details otherwise hidden by noise. Thus, they form a robust and reliable tool when conducting fault diagnosis and possibly toward system safety. • Fault identification from symbolically regressed inferential sensors. • Explainable inferential sensors derived with information-theoretic objective functions. • Inferential sensors are robust to system uncertainty and noise. • Symbolically regressed sensors provide better fault classification. [ABSTRACT FROM AUTHOR]

Numerical optimization is an indispensable part of the design process of laminated composite structures. Several optimality criteria-based algorithms exist which rely on a sequential resizing and scaling approach. This paper presents a novel design algorithm applicable for stiffness and eigenfrequency optimization of composite structures with concurrent consideration of resizing and scaling operations. A method is introduced that allows for an efficient consideration of nonlinear constraints. This is done by determining stable concurrent scaling parameters from first-order constraint change ratio estimations. Optimization is carried out using optimality criteria in three independent steps, namely with respect to fiber angles, ply thickness ratios, and total laminate thickness. Sensitivity analyses are performed analytically at low computational costs. Numerical examples demonstrate the efficiency and fast convergence of the method. Compared to established algorithms, the number of required function evaluations is reduced significantly. [ABSTRACT FROM AUTHOR]

This paper presents an evolutionary approach for the Robust Topology Optimization (RTO) of continuum structures under loading and material uncertainties. The method is based on an optimality criterion obtained from the stochastic linear elasticity problem in its weak form. The smooth structural topology is determined implicitly by an iso-value of the optimality criterion field. This iso-value is updated using an iterative approach to reach the solution of the RTO problem. The proposal permits to model the uncertainty using random variables with different probability distributions as well as random fields. The computational burden, due to the high dimension of the random field approximation, is efficiently addressed using anisotropic sparse grid stochastic collocation methods. The numerical results show the ability of the proposal to provide smooth and clearly defined structural boundaries. Such results also show that the method provides structural designs satisfying a trade-off between conflicting objectives in the RTO problem. [ABSTRACT FROM AUTHOR]

The popularity of precast concrete in construction is rising due to its capacity for improving building efficiency and quality in comparison to cast-in-situ concrete. While researchers have focused on enhancing constructability factors like logistics and sequencing, the need for developing standardization in this area remains evident. This paper describes a framework for studying the relationship between construction cost and standardization by optimizing precast component dimensions and rebar designs. The framework involves using Building Information Modeling techniques to extract semantic information from architectural plans, followed by a gradient-based Optimality Criteria method to optimize the sizing variables of precast components. Finally, a hybrid approach called NSGA-II-GD, which combines the Non-dominated Sorting Genetic Algorithm II and Great Deluge Algorithm, is used to optimize the rebar layout design of each precast component. The Results demonstrate that an optimal point exists between construction cost and standardization, particularly for components subjected to similar stresses. Additionally, the NSGA-II-GD algorithm improves the searching efficiency in terms of convergence, computational time, and searching space. • Develop a BIM-based framework for structural design optimization of precast elements. • Formulate the design optimization of construction cost and constructability of precast elements. • Integrate the Optimality Criteria method with NSGA-II-GD for element sizing and rebar detailing optimization. • Integrate NSGA-II with the Great Deluge Algorithm for rebar detailing optimization. • Show that the proposed method can identify the best trade-off for the precast building design. [ABSTRACT FROM AUTHOR]

We present a topology optimization based procedure aiming at the optimal placement (and design) of the supports in problems characterized by a time dependent construction process. More precisely, we focus on the solution of a time-dependent minimal compliance problem based on the classical Solid Isotropic Material with Penalization (SIMP) method. In particular, a continuous optimization problem with the state equation defined as the time-integral of a linear elasticity problem on a space-time domain is firstly introduced and the mean compliance over a time interval objective functional is then selected as objective function. The optimality conditions are derived and a fixed-point algorithm is introduced for the iterative computation of the optimal solution. Numerical examples showing the differences between a standard SIMP method, which only optimizes the shape at the final time, and the proposed time-dependent approach are presented and discussed. [ABSTRACT FROM AUTHOR]

A topology optimization approach based on the boundary element method (BEM) and the optimality criteria (OC) method is proposed for the optimal design of sound absorbing material distribution within sound barrier structures. The acoustical effect of the absorbing material is simplified as the acoustical impedance boundary condition. Based on the solid isotropic material with penalization (SIMP) method, a topology optimization model is established by selecting the densities of absorbing material elements as design variables, volumes of absorbing material as constraints, and the minimization of sound pressure at reference surface as design objective. A smoothed Heaviside-like function is proposed to help the SIMP method to obtain a clear 0-1 distribution. The BEM is applied for acoustic analysis and the sensitivities with respect to design variables are obtained by the direct differentiation method. The Burton-Miller formulation is used to overcome the fictitious eigen-frequency problem for exterior boundary-value problems. A relaxed form of OC is used for solving the optimization problem to find the optimal absorbing material distribution. Numerical tests are provided to illustrate the application of the optimization procedure for 2D sound barriers. Results show that the optimal distribution of the sound absorbing material is strongly frequency dependent, and performing an optimization in a frequency band is generally needed. [ABSTRACT FROM AUTHOR]

The subject of the paper is to investigate a new way for avoiding the development of checkerboard patterns in structural topology optimization, using an additional in-plane rotational freedom. The efficiency of a few, from the many existing formulations, with differing complexity are put into comparison, such as the standard 4 noded bilinear element, the Allman-type solution, the shell element from SAP2000 and finally an element constructed on the basis of micropolar theory. Since the emergence of checkerboarded regions is a general phenomenon, the optimization problem is as simple as possible, being a weight minimization with a compliance constraint, solved with the optimality criteria method and a FEM discretization of the design domain. [ABSTRACT FROM AUTHOR]

For optimal design most parameters may be classified in size, shape, and topology, such as simple density variables and parameters for surface description. Density and surface can be rather directly visualized. Extending the design to material design in sense of design of distributions of constitutive matrices, a practical visualization is more complicated but may be based on classical laminate analysis. In rotational transformation of constitutive matrices, some practical quantities are often termed invariants, but the invariance relates to an unchanged reference direction. Rotating this reference direction, the practical quantities do change and this point is clarified with derived rotational transformation for these practical quantities. The theoretical and numerical background for design of optimal anisotropic constitutive matrices are presented. Then design results are applied in a 2D visualization of optimized constitutive matrices that are distributed in a finite element model where each element has a specific reference direction. The visualized distributions of physical quantities are stiffest material direction, material stiffest longitudinal constitutive component, level of anisotropy, absolute or relative shear stiffness, and test of orthotropy. [ABSTRACT FROM AUTHOR]

Many industrial experiments involve random factors. The random blocks model defines a covariance structure in the data, thus generalized least square estimators of the parameters are used, and their covariance matrix is usually computed using the inverse of the generalized least square estimators information matrix. Many optimality criteria are based on this approximation of the covariance matrix. However, this approach underestimates the true covariance matrix of the parameters, and thus, the optimality criteria should be corrected in order to pay attention to the actual covariance. The bias in the estimation of the covariance matrix is negligible (or even null) for many models, and for this reason in those cases, it has no sense to deal with the corrected criteria because of the complexity of the calculations involved. But for some models, the correction does have importance, and thus, the modified criteria should be considered when designing; otherwise, the practitioner may risk to deal with poor designs. Some analytical results are presented for simpler models, and optimal designs taking into account the corrected variance will be computed and compared with those using the traditional approach for more complex models, showing that the loss in efficiency may be very important when the correction for the covariance matrix is ignored. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This article investigates topology optimization of a bi-material model for acoustic–structural coupled systems. The design variables are volume fractions of inclusion material in a bi-material model constructed by the microstructure-based design domain method (MDDM). The design objective is the minimization of sound pressure level (SPL) in an interior acoustic medium. Sensitivities of SPL with respect to topological design variables are derived concretely by the adjoint method. A relaxed form of optimality criteria (OC) is developed for solving the acoustic–structural coupled optimization problem to find the optimum bi-material distribution. Based on OC and the adjoint method, a topology optimization method to deal with large calculations in acoustic–structural coupled problems is proposed. Numerical examples are given to illustrate the applications of topology optimization for a bi-material plate under a low single-frequency excitation and an aerospace structure under a low frequency-band excitation, and to prove the efficiency of the adjoint method and the relaxed form of OC. [ABSTRACT FROM PUBLISHER]

Various types of failure, censored and accelerated life tests, are commonly employed for life testing in some manufacturing industries and products that are highly reliable. In this article, we consider the tampered failure rate model as one of such types that relate the distribution under use condition to the distribution under accelerated condition. It is assumed that the lifetimes of products under use condition have generalized Pareto distribution as a lifetime model. Some estimation methods such as graphical, moments, probability weighted moments, and maximum likelihood estimation methods for the parameters are discussed based on progressively type-I censored data. The determination of optimal stress change time is discussed under two different criteria of optimality. Finally, a Monte Carlo simulation study is carried out to examine the performance of the estimation methods and the optimality criteria. [ABSTRACT FROM PUBLISHER]

In this paper, we study self-relocated experimental design, when the lifetimes of the systems follow generalized inverted scale family of distributions (GIFD).We consider maximum likelilood estimations (MLEs) of the scale and shape parameters. We study generalized inverted exponential distribution (GIED) as a special case. Extensive simulations experiments are conducted to study he performances of the proposed estimators, and also to verify the small sample behavior of the jstimators based on asymptotic results. Further, we study the optimality of the self-relocated design tnd generalized type-II censoring scheme. Finally we carry out some cost analysis also, based on simulation study. [ABSTRACT FROM AUTHOR]

An optimality criteria (OC)-based algorithm for optimization of a general class of nonlinear programming (NLP) problems is presented. The algorithm is only applicable to problems where the objective and constraint functions satisfy certain monotonicity properties. For multiply constrained problems which satisfy these assumptions, the algorithm is attractive compared with existing NLP methods as well as prevalent OC methods, as the latter involve computationally expensive active set and step-size control strategies. The fixed point algorithm presented here is applicable not only to structural optimization problems but also to certain problems as occur in resource allocation and inventory models. Convergence aspects are discussed. The fixed point update or resizing formula is given physical significance, which brings out a strength and trim feature. The number of function evaluations remains independent of the number of variables, allowing the efficient solution of problems with large number of variables. [ABSTRACT FROM AUTHOR]

• The acoustic holography for any desired images is realized by introducing wave phase shifts. • The metamaterial-based hologram composed of helical units is invented. • A new optimization algorithm has been proposed for seek the phased arrays at the hologram plane. • The desired acoustic images with a high contrast ratio have been achieved numerically and experimentally. Holography is a technique to generate arbitrarily complex acoustic fields, fundamental to applications such as acoustic imaging, particle manipulation, and energy deposition. In this paper, we develop a new approach for designing acoustic holograms with high-resolution sound images against background noise interference. The metasurface-based holograms are composed of phased arrays, such as helical units, to adjust the propagating sound phase from 0 to 2π flexibly. The problem aims to seek the optimal phase distribution at the output of the metasurface, so that sounds focus a prescribed image at the projection plane. The projection plane is divided into the target and background pixels according to the desired resolution of images. The optimization problem is established to maximize the sound intensity of the target pixels and minimize that of the background pixels simultaneously. The optimality criterion is adopted to iteratively update the phase distribution in arrays based on the derived sensitivity. Finally, the effectiveness of the proposed approach is validated numerically and experimentally. [ABSTRACT FROM AUTHOR]

In this paper a successful topology optimization of a centrifugally loaded aero-engine part is presented. For the topology optimization, which is a nonlinear problem due to several contact regions, a self-developed topology optimization algorithm in combination with a commercial FE-solver is used. The goal of the optimization was the reduction of stresses in the structure. [ABSTRACT FROM AUTHOR]

In a free material formulation, the problem of minimizing a weighted sum of compliance's from multiple load cases, subject to an active constraint on material volume, is solved in a formulation with two optimality criteria. The first optimality criterion for the distribution of material volume densities is equal value for the weighted elastic energy densities, as a natural extension of the optimality criterion for a single load case. The second optimality criterion for the components of a constitutive matrix (of unit norm) is proportionality to corresponding weighted strain components with the same proportionality factor $\widehat \lambda $ for all the components, as shortly specified by $C_{i j k l} = \widehat \lambda \sum _{n} \eta _{n} (\epsilon _{i j})_{n} (\epsilon _{k l})_{n}$, in traditional notation (n indicate load case). These simple analytical results should be communicated, in spite of the practical objection against design for weighted sum of compliance's, as compared to worst case design and design considering strength. The application of the approach of the two optimality criteria is illustrated by a 2D example with 8 load cases. Stable and fast convergence is shown. [ABSTRACT FROM AUTHOR]

Highlights: [•] We suggest a new stiffener layout design method for plate/shell structures. [•] The method is combined with the bionic branch model and optimality criteria. [•] We derive an analytical iterative formula by the Kuhn-Tucker optimality condition. [•] We study problems with different design objectives, including multi-objectives. [•] The new approach is more effective and practicable than the current method. [ABSTRACT FROM AUTHOR]

A new algorithm for the solution of multimaterial topology optimization problems is introduced in the present study. The presented method is based on the splitting of a multiphase topology optimization problem into a series of binary phase topology optimization sub-problems which are solved partially, in a sequential manner, using a traditional binary phase topology optimization solver; internal solver. The coupling between these incomplete solutions is ensured using an outer iteration strategy based on the block coordinate descend method. The presented algorithm provides a general framework to extend the traditional binary phase topology optimization solvers for the solution of multiphase topology optimization problems. Interesting features of the presented algorithm are:generality, simplicity and the ease of implementation. The presented algorithm is used to solve multimaterial minimum structural and thermal compliance topology optimization problems based on the classical optimality criteria method. Details of MATLAB implementation are presented and the complete program listings are provided as the Supplementary Materials. The success and performance of the presented method are studied through several two dimensional numerical examples. [ABSTRACT FROM AUTHOR]

We provide an inequality relating the radial directional derivative and the subdifferential of proper lower semicontinuous functions, which extends the known formula for convex functions. We show that this property is equivalent to other subdifferential properties of Banach spaces, such as controlled dense subdifferentiability, optimality criterion, mean value inequality and separation principles. As an application, we obtain a first-order sufficient condition for optimality, which extends the known condition for differentiable functions in finite-dimensional spaces and which amounts to the maximal monotonicity of the subdifferential for convex lower semicontinuous functions. Finally, we establish a formula describing the subdifferential of the sum of a convex lower semicontinuous function with a convex inf-compact function in terms of the sum of their approximate ϵ-subdifferentials. Such a formula directly leads to the known formula relating the directional derivative of a convex lower semicontinuous function to its approximate ϵ-subdifferential. [ABSTRACT FROM AUTHOR]

This paper links the chemical kinetic models that obey the framework of nonlinear statistical models with optimal design theory. We provide the appropriate optimal designs for them, so that the involved parameters can be estimated as well as possible. Therefore, the D-optimality criterion is adopted, under the optimal design approach, for a number of models used in chemical kinetic applications. In the tables, the collected results are presented for 15 models. [ABSTRACT FROM AUTHOR]

Stiffness topology optimization is usually based on a state problem of linear elasticity, and there seems to be little discussion on what is the limit for such a small rotation-displacement assumption. We show that even for gross rotations that are in all practical aspects small (<3 deg), topology optimization based on a large deformation theory might generate different design concepts compared to what is obtained when small displacement linear elasticity is used. Furthermore, in large rotations, the choice of stiffness objective (potential energy or compliance), can be crucial for the optimal design concept. The paper considers topology optimization of hyperelastic bodies subjected simultaneously to external forces and prescribed non-zero displacements. In that respect it generalizes a recent contribution of ours to large deformations, but we note that the objectives of potential energy and compliance are no longer equivalent in the non-linear case. We use seven different hyperelastic strain energy functions and find that the numerical performance of the Kirchhoff-St.Venant model is in general significantly worse than the performance of the other six models, which are all modifications of this classical law that are equivalent in the limit of infinitesimal strains, but do not contain the well-known collapse in compression. Numerical results are presented for two different problem settings. [ABSTRACT FROM AUTHOR]

In this paper the nonlinear analysis and design optimization of guyed masts is addressed. The mast is modeled as a 3D truss and is supported by catenary cable elements that have nonlinear elastic behavior. For nonlinear static analysis, an innovative procedure is proposed that divides the structure into linear and nonlinear parts and analyzes them separately. The proposed method satisfies the equilibrium and compatibility by establishing and solution of a set of nonlinear equations. The optimization problem employs the sizes of members, initial cable tensions and the positions of anchor on the ground and tie level of cables on the mast as design variables. To facilitate the optimization solution, a compatible sensitivity analysis procedure is proposed. Sensitivities of objective function, displacement and strength constraints in the mast and cables, subjected to a variety of load combinations including dead, wind and ice loads are calculated. Numerical examples are provided to show the nonlinear analysis procedure and the applicability of the algorithm to optimum design of practical guyed masts. [ABSTRACT FROM AUTHOR]

The paper proposes a model of subjective expected utility with respect to the additive probability measure whose formalism is based on the formally logical principles of optimality, unlike the Anscombe-Aumann SEU model defined in behavioristic traditions. [ABSTRACT FROM AUTHOR]

We consider bilevel optimization from the optimistic point of view. Let the pair ( x, y) denote the variables. The main difficulty in studying such problems lies in the fact that the lower level contains a global constraint. In fact, a point ( x, y) is feasible if y solves a parametric optimization problem L( x). In this paper we restrict ourselves to the special case that the variable x is one-dimensional. We describe the generic structure of the feasible set M. Moreover, we discuss local reductions of the bilevel problem as well as corresponding optimality criteria. Finally, we point out typical problems that appear when trying to extend the ideas to higher dimensional x-dimensions. This will clarify the high intrinsic complexity of the general generic structure of the feasible set M and corresponding optimality conditions for the bilevel problem U. [ABSTRACT FROM AUTHOR]

This paper is concerned with design optimisation of cable-stayed bridges. Since cable-stayed bridges, due to the presence of cables, have nonlinear elastic behaviour and optimisation algorithms require frequent nonlinear analyses, an innovative fast and easy nonlinear analysis procedure is proposed. The solution procedure is based on dividing the structure into linear and nonlinear parts and determination of unknown forces at their interface by satisfaction of equilibrium and solution of a set of nonlinear compatibility equations. The analysis procedure is completely formulated and extended to P-? effect included problems. The optimality criteria (OC) method is used as the optimisation algorithm. Sensitivities of objective function, displacement and stress constraints in the deck, pylon and cables, subjected to a variety of load combinations including dead and moving loads of vehicles are calculated via the proposed sensitivity analysis procedure. Numerical examples are provided to show the nonlinear analysis procedure and its applicability to the optimum design of practical cable-stayed bridges. [ABSTRACT FROM AUTHOR]

Abstract: This paper presents a novel formulation for structural topology optimization in which both cost function and constraints are expressed in terms of an implicit design variable—the iso-line/surface threshold of a characteristic response function, such as a strain or mutual strain energy density function. A new material representation model is developed to implicitly describe material usage in a given design domain in terms of one implicit design variable. Based on the Karush–Kuhn–Tucker (KKT) necessary conditions, optimality criteria for finding solutions are established and then employed to develop a simple algorithm for one-material minimum mean compliance and compliant mechanism problems. The algorithm consists of sequentially moving iso-surface threshold (MIST) of chosen characteristic response function. Numerical examples are then presented to validate the proposed algorithm MIST for the minimum mean compliance, compliant mechanism, and fully stressed design problems. [Copyright &y& Elsevier]