Design optimization studies that model competition with other products in the market often use a small set of products to represent all competitors. We investigate the effect of competitor product representation on profit-maximizing design solutions. Specifically, we study the implications of replacing a large set of disaggregated elemental competitor products with a subset of competitor products or composite products. We derive first-order optimality conditions and show that optimal design (but not price) is independent of competitors when using logit and nested logit models (where preferences are homogeneous). However, this relationship differs in the case of random-coefficients logit models (where preferences are heterogeneous), and we demonstrate that profit-maximizing design solutions using latent-class or mixed-logit models can (but need not always) depend on the representation of competing products. We discuss factors that affect the magnitude of the difference between models with elemental and composite representations of competitors, including preference heterogeneity, cost function curvature, and competitor set specification. We present correction factors that ensure models using subsets or composite representation of competitors have optimal design solutions that match those of disaggregated elemental models. While optimal designs using logit and nested logit models are not affected by ad-hoc modeling decisions of competitor representation, the independence of optimal designs from competitors when using these models raises questions of when these models are appropriate to use.

System Reconfiguration is essential in complex systems management, as it is an enabler of system adaptability with regard to system evolutions. System evolutions have to be managed to ensure system effectiveness and efficiency through its whole life cycle, particularly when it comes to complex systems that take years of development and dozens of years of usage. In this context, system reconfiguration ensures system operation and maintains system “ilities” (e.g., reliability, availability, maintainability, testability, and safety). This research has been conducted in the context of a large international aerospace, space, ground transportation, defense, and security company. This research aims at supporting system reconfiguration during operations. Within current industrial practices, the development of reconfiguration support is challenging as it requires integrating data related to observations (from operations) and system design (from engineering). More specifically, there is a need to integrate and link relevant reconfiguration data concerning the system objectives, operational context, and level of functioning. This paper proposes integrating and linking this fundamental data within a reconfiguration method. MBSysRec is a multidisciplinary method that involves configuration generation and a multi-criteria decision-making method for configuration evaluation and selection to support system reconfiguration during operations. The method has been implemented on two projects based on historical data. Resulting configurations have been discussed and assessed by system reconfiguration experts. A SAR case study is used to demonstrate the method. The method is proven effective for finding relevant system configurations for reconfiguring the already deployed system to achieve search and rescue missions.

As Artificial Intelligence (AI) assistance tools become more ubiquitous in engineering design, it becomes increasingly necessary to understand the influence of AI assistance on the design process and design effectiveness. Previous work has shown the advantages of incorporating AI design agents to assist human designers. However, the influence of AI assistance on the behavior of designers during the design process is still unknown. This study examines the differences in participants' design process and effectiveness with and without AI assistance during a complex drone design task using the HyForm design research platform. Data collected from this study is analyzed to assess the design process and effectiveness using quantitative methods, such as Hidden Markov Models and network analysis. The results indicate that AI assistance is most beneficial when addressing moderately complex objectives but exhibits a reduced advantage in addressing highly complex objectives. During the design process, the individual designers working with AI assistance employ a relatively explorative search strategy, while the individual designers working without AI assistance devote more effort to parameter design.

Standard moving morphable component (MMC)-based topology optimization methods use free components with explicitly geometrical parameters as design units to obtain the optimal structural topology by moving, deforming and covering such components. In this study, we intend to present a method for geometrically nonlinear explicit topology optimization using moving wide Bezier components with constrained ends. Not only can the method efficiently avoid the convergence issues associated with nonlinear structural response analysis, but it can also alleviate the component disconnection issues associated with the standard MMC-based topology optimization methods. The numerical investigations proposed in this work indicate that the proposed method allows us to obtain results in accordance with the current literature with a more stable optimization process. In addition, the proposed method can easily achieve minimum length scale control without adding constraints.

Variable-axial fiber-reinforced composites allow for local customization of fiber orientation and thicknesses. Despite their significant potential for performance improvement over the conventional multiaxial composites and metals, they pose challenges in design optimization due to the vastly increased design freedom in material orientations. This paper presents an anisotropic topology optimization method for designing large-scale, 3D variable-axial lightweight composite structures subject to multiple load cases. The computational challenges associated with large-scale 3D anisotropic topology optimization with extremely low volume fraction are addressed by a tensor-based representation of 3D orientation that would avoid the 2π periodicity of angular representations such as Euler angles, and an adaptive meshing scheme, which, in conjunction with PDE regularization of the density variables, refines the mesh where structural members appear and coarsens where there is void. The proposed method is applied to designing a heavy-duty drone frame subject to complex multi-loading conditions. Finally, the manufacturability gaps between the optimized design and the fabrication-ready design for tailored fiber placement (TFP) is discussed, which motivates future work toward a fully automated design synthesis.

The components of complex systems such as automobiles or ships communicate via connectors, including wires, hoses, or pipes whose weight could substantially increase the total weight of the system. Hence, it is of paramount importance to lay out these connectors such that their overall weight is minimized. In this paper, a computationally efficient approach is proposed to optimize the layout of flexible connectors (e.g., cable harnesses) by minimizing their overall length while maximizing their common length. The approach provides a framework to mathematically model the cable harness layout optimization problem. A Multiobjective Genetic Algorithm (MOGA) solver is then applied to solve the optimization problem, which outputs a set of non-dominated solutions to the bi-objective problem. Finally, the effects of the workspace’s geometric structure on the optimal layouts of cable harnesses are discussed using sample test cases. The overarching objective of this study is to provide insight for designers of cable harnesses when deciding on the final layout of connectors considering aspects such as accessibility to and maintainability of these connectors.

This paper examines the impact of omitted variable bias (OVB) within consumer choice models on engineering design optimization solutions. Engineering products often have a multitude of attributes that influence consumers’ purchasing decisions, many of which are difficult to include in revealed-preference models due to a lack of data. Correlations among these omitted variables and product attributes included in the model can bias demand parameter estimates. However, engineering design optimization studies typically do not account for this bias. We examine the influence consumer choice OVB can have on design optimization results. We first mathematically derive how OVB propagates into optimal design solutions and characterize properties of optimization problems that affect the magnitude of the resulting error in solutions. We then demonstrate the impact of OVB on optimal designs using a case study of automotive powertrain design optimization. In the case study, we estimate two sets of choice models: one using only “typically observed” vehicle attributes commonly found in the literature, and one with an additional set of “typically unobserved” attributes gathered from Edmunds.com. We find that the model with omitted variables leads to, in some scenarios, substantial bias in parameter estimates (5–143%), which propagates up to 21% error in the optimal engine size.

A multifidelity surrogate (MFS) model is a data fusion method for the enhanced prediction of less intensively sampled primary variables of interest (i.e., high-fidelity (HF) samples) with the assistance of intensively sampled auxiliary variables (i.e., low-fidelity (LF) samples). In this article, an MFS model based on the gradient-enhanced radial basis function, termed gradient-enhanced multifidelity surrogate based on the radial basis function (GEMFS-RBF), is proposed to establish a mapping relationship between HF and LF samples. To identify the scaling factor and the undetermined coefficients in GEMFS-RBF, an expanded correlation matrix is constructed by considering the correlations between the acquired samples, the correlations between the gradients, and the correlations between the samples and their corresponding gradients. To evaluate the prediction accuracy of the GEMFS-RBF model, it is compared with the co-Kriging model, multifidelity surrogate based on the radial basis function (MFS-RBF) model, and two single-fidelity surrogate models. The influences of key factors (i.e., the correlations between the HF and LF functions, the subordinations between the sample sets) and the effect of the cost ratio on the performance of GEMFS-RBF are also investigated. It is observed that GEMFS-RBF presents a more acceptable accuracy rate and is less sensitive to the aforementioned factors than the other benchmark models in most cases in this article, which illustrates the practicability and robustness of the proposed GEMFS-RBF model.

Bayesian optimization (BO) is a low-cost global optimization tool for expensive black-box objective functions, where we learn from prior evaluated designs, update a posterior surrogate Gaussian process model, and select new designs for future evaluation using an acquisition function. This research focuses upon developing a BO model with multiple black-box objective functions. In the standard Multi-Objective optimization (MOO) problem, the weighted Tchebycheff method is efficiently used to find both convex and non-convex Pareto frontiers. This approach requires knowledge of utopia values before we start optimization. However, in the BO framework, since the functions are expensive to evaluate, it is very expensive to obtain the utopia values as a prior knowledge. Therefore, in this paper, we develop a MO-BO framework where we calibrate with multiple linear regression (MLR) models to estimate the utopia value for each objective as a function of design input variables; the models are updated iteratively with sampled training data from the proposed multi-objective BO. This iteratively estimated mean utopia values is used to formulate the weighted Tchebycheff multi-objective acquisition function. The proposed approach is implemented in optimizing thin tube geometries under constant loading of temperature and pressure, with minimizing the risk of creep-fatigue failure and design cost, along with risk-based and manufacturing constraints. Finally, the model accuracy with frequentist, Bayesian and without MLR-based calibration are compared to true Pareto solutions.

Ever since its introduction over five decades ago, geometric solid modelling has been crucial for engineering design purposes and is used in engineering software packages such as computer-aided design (CAD), computer-aided manufacturing (CAM), computer-aided engineering (CAE), etc. Solid models produced by CAD software have been used to transfer geometric information from designers to manufacturers. Since the emergence of additive manufacturing (AM), a CAD file can also be directly uploaded to a three-dimensional (3D) printer and used for production. AM techniques allow manufacturing of complex geometric objects such as bio-inspired structures and lattice structures. These structures are shapes inspired by nature and periodical geometric shapes consisting of struts interconnecting in nodes. Both structures have unique properties such as significantly reduced weight. However, geometric modelling of such structures has significant challenges due to the inability of current techniques to handle their geometric complexity. This calls for a novel modelling method that would allow engineers to design complex geometric objects. This survey paper reviews geometric modelling methods of complex structures to support bio-inspired design created for AM which includes discussing reasoning behind bio-inspired design, limitations of current modelling approaches applied to bio-inspired structures, challenges encountered with geometric modelling and opportunities that these challenges reveal. Based on the review, a need for a novel geometric modelling method for bio-inspired geometries produced by AM is identified. A framework for such bio-inspired geometric modelling method is proposed as a part of this work.

This work introduces a computational method for designing bone scaffolds for maximum bone growth. A mechanobiological model of bone adaptation is used to compute the bone growth, taking into account the shape of the defect, the applied loading, and the existing density distribution of the bone in which the scaffold has been implanted. Numerical homogenization and a geometry projection technique are used to efficiently obtain surrogates of the effective elastic and diffusive properties of the scaffold as a function of the scaffold design and the bone density. These property surrogates are in turn used to perform bone adaptation simulations of the scaffold–bone system for a sampling of scaffold designs. Surrogates of the bone growth in the scaffold at the end of the simulated time and of the strain energy of the scaffold at implantation time are subsequently constructed from these simulations. Using these surrogates, we optimize the design of a scaffold implanted in a rabbit femur to maximize volume bone growth into the scaffold while ensuring a minimum stiffness at implantation. The results of the optimization demonstrate the effectiveness of the proposed method by showing that maximizing bone growth with a constraint on structural compliance renders scaffold designs with better bone growth than what would be obtained by only minimizing compliance.

Multi-fidelity surrogate model-based engineering optimization has received much attention because it alleviates the computational burdens of expensive simulations or experiments. However, due to the nonlinearity of practical engineering problems, the initial sample set selected to produce the first set of data will almost inevitably miss certain features of the landscape, and thus, the construction of a useful surrogate often requires further, judicious infilling of some new samples. Sequential sampling strategies used to select new infilling samples during each iteration can gradually extend the data set and improve the accuracy of the initial model with an acceptable cost. In this paper, a sequential sampling generation method based on the Voronoi region and the sample density (SSGM-VRDS) is proposed. First, with a Monte Carlo-based approximation of a Voronoi tessellation for region division, Pearson correlation coefficients and cross-validation (CV) are employed to determine the candidate Voronoi region for infilling a new sample. Then, a relative sample density is defined to identify the position of the new infilling point at which the sample is the sparsest within the selected Voronoi region. A correction of this density is carried out concurrently through an expansion coefficient. The proposed method is applied to three numerical functions and a lightweight design problem via finite element analysis (FEA). Results suggest that the SSGM-VRDS strategy has outstanding effectiveness and efficiency in selecting a new sample for improving the accuracy of a surrogate model, as well as practicality for solving practical optimization problems.

Architected elastomeric beam networks have great potential for energy absorption, multi-resonant vibration isolation, and multi-bandgap elastic wave control, due to the reconfigurability and programmability of their mechanical buckling instabilities. However, navigating this design space is challenging due to bifurcations between mono- and bistable beam designs, inherent geometric nonlinearities, and the strong dependence of buckling properties on beam geometry. To investigate these challenges, we developed a Bayesian optimization framework to control the equilibrium states of an inclined elastomeric beam, while also tuning the energy to transition between these configurations. Leveraging symmetry to reduce the design space, the beam shape is parameterized using a Fourier series representation. A penalty method is developed to include monostable designs in objective functions with dependencies on bistable features, enabling monostable results to still be incorporated in the Gaussian process surrogate and contribute to the optimization process. Two objectives are optimized in this study, including the position of the second stable equilibrium configuration and the ratio of output to input energy between the two stable states. A scalarized multi-objective optimization is also carried out to study the trade-off between equilibrium position and the energetics of transition between the stable states. The predicted designs are qualitatively verified through experimental testing. Collectively, the study explores a new parameter space for beam buckling, introduces a penalty method to regularize between mono- and bistable domains, and provides a library of beams as building blocks to assemble and analyze in future studies.

Emulation plays an important role in engineering design. However, most emulators such as Gaussian processes (GPs) are exclusively developed for interpolation/regression and their performance significantly deteriorates in extrapolation. To address this shortcoming, we introduce evolutionary Gaussian processes (EGPs) that aim to increase the extrapolation capabilities of GPs. An EGP differs from a GP in that its training involves automatic discovery of some free-form symbolic bases that explain the data reasonably well. In our approach, this automatic discovery is achieved via evolutionary programming (EP) which is integrated with GP modeling via maximum likelihood estimation, bootstrap sampling, and singular value decomposition. As we demonstrate via examples that include a host of analytical functions as well as an engineering problem on materials modeling, EGP can improve the performance of ordinary GPs in terms of not only extrapolation, but also interpolation/regression and numerical stability.

Multi-objective optimization (MOO) problems with computationally expensive constraints are commonly seen in real-world engineering design. However, metamodel-based design optimization (MBDO) approaches for MOO are often not suitable for high-dimensional problems and often do not support expensive constraints. In this work, the situational adaptive Kreisselmeier and Steinhauser (SAKS) method was combined with a new multi-objective trust region optimizer (MTRO) strategy to form the SAKS-MTRO method for MOO problems with expensive black-box constraint functions. The SAKS method is an approach that hybridizes the modeling and aggregation of expensive constraints and adds an adaptive strategy to control the level of hybridization. The MTRO strategy uses a combination of objective decomposition and K-means clustering to handle MOO problems. SAKS-MTRO was benchmarked against four popular multi-objective optimizers and demonstrated superior performance on average. SAKS-MTRO was also applied to optimize the design of a semiconductor substrate and the design of an industrial recessed impeller.

We enhance the Bayesian optimization (BO) approach for simulation-based design of engineering systems consisting of multiple interconnected expensive simulation models. The goal is to find the global optimum design with minimal model evaluation costs. A commonly used approach is to treat the whole system as a single expensive model and apply an existing BO algorithm. This approach is inefficient due to the need to evaluate all the component models in each iteration. We propose a multi-model BO approach that dynamically and selectively evaluates one component model per iteration based on the uncertainty quantification of linked emulators (metamodels) and the knowledge gradient of system response as the acquisition function. Building on our basic formulation, we further solve problems with constraints and feedback couplings that often occur in real complex engineering design by penalizing the objective emulator and reformulating the original problem into a decoupled one. The superior efficiency of our approach is demonstrated through solving two analytical problems and the design optimization of a multidisciplinary electronic packaging system.

Owing to their tailorable physical properties, periodic cellular structures are considered promising materials for use in various engineering applications. To fully leverage the potential of such structures, it will be necessary to develop a design method that is capable of producing material layouts that are not only intricate but at the same time, readily manufacturable. This paper presents a topology optimization framework for designing well-connected and exact-sized multi-material cellular structures that are to be subjected to temperature change. In this framework, multi-material layouts within designable unit cells are represented using level-set functions and corresponding Boolean operations. The connectivity between exact-sized cells, advantageous in realizing the optimal designs, is guaranteed because of a common length scale assumed between these unit cells and the macrostructure. Increase in the number of degree-of-freedoms and concomitant storage requirements are minimized by applying the Guyan reduction method, in which the secondary degree-of-freedom is condensed out to reduce the size of the discretized model. The design capabilities of the proposed method were investigated using several numerical models. The optimized material layouts show that the presented method can create innovative designs facilitating the thermal expansion to improve the performance and enhance overall layouts’ stiffness in different ways, especially when the design is constituted of multiple materials.

While a majority of accidents and malfunctions in complex engineered systems are attributed to human error, a closer inspection would reveal that such mishaps often emerge as a result of complex interactions between the human- and component-related vulnerabilities. To fully understand and mitigate potential risks, the effects of such interactions between component failures and human errors (in addition to their independent effects) need to be considered early. Specifically, to facilitate risk-based design, severity of such failures need to be quantified early in the design process to determine overall risk and prioritize the most important hazards. However, existing risk assessment methods either quantify the risk of component failures or human errors in isolation or are only applicable during later design stages. This work intends to overcome this limitation by introducing an expected cost model to the Human Error and Functional Failure Reasoning (HEFFR) framework to facilitate the quantification of the effects of human error and component failures acting in tandem. This approach will allow designers to assess the risk of hazards emerging from human- and component-related failures occurring in combination and identify worst-case fault scenarios. A coolant tank case study is used to demonstrate this approach. The results show that the proposed approach can help designers quantify the effects of human error and component failures acting alone and in tandem, identify worst-case scenarios, and improve human-product interactions. However, the underlying likelihood and cost models are subject to uncertainties which may affect the assessments.

As a kind of imprecise probabilistic model, probability-box (P-box) model can deal with both aleatory and epistemic uncertainties in parameters effectively. The P-box can generally be categorized into two classes, namely, parameterized P-box and non-parameterized P-box. Currently, the researches involving P-boxes mainly aim at the parameterized P-box, while the works handling the non-parameterized P-box are relatively inadequate. This paper proposes an efficient uncertainty propagation analysis method based on cumulative distribution function discretization (CDFD) for problems with non-parameterized P-boxes, through which the bounds of statistical moments and the cumulative distribution function (CDF) of a response function with non-parameterized P-box variables can be obtained. First, a series of linear programming models are established for acquiring the lower and upper bounds of the first four origin moments of the response function. Second, based on the bounds of the origin moments, the CDF bounds for the response function can be obtained using Johnson distributions fitting and an optimization approach based on percentiles. Finally, the accuracy and efficiency of the proposed method are verified by investigating two numerical examples.

Metamodels instead of computer simulations are often adopted to reduce the computational cost in the uncertainty-based multilevel optimization. However, metamodel techniques may bring prediction discrepancy, which is defined as metamodeling uncertainty, due to the limited training data. An unreliable solution will be obtained when the metamodeling uncertainty is ignored, while an overly conservative solution, which contradicts the original intension of the design, may be got when both parametric and metamodeling uncertainty are treated concurrently. Hence, an adaptive sequential sampling framework is developed for the metamodeling uncertainty reduction of multilevel systems to obtain a solution that approximates the true solution. Based on the Kriging model for the probabilistic analytical target cascading (ATC), the proposed framework establishes a revised objective-oriented sampling criterion and sub-model selection criterion, which can realize the location of additional samples and the selection of subsystem requiring sequential samples. Within the sampling criterion, the metamodeling uncertainty is decomposed by the Karhunen–Loeve expansion into a set of stochastic variables, and then polynomial chaos expansion (PCE) is used for uncertainty quantification (UQ). The polynomial coefficients are encoded and integrated in the selection criterion to obtain subset sensitivity indices for the sub-model selection. The effectiveness of the developed framework for metamodeling uncertainty reduction is demonstrated on a mathematical example and an application.