Development of Game Theoretic Protocols for Multilevel Design

The effectiveness of the use of game theory in addressing multi-objective design problems has been illustrated. For the most part, researchers have focused on design problems at single level. In this paper, we illustrate the efficacy of using game theoretic protocols to model the relationship between multidisciplinary engineering teams and facilitate decision making at multiple levels. We will illustrate the protocols in the context of an underwater vehicle with three levels that span material and geometric modeling associated with microstructure mediated design of the material and vehicle.

Topology Optimization of Piezoelectric Energy Harvesting Devices Subjected to Stochastic Excitation

Converting ambient vibration energy into electrical energy using piezoelectric energy harvester has attracted much interest in the past decades. In this paper, topology optimization is applied to design the optimal layout of the piezoelectric energy harvesting devices. The objective function is defined as to maximize the energy harvesting performance over a range of ambient vibration frequencies. Pseudo excitation method (PEM) is applied to analyze structural stationary random responses. Sensitivity analysis is derived by the adjoint method. Numerical examples are presented to demonstrate the validity of the proposed approach.

An Engineering Design Strategy for Reconfigurable Products That Support Poverty Alleviation

Reconfigurable products can adapt to new and changing customer needs. One potential, high-impact, area for product reconfiguration is in the design of income-generating products for poverty alleviation. Non-reconfigurable income-generating products such as manual irrigation pumps have helped millions of people sustainably escape poverty. However, millions of other impoverished people are unwilling to invest in these relatively costly products because of the high perceived and actual financial risk involved. As a result, these individuals do not benefit from such technologies. Alternatively, when income-generating products are designed to be reconfigurable, the window of affordability can be expanded to attract more individuals, while simultaneously making the product adaptable to the changing customer needs that accompany an increased income. The method provided in this paper significantly reduces the risks associated with purchasing income-generating products while simultaneously allowing the initial purchase to serve as a foundation for future increases in income. The method presented builds on principles of multiobjective optimization and Pareto optimality, by allowing the product to move from one location on the Pareto frontier to another through the addition of modules and reconfiguration. Elements of product family design are applied as each instantiation of the reconfigurable product is considered in the overall design optimization of the product. The design of a modular irrigation pump for developing nations demonstrates the methodology.

Designing a Product Package Platform

An essential part of designing a successful product family is establishing a recognizable, familiar, product family identity. It is very often the case that consumers first identify products based on their physical embodiment. The Apple iPod, DeWalt power tools, and KitchenAid appliances are all examples of product families that have successfully branded themselves based on physical principles. While physical branding is often the first trait apparent to designers, there are some products that cannot be differentiated based on physical appearance. This is especially common for consumable products. For example, it is impossible to differentiate between diet Coke, Classic Coke, and Pepsi when each is poured into separate glasses. When differentiation is difficult to achieve from a product’s physical characteristics, the product’s package becomes a vital part of establishing branding and communicating membership to a product family while maintaining individual product identity. In this paper, product packaging is investigated with a focus on the graphic packaging components that identify product families. These components include: color, shape, typography, and imagery. Through the application of tools used in facilities layout planning, graph theory, social network theory, and display design theory an approach to determine an optimal arrangement of graphic components is achieved. This approach is validated using a web based survey that tracks user-package interactions across a range of commonly used cereal boxes.

System RBDO With Correlated Variables Using Probabilistic Re-Analysis and Local Metamodels

A simulation-based, system reliability-based design optimization (RBDO) method is presented that can handle problems with multiple failure regions and correlated random variables. Copulas are used to represent dependence between random variables. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a sequential trust-region optimization approach and local metamodels covering each trust region. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation per trust region. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing the use of a gradient-based optimizer. The PRRA method is based on importance sampling. One requirement for providing accurate results is that the support of the sampling PDF must contain the support of the joint PDF of the input random variables. The trust-region optimization approach satisfies this requirement. Local metamodels are constructed sequentially for each trust region taking advantage of the potential overlap of the trust regions. The metamodels are used to determine the value of the indicator function in MC simulation. An example with correlated input random variables demonstrates the accuracy and efficiency of the proposed RBDO method.

Computation of the Usage Contexts Coverage of a Jigsaw With CSP Techniques

In the context of the Usage Context Based Design (UCBD) of a product-service, a taxonomy of variables is suggested to setup the link between the design parameters of a product-service and the part of a set of expected usages that may be covered. This paper implements a physics-based model to provide a performance prediction for each usage context that also depends on the user skill. The physics describing the behavior and consequently the performances of a jigsaw are established. Simulating numerically the usage coverage is non trivial for two reasons: the presence of circular references in physical relations and the need to efficiently propagate value sets or domains instead of accurate values. For these two reasons, we modeled the usage coverage issue as a Constraint Satisfaction Problem and we result in the expected service performances and a value of a covered usage indicator.

Multiscale Variability and Uncertainty Quantification Based on a Generalized Multiscale Markov Model

Variability is inherent randomness in systems, whereas uncertainty is due to lack of knowledge. In this paper, a generalized multiscale Markov (GMM) model is proposed to quantify variability and uncertainty simultaneously in multiscale system analysis. The GMM model is based on a new imprecise probability theory that has the form of generalized interval, which is a Kaucher or modal extension of classical set-based intervals to represent uncertainties. The properties of the new definitions of independence and Bayesian inference are studied. Based on a new Bayes’ rule with generalized intervals, three cross-scale validation approaches that incorporate variability and uncertainty propagation are also developed.

Protocol-Based Multi-Agent Systems: Examining the Effect of Diversity, Dynamism, and Cooperation in Heuristic Optimization Approaches

Many heuristic optimization approaches have been developed to combat the ever-increasing complexity of engineering problems. In general, these approaches can be classified based on the diversity of the search strategies used, the amount of change to those search strategies during the optimization process, and the level of cooperation between the strategies. A review of the literature indicates that approaches which are simultaneously very diverse, highly dynamic, and cooperative are rare but have immense potential for finding high quality final solutions. In this work, a taxonomy of heuristic optimization approaches is introduced and used to motivate a new approach, entitled Protocol-based Multi-Agent Systems. This approach is found to produce final solutions of much higher quality when its implementation includes the use of multiple search protocols, the adaptation of those protocols during the optimization, and the cooperation between the protocols than when these characteristics are absent.

Tracing Pareto-Optimal Frontiers in Topology Optimization

In multi-objective topology optimization, a design is defined to be “pareto-optimal” if no other design exists that is better with respect to one objective, and as good with respect to others. This unfortunately suggests that unless other ‘better’ designs are found, one cannot declare a particular topology to be pareto-optimal. In this paper, we first show that a topology can be guaranteed to be (locally) pareto-optimal if certain inherent properties associated with the topological sensitivity field are satisfied, i.e., no further comparison is necessary. This, in turn, leads to a deterministic, i.e., non-stochastic, method for directly tracing pareto-optimal frontiers using the classic fixed-point iteration scheme. The proposed method can generate the full set of pareto-optimal topologies in a single-run, and is therefore both efficient and predictable, as illustrated through numerical examples.

Modified Reduced Gradient With Realizations Sorting for Hard Equality Constraints in Reliability-Based Design Optimization

In this work, the presence of equality constraints in reliability-based design optimization (RBDO) problems is studied. Relaxation of soft equality constraints in RBDO and its challenges are briefly discussed while the main focus is on hard equalities that can not be violated even under uncertainty. Direct elimination of hard equalities to reduce problem dimensions is usually suggested; however, for nonlinear or black-box functions, variable elimination requires expensive root-finding processes or inverse functions that are generally unavailable. We extend the reduced gradient methods in deterministic optimization to handle hard equalities in RBDO. The efficiency and accuracy of the first and the second order predictions in reduced gradient methods are compared. Results show the first order prediction being more efficient when realizations of random variables are available. A gradient-weighted sorting with these random samples is proposed to further improve the solution efficiency of the reduced gradient method. Feasible design realizations subject to hard equality constraints are then available to be implemented with the state-of-the-art sampling techniques for RBDO problems. Numerical and engineering examples show the strength and simplicity of the proposed method.