An Importance Sampling Approach for Time-Dependent Reliability

Reliability is an important engineering requirement for consistently delivering acceptable product performance through time. The reliability usually degrades with time increasing the lifecycle cost due to potential warranty costs, repairs and loss of market share. Reliability is the probability that the system will perform its intended function successfully for a specified time. In this article, we consider the first-passage reliability which accounts for the first time failure of non-repairable systems. Methods are available which provide an upper bound to the true reliability which may overestimate the true value considerably. The traditional Monte-Carlo simulation is accurate but computationally expensive. A computationally efficient importance sampling technique is presented to calculate the cumulative probability of failure for random dynamic systems excited by a stationary input random process. Time series modeling is used to characterize the input random process. A detailed example demonstrates the accuracy and efficiency of the proposed importance sampling method over the traditional Monte Carlo simulation.

Multiscale Design and Multiobjective Optimization of Orthopaedic Cellular Hip Implants

A multiscale design and multiobjective optimization procedure is developed to design a new type of graded cellular hip implant. We assume that the prosthesis design domain is occupied by a unit cell representing the building block of the implant. An optimization strategy seeks the best geometric parameters of the unit cell to minimize bone resorption and interface failure, two conflicting objective functions. Using the asymptotic homogenization method, the microstructure of the implant is replaced by a homogeneous medium with an effective constitutive tensor. This tensor is used to construct the stiffness matrix for the finite element modeling (FEM) solver that calculates the value of each objective function at each iteration. As an example, a 2D finite element model of a left implanted femur is developed. The relative density of the lattice material is the variable of the multiobjective optimization, which is solved through the non-dominated sorting genetic algorithm II (NSGA-II). The set of optimum relative density distributions is determined to minimize concurrently interface stress distribution and bone loss mass. The results show that the amount of bone resorption and the maximum value of interface stress can be reduced by over 70% and 50%, respectively, when compared to current fully dense titanium stem.

Identifying Product Scaling Principles: A Tool for Bioinspired Design and Beyond

There are countless products that perform the same function but are engineered to suit a different scale. Designers are often faced with the problem of taking a solution at one scale and mapping it to another. This frequently happens with design-by-analogy and bioinspired design. Despite various scaling laws for specific systems, there are no global principles for scaling systems, for example from a biological nano-scale to macro-scale. This is likely one of the reasons bioinspired design is difficult. Very often scaling laws assume the same physical principles are being used, but this study of products indicates that a variety of changes occur as scale changes, including changing the physical principles to meet a particular function. Empirical product research was used to determine a set of principles by observing and understanding numerous products to unearth new generalizations. The function a product performs is examined in various scales to view subtle and blatant differences. Principles are then determined. This study provides an initial step in creating new innovative designs based on existing solutions in nature or other products that occur at very different scales. Much further work is needed by studying additional products and bioinspired examples.

Topology Optimization of Spacers for Maximizing Permeate Flux on Membrane Surface in Reverse Osmosis Channel

The objective of this study is to design spacers using fluid topology optimization in 2D crossflow Reverse Osmosis (RO) membrane channel to improve the performance of RO processes. This study is an initial attempt to apply topology optimization to designing spacers in RO membrane channel. The performance was evaluated by the quantity of permeate flux penetrating both upper and lower membrane surfaces. A coupled Navier-Stokes and Convection-Diffusion model was employed to calculate the permeate flux. To get reliable solutions, stabilization methods were employed with standard finite element method. The nine reference models which consist of the combination of circle, rectangular, triangle shape and zigzag, cavity, submerge configuration of spacers were simulated. Such models were compared with new model designed by topology optimization. The permeate flux at both membrane surfaces was determined as an objective function. In addition, permissible pressure drop along the channel and spacer volume were used as constraints. As a result of topology optimization as the permissible pressure drop changes in channel, characteristics of spacer design development was founded. Spacer design based on topology optimization was reconstructed to a simple one considering manufactuability and characteristics of development spacer design. When a simplified design was compared with previous 9 models, new design has a better performance in terms of permeate flux and wall concentration at membrane surface.

Evaluating Genetic Algorithms on Welding Sequence Optimization With Respect to Dimensional Variation and Cycle Time

Spot welding is the predominant joining method in car body assembly. Spot welding sequences have a significant influence on the dimensional variation of resulting assemblies and ultimately on overall product quality. It also has a significant influence on welding robot cycle time and thus ultimately on manufacturing cost. In this work we evaluate the performance of Genetic Algorithms, GAs, on multi-criteria optimization of welding sequence with respect to dimensional assembly variation and welding robot cycle time. Reference assemblies are fully modelled in 3D including detailed fixtures, welding robots and weld guns. Dimensional variation is obtained using variation simulation and part measurement data. Cycle time is obtained using automatic robot path planning. GAs are not guaranteed to find the global optimum. Besides exhaustive calculations, there is no way to determine how close to the actual optimum a GA trial has reached. Furthermore, sequence fitness evaluations constitute the absolute majority of optimization computation running time and do thus need to be kept to a minimum. Therefore, for two industrial reference assemblies we investigate the number of fitness evaluations that is required to find a sequence that is optimal or a near-optimal with respect to the fitness function. The fitness function in this work is a single criterion based on a weighted and normalized combination of dimensional variation and cycle time. Both reference assemblies involves 7 spot welds which entails 7!=5040 possible welding sequences. For both reference assemblies, dimensional variation and cycle time is exhaustively calculated for all 5040 possible sequences, determining the optimal sequence, with respect to the fitness function, for a fact. Then a GA that utilizes Random Key Encoding is applied on both cases and the performance is recorded. It is found that in searching through about 1% of the possible sequences, optimum is reached in about half of the trials and 80–90% of the trials reach the ten best sequences. Furthermore the optimum of the single criterion fitness function entails dimensional variation and cycle time fairly close to their respective optimum. In conclusion, this work indicates that genetic algorithms are highly effective in optimizing welding sequence with respect to dimensional variation and cycle time.

Surrogate Modeling of Complex Systems Using Adaptive Hybrid Functions

This paper explores the effectiveness of the recently developed surrogate modeling method, the Adaptive Hybrid Functions (AHF), through its application to complex engineered systems design. The AHF is a hybrid surrogate modeling method that seeks to exploit the advantages of each component surrogate. In this paper, the AHF integrates three component surrogate models: (i) the Radial Basis Functions (RBF), (ii) the Extended Radial Basis Functions (E-RBF), and (iii) the Kriging model, by characterizing and evaluating the local measure of accuracy of each model. The AHF is applied to model complex engineering systems and an economic system, namely: (i) wind farm design; (ii) product family design (for universal electric motors); (iii) three-pane window design; and (iv) onshore wind farm cost estimation. We use three differing sampling techniques to investigate their influence on the quality of the resulting surrogates. These sampling techniques are (i) Latin Hypercube Sampling (LHS), (ii) Sobol’s quasirandom sequence, and (iii) Hammersley Sequence Sampling (HSS). Cross-validation is used to evaluate the accuracy of the resulting surrogate models. As expected, the accuracy of the surrogate model was found to improve with increase in the sample size. We also observed that, the Sobol’s and the LHS sampling techniques performed better in the case of high-dimensional problems, whereas the HSS sampling technique performed better in the case of low-dimensional problems. Overall, the AHF method was observed to provide acceptable-to-high accuracy in representing complex design systems.

Multidisciplinary Design Optimization of Modular Industrial Robots

This paper presents a multidisciplinary design optimization framework for modular industrial robots. An automated design framework, containing physics based high fidelity models for dynamic simulation and structural strength analyses are utilized and seamlessly integrated with a geometry model. The proposed framework utilizes well-established methods such as metamodeling and multi-level optimization in order to speed up the design optimization process. The contribution of the paper is to show that by applying a merger of well-established methods, the computational cost can be cut significantly, enabling search for truly novel concepts.

Learning Stylistic Desires and Generating Preferred Designs of Consumers Using Neural Networks and Genetic Algorithms

Consumers have different ideas of what makes a design stylish. Some consumers may want a sporty looking car, while others may want a rugged looking or a fuel-efficient looking car. Can computers learn what it means to satisfy those style-based goals and use this knowledge to generate designs that target style-based goals in design? An experiment was conducted where participants were asked to rate computer generated car profiles for sportiness, ruggedness, beauty, and fuel efficiency. This survey data is used as an indicator of consumer stylistic form preferences, and was used to train Artificial Neural Networks (ANN) for each of the four rating categories. The resulting ANNs were then inverted using a Genetic Algorithm (GA) in order to generate new designs that elicit targeted style goals from consumers.

Robustness Metrics for Time-Dependent Quality Characteristics

Quality characteristics (QC’s) are often treated static in robust design optimization while many of them are time dependent in reality. It is therefore desirable to define new robustness metrics for time-dependent QC’s. This work shows that using the robustness metrics of static QC’s for those of time-dependent QC’s may lead to erroneous design results. To this end, we propose the criteria of establishing new robustness metrics for time-dependent QC’s and then define new robustness metrics. Instead of using a point expected quality loss over the time period of interest, we use the expectation of the maximal quality loss over the time period to quantify the robustness for time-dependent QC’s. Through a four-bar function generator mechanism analysis, we demonstrate that the new robustness metrics can capture the full information of robustness of a time-dependent QC over a time interval. The new robustness metrics can then be used as objective functions for time-dependent robust design optimization.