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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 the correlation. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a 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 therefore, the use of a gradient-based optimizer. The PRRA method is based on importance sampling. It provides accurate results, if the support of the sampling PDF contains the support of the joint PDF of the input random variables. The sequential, trust-region optimization approach satisfies this requirement.

A uniaxial stress-strain curve obtained from a conventional tensile test is only valid up to the point of uniform elongation, beyond which a diffuse neck begins to develop, followed by localized necking and eventual fracture. However Finite Element Analysis for sheet metal forming requires an effective stress-strain curve that extends well beyond the diffuse necking point. Such an extension is usually accomplished by analytical curve fitting and extrapolation. Recent advancement in Digital Image Correlation (DIC) techniques allows direct measurement of full-range stress-strain curves by continuously analyzing the deformation within the diffuse neck zone until the material ruptures. However the stress-strain curve obtained this way is still approximate in nature. Its accuracy depends on the specimen size, the gage size for analysis, and the material response itself.

Piston design is a challenging engineering problem which involves complex physics and requires satisfying multiple performance objectives. Uncertainty in piston operating conditions and variability in piston design variables are inevitable and must be accounted for. The piston assembly can be a major source of engine mechanical friction and cold start noise, if not designed properly. In this paper, an analytical piston model is used in a deterministic and probabilistic (reliability-based) multi-objective design optimization process to obtain an optimal piston design. The model predicts piston performance in terms of scuffing, friction and noise, In order to keep the computational cost low, efficient and accurate metamodels of the piston performance metrics are used. The Pareto set of all optimal solutions is calculated allowing the designer to choose the “best” solution according to trade-offs among the multiple objectives.

Ti-alloy sheet is a high-modulus elastic-plastic material, about which the resilience in the cold-forming process is quite difficult to control. As a matter of fact, the procedure of cold-forming is composed of many cases such as tensile case and bending case. An expression of ultimate radius for bending-curvature is obtained based on tri-parameters elastic-plastic constitutive model. By classifying the cold-forming process, some typical cases of cold-forming are presented in this paper, and analytical solutions with a high precision of resilience for high-modulus elastic-plastic material such as Ti-alloy sheet under the different typical cases are obtained in this paper. The accurate analytical solutions of resilience for high-modulus elastic-plastic material presented in this paper will contribute to cold-forming process both in the mould-designing and optimizing of cold-forming procedure.

Vehicle restraint system design is a difficult optimization problem to solve because (1) the nature of the problem is highly nonlinear, non-convex, noisy, and discontinuous; (2) there are large numbers of discrete and continuous design variables; (3) a design has to meet safety performance requirements for multiple crash modes simultaneously, hence there are a large number of design constraints. Based on the above knowledge of the problem, it is understandable why design of experiment (DOE) does not produce a high-percentage of feasible solutions, and it is difficult for response surface methods (RSM) to capture the true landscape of the problem. Furthermore, in order to keep the restraint system more robust, the complexity of restraint system content needs to be minimized in addition to minimizing the relative risk score to achieve New Car Assessment Program (NCAP) 5-star rating.

Pareto optimal map concept has been applied to the optimization of the vehicle system control (VSC) strategy for a power-split hybrid electric vehicle (HEV) system. The methodology relies on an inner-loop optimization process to define Pareto maps of the best engine and electric motor/generator operating points given wheel power demand, vehicle speed, and battery power. Selected levels of model fidelity, from simple to very detailed, can be used to generate the Pareto maps. Optimal control is achieved by applying Pontryagin's minimum principle which is based on minimization of the Hamiltonian comprised of the rate of fuel consumption and a co-state variable multiplied by the rate of change of battery SOC. The approach delivers optimal control for lowest fuel consumption over a drive cycle while accounting for all critical vehicle operating constraints, e.g. battery charge balance and power limits, and engine speed and torque limits.

Implications of decision analysis (DA) on engineering design are important and well-documented. However, widespread adoption has not occurred. To that end, the authors recently proposed decision topologies (DT) as a visual method for representing decision situations and proved that they are entirely consistent with normative decision analysis. This paper addresses the practical issue of assessing the DTs of a designer using their responses. As in classical DA, this step is critical to encoding the DA's preferences so that further analysis and mathematical optimization can be performed on the correct set of preferences. We show how multi-attribute DTs can be directly assessed from DM responses. Furthermore, we show that preferences under uncertainty can be trivially incorporated and that topologies can be constructed using single attribute topologies similarly to multi-linear functions in utility analysis. This incremental construction simplifies the process of topology construction.

In vehicle design, response surface model (RSM) is commonly used as a surrogate of the high fidelity Finite Element (FE) model to reduce the computational time and improve the efficiency of design process. However, RSM introduces additional sources of uncertainty, such as model bias, which largely affect the reliability and robustness of the prediction results. The bias of RSM need to be addressed before the model is ready for extrapolation and design optimization. This paper further investigates the Bayesian inference based model extrapolation method which is previously proposed by the authors, and provides a systematic and integrated stochastic bias corrected model extrapolation and robustness design process under uncertainty. A real world vehicle design example is used to demonstrate the validity of the proposed method.

The objective of this paper focused on the modeling of an adaptive energy absorbing steering column which is the first phase of a study to develop a modeling methodology for an advanced steering wheel and column assembly. Early steering column designs often consisted of a simple long steel rod connecting the steering wheel to the steering gear box. In frontal collisions, a single-piece design steering column would often be displaced toward the driver as a result of front-end crush. Over time, engineers recognized the need to reduce the chance that a steering column would be displaced toward the driver in a frontal crash. As a result, collapsible, detachable, and other energy absorbing steering columns emerged as safer steering column designs. The safety-enhanced construction of the steering columns, whether collapsible, detachable, or other types, absorb rather than transfer frontal impact energy.

This paper presents the final phase of a study to develop the modeling methodology for an advanced steering assembly with a safety-enhanced steering wheel and an adaptive energy absorbing steering column. For passenger cars built before the 1960s, the steering column was designed to control vehicle direction with a simple rigid rod. In severe frontal crashes, this type of design would often be displaced rearward toward the driver due to front-end crush of the vehicle. Consequently, collapsible, detachable, and other energy absorbing steering columns emerged to address this type of kinematics. These safety-enhanced steering columns allow frontal impact energy to be absorbed by collapsing or breaking the steering columns, thus reducing the potential for rearward column movement in severe crashes. Recently, more advanced steering column designs have been developed that can adapt to different crash conditions including crash severity, occupant mass/size, seat position, and seatbelt usage.

The performance of an organic Rankine cycle (ORC) that recovers heat from the exhaust of a heavy-duty diesel engine was simulated. The work was an extension of a prior study that simulated the performance of an experimental ORC system developed and tested at Oak Ridge National laboratory (ORNL). The experimental data were used to set model parameters and validate the results of that simulation. For the current study the model was adapted to consider a 15 liter turbocharged engine versus the original 1.9 liter light-duty automotive turbodiesel studied by ORNL. Exhaust flow rate and temperature data for the heavy-duty engine were obtained from Southwest Research Institute (SwRI) for a range of steady-state engine speeds and loads without EGR. Because of the considerably higher exhaust gas flow rates of the heavy-duty engine, relative to the engine tested by ORNL, a different heat exchanger type was considered in order to keep exhaust pressure drop within practical bounds.

Motivated by a combination of increasing consumer demand for fuel efficient vehicles, more stringent greenhouse gas, and anticipated future Corporate Average Fuel Economy (CAFE) standards, automotive manufacturers are working to innovate in all areas of vehicle design to improve fuel efficiency. In addition to improving aerodynamics, enhancing internal combustion engines and transmission technologies, and developing alternative fuel vehicles, reducing vehicle weight by using lighter materials and/or higher strength materials has been identified as one of the strategies in future vehicle development. Weight reduction in vehicle components, subsystems and systems not only reduces the energy needed to overcome inertia forces but also triggers additional mass reduction elsewhere and enables mass reduction in full vehicle levels.

A new turbocharged 60° 2.7L 4V-V6 gasoline engine has been developed by Ford Motor Company for both pickup trucks and car applications. This engine was code named “Nano” due to its compact size; it features a 4-valves DOHC valvetrain, a CGI cylinder block, an Aluminum ladder, an integrated exhaust manifold and twin turbochargers. The goal of this engine is to deliver 120HP/L, ULEV70 emission, fuel efficiency improvements and leadership level NVH. This paper describes the upfront design and optimization process used for the NVH development of this engine. It showcases the use of analytical tools used to define the critical design features and discusses the NVH performance relative to competitive benchmarks.

The higher cylinder peak pressure and pressure rise rate of modern diesel and gasoline fueled engines tend to increase combustion noise while customers demand lower noise. The multiple degrees of freedom in engine control and calibration mean there is more scope to influence combustion noise but this must first be measured before it can be balanced with other attributes. An efficient means to realize this is to calculate combustion noise from the in-cylinder pressure measurements that are routinely acquired as part of the engine development process. This publication reviews the techniques required to ensure accurate and precise combustion noise measurements. First, the dynamic range must be maximized by using an analogue to digital converter with sufficient number of bits and selecting an appropriate range in the test equipment.

We have recently obtained experimental data and used them to develop computational models to quantify occupant impact responses and injury risks for military vehicles during frontal crashes. The number of experimental tests and model runs are however, relatively small due to their high cost. While this is true across the auto industry, it is particularly critical for the Army and other government agencies operating under tight budget constraints. In this study we investigate through statistical simulations how the injury risk varies if a large number of experimental tests were conducted. We show that the injury risk distribution is skewed to the right implying that, although most physical tests result in a small injury risk, there are occasional physical tests for which the injury risk is extremely large. We compute the probabilities of such events and use them to identify optimum design conditions to minimize such probabilities.

A common approach to the validation of simulation models focuses on validation throughout the entire design space. A more recent methodology validates designs as they are generated during a simulation-based optimization process. The latter method relies on validating the simulation model in a sequence of local domains. To improve its computational efficiency, this paper proposes an iterative process, where the size and shape of local domains at the current step are determined from a parametric bootstrap methodology involving maximum likelihood estimators of unknown model parameters from the previous step. Validation is carried out in the local domain at each step. The iterative process continues until the local domain does not change from iteration to iteration during the optimization process ensuring that a converged design optimum has been obtained.

Optimal material selection for a part becomes quite challenging with dynamically changing data from various sources. Multiple manufacturing locations with varying supplier capabilities add to the complexity. There is need to balance product attribute requirements with manufacturing feasibility, cost, sourcing, and vehicle program strategies. The sequential consideration of product attribute, manufacturing, and sourcing aspects tends to result in design churns. Ford R&A is developing a web based material recommender tool to help engineers with material selection integrating sourcing, manufacturing, and design considerations. This tool is designed to filter the list of materials for a specific part and provide a prioritized list of materials; and allow engineers to do weight and cost trade-off studies. The initial implementation of this material recommender tool employs simplified analytical calculators for evaluation of structural performance metrics of parts.

Understanding reliability is critical in design, maintenance and durability analysis of engineering systems. A reliability simulation methodology is presented in this paper for vehicle fleets using limited data. The method can be used to estimate the reliability of non-repairable as well as repairable systems. It can optimally allocate, based on a target system reliability, individual component reliabilities using a multi-objective optimization algorithm. The algorithm establishes a Pareto front that can be used for optimal tradeoff between reliability and the associated cost. The method uses Monte Carlo simulation to estimate the system failure rate and reliability as a function of time. The probability density functions (PDF) of the time between failures for all components of the system are estimated using either limited data or a user-supplied MTBF (mean time between failures) and its coefficient of variation.

A three-step process was developed to estimate fracture criteria for a human body model. The process was illustrated via example wherein skull fracture criteria were estimated for the Ford Human Body Model (FHBM)~a finite element model of a mid-sized human male. The studied loading condition was anterior-to-posterior, blunt (circular/planar) cylinder impact to the frontal bone. In Step 1, a conditional reference risk curve was derived via statistical analysis of the tests involving fractures in a recently reported dataset (Cormier et al., 2011a). Therein, Cormier et al., authors reported results for anterior-to-posterior dynamic loading of the frontal bone of rigidly supported heads of male post mortem human subjects, and fracture forces were measured in 22 cases. In Step 2, the FHBM head was used to conduct some underlying model validations relative to the Cormier tests. The model-based Force-at-Peak Stress was found to approximate the test-based Fracture Force.

Design optimization techniques are widely used to drive designs toward a global or a near global optimal solution. However, the achieved optimal solution often appears to be the only choice that an engineer/designer can select as the final design. This is caused by either problem topology or by the nature of optimization algorithms to converge quickly in local/global optimal or both. Problem topology can be unimodal or multimodal with many local and/or global optimal solutions. For multimodal problems, most global algorithms tend to exploit the global optimal solution quickly but at the same time leaving the engineer with only one choice of design. The paper explores the application of genetic algorithms (GA), simulated annealing (SA), and mixed integer problem sequential quadratic programming (MIPSQP) to find multiple local and global solutions using single objective optimization formulation.