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Technical Paper

Random Vibration Analysis Using Quasi-Random Bootstrapping

2018-04-03
2018-01-1104
Reliability analysis of engineering structures such as bridges, airplanes, and cars require calculation of small failure probabilities. These probabilities can be calculated using standard Monte Carlo simulation, but this method is impractical for most real-life systems because of its high computational cost. Many studies have focused on reducing the computational cost of a reliability assessment. These include bootstrapping, Separable Monte Carlo, Importance Sampling, and the Combined Approximations. The computational cost can also be reduced using an efficient method for deterministic analysis such as the mode superposition, mode acceleration, and the combined acceleration method. This paper presents and demonstrates a method that uses a combination of Sobol quasi-random sequences and bootstrapping to reduce the number of function calls. The study demonstrates that the use of quasi-random numbers in conjunction bootstrapping reduces dramatically computational cost.
Journal Article

Value of Information for Comparing Dependent Repairable Assemblies and Systems

2018-04-03
2018-01-1103
This article presents an approach for comparing alternative repairable systems and calculating the value of information obtained by testing a specified number of such systems. More specifically, an approach is presented to determine the value of information that comes from field testing a specified number of systems in order to appropriately estimate the reliability metric associated with each of the respective repairable systems. Here the reliability of a repairable system will be measured by its failure rate. In support of the decision-making effort, the failure rate is translated into an expected utility based on a utility curve that represents the risk tolerance of the decision-maker. The algorithm calculates the change of the expected value of the decision with the sample size. The change in the value of the decision represents the value of information obtained from testing.
Technical Paper

Inverse Modeling: Theory and Engineering Examples

2016-04-05
2016-01-0267
Over the last two decades inverse problems have become increasingly popular due to their widespread applications. This popularity continuously demands designers to find alternative methods, to solve the inverse problems, which are efficient and accurate. It is important to use effective techniques that are both accurate and computationally efficient. This paper presents a method for solving inverse problems through Artificial Neural Network (ANN) theory. The paper also presents a method to apply Grey Wolf optimizer (GWO) algorithm to inverse problems. GWO is a recent optimization method producing superior results. Both methods are then compared to traditional methods such as Particle Swarm Optimization (PSO) and Markov Chain Monte Carlo (MCMC). Four typical engineering design problems are used to compare the four methods. The results show that the GWO outperforms other methods both in terms of efficiency and accuracy.
Technical Paper

Combined Approximation for Efficient Reliability Analysis of Linear Dynamic Systems

2015-04-14
2015-01-0424
The Combined Approximation (CA) method is an efficient reanalysis method that aims at reducing the cost of optimization problems. The CA uses results of a single exact analysis, and it is suitable for different types of structures and design variables. The second author utilized CA to calculate the frequency response function of a system at a frequency of interest by using the results at a frequency in the vicinity of that frequency. He showed that the CA yields accurate results for small frequency perturbations. This work demonstrates a methodology that utilizes CA to reduce the cost of Monte Carlo simulation (MCs) of linear systems under random dynamic loads. The main idea is to divide the power spectral density function (PSD) of the input load into several frequency bins before calculating the load realizations.
Journal Article

Bootstrapping and Separable Monte Carlo Simulation Methods Tailored for Efficient Assessment of Probability of Failure of Structural Systems

2015-04-14
2015-01-0420
There is randomness in both the applied loads and the strength of systems. Therefore, to account for the uncertainty, the safety of the system must be quantified using its reliability. Monte Carlo Simulation (MCS) is widely used for probabilistic analysis because of its robustness. However, the high computational cost limits the accuracy of MCS. Smarslok et al. [2010] developed an improved sampling technique for reliability assessment called Separable Monte Carlo (SMC) that can significantly increase the accuracy of estimation without increasing the cost of sampling. However, this method was applied to time-invariant problems involving two random variables. This paper extends SMC to problems with multiple random variables and develops a novel method for estimation of the standard deviation of the probability of failure of a structure. The method is demonstrated and validated on reliability assessment of an offshore wind turbine under turbulent wind loads.
Journal Article

Managing the Computational Cost of Monte Carlo Simulation with Importance Sampling by Considering the Value of Information

2013-04-08
2013-01-0943
Importance Sampling is a popular method for reliability assessment. Although it is significantly more efficient than standard Monte Carlo simulation if a suitable sampling distribution is used, in many design problems it is too expensive. The authors have previously proposed a method to manage the computational cost in standard Monte Carlo simulation that views design as a choice among alternatives with uncertain reliabilities. Information from simulation has value only if it helps the designer make a better choice among the alternatives. This paper extends their method to Importance Sampling. First, the designer estimates the prior probability density functions of the reliabilities of the alternative designs and calculates the expected utility of the choice of the best design. Subsequently, the designer estimates the likelihood function of the probability of failure by performing an initial simulation with Importance Sampling.
Technical Paper

Modeling Dependence and Assessing the Effect of Uncertainty in Dependence in Probabilistic Analysis and Decision Under Uncertainty

2010-04-12
2010-01-0697
A complete probabilistic model of uncertainty in probabilistic analysis and design problems is the joint probability distribution of the random variables. Often, it is impractical to estimate this joint probability distribution because the mechanism of the dependence of the variables is not completely understood. This paper proposes modeling dependence by using copulas and demonstrates their representational power. It also compares this representation with a Monte-Carlo simulation using dispersive sampling.
Journal Article

An RBDO Method for Multiple Failure Region Problems using Probabilistic Reanalysis and Approximate Metamodels

2009-04-20
2009-01-0204
A Reliability-Based Design Optimization (RBDO) method for multiple failure regions is presented. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with an approximate global metamodel with local refinements. The latter serves as an indicator to determine the failure and safe regions. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. An “accurate-on-demand” metamodel is used in the PRRA that allows us to handle problems with multiple disjoint failure regions and potentially multiple most-probable points (MPP). The multiple failure regions are identified by using a clustering technique. A maximin “space-filling” sampling technique is used to construct the metamodel. A vibration absorber example highlights the potential of the proposed method.
Technical Paper

Grammatical Evolution Based Tool for Predicting Multivariable Response Surface for Laser Lap Welding

2008-04-14
2008-01-1372
The problem of predicting the quality of weld is critical to manufacturing. A great deal of data is collected under multiple conditions to predict the quality. The data generated at Daimler Chrysler has been used to develop a model based on grammatical evolution. Grammatical Evolution Technique is based on Genetic Algorithms and generates rules from the data which fit the data. This paper describes the development of a software tool that enables the user to choose input variables such as the metal types of top and bottom layers and their thickness, intensity and speed of laser beam, to generate a three dimensional map showing weld quality. A 3D weld quality surface can be generated in response to any of the two input variables picked from the set of defining input parameters. This tool will enable the user to pick the right set of input conditions to get an optimal weld quality. The tool is developed in Matlab with Graphical User Interface for the ease of operation.
Technical Paper

Analytical Modeling and Simulation of a Swash Plate Pump/Motor

2008-04-14
2008-01-0573
This paper presents a computer generated model of a hydraulic circuit that is typically seen in hybrid hydraulic vehicles (HHV's). HHV's have shown considerable potential for increasing fuel economy and decreasing emissions for mid-size and commercial trucks that exhibit urban driving habits. The aim of the present model is to aid in further optimizing the performance of the hybrid powertrain and serve as a baseline for future studies into the noise and vibration (NV) associated with the system. The model simulates the regenerative braking process of a parallel type hybrid hydraulic propulsion system. Regenerative braking captures and stores otherwise lost energy into an accumulator. This stored energy can then later be used to propel the vehicle, thus reducing the vehicle's reliance on a conventional internal combustion engine (ICE). This model will serve as a baseline for future developments and will be expanded and validated experimentally in ensuing research.
Technical Paper

Application of the Modal Compliance Technique to a Vehicle Body in White

2007-05-15
2007-01-2355
This paper describes the application of the modal compliance method to a complex structure such as a vehicle body in white, and the extension of the method from normal modes to the complex modes of a complete vehicle. In addition to the usual bending and torsion calculations, the paper also describes the application of the method to less usual tests such as second torsion, match-boxing and breathing. We also show how the method can be used to investigate the distribution of compliance throughout the structure.
Technical Paper

An Efficient Re-Analysis Methodology for Vibration of Large-Scale Structures

2007-05-15
2007-01-2326
Finite element analysis is a well-established methodology in structural dynamics. However, optimization and/or probabilistic studies can be prohibitively expensive because they require repeated FE analyses of large models. Various reanalysis methods have been proposed in order to calculate efficiently the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. The parametric reduced-order modeling (PROM) and the combined approximation (CA) methods are two re-analysis methods, which can handle large model parameter changes in a relatively efficient manner. Although both methods are promising by themselves, they can not handle large FE models with large numbers of DOF (e.g. 100,000) with a large number of design parameters (e.g. 50), which are common in practice. In this paper, the advantages and disadvantages of the PROM and CA methods are first discussed in detail.
Technical Paper

Validation of Vehicle NVH Performance using Experimental Modal Testing and In-Vehicle Dynamic Measurements

2007-05-15
2007-01-2320
NVH targets for future vehicles are often defined by utilizing a competitive benchmarking vehicle in conjunction with an existing production and/or reference vehicle. Mode management of full vehicle modes is one of the most effective and significant NVH strategies to achieve such targets. NVH dynamic characteristics of a full vehicle can be assessed and quantified through experimental modal testing for determination of global body mode resonance frequency, damping property, and mode shape. Major body modes identified from full vehicle modal testing are primarily dominated by the vehicle's body-in-white structure. Therefore, an estimate of BIW modes from full vehicle modes becomes essential, when only full vehicle modes from experimental modal testing exist. Establishing BIW targets for future vehicles confines the fundamental NVH behavior of the full vehicle.
Technical Paper

Transmission Mount Assembly Modelling for Load Simulation and Analysis

2007-04-16
2007-01-1348
Transmission mounts are usually tested as an assembly and typically only translational stiffnesses are provided. The torsional stiffness of the assembly is traditionally estimated based on experience in load simulation and analysis. This paper presents a procedure to estimate the torsional stiffness of the transmission mount assembly by using the test data. The effects of the torsional stiffness on the simulation results are also discussed.
Technical Paper

Robust Optimization of Engine Lubrication System

2007-04-16
2007-01-1568
The quality of engine lubrication depends upon how much oil is supplied and how the lubricant is pressurized to the lubricated components. These variables strongly affect the safe operation and lifespan of an engine. During the conceptual design stage of an engine, its lubrication system cannot be verified experimentally. It is highly desirable for design engineers to utilize computer simulations and robust design methodology in order to achieve their goal of optimizing the engine lubrication system. The heuristic design principle is a relatively routine resource for design engineers to pursue although it is time consuming and sacrifices valuable developing time. This paper introduces an unusual design methodology in which design engineers were involved in analyzing their own designs along with lubrication system analyst to establish a link between two sophisticated software packages.
Technical Paper

Sensitivity Analysis of Powertrain Cooling System Performance

2007-04-16
2007-01-0598
This paper identifies the difference in powertrain cooling system content levels using a nominal and a +3 Standard deviation maximum temperature design approach. Variation simulation analysis tools are used along with a 1-D cooling system performance model to predict resulting temperature distribution for different combinations of input variable populations. The analysis will show differential in powertrain cooling system content, mass, and impact to fuel economy for a nominal vs. +3 sigma design approach.
Technical Paper

Tailor-Welded Aluminum Blanks for Liftgate Inner

2007-04-16
2007-01-0421
Tailor welded steel blanks have long been applied in stamping of automotive parts such as door inner, b-pillar, rail, sill inner and liftgate inner, etc. However, there are few known tailor welded aluminum blanks in production. Traditional laser welding equipment simply does not have the capability to weld aluminum since aluminum has much higher reflectivity than steel. Welding quality is another issue since aluminum is highly susceptible to pin holes and undercut which leads to deterioration in formability. In addition, high amount of springback for aluminum panels can result in dimension control problem during assembly. A tailor-welded aluminum blank can help reducing dimension variability by reducing the need for assembly. In this paper, application of friction stir and plasma arc welded blanks on a liftgate inner will be discussed.
Technical Paper

Optimization of Head Impact Waveform to Minimize HIC

2007-04-16
2007-01-0759
To mitigate head impact injuries of vehicle occupants in impact accidents, the FMVSS 201 requires padding of vehicle interior so that under the free-moving-head-form impact, the head injury criterion (HIC) is below the limit. More recently, pedestrian head impact on the vehicle bonnet has been a subject being studied and regulated as requirements to the automobile manufacturers. Over the years, the square wave has been considered as the best waveform for head impacts, although it is impractical to achieve. This paper revisits the head impact topic and challenges the optimality of aiming at the square waveform. It studies several different simple waveforms, with the objective to achieve minimal HIC or minimal crush space required in head-form impacts. With that it is found that many other waveforms can be more efficient and more practical than the square wave, especially for the pedestrian impact.
Technical Paper

Effect of Cross Flow on Performance of a PEM Fuel Cell

2007-04-16
2007-01-0697
A serpentine flow channel is one of the most common and practical channel layouts for a PEM fuel cell since it ensures the removal of water produced in a cell. While the reactant flows along the flow channel, it can also leak or cross to neighboring channels via the porous gas diffusion layer due to a high pressure gradient. Such a cross flow leads to effective water removal in a gas diffusion layer thus enlarging the active area for reaction although this cross flow has largely been ignored in previous studies. In this study, neutron radiography is applied to investigate the liquid water accumulation and its effect on the performance of a PEM fuel cell. Liquid water tends to accumulate in the gas diffusion layer adjacent to the flow channel area while the liquid water formed in the gas diffusion layer next to the channel land area seems to be effectively removed by the cross leakage flow between the adjacent flow channels.
Technical Paper

Multi-Disciplinary Aerodynamics Analysis for Vehicles: Application of External Flow Simulations to Aerodynamics, Aeroacoustics and Thermal Management of a Pickup Truck

2007-04-16
2007-01-0100
During the design process for a vehicle, the CAD surface geometry becomes available at an early stage so that numerical assessment of aerodynamic performance may accompany the design of the vehicle's shape. Accurate prediction requires open grille models with detailed underhood and underbody geometry with a high level of detail on the upper body surface, such as moldings, trim and parting lines. These details are also needed for aeroacoustics simulations to compute wall-pressure fluctuations, and for thermal management simulations to compute underhood cooling, surface temperatures and heat exchanger effectiveness. This paper presents the results of a significant effort to capitalize on the investment required to build a detailed virtual model of a pickup truck in order to simultaneously assess performance factors for aerodynamics, aeroacoustics and thermal management.
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