Test/Analysis Correlation Using Design Sensitivity and Optimization

<p>The primary objective of this study is to develop new computational methods for robust design optimization (RDO) and reliability-based design optimization (RBDO) of high-dimensional, complex engineering systems. Four major research directions, all anchored in polynomial dimensional decomposition (PDD), have been defined to meet the objective. They involve: (1) development of new sensitivity analysis methods for RDO and RBDO; (2) development of novel optimization methods for solving RDO problems; (3) development of novel optimization methods for solving RBDO problems; and (4) development of a novel scheme and formulation to solve stochastic design optimization problems with both distributional and structural design parameters.</p> <p>The major achievements are as follows. Firstly, three new computational methods were developed for calculating design sensitivities of statistical moments and reliability of high-dimensional complex systems subject to random inputs. The first method represents a novel integration of PDD of a multivariate stochastic response function and score functions, leading to analytical expressions of design sensitivities of the first two moments. The second and third methods, relevant to probability distribution or reliability analysis, exploit two distinct combinations built on PDD: the PDD-SPA method, entailing the saddlepoint approximation (SPA) and score functions; and the PDD-MCS method, utilizing the embedded Monte Carlo simulation (MCS) of the PDD approximation and score functions. For all three methods developed, both the statistical moments or failure probabilities and their design sensitivities are both determined concurrently from a single stochastic analysis or simulation. Secondly, four new methods were developed for RDO of complex engineering systems. The methods involve PDD of a high-dimensional stochastic response for statistical moment analysis, a novel integration of PDD and score functions for calculating the second-moment sensitivities with respect to the design variables, and standard gradient-based optimization algorithms. The methods, depending on how statistical moment and sensitivity analyses are dovetailed with an optimization algorithm, encompass direct, single-step, sequential, and multi-point single-step design processes. Thirdly, two new methods were developed for RBDO of complex engineering systems. The methods involve an adaptive-sparse polynomial dimensional decomposition (AS-PDD) of a high-dimensional stochastic response for reliability analysis, a novel integration of AS-PDD and score functions for calculating the sensitivities of the failure probability with respect to design variables, and standard gradient-based optimization algorithms, resulting in a multi-point, single-step design process. The two methods, depending on how the failure probability and its design sensitivities are evaluated, exploit two distinct combinations built on AS-PDD: the AS-PDD-SPA method, entailing SPA and score functions; and the AS-PDD-MCS method, utilizing the embedded MCS of the AS-PDD approximation and score functions. In addition, a new method, named as the augmented PDD method, was developed for RDO and RBDO subject to mixed design variables, comprising both distributional and structural design variables. The method comprises a new augmented PDD of a high-dimensional stochastic response for statistical moment and reliability analyses; an integration of the augmented PDD, score functions, and finite-difference approximation for calculating the sensitivities of the first two moments and the failure probability with respect to distributional and structural design variables; and standard gradient-based optimization algorithms, leading to a multi-point, single-step design process.</p> <p>The innovative formulations of statistical moment and reliability analysis, design sensitivity analysis, and optimization algorithms have achieved not only highly accurate but also computationally efficient design solutions. Therefore, these new methods are capable of performing industrial-scale design optimization with numerous design variables.</p>

<div class="section abstract"><div class="htmlview paragraph">Evaluation of pedestrian leg protection performance using the Flex-PLI-GTR (Flexible Pedestrian Legform Impactor Global Technical Regulation) impactor is initiated in JNCAP in 2011. Therefore, a finite element (FE) model of Flex-PLI-GTR is needed for use in digital car development in order to satisfy pedestrian leg protection performance requirements. This paper describes the FE model of Flex-PLI-GTR that has been developed to meet this need.</div><div class="htmlview paragraph">There are three important features of this FE model for obtaining sufficient simulation accuracy. First, the shapes of all Flex-PLI-GTR structures were modeled in detail. Shape information of the inner structures was obtained by computerized tomography scanning and shape information of the inner structures of the outer skin was obtained by laser measurement. Furthermore, the shape of the wrapped skin was incorporated into the FE model based on a wrapping simulation. Second, the material and mechanical properties except the outer skin and rubber were set based on publicly released information without any tuning. The material properties of the outer skin and rubber were obtained experimentally using test pieces under different strain rates. The absence of tuning enables this FE model to be applied to different impact situations involving various velocities or impact angles. Third, pre-stressing of the outer skin and preloading of the springs in the knee structure were incorporated into the FE model by conducting preliminary simulations based on differences between before and after the skin is wrapped on the impactor. These measures have made it possible to represent faithfully the mechanical properties of the entire impactor.</div><div class="htmlview paragraph">A comparison of the results of pendulum impact tests and FE simulations verified that this FE model of Flex-PLI-GTR provides sufficient simulation accuracy. This FE model is now being used to evaluate pedestrian leg protection performance in the digital car development process.</div></div>

<div class="section abstract"><div class="htmlview paragraph">Plenum system of automotive vehicles draws atmospheric air using HVAC blower motor through air inlet grille at the bottom of the windshield and uses lower plenum for rainwater drainage after which air flow enters into awning and sugar scoop for evaporator air flow requirement. Awning and sugar scoop component is used in plenum air flow system to ensure the air flow with the required velocity that would meet the performance metric of total pressure drop of plenum air flow system. The optimal design of plenum component is essential since blower motor energy needs to be drawn from the expensive battery pack and any wastage of energy would lead to reduction in range of the Electric Vehicle. The conventional design process utilizes incremental design iteration, engineering intuition and requires significant effort from engineers to meet performance targets within the specified design space. This also may or may not ensure an optimal design.</div><div class="htmlview paragraph">In this work, a Machine learning tool with extreme gradient boost algorithm is used for development of a robust meta model that is used for quick prediction of awning and sugar scoop performance parameters such as total pressure drop and velocity of air prediction. On this response surface, application of a meta heuristic [<span class="xref">1</span>] based global optimization method is demonstrated which uses simplex homological global optimization (SHGO) and differential evolutionary (DE) method for optimum awning and sugar scoop design. Simplex homological global optimization (SHGO) is the concept of homology group growth which is used to solve a global and derivative free optimization problem of arbitrarily high dimensions. Similarly Differential evolution (DE) is a population-based metaheuristic search algorithm [<span class="xref">2</span>] that optimizes a problem which can quickly explore very large design spaces. Using these global optimization algorithms, it is observed that the optimized design of the awning and sugar scoop does result in significant reduction of total pressure drop that helps improve the required performance substantially compared to baseline design parameters within the given design space.</div></div>

This paper designs and optimizes a new structure hybrid material B‐pillar assembly. Establish a finite element analysis model for the side impact test of an electric vehicle to verify the model's accuracy. Construct a finite element model of the hybrid material B‐pillar assembly. Combined with the static performance analysis of the B‐pillar, the laminate design of the carbon fiber composite B‐pillar reinforcement plate and optimization. For the outer and inner panels of the B‐pillar, the surrogate model method and the multiobjective optimization method are combined to set 11 design variables and 13 responses. The optimal Latin hypercube design method was used to randomly sample each design variable and fit the radial basis function (RBF) approximate model. The modified second‐generation non‐dominated sorting genetic algorithm (MNSGA‐II) was used to carry out multiobjective optimization of the mixed material B‐pillar assembly, and the multicriteria decision‐making method was used to obtain the optimal solution for the Pareto solution set. A drop weight impact test was performed on the hybrid material B‐pillar assembly. The results showed that the peak collision force of the hybrid material B‐pillar was reduced by 43.7% compared with the original steel B‐pillar, the specific energy absorption was increased by 17.5%, and the side impact safety performance was better. After optimization, the weight of the mixed material B‐column was reduced by 26.44%. The improvement rates of the intrusion amount at P2 and the intrusion speed at P1 were 23.99% and 0.63%, respectively, and the lightweight effect and side impact safety were significantly improved.Highlights The finite element analysis parameters of carbon fiber composite materials were constructed through experiments, and the basis for simulation analysis under various working conditions of the B‐pillar based on performance‐driven optimization was established. A hybrid material B‐pillar design method is proposed, which consists of a variable‐thickness high‐strength steel B‐pillar outer plate, a variable‐thickness high‐strength steel B‐pillar inner plate, and a carbon fiber composite B‐pillar reinforcement plate. The super layer of the carbon fiber composite B‐pillar reinforcement plate was optimized and the laying plan of the carbon fiber composite B‐pillar reinforcement plate was determined. Performance‐driven optimization is adopted to realize the collaboration of multilevel design and optimization methods such as B‐pillar conceptual design, detailed design, and multiobjective optimization. A modified NSGA‐II algorithm was proposed and combined with the multicriteria decision‐making method and the entropy‐weighted gray relation analysis method to determine the Pareto optimal solution and the optimal design scheme for the mixed material B‐pillar.

A state space design sensitivity analysis and optimization method is presented in which problems of optimal design of machines are formulated in a setting that allows treatment of general design objectives and constraints. Synthesis of machines to perform both kinematic and kinetic functions is considered. A Cartesian coordinate formulation is employed for position, velocity, acceleration, and force analysis. An adjoint variable technique is employed to compute derivatives with respect to design of general cost and constraint functions that involve kinematic, force, and design variables. Linearization (or sequential quadratic programming) and gradient projection optimization algorithms are employed, using the design sensitivity analysis method developed, for design optimization. Four optimal design problems are solved to demonstrate use of the method.

Aircraft manufacturing companies have to consider multiple derivatives to satisfy various market requirements. They modify or extend an existing aircraft to meet the new market demands while keeping the development time and the cost to a minimum. Many researchers have studied the derivative design process, but these research considered the baseline and the derivatives together, while using the whole set of design variables. Therefore, an efficient process that can reduce the cost and the time for the aircraft derivative design is needed. In this dissertation, Aircraft Derivative Design Optimization process (ADDOPT) was developed which obtains the global changes from the local changes in the aircraft design to develop the aircraft derivatives efficiently. The sensitivity analysis was implemented to ignore design variables that have low impact on the objective function. This avoids wasting computational effort and time on low priority variables for design requirements and objectives. Additionally, the classification of uncertainty from its characteristics and sources of uncertainty involved in the aircraft design process were suggested to consider with design optimization. Uncertainty from the fidelity of analysis tools was applied in design optimization to increase the probability of optimization results. To handle uncertainty in low fidelity analysis tools on aircraft conceptual design optimization, Reliability Based Design Optimization (RBDO) and Possibility Based Design Optimization (PBDO) methods were performed. In this research, Extended Fourier Amplitude Sensitivity Test (eFAST) method was implemented in ADDOPT for Global Sensitivity Analysis (GSA) method and Collaborative Optimization (CO) based framework with RBDO and PBDO were also used. These methods were evaluated using numerical examples. ADDOPT was carried through on the civil jet aircraft derivative design. The objective of the optimization problem was to increase cruise range while satisfying the requirement such as the number of passengers. The proposed process reduced computation effort by reducing the number of design variables and achieved the target probability of failure when considering uncertainty from low fidelity analysis tools.

Aircraft manufacturing companies have to consider multiple derivatives to satisfy various market requirements. They modify or extend an existing aircraft to meet new market demands while keeping the development time and cost to a minimum. Many researchers have studied the derivative design process, but these research efforts consider baseline and derivative designs together, while using the whole set of design variables. Therefore, an efficient process that can reduce cost and time for aircraft derivative design is needed. In this research, a more efficient design process is proposed which obtains global changes from local changes in aircraft design in order to develop aircraft derivatives efficiently. Sensitivity analysis was introduced to remove unnecessary design variables that have a low impact on the objective function. This prevented wasting computational effort and time on low priority variables for design requirements and objectives. Additionally, uncertainty from the fidelity of analysis tools was considered in design optimization to increase the probability of optimization results. The Reliability Based Design Optimization (RBDO) and Possibility Based Design Optimization (PBDO) methods were proposed to handle the uncertainty in aircraft conceptual design optimization. In this paper, Collaborative Optimization (CO) based framework with RBDO and PBDO was implemented to consider uncertainty. The proposed method was applied for civil jet aircraft derivative design that increases cruise range and the number of passengers. The proposed process provided deterministic design optimization, RBDO, and PBDO results for given requirements.

<div class="section abstract"><div class="htmlview paragraph">The characteristics of suspension elastic elements (i.e., spring, damper and anti-roll bar) are directly related to the handling and ride comfort performances, how to tune the characteristics of suspensions' elastic elements is always a big issue in developing the chassis of a vehicle. In this paper, a multi-body dynamics model of a passenger car within MSC.ADAMS® is integrated with iSight FD®, an optimization tool, to carry out a multi-objective optimization for improving the behavior of vehicle handling and ride comfort. The characteristics of suspension elastic elements (i.e., spring, damper and anti-roll bar) are considered as design variables. For handling, the objectives are defined by the measurements from multi-body dynamics simulation of typical double lane change according to ISO3888 standard. For ride comfort, the frequency-weighted RMS (Root Mean Square) value of vertical acceleration of the front seat rail according to ISO2631 standard is set as the objective. The optimization methods which is suitable to the multi-objective trade-offs in vehicle development are discussed, and some simulation results about the cooperative optimization between handling & ride comfort are presented in this paper.</div></div>

Methodologies for greatly improving machine structural dynamics are presented in which design sensitivity analyses and evaluative parameters are used according to the fundamental procedures of the design optimization method based on clarification of competitive and cooperative relationships between characteristics. First, design sensitivity coefficients and evaluative parameters of structural dynamics are described. Then, design improvement methods of structural dynamics are proposed for the following three cases : (1) addition of elastic structural members, (2) addition of mass elements, and (3) substantial changes of joint design variables. Cases (1) and (2) correspond to the changes of the initial framework or configuration, and case (3) corresponds to the alteration of poor initial design variables. Finally, the methods are demonstrated with numerical examples for a machine tool structural model.

<div class="section abstract"><div class="htmlview paragraph">An Air intake system (AIS) is a duct system which leads the airflow going into the internal combustion engine. Combustion requires oxygen, and the more oxygen is provided into the combustion process the more power it will produce. The lower the air temperature, the higher its density, and hence there is more oxygen in a unit volume. The quality of air entering engine can be measured with the air temperature.</div><div class="htmlview paragraph">AIS design and routing influence the air charge temperature (ACT) at intake manifold runners and ACT is normally measured at AIS throttle body in reality. Higher ACT lead to inefficient combustion and can lead to spark retard. Optimization of AIS designs and reduction of ACT can improve engine performance and vehicle fuel economy.</div><div class="htmlview paragraph">High ACT can be a result of two different phenomena: <ul class="list disc"><li class="list-item"><div class="htmlview paragraph">Recirculation - Hot air from the underhood environment ingested into the dirty side of the air intake system. This is the result of the AIS snorkel not being isolated or sealed from the engine compartment hot air.</div></li><li class="list-item"><div class="htmlview paragraph">Underhood temperature rise - Air inside AIS is heated by the ducts walls because it is routed through a hot underhood environment. The longer the length and larger the diameter of the air induction system, and the higher duct skin temperatures, the worse the temperature rise.</div></li></ul></div><div class="htmlview paragraph">In this paper, it is planned to simulate and study the effects of following factors on ACT with CFD using a FCA production vehicle: <ul class="list disc"><li class="list-item"><div class="htmlview paragraph">Snorkel location: snorkel sucking fresh air at side air guide or snorkel sucking underhood hot recirculation air.</div></li><li class="list-item"><div class="htmlview paragraph">Exhaust hot end at front of an east-west engine or at the rear of the engine; these two arrangements will result in different underhood air temperatures and radiation to AIS surfaces.</div></li><li class="list-item"><div class="htmlview paragraph">Heat shield effects on ACT: heat shield blocks radiation from exhaust system to AIS surfaces, and hence reduces charge air heat pick from AIS duct walls.</div></li><li class="list-item"><div class="htmlview paragraph">The effects of other measures such as cutting holes on hood or fenders to lower engine compartment air temperatures.</div></li></ul></div><div class="htmlview paragraph">Although the airflow in vehicle AIS duct is transient in nature, steady CFD simulations will be performed to study the above cases for simplification, and CFD approach will be discussed in details. Vehicle test data will be used to validate the CFD models.</div><div class="htmlview paragraph">Finally, general practices of AIS development will be discussed, and future work on this topic will be outlined.</div></div>

<div class="htmlview paragraph">Increasingly, manufacturers are looking to computer simulation methods to accurately assess ride quality potential of new vehicle designs as they are being developed. This requires detailed multi-body dynamic models to be developed with sufficient fidelity to replicate ride relevant phenomenon. These models must have the capability to:</div> <div class="htmlview paragraph"> <ul class="list disc"> <li class="list-item"><div class="htmlview paragraph">Represent the distributed mass and elasticity of the vehicle structures (e.g. frame ladder, cab, and trailer).</div></li> <li class="list-item"><div class="htmlview paragraph">Include the non-linear behavior of shock absorbers and elastomeric components.</div></li> <li class="list-item"><div class="htmlview paragraph">Reproduce the fundamental system dynamics that influence ride.</div></li> <li class="list-item"><div class="htmlview paragraph">Provide output of the acceleration, velocity, and displacement measures needed to compute ride quality.</div></li> </ul> </div> <div class="htmlview paragraph">This paper discusses the development of an ADAMS multi-body dynamic model of a tractor semi-trailer for use as a predictive tool in evaluating ride quality design improvements. The model includes flexible representations of the frame, cab, and trailer generated from finite element models through the use of component mode synthesis. Non-linearities and viscoelastic effects associated with compliant elements and dampers are selectively incorporated using explicit functions and spline/surface interpolation. Road inputs into the suspension are generated via tire elements in contact with road profiles or by prescribing axle motions. Additionally, a ride quality algorithm is built into the model allowing virtual ride measurements to be taken and compared to physical test results.</div> <div class="htmlview paragraph">Construction and correlation of the model followed a multi-step process in which each of the major subsystems were built and validated to test results prior to incorporation in the full vehicle model. Ride data from a vehicle instrumented with 70 transducers was collected on highway routes and used to support full vehicle correlation.</div> <div class="htmlview paragraph">The ability of the model to predict ride quality variations due to changes in vehicle configuration was tested by evaluating several case studies. These results are presented along with details of the model construction and correlation process.</div>

<div class="section abstract"><div class="htmlview paragraph">A finite element model of a folded airbag with the module cover and steering wheel system was developed to estimate the injury numbers of a 5<sup>th</sup> percentile female dummy in an out-of-position (OOP) situation. The airbag model was correlated with static airbag deployments and standard force plate tests. The 5<sup>th</sup> percentile finite element dummy model developed by First Technology Safety Systems (FTSS) was used in the simulation.</div><div class="htmlview paragraph">The following two OOP tests were simulated with the airbag model including a validated steering wheel finite element model: <ol class="list nostyle"> <li class="list-item"> <span class="li-label">1.</span> <div class="htmlview paragraph">Chest on air bag module for maximum chest interaction from pressure loading (MS6-D) and</div></li> <li class="list-item"> <span class="li-label">2.</span> <div class="htmlview paragraph">Neck on air bag module for maximum neck interaction from membrane loading (MS8-D).</div></li></ol></div><div class="htmlview paragraph">These two simulations were then compared to the test results. Satisfactory correlation was found in both the cases.</div><div class="htmlview paragraph">This airbag mathematical model was then used in parametric studies to investigate the effects of airbag module design changes and occupant position mapping studies.</div></div>

When globally optimal designs are important and required sensitivity analysis is complicated, genetic algorithms can be effective alternatives to gradient-based optimization methods. Genetic algorithms are being used more widely in various engineering fields. However, when the design variables become large, standard genetic algorithms become difficult to use because of excessive computation time needed to obtain converged solutions. In this investigation, we consider two-dimensional structural topology optimizations based on finite element models as a large-size optimization problem. To expedite the solution convergence by orders of magnitude, the genetic algorithm in the multiscale multiresolution setting is proposed. By the multiscale setting, standard single-scale binary design variables are represented in multiple scales by the so-called Binary Wavelet Transform. Note that all genetic operators such as crossover and mutation must be redefined or modified for multiscaled design variables. A key advantage of using multiscale design variables is that the exploration of solution becomes more effective with them. If the multiresolution setting based on the multiscale variables is used, the design optimization can proceed from low to high resolution over several resolution stages where the information passing over resolutions is very effective. In this multiresolution approach, a converged population at a certain resolution level is reused as a part of the initial population at the next higher resolution level. In fact, we form the initial population in three groups: the converged population in the previous resolution, a randomly generated population and the mixture of the converged population and the random population. The detailed technique to generate the three groups is presented, which is an important part of the developed multiscale multiresolution genetic algorithm. The convergence improvement by the multiscale multiresolution approach was verified numerically with several numerical case studies.

<div class="htmlview paragraph">In this paper the development of statistical metamodels and statistical fast running models is presented first. They are utilized for propagating uncertainties in a multi-discipline design optimization process. Two main types of uncertainty can be considered in this manner: uncertainty due to variability in design variables or in random parameters; uncertainty due to the utilization of metamodels instead of the actual simulation models during the optimization process. The value of the new developments and their engagement in multi-discipline design optimization is demonstrated through a case study. An underwater vehicle is designed under four different disciplines, namely, noise radiation, self-noise due to TBL excitation, dynamic response due to propulsion impact loads, and response to an underwater detonation. The case study also demonstrates the value of the multi-discipline design optimization in identifying a system level optimum, and it emphasizes the importance of including uncertainties in the design optimization process.</div>

Mass customization necessitates increased product variety at the customers’ end but comparatively lesser part variety at the manufacturer’s end. Product platform concepts have been successful to achieve this goal at large. One of the popular methods for product platform formation is to scale one or more design variables called the scaling variables. Effective optimization methods are needed to identify proper values of the scaling variables. This paper presents a graph-based optimization method called the scalable platforms using ant colony optimization (SPACO) method for identifying appropriate values of the scaling variables. In the graph-based representation, each node signifies a sub-range of values for a design variable. This application includes the concept of multiplicity in node selection because there are multiple nodes corresponding to the discretized values of a given design variable. In the SPACO method, the overall decision is a result of the cumulative decisions, made by simple computing agents called the ants, over a number of iterations. The space search technique initially starts as a random search technique over the entire search space and progressively turns into an autocatalytic (positive feedback) probabilistic search technique as the solution matures. We use a family of universal electric motors, widely cited in the literature, to test the effectiveness of the proposed method. Our simulation results, when compared to the results reported in the literature, prove that SPACO method is a viable optimization method for determining the values of design variables for scalable platforms.