Application of Surrogate Based Optimisation in the Design of Automotive Body Structures

The rapid development of automotive industry requires manufacturers to continuously reduce the development cost and time and to enhance the product quality. Thus, modern automotive design pays more attention to using CAE analysis based optimisation techniques to drive the entire design flow. This thesis focuses on the optimisation design to improve the automotive crashworthiness and fatigue performances, aiming to enhance the optimisation efficiency, accuracy, reliability, and robustness etc. The detailed contents are as follows: (1) To excavate the potential of crash energy absorbers, the concept of functionally graded structure was introduced and multiobjective designs were implemented to this novel type of structures. First, note that the severe deformation takes place in the tubal corners, multi-cell tubes with a lateral thickness gradient were proposed to better enhance the crashworthiness. The results of crashworthiness analyses and optimisation showed that these functionally graded multi-cell tubes are preferable to a uniform multi-cell tube. Then, functionally graded foam filled tubes with different gradient patterns were analyzed and optimized subject to lateral impact and the results demonstrated that these structures can still behave better than uniform foam filled structures under lateral loading, which will broaden the application scope of functionally graded structures. Finally, dual functionally graded structures, i.e. functionally graded foam filled tubes with functionally graded thickness walls, were proposed and different combinations of gradients were compared. The results indicated that placing more material to tubal corners and the maximum density to the outmost layer are beneficial to achieve the best performance. (2) To make full use of training data, multiple ensembles of surrogate models were proposed to maximize the fatigue life of a truck cab, while the panel thicknesses were taken as design variables and the structural mass the constraint. Meanwhile, particle swarm optimisation was integrated with sequential quadratic programming to avoid the premature convergence. The results illustrated that the hybrid particle swarm optimisation and ensembles of surrogates enable to attain a more competent solution for fatigue optimisation. (3) As the conventional surrogate based optimisation largely depends on the number of initial sample data, sequential surrogate modeling was proposed to practical applications in automotive industry. (a) To maximize the fatigue life of spot-welded joints, an expected improvement based sequential surrogate modeling method was utilized. The results showed that by using this method the performance can be significantly improved with only a relatively small number of finite element analyses. (c) A multiojective sequential surrogate modeling method was proposed to address a multiobjective optimisation of a foam-filled double cylindrical structure. By adding the sequential points and updating the Kriging model adaptively, more accurate Pareto solutions are generated. (4) While various uncertainties are inevitably present in real-life optimisations, conventional deterministic optimisations could probably lead to the violation of constraints and the instability of performances. Therefore, nondeterministic optimisation methods were introduced to solve the automotive design problems. (a) A multiobjective reliability-based optimisation for design of a door was investigated. Based on analysis and design responses surface models, the structural mass was minimized and the vertical sag stiffness was maximized subjected to the probabilistic constraint. The results revealed that the Pareto frontier is divided into the sensitive region and insensitive region with respect to uncertainties, and the decision maker is recommended to select a solution from the insensitive region. Furthermore, the reduction of uncertainties can help improve the reliability but will increase the manufacturing cost, and the tradeoff between the reliability target and performance should be made. (b) A multiobjective uncertain optimisation of the foam-filled double cylindrical structure was conducted by considering randomness in the foam density and wall thicknesses. Multiobjective particle swarm optimisation and Monte Carlo simulation were integrated into the optimisation. The results proved that while the performances of the objectives are sacrificed slightly, the nondeterministic optimisation can enhance the robustness of the objectives and maintain the reliability of the constraint. (c) A multiobjective robust optimisation of the truck cab was performed by considering the uncertainty in material properties. The general version of dual response surface model, namely dual surrogate model, was proposed to approximate the means and standard deviations of the performances. Then, the multiobjective particle optimisation was used to generate the well-distributed Pareto frontier. Finally, a hybrid multi-criteria decision making model was proposed to select the best compromise solution considering both the fatigue performance and its robustness. During this PhD study, the following ideas are considered innovative: (1) Surrogate modeling and multiobjective optimisation were integrated to address the design problems of novel functionally graded structures, aiming to develop more advanced automotive energy absorbers. (2) The ensembles of surrogates and hybrid particle swarm optimisation were proposed for the design of a truck cab, which could make full use of training points and has a strong searching capacity. (3) Sequential surrogate modeling methods were introduced to several optimisation problems in the automotive industry so that the optimisations are less dependent on the number of initial training points and both the efficiency and accuracy are improved. (4) The surrogate based optimisation method was implemented to address various uncertainties in real life applications. Furthermore, a hybrid multi-criteria decision making model was proposed to make the best compromise between the performance and robustness

Uncertain design optimization of automobile structures: A survey

In real life, there are a lot of uncertainties in engineering structure design, and the potential uncertainties will have an important impact on the structural performance responses. Therefore, it is of great significance to consider the uncertainty in the initial stage of structural design to improve product performance. The consensus can be reached that the mechanical structure obtained by the reliability and robustness design optimization method considering uncertainty not only has low failure risk but also has highly stable performance. As a large mechanical system, the uncertainty design optimization of key vehicle structural performances is particularly important. This survey mainly discusses the current situation of the uncertain design optimization framework of automobile structures, and successively summarizes the uncertain design optimization of key automobile structures, uncertainty analysis methods, and multi-objective iterative optimization models. The uncertainty analysis method in the design optimization framework needs to consider the existing limited knowledge and limited test data. The importance of the interval model as a non-probabilistic model in the uncertainty analysis and optimization process is discussed. However, it should be noted that the interval model ignores the actual uncertainty distribution rule, which makes the design scheme still have some limitations. With the further improvement of design requirements, the efficiency, accuracy, and calculation cost of the entire design optimization framework of automobile structures need to be further improved iteratively. This survey will provide useful theoretical guidance for engineers and researchers in the automotive engineering field at the early stage of product development

Stresses and deformations in involute spur gears by finite element method

This thesis investigates the characteristics of an involute gear system including contact stresses, bending stresses, and the transmission errors of gears in mesh. Gearing is one of the most critical components in mechanical power transmission systems. Transmission error is considered to be one of the main contributors to noise and vibration in a gear set. Transmission error measurement has become popular as an area of research on gears and is possible method for quality control. To estimate transmission error in a gear system, the characteristics of involute spur gears were analyzed by using the finite element method. The contact stresses were examined using 2-D FEM models. The bending stresses in the tooth root were examined using a 3-D FEM model. Current methods of calculating gear contact stresses use Hertz’s equations, which were originally derived for contact between two cylinders. To enable the investigation of contact problems with FEM, the stiffness relationship between the two contact areas is usually established through a spring placed between the two contacting areas. This can be achieved by inserting a contact element placed in between the two areas where contact occurs. The results of the two dimensional FEM analyses from ANSYS are presented. These stresses were compared with the theoretical values. Both results agree very well. This indicates that the FEM model is accurate. This thesis also considers the variations of the whole gear body stiffness arising from the gear body rotation due to bending deflection, shearing displacement and contact deformation. Many different positions within the meshing cycle were investigated

Multi-objective optimization design for a battery pack of electric vehicle with surrogate models

In this investigation, a systematic surrogate-based optimization design framework for a battery pack is presented. An air-cooling battery pack equipped on electric vehicles is first designed. Finite element analysis (FEA) results of the baseline design show that global maximum stresses under x-axis and y-axis transient acceleration shock condition are both above the tensile limit of material. Selecting the panel and beam thickness of battery pack as design variables, with global maximum stress constraints in shock cases, a multi-objective optimization problem is implemented using metamodel technique and multi-objective particle-swarm-optimization (MOPSO) algorithm to simultaneously minimize the total mass and maximize the restrained basic frequency. It is found that 2nd order polynomial response surface (PRS), 3rd order PRS and radial basis function (RBF) are the most accurate and appropriate metamodels for restrained basic frequency, global maximum stresses under x-axis and y-axis shock conditions respectively. Results demonstrate that all the optimal solutions in Pareto Frontier have heavier weight and lower frequency compared with baseline design due to the restriction of global maximum stress response. Finally, two optimal schemes, “Knee Point” and “lightest weight”, satisfied both of the stress constraint conditions, show great consistency with FEA results and can be selected as alternative improved schemes

Multi-objective crashworthiness design optimization of a rollover protective structure by an improved constraint-handling technique

This study proposes a multi-objective optimization (MOO) strategy with an improved constraint-handling technique to improve the crashworthiness of an excavator rollover protective structure (ROPS). First, the experimental test under the ISO 12117 criteria is conducted and the developed numerical model is verified. Then, the amounts of energy absorption and the cross-sectional forces of components in the ROPS are analyzed. The main energy absorbing and load carrying components are identified. Finally, the thicknesses of the identified components are considered as the design variables. A multi-objective crashworthiness optimization process aims at improving the safety distance and reducing the total mass is designed by the finite element analysis-based surrogate model technique and a modified MOO algorithm. The proposed algorithm modifies the objective function values of an individual with its constraint violations and the true objective function values, of which adaptive penalty weights fed back from the constraint violations are used to keep the balance. Compared with the existing methods, it is found that the optimal solutions obtained by the proposed algorithm show superiority on convergence rate and diversity of distribution. The optimal results show that the safety distance is 27.42% higher while the total mass is 7.06% lower than those of the baseline design when it meets the requirements of ISO 12117. This study provides an alternative crashworthiness design route for the ROPS of the construction machines

Crack growth simulation in 13th row of compressor blades under foreign object damage and resonant vibration condition

In this study, the cracks growth rate in the 13th row of the T56 compressor blades was studied to investigate their fatigue life. For this purpose, the centrifugal and aerodynamic forces on the blade were calculated and then the resulting stress field was obtained by using finite element method. Then, the critical points of stress were determined and the initial semi-elliptical cracks were modeled at these points. After modeling of the initial crack, the stress intensity factor on the crack front was calculated by ANSYS software. Furthermore, the number of required cycles for the crack growth and blade fracture were calculated by applying Paris law to a certain value. After crack growth at this stage, a crack with new length was also modeled at the same point and all the mentioned stages for its growth, were repeated. In this paper, the modal analysis of the blade was conducted and normal frequencies with possible stimulation on compressor velocity were determined by Campbell Diagram. After determining the stress field at resonant frequency, all stages of crack growth were repeated under these conditions to calculate the fatigue life

Design Optimization of Composite Deployable Bridge Systems Using Hybrid Meta-heuristic Methods for Rapid Post-disaster Mobility

Recent decades have witnessed an increase in the transportation infrastructure damage caused by natural disasters such as earthquakes, high winds, floods, as well as man-made disasters. Such damages result in a disruption to the transportation infrastructure network; hence, limit the post-disaster relief operations. This led to the exigency of developing and using effective deployable bridge systems for rapid post-disaster mobility while minimizing the weight to capacity ratio. Recent researches for assessments of mobile bridging requirements concluded that current deployable metallic bridge systems are prone to their service life, unable to meet the increase in vehicle design loads, and any trials for the structures’ strengthening will sacrifice the ease of mobility. Therefore, this research focuses on developing a lightweight deployable bridge system using composite laminates for lightweight bridging in the aftermath of natural disaster. The research investigates the structural design optimization for composite laminate deployable bridge systems, as well as the design, development and testing of composite sandwich core sections that act as the compression bearing element in a deployable bridge treadway structure. The thesis is organized into two parts. The first part includes a new improved particle swarm meta-heuristic approach capable of effectively optimizing deployable bridge systems. The developed approach is extended to modify the technique for discrete design of composite laminates and maximum strength design of composite sandwich core sections. The second part focuses on developing, experimentally testing and numerically investigating the performance of different sandwich core configurations that will be used as the compression bearing element in a deployable fibre-reinforced polymer (FRP) bridge girder. The first part investigated different optimization algorithms used for structural optimization. The uncertainty in the effectiveness of the available methods to handle complex structural models emphasized the need to develop an enhanced version of Particle Swarm Optimizer (PSO) without performing multiple operations using different techniques. The new technique implements a better emulation for the attraction and repulsion behavior of the swarm. The new algorithm is called Controlled Diversity Particle Swarm Optimizer (CD-PSO). The algorithm improved the performance of the classical PSO in terms of solution stability, quality, convergence rate and computational time. The CD-PSO is then hybridized with the Response Surface Methodology (RSM) to redirect the swarm search for probing feasible solutions in hyperspace using only the design parameters of strong influence on the objective function. This is triggered when the algorithm fails to obtain good solutions using CD-PSO. The performance of CD-PSO is tested on benchmark structures and compared to others in the literature. Consequently, both techniques, CD-, and hybrid CD-PSO are examined for the minimum weight design of large-scale deployable bridge structure. Furthermore, a discrete version of the algorithm is created to handle the discrete nature of the composite laminate sandwich core design. The second part focuses on achieving an effective composite deployable bridge system, this is realized through maximizing shear strength, compression strength, and stiffness designs of light-weight composite sandwich cores of the treadway bridge’s compression deck. Different composite sandwich cores are investigated and their progressive failure is numerically evaluated. The performance of the sandwich cores is experimentally tested in terms of flatwise compressive strength, edgewise compressive strength and shear strength capacities. Further, the cores’ compression strength and shear strength capacities are numerically simulated and the results are validated with the experimental work. Based on the numerical and experimental tests findings, the sandwich cores plate properties are quantified for future implementation in optimized scaled deployable bridge treadway