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

Development of sustainable groundwater management methodologies to control saltwater intrusion into coastal aquifers with application to a tropical Pacific island country

Saltwater intrusion due to the over-exploitation of groundwater in coastal aquifers is a critical challenge facing groundwater-dependent coastal communities throughout the world. Sustainable management of coastal aquifers for maintaining abstracted groundwater quality within permissible salinity limits is regarded as an important groundwater management problem necessitating urgent reliable and optimal management methodologies. This study focuses on the development and evaluation of groundwater salinity prediction tools, coastal aquifer multi-objective management strategies, and adaptive management strategies using new prediction models, coupled simulation-optimization (S/O) models, and monitoring network design, respectively. Predicting the extent of saltwater intrusion into coastal aquifers in response to existing and changing pumping patterns is a prerequisite of any groundwater management framework. This study investigates the feasibility of using support vector machine regression (SVMR), an innovative artificial intelligence-based machine learning algorithm, to predict salinity at monitoring wells in an illustrative aquifer under variable groundwater pumping conditions. For evaluation purposes, the prediction results of SVMR are compared with well-established genetic programming (GP) based surrogate models. The prediction capabilities of the two learning machines are evaluated using several measures to ensure their practicality and generalisation ability. Also, a sensitivity analysis methodology is proposed for assessing the impact of pumping rates on salt concentrations at monitoring locations. The performance evaluations suggest that the predictive capability of SVMR is superior to that of GP models. The sensitivity analysis identifies a subset of the most influential pumping rates, which is used to construct new SVMR surrogate models with improved predictive capabilities. The improved predictive capability and generalisation ability of SVMR models, together with the ability to improve the accuracy of prediction by refining the dataset used for training, make the use of SVMR models more attractive. Coupled S/O models are efficient tools that are used for designing multi-objective coastal aquifer management strategies. This study applies a regional-scale coupled S/O methodology with a Pareto front clustering technique to prescribe optimal groundwater withdrawal patterns from the Bonriki aquifer in the Pacific Island of Kiribati. A numerical simulation model is developed, calibrated and validated using field data from the Bonriki aquifer. For computational feasibility, SVMR surrogate models are trained and tested utilizing input-output datasets generated using the flow and transport numerical simulation model. The developed surrogate models were externally coupled with a multi-objective genetic algorithm optimization (MOGA) model, as a substitute for the numerical model. The study area consisted of freshwater pumping wells for extracting groundwater. Pumping from barrier wells installed along the coastlines is also considered as a management option to hydraulically control saltwater intrusion. The objective of the multi-objective management model was to maximise pumping from production wells and minimize pumping from barrier wells (which provide a hydraulic barrier) to ensure that the water quality at different monitoring locations remains within pre-specified limits. The executed multi-objective coupled S/O model generated 700 Pareto-optimal solutions. Analysing a large set of Pareto-optimal solution is a challenging task for the decision-makers. Hence, the k-means clustering technique was utilized to reduce the large Pareto-optimal solution set and help solve the large-scale saltwater intrusion problem in the Bonriki aquifer. The S/O-based management models have delivered optimal saltwater intrusion management strategies. However, at times, uncertainties in the numerical simulation model due to uncertain aquifer parameters are not incorporated into the management models. The present study explicitly incorporates aquifer parameter uncertainty into a multi-objective management model for the optimal design of groundwater pumping strategies from the unconfined Bonriki aquifer. To achieve computational efficiency and feasibility of the management model, the calibrated numerical simulation model in the S/O model was is replaced with ensembles of SVMR surrogate models. Each SVMR standalone surrogate model in the ensemble is constructed using datasets from different numerical simulation models with different hydraulic conductivity and porosity values. These ensemble SVMR models were coupled to the MOGA model to solve the Bonriki aquifer management problem for ensuring sustainable withdrawal rates that maintain specified salinity limits. The executed optimization model presented a Pareto-front with 600 non-dominated optimal trade-off pumping solutions. The reliability of the management model, established after validation of the optimal solution results, suggests that the implemented constraints of the optimization problem were satisfied; i.e., the salinities at monitoring locations remained within the pre-specified limits. The correct implementation of a prescribed optimal management strategy based on the coupled S/O model is always a concern for decision-makers. The management strategy actually implemented in the field sometimes deviates from the recommended optimal strategy, resulting in field-level deviations. Monitoring such field-level deviations during actual implementation of the recommended optimal management strategy and sequentially updating the strategy using feedback information is an important step towards adaptive management of coastal groundwater resources. In this study, a three-phase adaptive management framework for a coastal aquifer subjected to saltwater intrusion is applied and evaluated for a regional-scale coastal aquifer study area. The methodology adopted includes three sequential components. First, an optimal management strategy (consisting of groundwater extraction from production and barrier wells) is derived and implemented for the optimal management of the aquifer. The implemented management strategy is obtained by solving a homogeneous ensemble-based coupled S/O model. Second, a regional-scale optimal monitoring network is designed for the aquifer system, which considers possible user noncompliance of a recommended management strategy and uncertainty in aquifer parameter estimates. A new monitoring network design is formulated to ensure that candidate monitoring wells are placed at high risk (highly contaminated) locations. In addition, a k-means clustering methodology is utilized to select candidate monitoring wells in areas representative of the entire model domain. Finally, feedback information in the form of salinity measurements at monitoring wells is used to sequentially modify pumping strategies for future time periods in the management horizon. The developed adaptive management framework is evaluated by applying it to the Bonriki aquifer system. Overall, the results of this study suggest that the implemented adaptive management strategy has the potential to address practical implementation issues arising due to user noncompliance, as well as deviations between predicted and actual consequences of implementing a management strategy, and uncertainty in aquifer parameters. The use of ensemble prediction models is known to be more accurate standalone prediction models. The present study develops and utilises homogeneous and heterogeneous ensemble models based on several standalone evolutionary algorithms, including artificial neural networks (ANN), GP, SVMR and Gaussian process regression (GPR). These models are used to predict groundwater salinity in the Bonriki aquifer. Standalone and ensemble prediction models are trained and validated using identical pumping and salinity concentration datasets generated by solving numerical 3D transient density-dependent coastal aquifer flow and transport numerical simulation models. After validation, the ensemble models are used to predict salinity concentration at selected monitoring wells in the modelled aquifer under variable groundwater pumping conditions. The predictive capabilities of the developed ensemble models are quantified using standard statistical procedures. The performance evaluation results suggest that the predictive capabilities of the standalone prediction models (ANN, GP, SVMR and GPR) are comparable to those of the groundwater variable-density flow and salt transport numerical simulation model. However, GPR standalone models had better predictive capabilities than the other standalone models. Also, SVMR and GPR standalone models were more efficient (in terms of computational training time) than other standalone models. In terms of ensemble models, the performance of the homogeneous GPR ensemble model was found to be superior to that of the other homogeneous and heterogeneous ensemble models. Employing data-driven predictive models as replacements for complex groundwater flow and transport models enables the prediction of future scenarios and also helps save computational time, effort and requirements when developing optimal coastal aquifer management strategies based on coupled S/O models. In this study, a new data-driven model, namely Group method for data handling (GMDH) approach is developed and utilized to predict salinity concentration in a coastal aquifer and, simultaneously, determine the most influential input predictor variables (pumping rates) that had the most impact onto the outcomes (salinity at monitoring locations). To confirm the importance of variables, three tests are conducted, in which new GMDH models are constructed using subsets of the original datasets. In TEST 1, new GMDH models are constructed using a set of most influential variables only. In TEST 2, a subset of 20 variables (10 most and 10 least influential variables) are used to develop new GMDH models. In TEST 3, a subset of the least influential variables is used to develop GMDH models. A performance evaluation demonstrates that the GMDH models developed using the entire dataset have reasonable predictive accuracy and efficiency. A comparison of the performance evaluations of the three tests highlights the importance of appropriately selecting input pumping rates when developing predictive models. These results suggest that incorporating the least influential variables decreases model accuracy; thus, only considering the most influential variables in salinity prediction models is beneficial and appropriate. This study also investigated the efficiency and viability of using artificial freshwater recharge (AFR) to increase fresh groundwater pumping rates from production wells. First, the effect of AFR on the inland encroachment of saline water is quantified for existing scenarios. Specifically, groundwater head and salinity differences at monitoring locations before and after artificial recharge are presented. Second, a multi-objective management model incorporating groundwater pumping and AFR is implemented to control groundwater salinization in an illustrative coastal aquifer system. A coupled SVMR-MOGA model is developed for prescribing optimal management strategies that incorporate AFR and groundwater pumping wells. The Pareto-optimal front obtained from the SVMR-MOGA optimization model presents a set of optimal solutions for the sustainable management of the coastal aquifer. The pumping strategies obtained as Pareto-optimal solutions with and without freshwater recharge shows that saltwater intrusion is sensitive to AFR. Also, the hydraulic head lenses created by AFR can be used as one practical option to control saltwater intrusion. The developed 3D saltwater intrusion model, the predictive capabilities of the developed SVMR models, and the feasibility of using the proposed coupled multi-objective SVMR-MOGA optimization model make the proposed methodology potentially suitable for solving large-scale regional saltwater intrusion management problems. Overall, the development and evaluation of various groundwater numerical simulation models, predictive models, multi-objective management strategies and adaptive methodologies will provide decision-makers with tools for the sustainable management of coastal aquifers. It is envisioned that the outcomes of this research will provide useful information to groundwater managers and stakeholders, and offer potential resolutions to policy-makers regarding the sustainable management of groundwater resources. The real-life case study of the Bonriki aquifer presented in this study provides the scientific community with a broader understanding of groundwater resource issues in coastal aquifers and establishes the practical utility of the developed management strategies