Application of Permutation Genetic Algorithm for Sequential Model Building–Model Validation Design of Experiments

YesThe work presented in this paper is motivated by a complex multivariate engineering problem associated with engine mapping experiments, which require efficient Design of Experiment (DoE) strategies to minimise expensive testing. The paper describes the development and evaluation of a Permutation Genetic Algorithm (PermGA) to support an exploration-based sequential DoE strategy for complex real-life engineering problems. A known PermGA was implemented to generate uniform OLH DoEs, and substantially extended to support generation of Model Building–Model Validation (MB-MV) sequences, by generating optimal infill sets of test points as OLH DoEs, that preserve good space filling and projection properties for the merged MB + MV test plan. The algorithm was further extended to address issues with non-orthogonal design spaces, which is a common problem in engineering applications. The effectiveness of the PermGA algorithm for the MB-MV OLH DoE sequence was evaluated through a theoretical benchmark problem based on the Six-Hump-Camel-Back (SHCB) function, as well as the Gasoline Direct Injection (GDI) engine steady state engine mapping problem that motivated this research. The case studies show that the algorithm is effective at delivering quasi-orthogonal space-filling DoEs with good properties even after several MB-MV iterations, while the improvement in model adequacy and accuracy can be monitored by the engineering analyst. The practical importance of this work, demonstrated through the engine case study, also is that significant reduction in the effort and cost of testing can be achieved.The research work presented in this paper was funded by the UK Technology Strategy Board (TSB) through the Carbon Reduction through Engine Optimization (CREO) project

Sampling CAD models via an extended teaching–learning-based optimization technique

The Teaching–Learning-Based Optimization (TLBO) algorithm of Rao et al. has been presented in recent years, which is a population-based algorithm and operates on the principle of teaching and learning. This algorithm is based on the influence of a teacher on the quality of learners in a population. In this study, TLBO is extended for constrained and unconstrained CAD model sampling which is called Sampling-TLBO (S-TLBO). Sampling CAD models in the design space can be useful for both designers and customers during the design stage. A good sampling technique should generate CAD models uniformly distributed in the entire design space so that designers or customers can well understand possible design options. To sample designs in a predefined design space, sub-populations are first generated each of which consists of separate learners. Teaching and learning phases are applied for each sub-population one by one which are based on a cost (fitness) function. Iterations are performed until change in the cost values becomes negligibly small. Teachers of each sub-population are regarded as sampled designs after the application of S-TLBO. For unconstrained design sampling, the cost function favors the generation of space-filling and Latin Hypercube designs. Space-filling is achieved using the Audze and Eglais’ technique. For constrained design sampling, a static constraint handling mechanism is utilized to penalize designs that do not satisfy the predefined design constraints. Four CAD models, a yacht hull, a wheel rim and two different wine glasses, are employed to validate the performance of the S-TLBO approach. Sampling is first done for unconstrained design spaces, whereby the models obtained are shown to users in order to learn their preferences which are represented in the form of geometric constraints. Samples in constrained design spaces are then generated. According to the experiments in this study, S-TLBO outperforms state-of-the-art techniques particularly when a high number of samples are generated

Evaluation of pairwise distances among points forming a regular orthogonal grid in a hypercube

Cartesian grid is a basic arrangement of points that form a regular orthogonal grid (ROG). In some applications, it is needed to evaluate all pairwise distances among ROG points. This paper focuses on ROG discretization of a unit hypercube of arbitrary dimension. A method for the fast enumeration of all pairwise distances and their counts for a high number of points arranged into high-dimensional ROG is presented. The proposed method exploits the regular and collapsible pattern of ROG to reduce the number of evaluated distances. The number of unique distances is identified and frequencies are determined using combinatorial rules. The measured computational speed-up compared to a nave approach corresponds to the presented theoretical analysis. The proposed method and algorithm may find applications in various fields. The paper shows application focused on the behaviour of various distance measures with the motivation to find the lower bounds on the criteria of point distribution uniformity in Monte Carlo integration

Efficient Approximation of Black-Box Functions and Pareto Sets.

In the case of time-consuming simulation models or other so-called black-box functions, we determine a metamodel which approximates the relation between the input- and output-variables of the simulation model. To solve multi-objective optimization problems, we approximate the Pareto set, i.e. the set of Pareto optimal solutions for which it is not possible to improve one objective without deteriorating another.

Maximin Designs for Computer Experiments.

Decision processes are nowadays often facilitated by simulation tools. In the field of engineering, for example, such tools are used to simulate the behavior of products and processes. Simulation runs, however, are often very time-consuming, and, hence, the number of simulation runs allowed is limited in practice. The problem then is to determine which simulation runs to perform such that the maximal amount of information about the product or process is obtained. This problem is addressed in the first part of the thesis. It is proposed to use so-called maximin Latin hypercube designs and many new results for this class of designs are obtained. In the second part, the case of multiple interrelated simulation tools is considered and a framework to deal with such tools is introduced. Important steps in this framework are the construction and the use of coordination methods and of nested designs in order to control the dependencies present between the various simulation tools

Application of Multidisciplinary Design Optimisation Frameworks for Engine Mapping and Calibration

With ever-increasing numbers of engine actuators to calibrate within increasingly stringent emissions legislation, the engine mapping and calibration task of identifying optimal actuator settings is much more difficult. The aim of this research is to evaluate the feasibility and effectiveness of the Multidisciplinary Design Optimisation (MDO) frameworks to optimise the multi-attribute steady state engine calibration optimisation problems. Accordingly, this research is concentrated on two aspects of the steady state engine calibration optimisation: 1) development of a sequential Design of Experiment (DoE) strategy to enhance the steady state engine mapping process, and 2) application of different MDO architectures to optimally calibrate the complex engine applications. The validation of this research is based on two case studies, the mapping and calibration optimisation of a JLR AJ133 Jaguar GDI engine; and calibration optimisation of an EU6 Jaguar passenger car diesel engine. These case studies illustrated that: -The proposed sequential DoE strategy offers a coherent framework for the engine mapping process including Screening, Model Building, and Model Validation sequences. Applying the DoE strategy for the GDI engine case study, the number of required engine test points was reduced by 30 – 50 %. - The MDO optimisation frameworks offer an effective approach for the steady state engine calibration, delivering a considerable fuel economy benefits. For instance, the MDO/ATC calibration solution reduced the fuel consumption over NEDC drive cycle for the GDI engine case study (i.e. with single injection strategy) by 7.11%, and for the diesel engine case study by 2.5%, compared to the benchmark solutions.UK Technology Strategy Board (TSB

A multi-criteria based selection method using non-dominated sorting for genetic algorithm based design

The paper presents a generative design approach, particularly for simulation-driven designs, using a genetic algorithm (GA), which is structured based on a novel offspring selection strategy. The proposed selection approach commences while enumerating the offsprings generated from the selected parents. Afterwards, a set of eminent offsprings is selected from the enumerated ones based on the following merit criteria: space-fillingness to generate as many distinct offsprings as possible, resemblance/non-resemblance of offsprings to the good/bad individuals, non-collapsingness to produce diverse simulation results and constrain-handling for the selection of offsprings satisfying design constraints. The selection problem itself is formulated as a multi-objective optimization problem. A greedy technique is employed based on non-dominated sorting, pruning, and selecting the representative solution. According to the experiments performed using three different application scenarios, namely simulation-driven product design, mechanical design and user-centred product design, the proposed selection technique outperforms the baseline GA selection techniques, such as tournament and ranking selections

Vehicle wakes subject to side wind conditions

Passenger vehicles are associated with travel flexibility, today it is clear that this flexibility impacts the environment. Passenger vehicles account for more than one-tenth of all greenhouse gasses in Europe with approximately a quarter of the vehicle\u27s energy consumption wasted as aerodynamic drag. Drag reduction has been and continues to be an active topic impacting fuel efficiency and electric vehicle range. This thesis is on aerodynamic drag of passenger vehicles in side wind conditions. The goal is to increase the knowledge of how vortical structures near the wake relate to the base pressure.\ua0 The presented work is focused on vehicle wakes and optimisation with the aim to aid in the design of future energy efficient vehicles.Vehicle wakes are often studied by comparing different configurations. The number of designs and possible combinations to be investigated is often limited due to time constraints. Instead of limiting the possible designs, optimisation was used to aid in the development of a low-drag reference geometry. A surrogate model-based optimisation method was developed and benchmarked against other common techniques. The surrogate model featured adaptively scaled Radial Basis Functions which performed well for the tested benchmark problems. The developed algorithm was used to optimise the geometry at the rear of a vehicle at yaw. This resulted in unexpected designs with good performance.The investigated geometries featured a base cavity with small angled surfaces, or kicks, at the trailing edge. This kick angle altered the wake balance, reducing the sensitivity to side wind. The wake\u27s unsteady behaviour changed when altering the cavity. Based on the results, it was not possible to find a consistent trend of the unsteadiness of the wake and its relation to drag alone. The results indicate that the improvements to the base pressure were primarily a result of altering the wake balance. The wake balance proved to be the most reliable indicator of drag, with and without additional side wind

Surrogate-based modeling strategy for design optimization of passenger car suspension system

The dynamic response of a Low-Fidelity (LoFi) vehicle model exhibits a discrepancy when compared to a High-Fidelity (HiFi) vehicle model. HiFi model construction involves complex state-space equations, a high degree of freedom, and requires a huge quantity of early data to completely define this model. This causes a delay and makes the computation process less efficient. On the other hand, the LoFi model developed using simpler state-space equations is faster and computationally cheaper. However, the response accuracy of this model is lower than that of HiFi. Due to this competence mismatch, it constrains the ability and integration of LoFi model or HiFi model applications in vehicle dynamics research. In previous researches, the proposed surrogate model has been completely replaced any physics-based model for subsequent engineering applications once it has been generated. However, this model has limitation to perform fine tuning either on LoFi or HiFi models. The primary aim of this research was to formulate a surrogate-based modeling strategy by tuning LoFi model for optimizing the design of the passenger car suspension system. The study began with the development of HiFi and LoFi models in Matlab, and their performances were verified by comparing the results produced by MSC Adams software. The LoFi model was used to determine the overall relationship between the suspension system's main elements, namely spring stiffness (Ks) and damper rate (Cs), and the design criteria, namely Body Acceleration (BAcc), Dynamic Tire Load (DTL), and Suspension Workspace (SWS). Based on the Design Criteria Space (DCS) map and recommendations from the literature, the Design Objective Space (DOS) map for a passenger car suspension system was established. Following that, three approaches to formulating surrogate models were introduced, namely the Response-Based Approach (RBA), the Variable-Based Approach (VBA), and the Parameter-Based Approach (PBA). The VBA for the Quadratic Transformation Scheme (QTS) was found to be the most suitable for the proposed newly surrogate model. Next, the surrogate model was linked to an optimization strategy to tune the suspension elements. Finally, a single optimal solution was obtained using the Min-Max method. The optimal tuning for the suspension elements of the chosen passenger car was Ks = 12535.6 N/m and Cs= 1416.7 Ns/m which increased the BAcc by 12.6% but at the expense of DTL performance by 6.4%, and keeping the SWS below the 7 mm restriction. In conclusion, the proposed surrogate-based modeling strategy could be a potential tool for optimizing the design of a passenger car suspension system