Tires, being the only component of the vehicle in contact with the road surface, are responsible for generating the forces for maintaining the vehicle pose, orientation and stability of the vehicle. Additionally, the on-board advanced chassis control systems require estimation of these tire-road interaction properties for their operation. Extraction of these properties becomes extremely important in handling limit maneuvers such as Double Lane Change (DLC) and cornering wherein the lateral force transfer is dependent upon these computations. This research focuses on the development of a high-fidelity vehicle-tire model and control algorithm framework for vehicle trajectory tracking for vehicles operating in this limit handling regime. This combined vehicle-tire model places an emphasis on the lateral dynamics of the vehicle by integrating the effects of relaxation length on the contact patch force generation. The vertical dynamics of the vehicle have also been analyzed, and a novel double damper has been mathematically modeled and experimentally validated. Different control algorithms, both classical and machine learning-based, have been developed for optimizing this vertical dynamics model. Experimental data has been collected by instrumenting a vehicle with in-tire accelerometers, IMU, GPS, and encoders for slalom and lane change maneuvers. Different state estimation techniques have been developed to predict the vehicle side slip angle, tire slip angle, and normal load to further assist the developed vehicle-tire model. To make the entire framework more robust, Machine Learning algorithms have been developed to classify between different levels of tire wear. The effect of tire tread wear on the pneumatic trail of the tire has been further evaluated, which affects the aligning moment and lateral force generation. Finally, a Model Predictive Control (MPC) framework has been developed to compare the performance between the conventional vehicle models and the developed vehicle models in tracking a reference trajectory. / Doctor of Philosophy / In our rapidly advancing world, self-driving or autonomous vehicles are no longer a vision of the future but a reality of today. As we grow more reliant on these vehicles, ensuring their safety and reliability becomes increasingly critical. Unlike traditional vehicles, self-driving cars operate without human intervention. Consequently, the onus of passenger and pedestrian safety falls squarely on the vehicle's control systems. The efficiency and effectiveness of these control systems are pivotal in preventing accidents and ensuring a smooth ride. One vital aspect of these control systems lies in understanding the tires' behavior, the only parts of the vehicle that are in contact with the road surface. A tire's interaction with the road surface significantly impacts the vehicle's handling and stability. Information such as how much of the tire is in contact with the road, the forces and moments generated at this contact point, becomes valuable for optimizing the vehicle's performance. This is particularly crucial when a vehicle is turning or cornering, where the forces developed between the tires and the road are key to maintaining control and stability. In this research, a framework has been designed to improve the vehicle performance, primarily by improving the modeling of tire lag dynamics. This refers to the delay or 'lag' between a change in tire conditions (such as pressure, wear, and temperature) and the corresponding change in tire behavior. In addition, in this research a vertical dynamics model of the vehicle has also been developed incorporated with a novel double damper suspension system. To complete the entire framework, the effect of tire wear over time and how this affects its performance and safety characteristics has also been examined. By estimating and understanding this wear, we can predict how it will affect the dynamic properties of the tire, thus improving the reliability and efficiency of our autonomous vehicles. The last piece of this framework comprises the development of an MPC controller to track a reference trajectory and evaluate the performance of the developed model.

O escopo do trabalho é a modelagem de um coxim elastomérico de motor, elemento que possui papel fundamental no isolamento vibracional do conjunto motor e transmissão. O estudo do comportamento mecânico de materiais elastoméricos é um campo que é desenvolvido a muitos anos devida complexidade e não-linearidade desses componentes; e modelos matemáticos fiéis são diferenciais competitivos. Assim essa dissertação tem como objetivo principal propor a modelagem de um coxim de motor elastomérico utilizando a técnica de redes neurais para generalizar a função de transferência entre o deslocamento do coxim e a aceleração vertical de motor. Duas abordagens de treinamento - dados experimentais coletados em bancada hidráulica uniaxial e dados experimentais coletados em campo - são apresentadas com o intuito de identificar a condição que a rede neural apresenta melhor performance de generalização. Para tal comparação uma métrica baseada em área da densidade espectral de potência é apresentada para quantificar o desempenho do modelo na faixa de frequência estudada (0-40 Hz). Finalmente é realizada uma comparação com um modelo mecânico composto por molas e amortecedores combinados. Os resultados demonstram que tanto o treinamento realizado com dados de bancada quanto o modelo mecânico apresentam boa correlação de 0 Hz a 14 Hz enquanto o treinamento realizado com dados de campo tem boa correlação de 0 Hz a 14 Hz e de 23 Hz a 40 Hz uma vez que essa abordagem tem capacidade de capturar a histerese e parte da não linearidade da borracha. É demonstrado que na faixa de frequência na qual todos modelos não foram capazes de generalizar existe modo de vibrar onde um nó no coxim estudado que dificulta a modelagem. Conclui-se que a técnica de redes neurais possui grande potencial em sua utilização, apresentando resultados bastante satisfatórios, além de outras vantagens, como a velocidade de processamento da rede treinada. / This dissertation scope is the modeling of an elastomeric mount, element which has primordial role on powertrain vibration isolation. The study of the mechanic behavior of those elastomeric materials is a field being studied for several years agor since its complexity and non-linarity of those components; and a reliable math models are competitive edge. So this dissertation has as main object purpose the modeling of an elastomeric engine mount using neural networks technician to predict the transfer function between the mount displacement and engine vertical accelerationTwo training approachs experimental data gathered in a uniaxial hydraulic bench and experimental data gathered in field are presented with the objective of identify the condition which the neural network presents better prediction performance. So this comparison being made a metric based on power density spectral area is presented to quantify the performance on the frequency range studied (0-40 Hz). Finally a comparison is made with a mechanical model composed per springs and dumpers combined. The results show that even the training made with the bench data and the mechnical model present good correlation from 0 Hz to 14 Hz while the training made with field data has good correlation from 0 Hz to 14 Hz and 23 Hz to 40 Hz once this approach has the ability to capture the hysteresis and part of rubber non-linearity. It is demonstrated that the frequency range where all the models are not capable to predict, there is a vibration mode where there is a node on the studied mount which dificults the modeling. The conclusion is that the neural network technique has great potential on its usage, presenting very satisfactory results, among other vantages as the processing speed after the network is trained.

O escopo do trabalho é a modelagem de um coxim elastomérico de motor, elemento que possui papel fundamental no isolamento vibracional do conjunto motor e transmissão. O estudo do comportamento mecânico de materiais elastoméricos é um campo que é desenvolvido a muitos anos devida complexidade e não-linearidade desses componentes; e modelos matemáticos fiéis são diferenciais competitivos. Assim essa dissertação tem como objetivo principal propor a modelagem de um coxim de motor elastomérico utilizando a técnica de redes neurais para generalizar a função de transferência entre o deslocamento do coxim e a aceleração vertical de motor. Duas abordagens de treinamento - dados experimentais coletados em bancada hidráulica uniaxial e dados experimentais coletados em campo - são apresentadas com o intuito de identificar a condição que a rede neural apresenta melhor performance de generalização. Para tal comparação uma métrica baseada em área da densidade espectral de potência é apresentada para quantificar o desempenho do modelo na faixa de frequência estudada (0-40 Hz). Finalmente é realizada uma comparação com um modelo mecânico composto por molas e amortecedores combinados. Os resultados demonstram que tanto o treinamento realizado com dados de bancada quanto o modelo mecânico apresentam boa correlação de 0 Hz a 14 Hz enquanto o treinamento realizado com dados de campo tem boa correlação de 0 Hz a 14 Hz e de 23 Hz a 40 Hz uma vez que essa abordagem tem capacidade de capturar a histerese e parte da não linearidade da borracha. É demonstrado que na faixa de frequência na qual todos modelos não foram capazes de generalizar existe modo de vibrar onde um nó no coxim estudado que dificulta a modelagem. Conclui-se que a técnica de redes neurais possui grande potencial em sua utilização, apresentando resultados bastante satisfatórios, além de outras vantagens, como a velocidade de processamento da rede treinada. / This dissertation scope is the modeling of an elastomeric mount, element which has primordial role on powertrain vibration isolation. The study of the mechanic behavior of those elastomeric materials is a field being studied for several years agor since its complexity and non-linarity of those components; and a reliable math models are competitive edge. So this dissertation has as main object purpose the modeling of an elastomeric engine mount using neural networks technician to predict the transfer function between the mount displacement and engine vertical accelerationTwo training approachs experimental data gathered in a uniaxial hydraulic bench and experimental data gathered in field are presented with the objective of identify the condition which the neural network presents better prediction performance. So this comparison being made a metric based on power density spectral area is presented to quantify the performance on the frequency range studied (0-40 Hz). Finally a comparison is made with a mechanical model composed per springs and dumpers combined. The results show that even the training made with the bench data and the mechnical model present good correlation from 0 Hz to 14 Hz while the training made with field data has good correlation from 0 Hz to 14 Hz and 23 Hz to 40 Hz once this approach has the ability to capture the hysteresis and part of rubber non-linearity. It is demonstrated that the frequency range where all the models are not capable to predict, there is a vibration mode where there is a node on the studied mount which dificults the modeling. The conclusion is that the neural network technique has great potential on its usage, presenting very satisfactory results, among other vantages as the processing speed after the network is trained.

Obtaining the modal parameters of a deflected and rolling tire represents a challenge due to the complex vibration characteristics that cause the tire's symmetry distortion and the natural frequencies' bifurcation phenomena. The modal parameters are usually extracted using a detailed finite element model. The main issue with full modal models (FEA, for example) is the inability to integrate the tire modal model with the vehicle models to tune the suspension system for optimal ride comfort. An in-plane rigid–elastic-coupled tire model was used to examine the 200 DOF finite difference method (FDM) modal analysis accuracy under non-ground contact and non-rotating conditions. The discrete in-plane rigid–elastic-coupled tire model was modified to include the contact patch restriction, centrifugal force, Doppler, and Coriolis effects, covering a range of 0-300 Hz. As a result, the influence of the contact patch and the rotating tire conditions on the natural frequencies and modes were obtained through modal analysis. The in-plane rigid–elastic-coupled modal model with varying conditions was created that connects any two DOFs around the tire's tread or sidewall as inputs or outputs. The vertical movement of the wheel was incorporated into the in-plane rigid–elastic-coupled tire modal model to extract the transfer function (TF) that connects road irregularities as an input to the wheel's vertical movement as an output. The TF was utilized in a quasi-static manner to obtain the tire's enveloping characteristics rolling over short wavelength obstacles as a direct function of vertical wheel displacement under varying contact patch length constraints. The tire modal model was implemented with the quarter car model to obtain the vehicle response rolling over short wavelength obstacles. Finally, a sensitivity analysis was performed to examine the influence of tire parameters and pretension forces on natural frequencies. / Doctor of Philosophy / The goal of vehicle manufacturers is to predict the vehicle's behavior under various driving conditions using mathematical models and simulation. Automotive companies rely heavily on computational simulation tools instead of real-time tests to shorten the product development cycle and reduce costs. However, the interaction between the tire and the road is one of the most critical aspects to consider when evaluating automobile stability and performance. The tires are responsible for generating the forces and moments that drive and maneuver the vehicle. Tires are complex products due to their intricate design, and their characteristics are affected by many factors such as vertical load, inflation pressure, speed, and a road with an uneven surface profile. Consequently, this project aims to describe the influence of various driving circumstances and load conditions on tire properties, as well as to develop a model that can represent the vertical tire and vehicle behavior while traveling over a cleat under different vehicle loads.

Esta Tese propõe uma nova ferramenta para Otimização Robusta Multiobjetivo por Análise de Intervalo Não Probabilística (Non-probabilistic Interval Analysis for Multiobjective Robust Design Optimization ou NPIA-MORDO). A ferramenta desenvolvida visa à otimização dos parâmetros concentrados de suspensão em um modelo veicular completo, submetido a uma manobra direcional percorrendo diferentes perfis de pista, a fim de garantir maior conforto e segurança ao motorista. O modelo multicorpo possui 15 graus de liberdade (15-GDL), dentre os quais onze pertencem ao veículo e assento, e quatro, ao modelo biodinâmico do motorista. A função multiobjetivo é composta por objetivos conflitantes e as suas tolerâncias, como a raiz do valor quadrático médio (root mean square ou RMS) da aceleração lateral e da aceleração vertical do assento do motorista, desenvolvidas durante a manobra de dupla troca de faixa (Double Lane Change ou DLC). O curso da suspensão e a aderência dos pneus à pista são tratados como restrições do problema de otimização. As incertezas são quantificadas no comportamento do sistema pela análise de intervalo não probabilística, por intermédio do Método dos Níveis de Corte-α (α-Cut Levels) para o nível α zero (de maior dispersão), e realizada concomitantemente ao processo de otimização multiobjetivo. Essas incertezas são aplicáveis tanto nos parâmetros do problema quanto nas variáveis de projeto. Para fins de validação do modelo, desenvolvido em ambiente MATLAB®, a trajetória do centro de gravidade da carroceria durante a manobra é comparada com o software CARSIM®, assim como as forças laterais e verticais dos pneus. Os resultados obtidos são exibidos em diversos gráficos a partir da fronteira de Pareto entre os múltiplos objetivos do modelo avaliado Os indivíduos da fronteira de Pareto satisfazem as condições do problema, e a função multiobjetivo obtida pela agregação dos múltiplos objetivos resulta em uma diferença de 1,66% entre os indivíduos com o menor e o maior valor agregado obtido. A partir das variáveis de projeto do melhor indivíduo da fronteira, gráficos são gerados para cada grau de liberdade do modelo, ilustrando o histórico dos deslocamentos, velocidades e acelerações. Para esse caso, a aceleração RMS vertical no assento do motorista é de 1,041 m/s² e a sua tolerância é de 0,631 m/s². Já a aceleração RMS lateral no assento do motorista é de 1,908 m/s² e a sua tolerância é de 0,168 m/s². Os resultados obtidos pelo NPIA-MORDO confirmam que é possível agregar as incertezas dos parâmetros e das variáveis de projeto à medida que se realiza a otimização externa, evitando a necessidade de análises posteriores de propagação de incertezas. A análise de intervalo não probabilística empregada pela ferramenta é uma alternativa viável de medida de dispersão se comparada com o desvio padrão, por não utilizar uma função de distribuição de probabilidades prévia e por aproximar-se da realidade na indústria automotiva, onde as tolerâncias são preferencialmente utilizadas. / This thesis proposes the development of a new tool for Non-probabilistic Interval Analysis for Multi-objective Robust Design Optimization (NPIA-MORDO). The developed tool aims at optimizing the lumped parameters of suspension in a full vehicle model, subjected to a double-lane change (DLC) maneuver throughout different random road profiles, to ensure comfort and safety to the driver. The multi-body model has 15 degrees of freedom (15-DOF) where 11-DOF represents the vehicle and its seat and 4-DOF represents the driver's biodynamic model. A multi-objective function is composed by conflicted objectives and their tolerances, like the root mean square (RMS) lateral and vertical acceleration in the driver’s seat, both generated during the double-lane change maneuver. The suspension working space and the road holding capacity are used as constraints for the optimization problem. On the other hand, the uncertainties in the system are quantified using a non-probabilistic interval analysis with the α-Cut Levels Method for zero α-level (the most uncertainty one), performed concurrently in the multi-objective optimization process. These uncertainties are both applied to the system parameters and design variables to ensure the robustness in results. For purposes of validation in the model, developed in MATLAB®, the path of the car’s body center of gravity during the maneuver is compared with the commercial software CARSIM®, as well as the lateral and vertical forces from the tires. The results are showed in many graphics obtained from the Pareto front between the multiple conflicting objectives of the evaluated model. The obtained solutions from the Pareto Front satisfy the conditions of the evaluated problem, and the aggregated multi-objective function results in a difference of 1.66% for the worst to the best solution. From the design variables of the best solution choose from the Pareto front, graphics are created for each degree of freedom, showing the time histories for displacements, velocities and accelerations. In this particular case, the RMS vertical acceleration in the driver’s seat is 1.041 m/s² and its tolerance is 0.631 m/s², but the RMS lateral acceleration in the driver’s seat is 1.908 m/s² and its tolerance is 0.168 m/s². The overall results obtained from NPIA-MORDO assure that is possible take into account the uncertainties from the system parameters and design variables as the external optimization loop is performed, reducing the efforts in subsequent evaluations. The non-probabilistic interval analysis performed by the proposed tool is a feasible choice to evaluate the uncertainty if compared to the standard deviation, because there is no need of previous well-known based probability distribution and because it reaches the practical needs from the automotive industry, where the tolerances are preferable.

Esta Tese propõe uma nova ferramenta para Otimização Robusta Multiobjetivo por Análise de Intervalo Não Probabilística (Non-probabilistic Interval Analysis for Multiobjective Robust Design Optimization ou NPIA-MORDO). A ferramenta desenvolvida visa à otimização dos parâmetros concentrados de suspensão em um modelo veicular completo, submetido a uma manobra direcional percorrendo diferentes perfis de pista, a fim de garantir maior conforto e segurança ao motorista. O modelo multicorpo possui 15 graus de liberdade (15-GDL), dentre os quais onze pertencem ao veículo e assento, e quatro, ao modelo biodinâmico do motorista. A função multiobjetivo é composta por objetivos conflitantes e as suas tolerâncias, como a raiz do valor quadrático médio (root mean square ou RMS) da aceleração lateral e da aceleração vertical do assento do motorista, desenvolvidas durante a manobra de dupla troca de faixa (Double Lane Change ou DLC). O curso da suspensão e a aderência dos pneus à pista são tratados como restrições do problema de otimização. As incertezas são quantificadas no comportamento do sistema pela análise de intervalo não probabilística, por intermédio do Método dos Níveis de Corte-α (α-Cut Levels) para o nível α zero (de maior dispersão), e realizada concomitantemente ao processo de otimização multiobjetivo. Essas incertezas são aplicáveis tanto nos parâmetros do problema quanto nas variáveis de projeto. Para fins de validação do modelo, desenvolvido em ambiente MATLAB®, a trajetória do centro de gravidade da carroceria durante a manobra é comparada com o software CARSIM®, assim como as forças laterais e verticais dos pneus. Os resultados obtidos são exibidos em diversos gráficos a partir da fronteira de Pareto entre os múltiplos objetivos do modelo avaliado Os indivíduos da fronteira de Pareto satisfazem as condições do problema, e a função multiobjetivo obtida pela agregação dos múltiplos objetivos resulta em uma diferença de 1,66% entre os indivíduos com o menor e o maior valor agregado obtido. A partir das variáveis de projeto do melhor indivíduo da fronteira, gráficos são gerados para cada grau de liberdade do modelo, ilustrando o histórico dos deslocamentos, velocidades e acelerações. Para esse caso, a aceleração RMS vertical no assento do motorista é de 1,041 m/s² e a sua tolerância é de 0,631 m/s². Já a aceleração RMS lateral no assento do motorista é de 1,908 m/s² e a sua tolerância é de 0,168 m/s². Os resultados obtidos pelo NPIA-MORDO confirmam que é possível agregar as incertezas dos parâmetros e das variáveis de projeto à medida que se realiza a otimização externa, evitando a necessidade de análises posteriores de propagação de incertezas. A análise de intervalo não probabilística empregada pela ferramenta é uma alternativa viável de medida de dispersão se comparada com o desvio padrão, por não utilizar uma função de distribuição de probabilidades prévia e por aproximar-se da realidade na indústria automotiva, onde as tolerâncias são preferencialmente utilizadas. / This thesis proposes the development of a new tool for Non-probabilistic Interval Analysis for Multi-objective Robust Design Optimization (NPIA-MORDO). The developed tool aims at optimizing the lumped parameters of suspension in a full vehicle model, subjected to a double-lane change (DLC) maneuver throughout different random road profiles, to ensure comfort and safety to the driver. The multi-body model has 15 degrees of freedom (15-DOF) where 11-DOF represents the vehicle and its seat and 4-DOF represents the driver's biodynamic model. A multi-objective function is composed by conflicted objectives and their tolerances, like the root mean square (RMS) lateral and vertical acceleration in the driver’s seat, both generated during the double-lane change maneuver. The suspension working space and the road holding capacity are used as constraints for the optimization problem. On the other hand, the uncertainties in the system are quantified using a non-probabilistic interval analysis with the α-Cut Levels Method for zero α-level (the most uncertainty one), performed concurrently in the multi-objective optimization process. These uncertainties are both applied to the system parameters and design variables to ensure the robustness in results. For purposes of validation in the model, developed in MATLAB®, the path of the car’s body center of gravity during the maneuver is compared with the commercial software CARSIM®, as well as the lateral and vertical forces from the tires. The results are showed in many graphics obtained from the Pareto front between the multiple conflicting objectives of the evaluated model. The obtained solutions from the Pareto Front satisfy the conditions of the evaluated problem, and the aggregated multi-objective function results in a difference of 1.66% for the worst to the best solution. From the design variables of the best solution choose from the Pareto front, graphics are created for each degree of freedom, showing the time histories for displacements, velocities and accelerations. In this particular case, the RMS vertical acceleration in the driver’s seat is 1.041 m/s² and its tolerance is 0.631 m/s², but the RMS lateral acceleration in the driver’s seat is 1.908 m/s² and its tolerance is 0.168 m/s². The overall results obtained from NPIA-MORDO assure that is possible take into account the uncertainties from the system parameters and design variables as the external optimization loop is performed, reducing the efforts in subsequent evaluations. The non-probabilistic interval analysis performed by the proposed tool is a feasible choice to evaluate the uncertainty if compared to the standard deviation, because there is no need of previous well-known based probability distribution and because it reaches the practical needs from the automotive industry, where the tolerances are preferable.

Esta Tese propõe uma nova ferramenta para Otimização Robusta Multiobjetivo por Análise de Intervalo Não Probabilística (Non-probabilistic Interval Analysis for Multiobjective Robust Design Optimization ou NPIA-MORDO). A ferramenta desenvolvida visa à otimização dos parâmetros concentrados de suspensão em um modelo veicular completo, submetido a uma manobra direcional percorrendo diferentes perfis de pista, a fim de garantir maior conforto e segurança ao motorista. O modelo multicorpo possui 15 graus de liberdade (15-GDL), dentre os quais onze pertencem ao veículo e assento, e quatro, ao modelo biodinâmico do motorista. A função multiobjetivo é composta por objetivos conflitantes e as suas tolerâncias, como a raiz do valor quadrático médio (root mean square ou RMS) da aceleração lateral e da aceleração vertical do assento do motorista, desenvolvidas durante a manobra de dupla troca de faixa (Double Lane Change ou DLC). O curso da suspensão e a aderência dos pneus à pista são tratados como restrições do problema de otimização. As incertezas são quantificadas no comportamento do sistema pela análise de intervalo não probabilística, por intermédio do Método dos Níveis de Corte-α (α-Cut Levels) para o nível α zero (de maior dispersão), e realizada concomitantemente ao processo de otimização multiobjetivo. Essas incertezas são aplicáveis tanto nos parâmetros do problema quanto nas variáveis de projeto. Para fins de validação do modelo, desenvolvido em ambiente MATLAB®, a trajetória do centro de gravidade da carroceria durante a manobra é comparada com o software CARSIM®, assim como as forças laterais e verticais dos pneus. Os resultados obtidos são exibidos em diversos gráficos a partir da fronteira de Pareto entre os múltiplos objetivos do modelo avaliado Os indivíduos da fronteira de Pareto satisfazem as condições do problema, e a função multiobjetivo obtida pela agregação dos múltiplos objetivos resulta em uma diferença de 1,66% entre os indivíduos com o menor e o maior valor agregado obtido. A partir das variáveis de projeto do melhor indivíduo da fronteira, gráficos são gerados para cada grau de liberdade do modelo, ilustrando o histórico dos deslocamentos, velocidades e acelerações. Para esse caso, a aceleração RMS vertical no assento do motorista é de 1,041 m/s² e a sua tolerância é de 0,631 m/s². Já a aceleração RMS lateral no assento do motorista é de 1,908 m/s² e a sua tolerância é de 0,168 m/s². Os resultados obtidos pelo NPIA-MORDO confirmam que é possível agregar as incertezas dos parâmetros e das variáveis de projeto à medida que se realiza a otimização externa, evitando a necessidade de análises posteriores de propagação de incertezas. A análise de intervalo não probabilística empregada pela ferramenta é uma alternativa viável de medida de dispersão se comparada com o desvio padrão, por não utilizar uma função de distribuição de probabilidades prévia e por aproximar-se da realidade na indústria automotiva, onde as tolerâncias são preferencialmente utilizadas. / This thesis proposes the development of a new tool for Non-probabilistic Interval Analysis for Multi-objective Robust Design Optimization (NPIA-MORDO). The developed tool aims at optimizing the lumped parameters of suspension in a full vehicle model, subjected to a double-lane change (DLC) maneuver throughout different random road profiles, to ensure comfort and safety to the driver. The multi-body model has 15 degrees of freedom (15-DOF) where 11-DOF represents the vehicle and its seat and 4-DOF represents the driver's biodynamic model. A multi-objective function is composed by conflicted objectives and their tolerances, like the root mean square (RMS) lateral and vertical acceleration in the driver’s seat, both generated during the double-lane change maneuver. The suspension working space and the road holding capacity are used as constraints for the optimization problem. On the other hand, the uncertainties in the system are quantified using a non-probabilistic interval analysis with the α-Cut Levels Method for zero α-level (the most uncertainty one), performed concurrently in the multi-objective optimization process. These uncertainties are both applied to the system parameters and design variables to ensure the robustness in results. For purposes of validation in the model, developed in MATLAB®, the path of the car’s body center of gravity during the maneuver is compared with the commercial software CARSIM®, as well as the lateral and vertical forces from the tires. The results are showed in many graphics obtained from the Pareto front between the multiple conflicting objectives of the evaluated model. The obtained solutions from the Pareto Front satisfy the conditions of the evaluated problem, and the aggregated multi-objective function results in a difference of 1.66% for the worst to the best solution. From the design variables of the best solution choose from the Pareto front, graphics are created for each degree of freedom, showing the time histories for displacements, velocities and accelerations. In this particular case, the RMS vertical acceleration in the driver’s seat is 1.041 m/s² and its tolerance is 0.631 m/s², but the RMS lateral acceleration in the driver’s seat is 1.908 m/s² and its tolerance is 0.168 m/s². The overall results obtained from NPIA-MORDO assure that is possible take into account the uncertainties from the system parameters and design variables as the external optimization loop is performed, reducing the efforts in subsequent evaluations. The non-probabilistic interval analysis performed by the proposed tool is a feasible choice to evaluate the uncertainty if compared to the standard deviation, because there is no need of previous well-known based probability distribution and because it reaches the practical needs from the automotive industry, where the tolerances are preferable.

The object of this master thesis is testing of vehicle using four post rig. The main goal is to make a research about testing and tuning vehicle characteristics on four post rig in order to implement them for testing of TU Brno Racing’s Formula Student racecar. The main method of testing, input signals and measurement description are presented in this thesis. The different methods of analysis of testing data to find best tuning of damper and spring stiffness for different race disciplines are described. In the last part of this work, quarter car model and multibody model in MSC Adams Car is created. Input parameters of model are based on measurements from real car/ component testing, including damper characteristics and static tire radial stiffness for best fit with the characteristics of real vehicle. The measurements themselves were also described in separate chapter of this thesis. The last but not the least goal was to compare these simulations with measurements, made od real four post rig in order to decide whether car model is suitable for racecar development.