Otimização paramétrica robusta multiobjetivo aplicada em suspensão veicular

A presente dissertação aplica uma metodologia de otimização robusta multiobjetivo ao problema da otimização de parâmetros da suspensão de um modelo numérico de meio carro com 5 graus de liberdade. A fim de aumentar o conforto do motorista do veículo sem prejudicar a dirigibilidade, a função objetivo escolhida foi a aceleração rms ponderada conforme a norma ISO 2631 (1997) com restrição no espaço de trabalho da suspensão. A otimização robusta é baseada em uma abordagem probabilística, mais completa do que aquela baseada em intervalos. A solução é comparada com uma otimização determinística, que não leva em consideração as incertezas. O estudo leva em conta diferentes aproximações presentes na literatura para a média e desvio padrão da função e da restrição, comparando os benefícios e prejuízos dos métodos. A solução gerada pela otimização robusta multiobjetivo escolhida resulta em uma média de aceleração rms ponderada de 0,205 /ଶ, contra 0,183 /ଶ da otimização determinística. Estas soluções, robusta e determinística, representam uma redução de 85,25% e 86,82% da aceleração da configuração de referência, respectivamente. No entanto, a probabilidade de falha calculada a partir do método de Monte Carlo com 25000 amostras mostrou que a otimização robusta permaneceu dentro do intervalo de segurança aceitável do espaço de trabalho da suspensão que foi estipulado em 10%, com apenas 8,69% de chance de falha da restrição, contra 66,23% de chance de falha para a solução determinística.This dissertation applies a multiobjective robust optimization methodology to the suspension optimization problem of a 5 degrees of freedom half-car numerical model. In order to increase the driver’s comfort without compromising the drivability, the chosen objective function was the weighted rms acceleration according to ISO 2631 (1997) with constrain regarding the suspension working space. The robust optimization is based in a probabilistic approach, more complete compared to the interval based approach. The study accounts for different approximation approaches present in the literature for the mean and deviation of function and constrain, comparing the advantages and disadvantages of each method. The chosen solution generated by the multiobjective robust optimization results in a mean for weighted rms acceleration of 0.205 /² against 0.183 /ଶ for the deterministic solution. These solutions, robust and deterministic, represent a reduction of 85.25% and 86.82% of the acceleration of the reference configuration, respectively. However, the failure probability calculated with the Monte Carlo method using 25000 samples, show that the robust optimization remained within the acceptable safety range of the suspension workspace which has been set to 10%, with an 8.69% chance of failure, against 66.23% chance of failure for the deterministic solution

An efficient anti-optimization approach for uncertainty analysis in composite laminates

This work presents an efficient approach to quantify uncertainties in composite laminates using the interval analysis, anti-optimization technique, and the α-cut procedure. The solutions are compared with the traditional and robust Monte Carlo method in 3 cases scenarios: natural frequencies, buckling, and strength safe factor. For natural frequencies and buckling loads, the presented Interval based methodology showed 2.5% to 4.5% larger error values when compared to the Monte Carlo method using the same number of function calls. This implies a larger uncertain area, and hence, a better solution. For the strength test using Tsai-Wu failure theory, the error values are even greater: 22% to 46%. A violation of the failure limit was detected by the proposed Interval based approach, but not detected by Monte Carlo method. The solutions show that the presented methodology yields a safer and more precise analysis when compared to the traditional Monte Carlo approach

An interval-based algorithm for uncertainty quantification in composite structures

Composite materials have been used extensively in the aeronautical and automotive industries. Despite the improved knowledge about the mechanical and dynamic behavior and modes of failure, it is still not well explained some variability from experimental data obtained for, a priory, and nominally identical specimens. Epistemic and aleatory uncertainties are alleged as the main causes for these discrepancies besides the uncertainties from modeling. Regarding the structural damping of such structures, the phenomena involved are not completely revealed nor modeled. This paper presents an interval-based algorithm for uncertainty quantification in composite structures. The α-cut procedures are used to account for the several levels of uncertainty present in material properties, geometrical imperfections and external loading. Due to the lack of reliable statistical information about such uncertainties, the interval-based approach is used in this study and compared with the robust solution by Monte Carlo simulations

A novel multi-objective quantum particle swarm algorithm for suspension optimization

In this paper, a novel multi-objective archive-based Quantum Particle Optimizer (MOQPSO) is proposed for solving suspension optimization problems. The algorithm has been adapted from the well-knownsingle objectiveQPSOby substantialmodifications in the core equations and implementation of new multi-objectivemechanisms. The novel algorithmMOQPSO and the long-establishedNSGA-II andCOGA-II (Compressed-ObjectiveGenetic Algorithm with Convergence Detection) are compared. Two situations are considered in this paper: a simple half-car suspension model and a bus suspension model. The numerical model of the bus allows complex dynamic interactions not considered in previous studies. The suitability of the solution is evaluated based on vibration-related ISO Standards, and the efficiency of the proposed algorithm is tested by dominance comparison. For a specifically chosen Pareto front solution found by MOQPSO in the second case, the passengers and driver accelerations attenuated about 50% and 33%, respectively, regarding non-optimal suspension parameters. All solutions found by NSGA-II are dominated by those found byMOQPSO,which presented a Pareto front noticeably wider for the same number of objective function calls

Multi-objective optimization of bus suspension parameters based on quantum particle model

Este trabalho fornece um estudo multiobjetivo sobre redução da vibração nos passageiros e no motorista de um ônibus. Um modelo numérico de ônibus com treze graus de liberdade, incluindo dinâmica lateral, é acoplado ao algoritmo de otimização multiobjetivo NSGA-II (Nondominated Sorting Genetic Algorithm) e um novo algoritmo proposto, MOQPSO (Multi-objective Quantum Particle Swarm Optimization). Três assentos são estrategicamente selecionados a fim de investigar a atenuação da vibração. Dez parâmetros de rigidez e amortecimento são selecionados como variáveis de projeto para compor o processo de otimização, a fim de reduzir a vibração nos passageiros e averiguar o comportamento das curvas de Pareto geradas pelos algoritmos. O ônibus é submetido à manobra DLC (double lane change, ISO 3888, 2002) e a uma pista rugosa classe C (ISO 8606, 1995) a fim de promover excitações majoritariamente laterais e verticais, respectivamente. Normas para vibração (ISO 2631, 1997) são usadas na avaliação e comparação das soluções. Os resultados mostram que os novos parâmetros obtidos pela otimização geram atenuações de vibração que são superiores àquelas usando valores nominais. O algoritmo proposto no presente estudo mostrou-se adequado, uma vez que sua Fronteira de Pareto se mostrou mais ampla e avançada do que aquela obtida pelo já consolidado NSGA-II com o mesmo custo computacional.This work provides a multiobjective study on vibration reduction for passengers and a bus driver. A numerical model of bus with thirteen degrees of freedom, including lateral dynamics, is coupled to the NSGA-II (Non-dominated Sorting Genetic Algorithm) and a novel proposed algorithm, MOQPSO (Multi-objective Quantum Particle Swarm Optimization). Three seats are strategically selected in order to investigate vibration attenuation. Ten parameters of stiffness and damping are selected as design variables to compose the optimization process in order to reduce the vibration in the passengers and to investigate the behavior of the Pareto curves generated by the algorithms. The bus is subjected to the DLC maneuver (ISO 3888, 2002) and to a class C track (ISO 8606, 1995) in order to generate mainly lateral and vertical excitations, respectively. Vibration standards (ISO 2631, 1997) are used to evaluate and compare the solutions. The results show that the new parameters obtained by the optimization generate vibration attenuations that are superior when compared to those using the nominal values. The algorithm proposed in the present study was proven suitable, since its Pareto frontier was wider and more advanced than the one obtained by the already consolidated NSGA-II with the same computational cost

Multi-objective optimization of bus suspension parameters based on quantum particle model

Este trabalho fornece um estudo multiobjetivo sobre redução da vibração nos passageiros e no motorista de um ônibus. Um modelo numérico de ônibus com treze graus de liberdade, incluindo dinâmica lateral, é acoplado ao algoritmo de otimização multiobjetivo NSGA-II (Nondominated Sorting Genetic Algorithm) e um novo algoritmo proposto, MOQPSO (Multi-objective Quantum Particle Swarm Optimization). Três assentos são estrategicamente selecionados a fim de investigar a atenuação da vibração. Dez parâmetros de rigidez e amortecimento são selecionados como variáveis de projeto para compor o processo de otimização, a fim de reduzir a vibração nos passageiros e averiguar o comportamento das curvas de Pareto geradas pelos algoritmos. O ônibus é submetido à manobra DLC (double lane change, ISO 3888, 2002) e a uma pista rugosa classe C (ISO 8606, 1995) a fim de promover excitações majoritariamente laterais e verticais, respectivamente. Normas para vibração (ISO 2631, 1997) são usadas na avaliação e comparação das soluções. Os resultados mostram que os novos parâmetros obtidos pela otimização geram atenuações de vibração que são superiores àquelas usando valores nominais. O algoritmo proposto no presente estudo mostrou-se adequado, uma vez que sua Fronteira de Pareto se mostrou mais ampla e avançada do que aquela obtida pelo já consolidado NSGA-II com o mesmo custo computacional.This work provides a multiobjective study on vibration reduction for passengers and a bus driver. A numerical model of bus with thirteen degrees of freedom, including lateral dynamics, is coupled to the NSGA-II (Non-dominated Sorting Genetic Algorithm) and a novel proposed algorithm, MOQPSO (Multi-objective Quantum Particle Swarm Optimization). Three seats are strategically selected in order to investigate vibration attenuation. Ten parameters of stiffness and damping are selected as design variables to compose the optimization process in order to reduce the vibration in the passengers and to investigate the behavior of the Pareto curves generated by the algorithms. The bus is subjected to the DLC maneuver (ISO 3888, 2002) and to a class C track (ISO 8606, 1995) in order to generate mainly lateral and vertical excitations, respectively. Vibration standards (ISO 2631, 1997) are used to evaluate and compare the solutions. The results show that the new parameters obtained by the optimization generate vibration attenuations that are superior when compared to those using the nominal values. The algorithm proposed in the present study was proven suitable, since its Pareto frontier was wider and more advanced than the one obtained by the already consolidated NSGA-II with the same computational cost

An interval-based algorithm for uncertainty quantification in composite structures

Composite materials have been used extensively in the aeronautical and automotive industries. Despite the improved knowledge about the mechanical and dynamic behavior and modes of failure, it is still not well explained some variability from experimental data obtained for, a priory, and nominally identical specimens. Epistemic and aleatory uncertainties are alleged as the main causes for these discrepancies besides the uncertainties from modeling. Regarding the structural damping of such structures, the phenomena involved are not completely revealed nor modeled. This paper presents an interval-based algorithm for uncertainty quantification in composite structures. The α-cut procedures are used to account for the several levels of uncertainty present in material properties, geometrical imperfections and external loading. Due to the lack of reliable statistical information about such uncertainties, the interval-based approach is used in this study and compared with the robust solution by Monte Carlo simulations