Search Results

A simple, design-oriented model of joints in vehicles structures is developed. This model accounts for the flexibility, the offsets of rotation centers of joint branches from geometric center, and the coupling between rotations of a joint branch in different planes. A family of joint models with different levels of complexity is also defined. A probabilistic system identification is used to estimate the joint model parameters by using the measured displacements. Statistical tools which identify important parameters are also presented. The identification methodology is applied to the estimation of parameters of a B-pillar to rocker joint.

Design optimization often relies on computational models, which are subjected to a validation process to ensure their accuracy. Because validation of computer models in the entire design space can be costly, we have previously proposed an approach where design optimization and model validation, are concurrently performed using a sequential approach with variable-size local domains. We used test data and statistical bootstrap methods to size each local domain where the prediction model is considered validated and where design optimization is performed. The method proceeds iteratively until the optimum design is obtained. This method however, requires test data to be available in each local domain along the optimization path. In this paper, we refine our methodology by using polynomial regression to predict the size and shape of a local domain at some steps along the optimization process without using test data.

An efficient approach for Reliability-Based Design Optimization (RBDO) of series systems is presented. A modified formulation of the RBDO problem is employed in which the required reliabilities of the failure modes of a system are design variables. This allows for an optimal apportionment of the reliability of a system among its failure modes. A sequential optimization and reliability assessment method is used to efficiently determine the optimum design. Here, the constraints on the reliabilities of the failure modes of the RBDO problem are replaced with deterministic constraints. The method is demonstrated on an example problem that has been solved in a previous study that did not treat the required reliability levels of the failure modes as design variables. The new approach finds designs with lower mass than designs found in the previous study without reducing their system reliability.

A simulation-based, system reliability-based design optimization (RBDO) method is presented that can handle problems with multiple failure regions and correlated random variables. Copulas are used to represent the correlation. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with a trust-region optimization approach and local metamodels covering each trust region. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation per trust region. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. The PRRA method is based on importance sampling. It provides accurate results, if the support of the sampling PDF contains the support of the joint PDF of the input random variables. The sequential, trust-region optimization approach satisfies this requirement.

Understanding reliability is critical in design, maintenance and durability analysis of engineering systems. A reliability simulation methodology is presented in this paper for vehicle fleets using limited data. The method can be used to estimate the reliability of non-repairable as well as repairable systems. It can optimally allocate, based on a target system reliability, individual component reliabilities using a multi-objective optimization algorithm. The algorithm establishes a Pareto front that can be used for optimal tradeoff between reliability and the associated cost. The method uses Monte Carlo simulation to estimate the system failure rate and reliability as a function of time. The probability density functions (PDF) of the time between failures for all components of the system are estimated using either limited data or a user-supplied MTBF (mean time between failures) and its coefficient of variation.

Using the total probability theorem, we propose a method to calculate the failure rate of a linear vibratory system with random parameters excited by stationary Gaussian processes. The response of such a system is non-stationary because of the randomness of the input parameters. A space-filling design, such as optimal symmetric Latin hypercube sampling or maximin, is first used to sample the input parameter space. For each design point, the output process is stationary and Gaussian. We present two approaches to calculate the corresponding conditional probability of failure. A Kriging metamodel is then created between the input parameters and the output conditional probabilities allowing us to estimate the conditional probabilities for any set of input parameters. The total probability theorem is finally applied to calculate the time-dependent probability of failure and the failure rate of the dynamic system. The proposed method is demonstrated using a vibratory system.

Finite element analysis is a well-established methodology in structural dynamics. However, optimization and/or probabilistic studies can be prohibitively expensive because they require repeated FE analyses of large models. Various reanalysis methods have been proposed in order to calculate efficiently the dynamic response of a structure after a baseline design has been modified, without recalculating the new response. The parametric reduced-order modeling (PROM) and the combined approximation (CA) methods are two re-analysis methods, which can handle large model parameter changes in a relatively efficient manner. Although both methods are promising by themselves, they can not handle large FE models with large numbers of DOF (e.g. 100,000) with a large number of design parameters (e.g. 50), which are common in practice. In this paper, the advantages and disadvantages of the PROM and CA methods are first discussed in detail.

A Reliability-Based Design Optimization (RBDO) method for multiple failure regions is presented. The method uses a Probabilistic Re-Analysis (PRRA) approach in conjunction with an approximate global metamodel with local refinements. The latter serves as an indicator to determine the failure and safe regions. PRRA calculates very efficiently the system reliability of a design by performing a single Monte Carlo (MC) simulation. Although PRRA is based on MC simulation, it calculates “smooth” sensitivity derivatives, allowing therefore, the use of a gradient-based optimizer. An “accurate-on-demand” metamodel is used in the PRRA that allows us to handle problems with multiple disjoint failure regions and potentially multiple most-probable points (MPP). The multiple failure regions are identified by using a clustering technique. A maximin “space-filling” sampling technique is used to construct the metamodel. A vibration absorber example highlights the potential of the proposed method.

In reliability design, often, there is scarce data for constructing probabilistic models. Probabilistic models whose parameters vary in known intervals could be more suitable than Bayesian models because the former models do not require making assumptions that are not supported by the available evidence. If we use models whose parameters vary in intervals we need to calculate upper and lower bounds of the failure probability (or reliability) of a system in order to make design decisions. Monte Carlo simulation can be used for this purpose, but it is too expensive for all but very simple systems. This paper proposes an efficient Monte-Carlo simulation approach for estimation of upper and lower probabilities. This approach is based on two ideas: a) use an efficient approach for reliability reanalysis of a system, which is introduced in this paper, and b) approximate the probability distribution of the minimum and maximum failure probabilities using extreme value statistics.

There is randomness in both the applied loads and the strength of systems. Therefore, to account for the uncertainty, the safety of the system must be quantified using its reliability. Monte Carlo Simulation (MCS) is widely used for probabilistic analysis because of its robustness. However, the high computational cost limits the accuracy of MCS. Smarslok et al. [2010] developed an improved sampling technique for reliability assessment called Separable Monte Carlo (SMC) that can significantly increase the accuracy of estimation without increasing the cost of sampling. However, this method was applied to time-invariant problems involving two random variables. This paper extends SMC to problems with multiple random variables and develops a novel method for estimation of the standard deviation of the probability of failure of a structure. The method is demonstrated and validated on reliability assessment of an offshore wind turbine under turbulent wind loads.

The Combined Approximation (CA) method is an efficient reanalysis method that aims at reducing the cost of optimization problems. The CA uses results of a single exact analysis, and it is suitable for different types of structures and design variables. The second author utilized CA to calculate the frequency response function of a system at a frequency of interest by using the results at a frequency in the vicinity of that frequency. He showed that the CA yields accurate results for small frequency perturbations. This work demonstrates a methodology that utilizes CA to reduce the cost of Monte Carlo simulation (MCs) of linear systems under random dynamic loads. The main idea is to divide the power spectral density function (PSD) of the input load into several frequency bins before calculating the load realizations.

This paper outlines a real-time hierarchical control allocation algorithm for multi-axle land vehicles with independent hub motor wheel drives. At the top level, the driver’s input such as pedal position or steering wheel position are interpreted into desired global state responses based on a reference model. Then, a locally linearized rigid body model is used to design a linear quadratic regulator that generates the desired global control efforts, i.e., the total tire forces and moments required track the desired state responses. At the lower level, an optimal control allocation algorithm coordinates the motor torques in such a manner that the forces generated at tire-road contacts produce the desired global control efforts under some physical constraints of the actuation and the tire/wheel dynamics. The performance of the proposed control system design is verified via simulation analysis of a 3-axle heavy vehicle with independent hub-motor drives.

This paper presents a methodology to evaluate and optimize discrete event systems, such as an assembly line or a call center. First, the methodology estimates the performance of a system for a single probability distribution of the inputs. Probabilistic Reanalysis (PRRA) uses this information to evaluate the effect of changes in the system configuration on its performance. PRRA is integrated with a program to optimize the system. The proposed methodology is dramatically more efficient than one requiring a new Monte Carlo simulation each time we change the system. We demonstrate the approach on a drilling center and an electronic parts factory.

Reliability assessment of dynamic systems with low failure probability can be very expensive. This paper presents and demonstrates a method that uses the Metropolis-Hastings algorithm to sample from an optimal probability density function (PDF) of the random variables. This function is the true PDF truncated over the failure region. For a system subjected to time varying excitation, Shinozuka's method is employed to generate time histories of the excitation. Random values of the frequencies and the phase angles of the excitation are drawn from the optimal PDF. It is shown that running the subset simulation by the proposed approach, which uses Shinozuka's method, is more efficient than the original subset simulation. The main reasons are that the approach involves only 10 to 20 random variables, and it takes advantage of the symmetry of the expression of the displacement as a function of the inputs. The paper demonstrates the method on two examples.

It is challenging to perform probabilistic analysis and design of large-scale structures because probabilistic analysis requires repeated finite element analyses of large models and each analysis is expensive. This paper presents a methodology for probabilistic analysis and reliability based design optimization of large scale structures that consists of two re-analysis methods; one for estimating the deterministic vibratory response and another for estimating the probability of the response exceeding a certain level. The deterministic re-analysis method can analyze efficiently large-scale finite element models consisting of tens or hundreds of thousand degrees of freedom and large numbers of design variables that vary in a wide range. The probabilistic re-analysis method calculates very efficiently the system reliability for many probability distributions of the design variables by performing a single Monte Carlo simulation.

In design of real-life systems, such as the suspension of a car, an offshore platform or a wind turbine, there are significant uncertainties in the model of the inputs. For example, scarcity of data leads to inaccuracies in the power spectral density function of the waves and the probability distribution of the wind speed. Therefore, it is necessary to evaluate the performance and safety of a system for different probability distributions. This is computationally expensive or even impractical. This paper presents a methodology to assess efficiently the fatigue life of structures for different power spectra of the applied loads. We accomplish that by reweighting the incremental damage calculated in one simulation. We demonstrate the accuracy and efficiency of the proposed method on an example which involves a nonlinear quarter car under a random dynamic load. The fatigue life of the suspension spring under loads generated by a sampling spectrum is calculated.

This paper investigates the potential of Evidence Theory (ET) and Bayesian Theory (BT) for decision under uncertainty, when the evidence about uncertainty is imprecise. The basic concepts of ET and BT are introduced and the ways these theories model uncertainties, propagate them through systems and assess the safety of these systems are presented. ET and BT approaches are demonstrated and compared on examples involving an algebraic function when the evidence about the input variables consists of intervals provided by experts. It is recommended that a decision maker compute both the Bayesian probability of events and their lower and upper probabilities using ET when evidence from experts is imprecise. A large gap between the lower and upper probability suggests that more information should be collected before making a decision. If this is not feasible, then Bayesian probabilities can help make a decision.

In reliability design, often, there is scarce data for constructing probabilistic models. It is particularly challenging to model uncertainty in variables when the type of their probability distribution is unknown. Moreover, it is expensive to estimate the upper and lower bounds of the reliability of a system involving such variables. A method for modeling uncertainty by using Polynomial Chaos Expansion is presented. The method requires specifying bounds for statistical summaries such as the first four moments and credible intervals. A constrained optimization problem, in which decision variables are the coefficients of the Polynomial Chaos Expansion approximation, is formulated and solved in order to estimate the minimum and maximum values of a system’s reliability. This problem is solved efficiently by employing a probabilistic re-analysis approach to approximate the system reliability as a function of the moments of the random variables.

In the recent years world-wide automotive manufacturers are continuously working in the research of the suiTable technical solutions to meet upcoming stringent carbon dioxide (CO2) emission targets, defined by regulatory authorities across the world. Many technologies have been already developed, or are currently under study, to meet the legislated targets. To meet this objective, the generation of tumble at intake stroke and the conservation of turbulence intensity at the end of compression stroke inside the combustion chamber have a significant role in the contribution towards accelerating the burning rate, increasing the thermal efficiency and reducing the cyclic variability [1]. Tumble generation is mainly attained by intake port design, and conservation is achieved during the end of compression stroke 690 ~ 720 crank angles (CA) which is strictly affected by the piston bowl geometry and pentroof combustion chamber shape.

In recent years, world-wide automotive manufacturers have been continuously working in the research of suitable technical solutions to meet upcoming stringent carbon dioxide (CO2) emission targets, as defined by international regulatory authorities. Many technologies have been already developed, or are currently under study, to meet legislated targets. In-line with above objective, the enhancement of turbulence intensity inside the combustion chamber has a significant importance which contributes to accelerating the burning rate, to increase the thermal efficiency and to reduce the cyclic variability [9]. Turbulence generation is mainly achieved during the intake stroke which is strictly affected by the intake port geometry, orientation and to certain extends by combustion chamber masking. Conservation of turbulence intensity till 700~720 crank angle (CA) is achieved by optimized shape of combustion chamber geometry and piston bowl shape.