Estimation of Uncertain Vehicle Center of Gravity using Polynomial Chaos Expansions (original) (raw)
Center for Vehicle Systems and Safety, Virginia Tech, Blacksburg, VA 24061-0238 ABSTRACT This is the second part of a two-part article. In the first part, a new computational approach for parameter estimation was proposed based on the application of the polynomial chaos theory. The maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. In this part, the new parameter estimation method is illustrated on a nonlinear four-degree-of-freedom roll plane model of a vehicle in which an uncertain mass with an uncertain position is added on the roll bar. The value of the mass and its position are estimated from periodic observations of the displacements and velocities across the suspensions. Appropriate excitations are needed in order to obtain accurate results. For some excitations, different combinations of uncertain parameters lead to essentially the same time responses, and no estimation method can work without additional information. Regularization techniques can still yield most likely values among the possible combinations of uncertain parameters resulting in the same time responses than the ones observed. When using appropriate excitations, the results obtained with this approach are close to the actual values of the parameters. The accuracy of the estimations has been shown to be sensitive to the number of terms used in the polynomial expressions and to the number of collocation points, and thus it may become computationally expensive when a very high accuracy of the results is desired. However, the noise level in the measurements affects the accuracy of the estimations as well. Therefore, it is usually not necessary to use a large number of terms in the polynomial expressions and a very large number of collocation points since the addition of extra precision eventually affects the results less than the effect of the measurement noise. Possible applications of this theory to the field of vehicle dynamics simulations include the estimation of mass, inertia properties, as well as other parameters of interest.
2016
Computer models and simulations have become an indispensable tool for solving complex problems in many parts of vehicle development including powertrain engineering, mobility assessment, survivability analysis, and manufacturing and life cycle assessment. As computational power has increased and model accuracy has improved, engineers have come to depend on simulations to investigate and characterize systems. This raises the importance of model calibration and validation. Calibration is the process of tuning model parameters which are not directly measured in physical tests. These parameters maybe physical properties (material and soil properties, manufactured dimensions, engine operating points) which are difficult to measure or entirely non-physical model parameters. Calibration is necessary to ensure that models and simulation results are as close to physical reality as possible given modeling limitations and assumptions. This paper presents a calibration framework which implement...
2020
Online simulations conducted in vehicles can enable predictive control of automotive systems. This capability can be especially valuable for complex propulsion systems to manage performance, safety, and efficiency under changing drive conditions. Reliable online simulations require accurate models. However, modeling errors are unavoidable, and the inputs from the driver and environment are subject to uncertainty and generally unknown a priori, rendering the system stochastic. Furthermore, limited computing resources in a vehicle can prohibit solving stochastic systems, posing a major challenge. This paper seeks to alleviate these computational bottlenecks by utilizing generalized Polynomial Chaos to efficiently propagate and quantify uncertainty without loss of accuracy for online propulsion system simulations. To demonstrate the effectiveness of this method, uncertainty quantification is performed for simulations of vehicle launch where both model and input uncertainties are considered. A standard Monte Carlo method is used as a baseline for comparison. It is shown that, for the same accuracy, the proposed method is more than two orders of magnitude faster than a Monte Carlo method. A variance-based sensitivity analysis is also used to quantify the statistical contribution from each uncertainty source to the output. The outcome suggests that the proposed method is wellsuited to automotive applications where fast and accurate onboard simulation capabilities are required.
Calculating Invariant Loads for System Simulation In Vehicle Engineering
Multiobody Dynamics …, 2009
© Fraunhofer-Institut für Techno-und Wirtschaftsmathematik ITWM 2009 ISSN 1434-9973 Bericht 161 (2009) Alle Rechte vorbehalten. Ohne ausdrückliche schriftliche Genehmigung des Herausgebers ist es nicht gestattet, das Buch oder Teile daraus in irgendeiner Form durch Fotokopie, ...
A Vehicle Dynamics Design and Simulation Tool for Capstone Projects
2011 ASEE Annual Conference & Exposition Proceedings
is an Associate Professor of Mechanical Engineering at Milwaukee School of Engineering (MSOE). Before coming to MSOE, he spent more than twenty years as a special machine designer and was involved with the design, construction and installation of machines and manufacturing automation equipment for automotive, aerospace, and defense industry clients. Dr. Pakkala earned a Bachelor of Science degree in mechanical engineering from Michigan State University. His Master of Science and Ph.D. degrees in electrical engineering from Michigan Technological University were in the area of dynamic control theory and system identification. He has published papers in fluid mechanics, internal combustion engine controls, system identification, and engineering education. He consults in the areas of manufacturing engineering and in vehicle crash reconstruction. He is currently the director of an exchange program for mechanical engineering students between MSOE and the Fachhochschule Lbeck in Lbeck, Germany.
Dynamic Simulation of Vehicle Maneuvers for Loads Analysis
AIAA AVIATION 2020 FORUM, 2020
Testing critical loads during specific dynamic maneuvers is essential to aircraft structural design, and several such dynamic load cases must be demonstrated during the certification process. A simulation capability is developed in this work to calculate critical loads on the vertical tail of a business jet resulting from yaw maneuvers required for certification. The data produced from these simulations can be used to inform future structural design decisions. Models for the pilot and flight control system are developed to simulate the pilot control actions needed to perform the maneuvers within the boundaries of pilot capabilities and flight control system limits. Aerodynamic and propulsive data are used to calculate the forces and moments on the aircraft and solve the 6-degree of freedom equations of motion to accurately model the aircraft's trajectory. Sectional aerodynamic characteristics of the horizontal and vertical tail are used to calculate the structural loads at each section of the tail. The summation of these forces and moments yields the loads at the vertical tail root, which can be used to assess the structural design of the tail. The simulation is demonstrated on a T-tail business jet with three weight conditions and at flight conditions throughout the flight test envelope. The ultimate loading conditions and the number of control application cycles required to reach ultimate loads at the vertical tail are determined using the maneuver simulation.
Design and Simulation of a Formula Vehicle - The Role of CAE
Automobile sector is one of the most blooming sectors now-a-days. With the advent of computer assisted engineering and the blend of classic methodologies combined together to bring the most durable result about pre-manufacturing analysis and design optimization. This paper presents an overview of the role of Computer Assisted Engineering in the Design and Simulation of a Formula Vehicle.
A Polynomial-Chaos-Based Bayesian Approach for Estimating Uncertain Parameters of Mechanical Systems
Volume 3: 19th International Conference on Design Theory and Methodology; 1st International Conference on Micro- and Nanosystems; and 9th International Conference on Advanced Vehicle Tire Technologies, Parts A and B, 2007
Center for Vehicle Systems and Safety, Virginia Tech, Blacksburg, VA 24061-0238 ABSTRACT This is the second part of a two-part article. In the first part, a new computational approach for parameter estimation was proposed based on the application of the polynomial chaos theory. The maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. In this part, the new parameter estimation method is illustrated on a nonlinear four-degree-of-freedom roll plane model of a vehicle in which an uncertain mass with an uncertain position is added on the roll bar. The value of the mass and its position are estimated from periodic observations of the displacements and velocities across the suspensions. Appropriate excitations are needed in order to obtain accurate results. For some excitations, different combinations of uncertain parameters lead to essentially the same time responses, and no estimation method can work without additional information. Regularization techniques can still yield most likely values among the possible combinations of uncertain parameters resulting in the same time responses than the ones observed. When using appropriate excitations, the results obtained with this approach are close to the actual values of the parameters. The accuracy of the estimations has been shown to be sensitive to the number of terms used in the polynomial expressions and to the number of collocation points, and thus it may become computationally expensive when a very high accuracy of the results is desired. However, the noise level in the measurements affects the accuracy of the estimations as well. Therefore, it is usually not necessary to use a large number of terms in the polynomial expressions and a very large number of collocation points since the addition of extra precision eventually affects the results less than the effect of the measurement noise. Possible applications of this theory to the field of vehicle dynamics simulations include the estimation of mass, inertia properties, as well as other parameters of interest.
Simulation for next generation vehicles
The major industrial countries have defined new requirements and guidelines for the 21st century: a sensible reduction of the air pollution caused by the vehicles and the migration to renewable energy sources. In this fast-changing scenario, optimization of the single component in terms of weight or efficiency and system integration are playing a key role; only by means of advanced simulation software platforms, it is possible to fulfill the new challenges.
Fidelity of using scaled vehicles for chassis dynamic studies
Vehicle System Dynamics, 2009
There are many situations where physical testing of a vehicle or vehicle controller is necessary, yet use of a full-size vehicle is not practical. Some situations include implementation testing of novel actuation strategies, analyzing the behavior of chassis feedback control under system faults, or near-unstable situations such as limit handling under driver-assist feedback control. Historically, many have advocated the use of scale vehicles as surrogates for larger vehicles. This article presents analysis and experimental testing that examines the fidelity of using scaled vehicles for vehicle chassis dynamics and control studies. In support of this effort, this work introduces an experimental system called the Pennsylvania State University Rolling Roadway Simulator (the PURRS). In the PURRS, a custom-built scale-sized vehicle is freely driven on a moving roadway surface. While others have used scale-vehicle rolling roadway simulators in the past, this work is the first to attempt to directly match the planar dynamic performance of the scale-sized vehicle to a specific full-sized vehicle by careful design of the scale vehicle. This article explains details of this effort including vehicle dynamic modeling, detailed measurement of model parameters, conditions for dynamic similitude, validation of the resulting experimental vehicle in the time, frequency, and dimensionless domains. The results of the dynamic comparisons between scale-and full-sized vehicles clearly illustrate operational regimes where agreement is quite good, and other regimes where agreement is quite poor. Both are useful to understand the applicability of scale-vehicle results to full-size vehicle analysis. 2 S. Lapapong et al.