A Framework for Problem Standardization and Algorithm Comparison in Multibody System

2014 ◽  
Author(s):  
Ying Lu ◽  
Jedediyah Williams ◽  
Jeff Trinkle ◽  
Claude Lacoursière
Keyword(s):  
Estimation Error ◽  
Nonlinear Problems ◽  
Simulation Method ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Simulation Design ◽  
Solution Algorithms ◽  
Algorithm Comparison ◽  
Simulation Problem ◽  
User Friendly

The underlying dynamic model of multibody systems takes the form of a differential Complementarity Problem (dCP), which is nonsmooth and thus challenging to integrate. The dCP is typically solved by discretizing it in time, thus converting the simulation problem into the problem of solving a sequence of complementarity problems (CPs). Because the CPs are difficult to solve, many modelling options that affect the dCPs and CPs have been tested, and some reformulation and relaxation options affecting the properties of the CPs and solvers have been studied in the hopes to find the “best” simulation method. One challenge within the existing literature is that there is no standard set of benchmark simulations. In this paper, we propose a framework of Benchmark Problems for Multibody Dynamics (BPMD) to support the fair testing of various simulation algorithms. We designed and constructed a BPMD database and collected an initial set of solution algorithms for testing. The data stored for each simulation problem is sufficient to construct the CPs corresponding to several different simulation design decisions. Once the CPs are constructed from the data, there are several solver options including the PATH solver, nonsmooth Newton methods, fixed-point iteration methods for nonlinear problems, and Lemke’s algorithm for linear problems. Additionally, a user-friendly interface is provided to add customized models and solvers. As an example benchmark comparison, we use data from physical planar grasping experiments. Using the input from a physical experiment to drive the simulation, uncertain model parameters such as friction coefficients are determined. This is repeated for different simulation methods and the parameter estimation error serves as a measure of the suitability of each method to predict the observed physical behavior.

scholarly journals Real-time automatic uncertainty estimation of coseismic single rectangular fault model using GNSS data

2021 ◽  
Vol 73 (1) ◽  
Author(s):  
Keitaro Ohno ◽  
Yusaku Ohta ◽  
Satoshi Kawamoto ◽  
Satoshi Abe ◽  
Ryota Hino ◽  
...  
Keyword(s):  
Real Time ◽  
Disaster Response ◽  
Order Approximation ◽  
Nonlinear Problems ◽  
Large Earthquake ◽  
Fault Model ◽  
Deformation Monitoring ◽  
Model Parameters ◽  
The Sea Of Japan ◽  
Plate Interface

AbstractRapid estimation of the coseismic fault model for medium-to-large-sized earthquakes is key for disaster response. To estimate the coseismic fault model for large earthquakes, the Geospatial Information Authority of Japan and Tohoku University have jointly developed a real-time GEONET analysis system for rapid deformation monitoring (REGARD). REGARD can estimate the single rectangular fault model and slip distribution along the assumed plate interface. The single rectangular fault model is useful as a first-order approximation of a medium-to-large earthquake. However, in its estimation, it is difficult to obtain accurate results for model parameters due to the strong effect of initial values. To solve this problem, this study proposes a new method to estimate the coseismic fault model and model uncertainties in real time based on the Bayesian inversion approach using the Markov Chain Monte Carlo (MCMC) method. The MCMC approach is computationally expensive and hyperparameters should be defined in advance via trial and error. The sampling efficiency was improved using a parallel tempering method, and an automatic definition method for hyperparameters was developed for real-time use. The calculation time was within 30 s for 1 × 106 samples using a typical single LINUX server, which can implement real-time analysis, similar to REGARD. The reliability of the developed method was evaluated using data from recent earthquakes (2016 Kumamoto and 2019 Yamagata-Oki earthquakes). Simulations of the earthquakes in the Sea of Japan were also conducted exhaustively. The results showed an advantage over the maximum likelihood approach with a priori information, which has initial value dependence in nonlinear problems. In terms of application to data with a small signal-to-noise ratio, the results suggest the possibility of using several conjugate fault models. There is a tradeoff between the fault area and slip amount, especially for offshore earthquakes, which means that quantification of the uncertainty enables us to evaluate the reliability of the fault model estimation results in real time.

scholarly journals Study on Friction in Automotive Shock Absorbers Part 1: Friction Simulation Using a Dynamic Friction Model in the Contact Zone of an FEM Model

Vehicles ◽  
2021 ◽  
Vol 3 (2) ◽  
pp. 212-232
Author(s):  
Ludwig Herzog ◽  
Klaus Augsburg
Keyword(s):  
Ride Comfort ◽  
Viscous Friction ◽  
Simulation Method ◽  
Friction Model ◽  
Model Parameters ◽  
Dynamic Friction ◽  
Friction Modeling ◽  
Shock Absorbers ◽  
Operation Conditions ◽  
Wide Range

The important change in the transition from partial to high automation is that a vehicle can drive autonomously, without active human involvement. This fact increases the current requirements regarding ride comfort and dictates new challenges for automotive shock absorbers. There exist two common types of automotive shock absorber with two friction types: The intended viscous friction dissipates the chassis vibrations, while the unwanted solid body friction is generated by the rubbing of the damper’s seals and guides during actuation. The latter so-called static friction impairs ride comfort and demands appropriate friction modeling for the control of adaptive or active suspension systems. In this article, a simulation approach is introduced to model damper friction based on the most friction-relevant parameters. Since damper friction is highly dependent on geometry, which can vary widely, three-dimensional (3D) structural FEM is used to determine the deformations of the damper parts resulting from mounting and varying operation conditions. In the respective contact zones, a dynamic friction model is applied and parameterized based on the single friction point measurements. Subsequent to the parameterization of the overall friction model with geometry data, operation conditions, material properties and friction model parameters, single friction point simulations are performed, analyzed and validated against single friction point measurements. It is shown that this simulation method allows for friction prediction with high accuracy. Consequently, its application enables a wide range of parameters relevant to damper friction to be investigated with significantly increased development efficiency.

Nonintrusive Global Sensitivity Analysis for Linear Systems With Process Noise

2019 ◽  
Vol 14 (2) ◽  
Author(s):  
Souransu Nandi ◽  
Tarunraj Singh
Keyword(s):  
Sensitivity Analysis ◽  
Linear Systems ◽  
Global Sensitivity Analysis ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Parameter Uncertainties ◽  
Sobol Indices ◽  
Global Sensitivity ◽  
Time Invariant ◽  
The Impact

The focus of this paper is on the global sensitivity analysis (GSA) of linear systems with time-invariant model parameter uncertainties and driven by stochastic inputs. The Sobol' indices of the evolving mean and variance estimates of states are used to assess the impact of the time-invariant uncertain model parameters and the statistics of the stochastic input on the uncertainty of the output. Numerical results on two benchmark problems help illustrate that it is conceivable that parameters, which are not so significant in contributing to the uncertainty of the mean, can be extremely significant in contributing to the uncertainty of the variances. The paper uses a polynomial chaos (PC) approach to synthesize a surrogate probabilistic model of the stochastic system after using Lagrange interpolation polynomials (LIPs) as PC bases. The Sobol' indices are then directly evaluated from the PC coefficients. Although this concept is not new, a novel interpretation of stochastic collocation-based PC and intrusive PC is presented where they are shown to represent identical probabilistic models when the system under consideration is linear. This result now permits treating linear models as black boxes to develop intrusive PC surrogates.

Halton Based Initial Distribution in Artificial Bee Colony Algorithm and its Application in Software Effort Estimation

2012 ◽  
Vol 3 (2) ◽  
pp. 86-106 ◽  
Author(s):  
Tarun Kumar Sharma ◽  
Millie Pant
Keyword(s):  
Optimization Algorithm ◽  
Artificial Bee Colony ◽  
Real Life ◽  
Initial Distribution ◽  
Benchmark Problems ◽  
Model Parameters ◽  
Random Numbers ◽  
Initial Population ◽  
Effort Estimation ◽  
Bee Colony

Artificial Bee Colony (ABC) is an optimization algorithm that simulates the foraging behavior of honey bees. It is a population based search technique whose performance depends largely on the distribution of initial population. Generally, uniform distributions are preferred since they best reflect the lack of knowledge about the optimum’s location. Moreover, these are easy to generate as most of the programming languages have an inbuilt function for generating uniformly distributed random numbers. However, in case of a population dependent optimization algorithm like that of ABC, random numbers having uniform probability distribution may not be a good choice as they may not be able exploit the search space fully. This paper uses quasi random numbers based on Halton sequence for the initial distribution and have compared the simulation results with initial population generated using uniform distribution. The proposed variant, termed as Halton based ABC (H-ABC), is validated on a set of 15 standard benchmark problems, 6 nontraditional shifted benchmark functions proposed at the special session of CEC2008, and has been used for solving the real life problem of estimating the cost model parameters. Numerical results indicate the competence of the proposed algorithm.

scholarly journals Vehicle Velocity Estimation Fusion with Kinematic Integral and Empirical Correction on Multi-Timescales

Energies ◽  
2019 ◽  
Vol 12 (7) ◽  
pp. 1242
Author(s):  
Jiangyi Lv ◽  
Hongwen He ◽  
Wei Liu ◽  
Yong Chen ◽  
Fengchun Sun
Keyword(s):  
Autonomous Vehicles ◽  
Estimation Error ◽  
Longitudinal Velocity ◽  
Estimation Method ◽  
Velocity Estimation ◽  
Model Parameters ◽  
Lateral Velocity ◽  
Empirical Correction ◽  
Vehicle Velocity ◽  
Wide Range

Accurate and reliable vehicle velocity estimation is greatly motivated by the increasing demands of high-precision motion control for autonomous vehicles and the decreasing cost of the required multi-axis IMU sensors. A practical estimation method for the longitudinal and lateral velocities of electric vehicles is proposed. Two reliable driving empirical judgements about the velocities are extracted from the signals of the ordinary onboard vehicle sensors, which correct the integral errors of the corresponding kinematic equations on a long timescale. Meanwhile, the additive biases of the measured accelerations are estimated recursively by comparing the integral of the measured accelerations with the difference of the estimated velocities between the adjacent strong empirical correction instants, which further compensates the kinematic integral error on short timescale. The algorithm is verified by both the CarSim-Simulink co-simulation and the controller-in-the-loop test under the CarMaker-RoadBox environment. The results show that the velocities can be accurately and reliably estimated under a wide range of driving conditions without prior knowledge of the tire-model and other unavailable signals or frequently changeable model parameters. The relative estimation error of the longitudinal velocity and the absolute estimation error of the lateral velocity are kept within 2% and 0.5 km/h, respectively.

scholarly journals Sensor Placement via Optimal Experiment Design in EMI Sensing of Metallic Objects

2016 ◽  
Vol 2016 ◽  
pp. 1-14
Author(s):  
Lin-Ping Song ◽  
Leonard R. Pasion ◽  
Nicolas Lhomme ◽  
Douglas W. Oldenburg
Keyword(s):  
Experimental Design ◽  
Field Experiments ◽  
Information Gain ◽  
Estimation Error ◽  
Sensor Placement ◽  
Model Parameters ◽  
Placement Problem ◽  
Empirical Survey ◽  
Optimal Experiment ◽  
Linearized Model

This work, under the optimal experimental design framework, investigates the sensor placement problem that aims to guide electromagnetic induction (EMI) sensing of multiple objects. We use the linearized model covariance matrix as a measure of estimation error to present a sequential experimental design (SED) technique. The technique recursively minimizes data misfit to update model parameters and maximizes an information gain function for a future survey relative to previous surveys. The fundamental process of the SED seeks to increase weighted sensitivities to targets when placing sensors. The synthetic and field experiments demonstrate that SED can be used to guide the sensing process for an effective interrogation. It also can serve as a theoretic basis to improve empirical survey operation. We further study the sensitivity of the SED to the number of objects within the sensing range. The tests suggest that an appropriately overrepresented model about expected anomalies might be a feasible choice.

scholarly journals Optimal solution error covariance in highly nonlinear problems of variational data assimilation

2012 ◽  
Vol 19 (2) ◽  
pp. 177-184 ◽  
Author(s):  
V. Shutyaev ◽  
I. Gejadze ◽  
G. J. M. Copeland ◽  
F.-X. Le Dimet
Keyword(s):  
Nonlinear Dynamics ◽  
Data Assimilation ◽  
Optimal Solution ◽  
Nonlinear Problems ◽  
Variational Data Assimilation ◽  
Model Parameters ◽  
Efficient Computation ◽  
Viscous Term ◽  
Highly Nonlinear ◽  
The Cost

Abstract. The problem of variational data assimilation (DA) for a nonlinear evolution model is formulated as an optimal control problem to find the initial condition, boundary conditions and/or model parameters. The input data contain observation and background errors, hence there is an error in the optimal solution. For mildly nonlinear dynamics, the covariance matrix of the optimal solution error can be approximated by the inverse Hessian of the cost function. For problems with strongly nonlinear dynamics, a new statistical method based on the computation of a sample of inverse Hessians is suggested. This method relies on the efficient computation of the inverse Hessian by means of iterative methods (Lanczos and quasi-Newton BFGS) with preconditioning. Numerical examples are presented for the model governed by the Burgers equation with a nonlinear viscous term.

Development of an advanced turbocharger simulation method for cycle simulation of turbocharged internal combustion engines

2009 ◽  
Vol 223 (5) ◽  
pp. 661-672 ◽  
Author(s):  
W Zhuge ◽  
Y Zhang ◽  
X Zheng ◽  
M Yang ◽  
Y He
Keyword(s):  
Internal Combustion Engines ◽  
Flow Model ◽  
Predictive Accuracy ◽  
Integrated Design ◽  
Simulation Method ◽  
Low Flow ◽  
Model Parameters ◽  
Cycle Simulation ◽  
Cent Error ◽  
Engine Cycle

An advanced turbocharger simulation method for engine cycle simulation was developed on the basis of the compressor two-zone flow model and the turbine mean-line flow model. The method can be used for turbocharger and engine integrated design without turbocharger test maps. The sensitivities of the simulation model parameters on turbocharger simulation were analysed to determine the key modelling parameters. The simulation method was validated against turbocharger test data. Results show that the methods can predict the turbocharger performance with a good accuracy, less than 5 per cent error in general for both the compressor and the turbine. In comparison with the map-based extrapolation methods commonly used in engine cycle simulation tools such as GT-POWER®, the turbocharger simulation method showed significant improvement in predictive accuracy to simulate the turbocharger performance, especially in low-flow and low-operating-speed conditions.

Element-Independent Pure Deformational and Co-Rotational Methods for Triangular Shell Elements in Geometrically Nonlinear Analysis

2018 ◽  
Vol 18 (05) ◽  
pp. 1850065 ◽  
Author(s):  
Y. Q. Tang ◽  
Y. P. Liu ◽  
S. L. Chan
Keyword(s):  
Nonlinear Analysis ◽  
Nonlinear Problems ◽  
Shell Element ◽  
Benchmark Problems ◽  
Element Formulation ◽  
Geometrically Nonlinear ◽  
Plate Element ◽  
Membrane Element ◽  
Geometrically Nonlinear Analysis ◽  
Shell Elements

Proposed herein is a novel pure deformational method for triangular shell elements that can decrease the element quantities and simplify the element formulation. This approach has computational advantages over the conventional finite element method for linear and nonlinear problems. In the element level, this method saves time for computing stresses, internal forces and stiffness matrices. A flat shell element is formed by a membrane element and a plate element, so that the pure deformational membrane and plate elements are derived and discussed separately in this paper. Also, it is very convenient to incorporate the proposed pure deformational method into the element-independent co-rotational (EICR) framework for geometrically nonlinear analysis. Thus, on the basis of the pure deformational method, a novel EICR formulation is proposed which is simpler and has more clear physical characteristics than the traditional formulation. In addition, a triangular membrane element with drilling rotations and the discrete Kirchhoff triangular plate element are used to verify the proposed pure deformational method, although several benchmark problems are employed to verify the robustness and accuracy of the proposed EICR formulations.

Application of line sampling simulation method to reliability benchmark problems

2007 ◽  
Vol 29 (3) ◽  
pp. 208-221 ◽  
Author(s):  
H.J. Pradlwarter ◽  
G.I. Schuëller ◽  
P.S. Koutsourelakis ◽  
D.C. Charmpis
Keyword(s):  
Simulation Method ◽  
Benchmark Problems ◽  
Line Sampling
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