MBSVT: Software for Modeling, Sensitivity Analysis, and Optimization of Multibody Systems at Virginia Tech

2014 ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Virginia Tech ◽  
Benchmark Problems ◽  
Adjoint Sensitivity ◽  
Normal Contact ◽  
Penalty Formulation ◽  
Sensitivity Equations ◽  
External Forces

This paper introduces MBSVT (Multibody Systems at Virginia Tech), as a software library for the kinematic and dynamic simulation of multibody systems, with forward kinematics and dynamics, direct and adjoint sensitivity analysis, and optimization capabilities. The MBSVT software was developed in Fortran 2003 as a collection of Fortran modules and it was tested on several different platforms using multiple compilers. The kinematic library includes dot-1 constraint, revolute, spherical, Euler, and translational joints, as well as distance and coordinates driving constraints. The forward dynamics uses the penalty formulation to write the equations of motion and both explicit and implicit Runge-Kutta numerical integrators are implemented to integrate the equations. The library implements external forces, such as translational spring-damper-actuator, bump stop, linear normal contact, and basic tire force. Direct and adjoint sensitivity equations are implemented for the penalty formulation. The L-BFGS-B quasi-Newton optimization algorithm [1] is integrated with the library, to carry out the optimization tasks. MBSVT also provides a connection with Matlab by means of the Matlab engine. 3D rendering is available via the graphic library MBSVT-viz based on OpenSceneGraph. The collection of benchmark problems provided includes a crank-slider mechanism, 2D and 3D excavators models, a vehicle suspension, and full vehicle model. The distribution includes a Cmake list, gfortran make files, MSV2010 project files, and a collection of training problems. Detailed doxygen documentation for the MBSVT library is available in html and pdf formats.

scholarly journals Dynamic Response Optimization of Complex Multibody Systems in a Penalty Formulation Using Adjoint Sensitivity

2015 ◽  
Vol 10 (3) ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Dynamics ◽  
Multibody Systems ◽  
Real Life ◽  
Design Parameters ◽  
Vehicle Model ◽  
Adjoint Sensitivity ◽  
Penalty Formulation ◽  
Sensitivity Approach ◽  
Dynamic Performance Analysis

Multibody dynamics simulations are currently widely accepted as valuable means for dynamic performance analysis of mechanical systems. The evolution of theoretical and computational aspects of the multibody dynamics discipline makes it conducive these days for other types of applications, in addition to pure simulations. One very important such application is design optimization for multibody systems. In this paper, we focus on gradient-based optimization in order to find local minima. Gradients are calculated efficiently via adjoint sensitivity analysis techniques. Current approaches have limitations in terms of efficiently performing sensitivity analysis for complex systems with respect to multiple design parameters. To improve the state of the art, the adjoint sensitivity approach of multibody systems in the context of the penalty formulation is developed in this study. The new theory developed is then demonstrated on one academic case study, a five-bar mechanism, and on one real-life system, a 14 degree of freedom (DOF) vehicle model. The five-bar mechanism is used to validate the sensitivity approach derived in this paper. The full vehicle model is used to demonstrate the capability of the new approach developed to perform sensitivity analysis and optimization for large and complex multibody systems with respect to multiple design parameters with high efficiency.

Direct and Adjoint Sensitivity Analysis of Ordinary Differential Equation Multibody Formulations

2014 ◽  
Vol 10 (1) ◽  
Author(s):  
Daniel Dopico ◽  
Yitao Zhu ◽  
Adrian Sandu ◽  
Corina Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Dynamics ◽  
Multibody Systems ◽  
Third Party ◽  
Adjoint Sensitivity ◽  
Numerical Errors ◽  
The Third ◽  
Sensitivity Equations ◽  
Perform Sensitivity Analysis ◽  
Analytical Approaches

Sensitivity analysis of multibody systems is essential for several applications, such as dynamics-based design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences. This procedure is computationally expensive when the number of parameters is large, and numerical errors can severely limit its accuracy. This paper explores several analytical approaches to perform sensitivity analysis of multibody systems. Direct and adjoint sensitivity equations are developed in the context of Maggi's formulation of multibody dynamics equations. The approach can be generalized to other formulations of multibody dynamics as systems of ordinary differential equations (ODEs). The sensitivity equations are validated numerically against the third party code fatode and against finite difference solutions with real and complex perturbations.

DynManto: A Matlab Toolbox for the Simulation and Analysis of Multibody Systems

2020 ◽  
Author(s):  
Alexander Held ◽  
Ali Moghadasi ◽  
Robert Seifried
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
The Body ◽  
Computationally Efficient ◽  
Adjoint Sensitivity ◽  
Modeling And Analysis ◽  
Gradient Based ◽  
Data Files ◽  
Parameter Identifications

Abstract The Dynamic Modeling and Analysis Toolbox DynManto is an acedemic Matlab code which allows the modeling, simulation and sensitivity analysis of spatial multibody systems. The kinematics of rigid and flexible bodies is described by the floating frame of reference formulation and the body properties are provided by standard input data files. In this way the evaluation of the equations of motion is computationally efficient and an arbitrary parameterization of the system can be achieved. The latter is important in the automated adjoint sensitivity analysis of multibody systems, which yields gradient information for system analyses, parameter identifications or gradient-based optimizations. The capabilities of DynManto are demonstrated by the application examples of a flexible two-arm manipulator and Chebyshev’s Lambda Mechanism.

Direct and Adjoint Sensitivity Analysis of Multibody Systems Using Maggi’s Equations

2013 ◽  
Author(s):  
Daniel Dopico ◽  
Yitao Zhu ◽  
Adrian Sandu ◽  
Corina Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Multibody Systems ◽  
Equations Of Motion ◽  
Third Party ◽  
Adjoint Sensitivity Analysis ◽  
Adjoint Sensitivity ◽  
Dynamics Of Multibody Systems ◽  
Dynamical Optimization ◽  
Analytical Expressions ◽  
Coordinate Partitioning

The importance of the sensitivity analysis of multibody systems for several applications is well known, concretely design optimization based on the dynamics of multibody systems usually requires the sensitivity analysis of the equations of motion. A broad range of methods for the dynamics of multibody systems include the state space formulations based on Maggis equations, nullspace methods or coordinate partitioning. Dynamic sensitivities, when needed, are often calculated by means of finite differences but, depending of the number of parameters involved, this procedure can be very demanding in terms of CPU time and the accuracy obtained can be very poor in many cases. In this paper, several ways to perform the sensitivity analysis are explored and analytical expressions for the direct and adjoint sensitivity analysis of multibody systems are presented, all of them based on Maggi’s formulations. Moreover, two different approaches to the adjoint sensitivity analysis of multibody systems are presented. Although particularized to one formulation, the general expressions provided in the paper, are intended to be easily generalized and applied to any other formulation that can be expressed as an ODE-like system of equations, including penalty formulations. Besides, to check the validity and correctness of the proposed equations, the solutions of all the methods proposed are compared: 1) between them, 2) with the third party code FATODE and 3) with the numerical solution using real and complex perturbations. Finally, all the techniques proposed are applied to the dynamical optimization of a multibody system.

Direct Sensitivity Analysis of Spatial Multibody Systems With Joint Friction Using Index-1 Formulation

2021 ◽  
Author(s):  
Adwait Verulkar ◽  
Corina Sandu ◽  
Daniel Dopico ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Dynamic Systems ◽  
Multibody Systems ◽  
Friction Model ◽  
Design Parameters ◽  
Adjoint Sensitivity ◽  
Joint Friction ◽  
Multibody Dynamic ◽  
Model Dynamics ◽  
Direct Sensitivity

Abstract Sensitivity analysis is one of the most prominent gradient based optimization techniques for mechanical systems. Model sensitivities are the derivatives of the generalized coordinates defining the motion of the system in time with respect to the system design parameters. These sensitivities can be calculated using finite differences, but the accuracy and computational inefficiency of this method limits its use. Hence, the methodologies of direct and adjoint sensitivity analysis have gained prominence. Recent research has presented computationally efficient methodologies for both direct and adjoint sensitivity analysis of complex multibody dynamic systems. The contribution of this article is in the development of the mathematical framework for conducting the direct sensitivity analysis of multibody dynamic systems with joint friction using the index-1 formulation. For modeling friction in multibody systems, the Brown and McPhee friction model has been used. This model incorporates the effects of both static and dynamic friction on the model dynamics. A case study has been conducted on a spatial slider-crank mechanism to illustrate the application of this methodology to real-world systems. Using computer models, with and without joint friction, effect of friction on the dynamics and model sensitivities has been demonstrated. The sensitivities of slider velocity have been computed with respect to the design parameters of crank length, rod length, and the parameters defining the friction model. Due to the highly non-linear nature of friction, the model dynamics are more sensitive during the transition phases, where the friction coefficient changes from static to dynamic and vice versa.

Dynamics Study and Sensitivity Analysis of Flexible Multibody Systems With Interval Parameters

2016 ◽  
Author(s):  
Wang Zhe ◽  
Qiang Tian ◽  
Hiayan Hu
Keyword(s):  
Sensitivity Analysis ◽  
Surrogate Model ◽  
Multibody Systems ◽  
Differential Algebraic Equations ◽  
Flexible Multibody Systems ◽  
Computational Time ◽  
Interval Parameters ◽  
Computation Efficiency ◽  
Sensitivity Equations ◽  
Flexible Multibody

The dynamics of flexible multibody systems with interval parameters is studied based on a non-intrusive computation methodology. The Absolute Nodal Coordinate Formulation (ANCF) is used to model the rigid-flexible multibody system, including the finite elements of the ANCF and the ANCF Reference Nodes (ANCF-RNs). The Chebyshev sampling methods including Chebyshev tensor product (CTP) sampling method and Chebyshev collocation method (CCM), are utilized to generate the Chebyshev surrogate model for Interval Differential Algebraic Equations (IDAEs). For purpose of preventing the interval explosion problem and maintaining computation efficiency, the interval bounds of the IDAEs are determined by scanning the deduced Chebyshev surrogate model. To further improve the computation efficiency, OpenMP directives are also used to parallelize the solving process of the Differential Algebraic Equations (DAEs) by fixing the uncertain interval parameter at the given sampling points. The sensitivity analysis of flexible multibody systems with interval parameters is initially performed by using the direct differentiation method. The direct differentiation method differentiates the dynamic equations with respect to the design variable, which yields the system sensitivity equations governed by DAEs. The generalized alpha method is introduced to integrate the sensitivity DAEs. The sensitivity equations of flexible multibody systems with interval parameters are also described by the IDAEs. Based on the continuum mechanics, the computational efficient analytical formulations for the derivative items of the system sensitivity equations are deduced. Three examples are studied to validate the proposed methodology, including the complicated spatial rigid-flexible multibody systems with a large number of uncertain interval parameters, the flexible system with uncertain interval clearance size joint, and the first order sensitivity analysis of flexible multibody systems with interval parameters. Firstly, the dynamics analysis of a six-arm space robot with six interval parameters is performed. For this case study, the interval dynamics cannot be obtained by directly scanning the IDAEs because extremely huge sets of DAEs with deterministic samples have to be solved. The estimated total computational time for solving the scanned IDAEs will be 1850 days! However, the computational time for solving the scanned Chebyshev surrogate model is 9796.97 seconds. It shows the effectiveness of the proposed computation methodology. Then, the nonlinear dynamics of a planar slider-crank mechanism with uncertain interval clearance size joint is studied in this work. The kinetics model of the revolute clearance joints is formulated under the ANCF-RN framework. Moreover, the influence of the LuGre and the modified Coulomb’s friction force models on the system’s dynamic response is investigated. By analyzing the bounds of dynamic response, the bifurcation diagrams are observed. It must be highlighted that with increasing the size of clearance, it does not automatically lead to unstable behaviors. Finally, the first order sensitivity analysis of flexible multibody systems with interval parameters is also studied in this work. The third one of a flexible mechanism with interval parameters is used to perform the sensitivity analysis.

Computing Sensitivity Analysis of Vehicle Dynamics Based on Multibody Models

2013 ◽  
Author(s):  
Yitao Zhu ◽  
Daniel Dopico ◽  
Corina Sandu ◽  
Adrian Sandu
Keyword(s):  
Sensitivity Analysis ◽  
Vehicle Dynamics ◽  
Multibody Systems ◽  
Dynamics Simulation ◽  
Adjoint Sensitivity ◽  
Analysis And Design ◽  
Systems Analysis And Design ◽  
Dynamics Of Multibody Systems ◽  
Direct Sensitivity ◽  
Vehicle Suspension System

Vehicle dynamics simulation based on multibody dynamics techniques has become a powerful tool for vehicle systems analysis and design. As this approach evolves, more and more details are required to increase the accuracy of the simulations, to improve their efficiency, or to provide more information that will allow various types of analyses. One very important direction is the optimization of multibody systems. Sensitivity analysis of the dynamics of multibody systems is essential for design optimization. Dynamic sensitivities, when needed, are often calculated by means of finite differences but, depending of the number of parameters involved, this procedure can be very demanding in terms of time and the accuracy obtained can be very poor in many cases if real perturbations are used. In this paper, several ways to perform the sensitivity analysis of multibody systems are explored including the direct sensitivity approaches and the adjoint sensitivity ones. Finally, the techniques proposed are applied to the dynamical optimization of a five bar mechanism and a vehicle suspension system.

Simulations of Gear-Rolling Element Bearing Interactions in Geared Transmissions

2003 ◽  
Author(s):  
F. Lahmar ◽  
P. Velex
Keyword(s):  
Equations Of Motion ◽  
Rolling Element Bearing ◽  
Integration Scheme ◽  
Time Step ◽  
Normal Contact ◽  
Contact Algorithm ◽  
Rolling Element ◽  
Non Linear ◽  
External Forces ◽  
Gear Rolling

The modular model of geared systems presented in this paper makes it possible to simultaneously account for the contact conditions in gears and rolling element bearings. Gears are modeled as two rigid cylinders connected by distributed mesh stiffnesses while ball and roller bearings contribute to the equations of motion as time-varying, non-linear external forces. Solutions are obtained by combining a Newmark time-step integration scheme, a Newton-Raphson method for ball bearing non-linearity and a normal contact algorithm that deals with the contact problem between the teeth. It is found that the static gear-bearing couplings are generally more important than the dynamic couplings with a significant influence of the gear on the bearing response. Finally, it is shown that, in certain conditions, bearings can generate non-linear parametric excitations of the same orders of magnitude as those associated with the meshing of helical gears.

Logarithmic Complexity Sensitivity Analysis of Flexible Multibody Systems

2009 ◽  
Author(s):  
Kishor D. Bhalerao ◽  
Mohammad Poursina ◽  
Kurt S. Anderson
Keyword(s):  
Sensitivity Analysis ◽  
Data Storage ◽  
Multibody Systems ◽  
Parallel Implementation ◽  
Equations Of Motion ◽  
Flexible Multibody Systems ◽  
Divide And Conquer ◽  
Dynamics Simulation ◽  
Modal Shape ◽  
Flexible Multibody

This paper presents a recursive direct differentiation method for sensitivity analysis of flexible multibody systems. Large rotations and translations in the system are modeled as rigid body degrees of freedom while the deformation field within each body is approximated by superposition of modal shape functions. The equations of motion for the flexible members are differentiated at body level and the sensitivity information is generated via a recursive divide and conquer scheme. The number of differentiations required in this method is minimal. The method works concurrently with the forward dynamics simulation of the system and requires minimum data storage. The use of divide and conquer framework makes the method linear and logarithmic in complexity for serial and parallel implementation, respectively, and ideally suited for general topologies. The method is applied to a flexible two arm robotic manipulator to calculate sensitivity information and the results are compared with the finite difference approach.

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