A Unit-Consistent Error Measure for Multibody Systems With Unilateral Constraints

2019 ◽  
Vol 14 (5) ◽  
Author(s):  
Andreas Enzenhöfer ◽  
Albert Peiret ◽  
Marek Teichmann ◽  
József Kövecses
Keyword(s):  
Multibody Systems ◽  
Reference Trajectory ◽  
Unilateral Constraints ◽  
Error Measure ◽  
Energy Error ◽  
Error Measures ◽  
Unilateral Contacts ◽  
Mixed Linear Complementarity Problem ◽  
Consistent Error ◽  
Real Time Simulations

Modeling multibody systems subject to unilateral contacts and friction efficiently is challenging, and dynamic formulations based on the mixed linear complementarity problem (MLCP) are commonly used for this purpose. The accuracy of the MLCP solution method can be evaluated by determining the error introduced by it. In this paper, we find that commonly used MLCP error measures suffer from unit inconsistency leading to the error lacking any physical meaning. We propose a unit-consistent error measure, which computes energy error components for each constraint dependent on the inverse effective mass and compliance. It is shown by means of a simple example that the unit consistency issue does not occur using this proposed error measure. Simulation results confirm that the error decreases with convergence toward the solution. If a pivoting algorithm does not find a solution of the MLCP due to an iteration limit, e.g., in real-time simulations, choosing the result with the least error can reduce the risk of simulation instabilities and deviation from the reference trajectory.

A Unit-Consistent Error Measure for Mixed Linear Complementarity Problems in Multibody Dynamics With Contact

2018 ◽  
Author(s):  
Andreas Enzenhöfer ◽  
Albert Peiret ◽  
Marek Teichmann ◽  
József Kövecses
Keyword(s):  
Linear Complementarity Problems ◽  
Linear Complementarity ◽  
Error Measure ◽  
Energy Error ◽  
Error Measures ◽  
Pivoting Algorithm ◽  
Unilateral Contacts ◽  
Mixed Linear Complementarity Problem ◽  
Consistent Error ◽  
Real Time Simulations

Modeling multibody systems subject to unilateral contacts and friction efficiently is challenging, and dynamic formulations based on the mixed linear complementarity problem (MLCP) are commonly used for this purpose. The accuracy of the MLCP solution method can be evaluated by determining the error introduced by it. In this paper, we find that commonly used MLCP error measures suffer from unit inconsistency leading to the error lacking any physical meaning. We propose a unit-consistent error measure which computes energy error components for each constraint dependent on the inverse effective mass and compliance. It is shown by means of a simple example that the unit consistency issue does not occur using this proposed error measure. Simulation results confirm that the error decreases with convergence toward the solution. If a pivoting algorithm does not find a solution of the MLCP due to an iteration limit, e.g. in real-time simulations, choosing the result with the least error can reduce the risk of simulation instabilities.

Dynamics of Roller Coasters

2005 ◽  
Author(s):  
Friedrich Pfeiffer
Keyword(s):  
Multibody Systems ◽  
Multibody System ◽  
Roller Coaster ◽  
Stick Slip ◽  
Unilateral Contacts ◽  
Raceway Design ◽  
Impacts With Friction

Roller coasters are dynamically multibody systems with unilateral contacts due to the usual raceway design including straight parts and bends. In running down such tracks and passing parts of the track with changing curvature impacts with friction are generated in the track-wheel contacts. The impacts are always connected with large overloads of the wheels sometimes leading to damages. To investigate these problems the roller coaster carriages are modelled as a non-smooth multibody system with impacts and stick-slip processes. The results in terms of wheel loads are used to improve wheel design.

scholarly journals Alopex: A Correlation-Based Learning Algorithm for Feedforward and Recurrent Neural Networks

1994 ◽  
Vol 6 (3) ◽  
pp. 469-490 ◽  
Author(s):  
K. P. Unnikrishnan ◽  
K. P. Venugopal
Keyword(s):  
Neural Networks ◽  
Gradient Descent ◽  
Transfer Functions ◽  
Learning Algorithm ◽  
Recurrent Networks ◽  
Error Measure ◽  
Scaling Properties ◽  
Error Measures ◽  
Local Correlations ◽  
Temperature Parameter

We present a learning algorithm for neural networks, called Alopex. Instead of error gradient, Alopex uses local correlations between changes in individual weights and changes in the global error measure. The algorithm does not make any assumptions about transfer functions of individual neurons, and does not explicitly depend on the functional form of the error measure. Hence, it can be used in networks with arbitrary transfer functions and for minimizing a large class of error measures. The learning algorithm is the same for feedforward and recurrent networks. All the weights in a network are updated simultaneously, using only local computations. This allows complete parallelization of the algorithm. The algorithm is stochastic and it uses a “temperature” parameter in a manner similar to that in simulated annealing. A heuristic “annealing schedule” is presented that is effective in finding global minima of error surfaces. In this paper, we report extensive simulation studies illustrating these advantages and show that learning times are comparable to those for standard gradient descent methods. Feedforward networks trained with Alopex are used to solve the MONK's problems and symmetry problems. Recurrent networks trained with the same algorithm are used for solving temporal XOR problems. Scaling properties of the algorithm are demonstrated using encoder problems of different sizes and advantages of appropriate error measures are illustrated using a variety of problems.

A Regularized Contact Model for Multibody System Simulation

2016 ◽  
Author(s):  
Albert Peiret ◽  
Farnood Gholami ◽  
József Kövecses ◽  
Josep M. Font-Llagunes
Keyword(s):  
Multibody Systems ◽  
Large Scale ◽  
Multibody System ◽  
Linear Complementarity Problems ◽  
Friction Model ◽  
Computational Performance ◽  
Unilateral Contacts ◽  
Wheel Model ◽  
Friction Models ◽  
Coulomb Model

Simulation of large-scale multibody systems with unilateral contacts requires formulations with which good computational performance can be achieved. The availability of many solver algorithms for Linear Complementarity Problems (LCP) makes the LCP-based formulations a good candidate for this. However, considering friction in contacts asks for new friction models compatible with this kind of formulations. Here, a new, regularized friction model is presented to approximate the Coulomb model, which allows to formulate the multibody system dynamics as a LCP with bounds. Moreover, a bristle approach is used to approximate the stiction force, so that it improves the numerical behaviour of the system and makes it able to handle redundancy coming from the friction interfaces. Several examples using a 3D wheel model has been carried out, and the proposed friction model shows a better approximation of the Coulomb model compared to other LCP-based formulations.

scholarly journals Fuzzy set based error measure for hydrologic model evaluation

2005 ◽  
Vol 7 (3) ◽  
pp. 199-208 ◽  
Author(s):  
Ramesh Teegavarapu ◽  
Amin Elshorbagy
Keyword(s):  
Fuzzy Set ◽  
Mean Squared Error ◽  
Predictive Accuracy ◽  
Selection Process ◽  
Real Life ◽  
Hydrologic Model ◽  
Error Measure ◽  
Hydrologic Time Series ◽  
Error Measures ◽  
Hydrologic Condition

Traditional error measures (e.g. mean squared error, mean relative error) are often used in the field of water resources to evaluate the performance of models developed for modeling various hydrological processes. However, these measures may not always provide a comprehensive assessment of the performance of the model intended for a specific application. A new error measure is proposed and developed in this paper to fill the gap left by existing traditional error measures for performance evaluation. The measure quantifies the error that corresponds to the hydrologic condition and model application under consideration and also facilitates selection of the best model whenever multiple models are available for that application. Fuzzy set theory is used to model the modeler's perceptions of predictive accuracy in specific applications. The development of the error measure is primarily intended for use with models that provide hydrologic time series predictions. Hypothetical and real-life examples are used to illustrate and evaluate this measure. Results indicate that use of this measure is rational and meaningful in the selection process of an appropriate model from a set of competing models.

Structures With Multiple Rigid Configurations Due to Prestress and Unilateral Contacts

2021 ◽  
Author(s):  
Charles Dorn ◽  
Yang Li ◽  
Sergio Pellegrino
Keyword(s):  
Degree Of Freedom ◽  
Multiple Equilibrium ◽  
Multiple Target ◽  
Unilateral Constraints ◽  
Equilibrium Configurations ◽  
Unilateral Contacts ◽  
Reaction Forces ◽  
Rf Antenna ◽  
Four Bar Linkage ◽  
Multiple Configurations

Abstract This paper presents structures with multiple equilibrium configurations arising from the combination of a state of prestress and unilateral contacts. A design problem is posed where preloaded elastic springs and unilateral constraints are embedded throughout a mechanism. The spring parameters are designed such that multiple target configurations are immobilized due to contact. In each of these configurations, the spring forces maintain compressive reaction forces, immobilizing the structure. Each immobilized configuration can rigidly resist perturbation forces up to some finite magnitude where contact is lost. Hence, this case of multiple configurations in equilibrium due to the combination of prestress and contact is referred to as multi-configuration rigidity. Two examples of structures exhibiting multi-configuration rigidity are presented. First, a four bar linkage with a single kinematic degree of freedom is used to introduce the concept. In the context of the linkage, multi-configuration rigidity is compared to multi-stability, exhibiting the key differences between the two concepts. Then, a 24-degree-of-freedom kirigami surface is presented that can morph between flat and spherical configurations, motivated by RF antenna applications. By embedding torsional springs and fold angle stops throughout the structure, flat and spherical configurations are made rigid. Actuation between the configurations can easily be achieved by snapping the structure between the rigid configurations.

A Fast Algorithm for Contact Dynamics of Multibody Systems Using the Box Friction Model

2016 ◽  
Vol 12 (1) ◽  
Author(s):  
Farnood Gholami ◽  
Mostafa Nasri ◽  
József Kövecses ◽  
Marek Teichmann
Keyword(s):  
Complementarity Problem ◽  
Multibody Systems ◽  
Friction Model ◽  
Contact Dynamics ◽  
Redundant Constraints ◽  
Solution Algorithms ◽  
Mixed Complementarity Problem ◽  
Dynamics Of Multibody Systems ◽  
Novel Approach ◽  
Mixed Linear Complementarity Problem

One of the major challenges in dynamics of multibody systems is to handle redundant constraints appropriately. The box friction model is one of the existing approaches to formulate the contact and friction phenomenon as a mixed linear complementarity problem (MLCP). In this setting, the contact redundancy can be handled by relaxing the constraints, but such a technique might suffer from certain drawbacks, specially in the case of large number of redundant constraints. Most of the common pivoting algorithms used to solve the resulting mixed complementarity problem might not converge when the relaxation terms are chosen as small as they should be. To overcome the aforementioned shortcoming, we propose a novel approach which takes advantage of the sparse structure of the formulated MLCP. This novel approach reduces the sensitivity of the solution of the problem to the relaxation terms and decreases the number of required pivots to obtain the solution, leading to shorter computational times. Furthermore, as a result of the proposed approach, much smaller relaxation terms can be used while the solution algorithms converge.

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