Treatment of Constrained Multibody Dynamic Systems with Uncertainties

Sandu, Corina; Sandu, Adrian; Chan, Brendan J.; Ahmadian, Mehdi

doi:10.4271/2005-01-0936

Cited by 11 publications

(4 citation statements)

References 45 publications

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“…X respectively Y axes are in the plane of the sensor, the Z axis is vertical. [6,13] It is generally thought one of the X or Y The loading force P or the moment M in the middle of a beam embedded at both ends. Torques diagrams considering the two situations are shown in figure 3 have an area with constant or slowly varying values of specific strains where strain gauge transducers are installed onto (TER) was considered a variation of the section (double tapered beam).…”

Section: Applied Mechanics and Materials Vol 762mentioning

confidence: 99%

Adaptation to Rough Terrains by Using Force Sensing on the MERO Modular Walking Robots

Ion

Găvan

Curaj

et al. 2015

AMM

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The last years a large number of vehicles have been developed for their mobility characteristics over rough terrains. The new modular walking robot MERO* (MEchanism Robot- *Pelecudi Ch et.al.) by reconfiguring their architecture are built to displace the heavy loads on the rough terrains. The main characteristic of the modular walking robot is that they are able to move away on not arranged, horizontal and rough terrains. The modular mechatronic system protect much better the environment when its contact with the soil is discrete, a fact that limits appreciately he area that is crushed. Operation of autonomous walking robot MERO movement implies the existence of a close link between planning movements, environmental perception and executions order to obtain an appropriate behaviour in weakly structured environments. For further acquisition of terrain information, we propose installed active force sensor for terminal leg. This paper describes the detailed design and the prototype characterization of a novel tactile sensor force/moment sensor for MERO an intelligent walking robot’s .

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Section: Applied Mechanics and Materials Vol 762mentioning

confidence: 99%

Adaptation to Rough Terrains by Using Force Sensing on the MERO Modular Walking Robots

Ion

Găvan

Curaj

et al. 2015

AMM

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“…Xiu extended the approach to general formulations based on Wiener‐askey polynomials family (Xiu and Karniadakis, 2002a), and applied it to fluid mechanics (Xiu et al , 2002; Xiu and Karniadakis, 2002b, 2003). Sandu et al applied for the first time the polynomial chaos method to multi‐body dynamic systems (Sandu et al 2004, 2005, 2006a, b), terramechanics (Li et al , 2005; Sandu et al , 2006c) and parameter estimation (Blanchard et al , 2007a, b). Saad et al (2007) coupled the polynomial chaos theory with the EnKF to indentify unknown variables in a non‐parametric stochastic representation of the nonlinearities in a shear building model.…”

Section: Introductionmentioning

confidence: 99%

Parameter estimation for mechanical systems via an explicit representation of uncertainty

Blanchard

Sandu

2009

Engineering Computations

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Purpose -To propose a new computational approach for parameter estimation in the Bayesian framework. Aposteriori PDFs are obtained using the polynomial chaos theory for propagating uncertainties through system dynamics. The new method has the advantage of being able to deal with large parametric uncertainties, non-Gaussian probability densities, and nonlinear dynamics.Design/methodology/approach -The maximum likelihood estimates are obtained by minimizing a cost function derived from the Bayesian theorem. Direct stochastic collocation is used as a less computationally expensive alternative to the traditional Galerkin approach to propagate the uncertainties through the system in the polynomial chaos framework. Findings -The new approach is explained and is applied to very simple mechanical systems in order to illustrate how the Bayesian cost function can be affected by the noise level in the measurements, by undersampling, non-identifiablily of the system, non-observability, and by excitation signals that are not rich enough. When the system is non-identifiable and an apriori knowledge of the parameter uncertainties is available, 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.Originality/value -The polynomial chaos method has been shown to be considerably more efficient than Monte Carlo in the simulation of systems with a small number of uncertain parameters. To the best of our knowledge, it is the first time the polynomial chaos theory has been applied to Bayesian estimation. Paper type Research paper  = probability distribution of the multidimensional random variable  . K  = standard deviation for the stiffness distribution M  = standard deviation for the mass distribution meas  = standard deviation of the measurement oscillation frequency obs   = frequency of the forcing function (radians s -1 ) n  = natural frequency (radians s -1 ) obs  = measured oscillation frequency (radians s -1 )  = multi-dimensional random variable  = space of possible value for the unknown variables  = generalized Askey-Wiener polynomial chaoses Subscripts nom = nominal value, i.e., value obtained when 0   Superscripts ref = reference value used to generate observations 4 uncertainties through covariance matrices at the same time. In order to approximate PDFs propagated through the system, linearization using the EKF (Blanchard et al., 2007b) and Monte Carlo techniques using the EnKF (Saad et al., 2007) are common approaches. 10 mismatch J is usually the most important component of the cost function, but apriori J is useful when mismatch Jdoes not contain enough information in order to find a clear minimum value for our cost function. This is illustrated in the next section of this article. Mass-spring system with uncertain initial velocityThis section applies the Bayesian approach to the simple mass-spring system shown in Figure 1.

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“…Xiu and Karniadakis [11] extended the approach to general formulations based on Wiener-Askey polynomials family, and applied it to fluid mechanics [12][13][14]. Sandu et al [3,4,15,16] applied for the first time the polynomial chaos method to multibody dynamic systems, terramechanics [17,18], and parameter estimation in the time domain for fixed parameters [19,20]. In their groundbreaking work, Soize and Ghanem [21] described mathematical settings for characterizing problems for which random uncertainties have arbitrary probability densities.…”

Section: Introductionmentioning

confidence: 99%

Polynomial chaos-based parameter estimation methods applied to a vehicle system

Blanchard

Sandu

2009

Proceedings of the Institution of Mechanical Engineers, Part K:

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Parameter estimation for large systems is a difficult problem, and the solution approaches are computationally expensive. The polynomial chaos approach has been shown to be more efficient than Monte Carlo for quantifying the effects of uncertainties on the system response. This article compares two new computational approaches for parameter estimation based on the polynomial chaos theory for parameter estimation: a Bayesian approach, and an approach using an extended Kalman filter (EKF) to obtain the polynomial chaos representation of the uncertain states and the uncertain parameters. The two methods are applied to a non-linear 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. When using appropriate excitations, the results obtained with both approaches are close to the actual values of the parameters, and both approaches can work with noisy measurements. The EKF approach has an advantage over the Bayesian approach: the estimation comes in the form of a posteriori probability densities of the estimated parameters. However, it can yield poor estimations when dealing with non-identifiable systems, and it is recommended to repeat the estimation with different sampling rates in order to verify the coherence of the results with the EKF approach. The Bayesian approach is more robust, can recognize non-identifiability, and use regularization techniques if necessary.

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Treatment of Constrained Multibody Dynamic Systems with Uncertainties

Cited by 11 publications

References 45 publications

Adaptation to Rough Terrains by Using Force Sensing on the MERO Modular Walking Robots

Adaptation to Rough Terrains by Using Force Sensing on the MERO Modular Walking Robots

Parameter estimation for mechanical systems via an explicit representation of uncertainty

Polynomial chaos-based parameter estimation methods applied to a vehicle system

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