This work proposes an augmented extended Kalman filter based state-input estimator for mechanical systems defined by implicit equations of motion which is then applied to estimate the six wheel center loads and the strain field on a vehicle suspension test rig.Implicit equations of motion typically arise in the definition of flexible multibody models and also in their time resolution, because implicit time-discretization schemes are normally employed to obtain a stable solution. The presented methodology can be applied to such case and analytical expressions are derived for the necessary linearizations, providing the means for a computationally efficient estimation procedure.The six wheel center loads and the strain field on a vehicle suspension system are valuable quantities during the vehicle design phase (e.g. for durability analysis), hence they are often directly measured during elaborate full vehicle testing campaigns. This work demonstrates that a flexible multibody model representation allows to accurately reconstruct the time domain signals of the six loads and of the full strain field, starting from a minimal set of six measured strains, hence providing an appealing alternative to direct measurement methods. The experimental validation on the suspension test rig shows that all estimated quantities can be accurately reconstructed, given that the system simulation model incorporates an adequate level of accuracy.

A novel nonlinear parametric model order reduction technique for the solution of contact problems in flexible multibody dynamics is presented. These problems are characterized by significant variations in the location and size of the contact area and typically require high-dimensional finite element models having multiple inputs and outputs to be solved. The presented technique draws from the fields of nonlinear and parametric model reduction to construct a reduced-order model whose dimensions are insensitive to the dimensions of the full-order model. The solution of interest is approximated in a lower-dimensional subspace spanned by a constant set of eigenvectors augmented with a parameter-dependent set of global contact shapes. The latter represent deformation patterns of the interacting bodies obtained from a series of static contact analyses. The set of global contact shapes is parameterized with respect to the system configuration and therefore continuously varies in time. An energy-consistent formulation is assured by explicitly taking into account the dynamic parameter variability in the derivation of the equations of motion. The performance of the novel technique is demonstrated by simulating a dynamic gear contact problem and comparing results against traditional model reduction techniques as well as commercial nonlinear finite element software. Copyright NLPMOR METHOD FOR EFFICIENT GEAR SIMULATIONS 1163 meshes. These approaches separate the bulk deformation of the interacting components from the nonlinear local displacement field at the contact surfaces, computing the former using linear FE on a coarse mesh and obtaining the latter from classical contact theory. Most notably, Vijayakar [3] combines traditional FE with the Boussinesq solution for a point-load acting on an infinite halfspace, whereas Andersson and Vedmar [2] compute the local deformation due to Hertzian contact pressure using a formula derived by Weber and Banaschek [4]. Although these approaches require significantly less degrees of freedom as compared to traditional FE-based contact simulations, the procedure of matching the analytical and FE solutions at a certain depth below the contact surface is computationally involved, resulting in relatively high costs per time increment [5]. Moreover, an energy-consistent adaptation of these approaches to the formalism of flexible multibody dynamics (FMBS) has yet to be pursued. Finally, the question as to whether an infinite half-space serves as a good approximation of the actual contact zone is highly case-specific.The use of conventional FE to represent flexible bodies in multibody simulations can be rendered practical with the aid of model order reduction (MOR) techniques. These techniques originated from the fields of control theory [6] and structural dynamics [7] and were primarily designed for reducing the sizes of, respectively, first-order and second-order linear systems. Using the floating frame of reference formulation [8], the linear elastic deformation of a flexible body is separate...

The potential of the Augmented Kalman Filter algorithm is tested in this paper for joint state-input estimation in structural dynamics field. In view of inverse load identification, the filter is compared with the Transfer Path Analysis Matrix Inversion technique, commonly used for industrial applications. An existing Optimal Sensor Placement strategy for Kalman Filter is adopted and validated on real experimental data. The advantages of the proposed methods, through strain measurements information, are identified in the effort needed for data-acquisition and data-processing. The effectiveness of the filter and the quality of the results are demonstrated in this paper for an industrial test-case, such as a rear twistbeam suspension.