Multibody model based estimation of multiple loads and strain field on a vehicle suspension system

Abstract

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.

State and Force Estimation on a Rotating Helicopter Blade through a Kalman-Based Approach

“…Starting from this layout, a coupled multibody-aerodynamic simulation was performed and position/velocity sensor data were stored by applying additive white Gaussian noise, which defines the covariance matrix R. The missing information was on the model covariance Q. In previous work [25,27], a higher source of uncertainties was considered on the load states, such that Q p Q x . This was a valuable assumption, since we can assume that the model used was accurate enough, but no information on the external loads is available.…”

“…The main principle is the linearization of the non-linear system around the current estimated state using a first-order truncation of the Taylor series expansion of the model equations. Some references on the application of the EKF can be found in [23][24][25]. The UKF is instead a recursive estimator that addresses some of the approximation issues of the EKF.…”

“…The DKF operates in two estimation stages, while the AKF estimates the states and the inputs simultaneously by introducing an augmented state vector and this defines a reduction of the computational cost. The AKF has been applied in many fields and was recently demonstrated to give accurate results for automotive applications [25,27]. The results showed that, when the adopted structural model was not accurate enough, the AKF still provided a good estimation of the states at the expense of the loads' accuracy.…”

A noninvasive system‐level model order reduction scheme for flexible multibody simulation

“…For many industrial applications, the small deformation assumption in particular has led to the development of range of efficient descriptions like the floating‐frame‐of‐reference component mode synthesis (FFR‐CMS) and generalized component mode synthesis approaches (GCMS), and more recently the flexible natural coordinate formulation (FNCF) . The possibility of these methods for effectively describing the system‐level dynamics at a feasible computational cost, in contrast to more general nonlinear finite element approaches, has led to an increasing interest in exploiting (flexible) multibody simulation paradigms in a range of novel frameworks like: model‐based state‐estimation and model‐based control and design …”

“…Current flexible multibody approaches, however, typically lead to differential algebraic equations (DAE) with tens to hundreds of degrees‐of‐freedom (DOFs), even after component‐level model order reduction. This differential algebraic structure can be resolved into a set of ordinary DAEs through a penalty formulation, instead of a Lagrange multiplier formulation, but this is often a numerically poorly conditioned approach and has several issues when redundant rotational parameterizations (like the ominous Euler parameters) are employed.…”