Real-world products and physics-based simulations are becoming interconnected. In particular, real-time capable dynamic simulation has made it possible for simulation models to run in parallel and simultaneously with operating machinery. This capability combined with state observer techniques such as Kalman filtering have enabled the synchronization between simulation and the real world. State estimator techniques can be applied to estimate unmeasured quantities, also referred as virtual sensing, or to enhance the quality of measured signals. Although synchronized models could be used in a number of ways, value creation and business model development are currently defining the most practical and beneficial use cases from a business perspective. The research reported here reveals the communication and collaboration methods that lead to economically relevant technology solutions. Two case examples are given that demonstrate the proposed methodology. The work benefited from the broad perspective of researchers from different backgrounds and the joint effort to drive the technology development towards business relevant cases.

Multibody system dynamics approaches together with state estimation methods can reduce the need for a large number of sensors, especially in the digital twin of working mobile machinery. To demonstrate this, a hydraulically actuated machine was modeled using the double-step semi-recursive multibody formulation and lumped fluid theory in terms of system independent states. Next, because of the high non-linearity of the modeled system and with respect to the reported performance degradation of the Extended Kalman Filters (EKF), which are mostly related to the linearization procedure of this filter, the Unscented Kalman Filter (UKF) was implemented to achieve high accuracy and performance. The methodology of the proposed approaches was applied to a mobile log crane model PATU 655. The implementation of the proposed estimation algorithms is demonstrated with three different multibody based simulation models: the synthetic real system producing the artificial measurements, the simulation model, and the estimation model. Encoders and pressure sensors, installed on the synthetic real system, provided synthetic sensor measurement data. To mimic real-world conditions, the estimation and simulation models used in the processing of the state estimation algorithm were assumed to have errors in the initial conditions and force model. The proposed UKF was applied to the estimation model with the synthetic sensor measurement data. The minimum percent normalized root mean square errors in the associated measured and unmeasured states of case example were 0.11% and 1.86%, respectively. The UKF using the multibody system dynamics formulations is able to estimate the case example states despite 15% and 60% errors in mass and inertial properties of bodies and Payload, respectively, confirming the accuracy and performance of the algorithm.INDEX TERMS state estimation, multibody system dynamics, hydraulic actuators, unscented Kalman filter, working machine, digital twin

This study investigates the discrete extended Kalman filter as applied to multibody systems and focuses on accurate formulation of the state-transition model in the framework. The proposed state-transition model is based on the coordinate-partitioning method and linearization of the multibody equations of motion. The approach utilizes the synergies between the integration of states and estimator covariances without overly simplifying the integrator structure. The proposed method is analyzed with a forward dynamics analysis of a four-bar mechanism. The results show that the stability of the state-transition model in the forward dynamics analysis is significantly enhanced with the proposed method compared with the forward Euler-based methods. The computational efficiency of the novel method was significantly lower in comparison to forward Euler-based methods, which was found to be mainly due to the computation of the Jacobian matrix of the nonlinear state equation. However, the increase in computational cost can be considered acceptable in Kalman-filtering applications, where the exact Jacobian of the state equation is needed.

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