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We develop a cluster‐based model order reduction (called C‐pRBMOR) approach for efficient homogenization of bones, compatible with a large variety of generalized standard material (GSM) models. To this end, the pRBMOR approach based on a mixed incremental potential formulation is extended to a clustered version for a significantly improved computational efficiency. The microscopic modeling of bones falls into a mixed incremental class of the GSM framework, originating from two potentials. An offline phase of the C‐pRBMOR approach includes both a clustering analysis spatially decomposing the micro‐domain within an RVE and a space–time decomposition of the microscopic plastic strain fields. A comparative study on two different clustering approaches and two algorithms for mode identification is additionally conducted. For an online analysis, a cluster‐enhanced version of evolution equations for the reduced variables is derived from an effective incremental variational formulation, rendering a very small set of nonlinear equations to be numerically solved. Several numerical examples show the effectiveness of the C‐pRBMOR approach. A striking acceleration rate beyond 104 against conventional FE computations and that beyond 103 against the original pRBMOR approach are observed. [ABSTRACT FROM AUTHOR]

Fast state estimation for nonlinear systems has been a key issue in control theory and the recently developed predefined‐time stability acts as an effective tool for the problem. However, the studies of predefined‐time state observer for nonlinear systems are rare. In this article, we consider the predefined‐time extended state observer (PTESO) design for a class of high‐order strict‐feedback systems subject to Hölder continuous nonlinearities and lumped disturbance. By developing an adaptive mechanism and using time‐varying functions, a class of adaptive PTESOs is designed to estimate the unavailable states and the lumped disturbance, in which the convergence time can be tightly and explicitly preset by only one parameter, irrelevant to the initial conditions. The adaptive mechanism is used to improve the transient performance under wide‐range lumped disturbance. Moreover, thanks to the design of the time‐varying gains, the PTESO could realize fast observation with trivial peaking observation errors. Finally, simulation results are provided to illustrate the effectiveness of the proposed observer. [ABSTRACT FROM AUTHOR]

We present a reduced order model for efficient nonlinear homogenization of bones, accounting for strength difference effects and containing some well‐known plasticity models (like von Mises or Drucker‐Prager) as special cases. The reduced order homogenization is done by using a cluster‐based model order reduction technique, called cluster‐based nonuniform transformation field analysis. For an offline phase, a space–time decomposition is performed on the mesoscopic plastic strain fields, while a clustering analysis is employed for a spatial decomposition of the mesoscale RVE model. A volumetric‐deviatoric split is additionally introduced to capture the enriched characteristics of the mesoscopic plastic strain fields. For an online analysis, the reduced order model is formulated in a unified minimization problem, which is compatible with a large variety of material models. Both cortical and trabecular bones are considered for numerical experiments. Compared to conventional FE‐based RVE computations, the developed reduced order model renders a considerable acceleration rate beyond 103, while maintaining a sufficient accuracy level. [ABSTRACT FROM AUTHOR]

This article studies the predefined‐time observation problem of generalized strict‐feedback second‐order systems commonly encountered in practice. A nonaffine control input, a matched perturbation, and nonlinear functions satisfying the Hölder growth condition are considered. A class of adaptive predefined‐time observers (PTOs) is designed to reconstruct unknown states and lumped perturbations based on a barrier function and specific time‐varying functions. Distinct from existing observers for strict‐feedback systems, the PTO accomplishes a complete reconstruction in a predefined time with trivial peaking observation errors. Furthermore, the upper bound of the settling time of the PTO is tightly and explicitly predefined by only one design parameter, and is irrelevant to the initial conditions. Hence, tuning procedures for the physically realizable temporal demands become less conservative and more straightforward. Moreover, the adaptive coefficients of the PTO are self‐adjusted along with the magnitude of perturbation, efficiently improving the transient performance under wide‐range perturbations. Finally, numerical simulations on a robot manipulator system demonstrate the effectiveness of the PTO. [ABSTRACT FROM AUTHOR]

Conventional vibration displacement monitoring equipment was expensive, limited by the installation location and space of sensors, and was difficult to be widely used in the industrial field. Due to the integral operation relationship between acceleration and displacement, and the relatively easily measured acceleration signal, the acceleration frequency domain integral method was studied, and a set of simple and high precision vibration displacement measurement system was developed by using Lab VIEW virtual instrument platform and MATLAB. In order to further verify the effectiveness of the current system, the displacement measured by the current system was compared with that measured by digital image correlation (DIC) with the vibration platform as the experimental object. Experimental results show that the current low cost vibration displacement measurement system has high precision. [ABSTRACT FROM AUTHOR]

Summary: Homogenization methods are drawing increasing attention for simulation of heterogeneous materials like composites. For balancing the accuracy and the numerical efficiency of such strategies, we deal with both model and discretization errors of the finite element method (FEM) on a macroscale. Within a framework of goal‐oriented adaptivity, we consider linear elastic heterogeneous materials, for which first‐order homogenization schemes apply. A novel model hierarchy is proposed based on mean‐field and full‐field homogenization methods. For the former, we consider several well‐established schemes like Mori‐Tanaka or self‐consistent as basic models, and for the latter, as superior models, unit cell problems are solved via the FEM under an a priori chosen boundary condition. For a further stage of the model hierarchy, we consider hierarchical unit cells within the frame of the FEM toward an adaptive selection of the unit cell size. By means of several numerical examples, we illustrate the effectiveness of the proposed adaptive approach. [ABSTRACT FROM AUTHOR]