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This article aims to present a direct solution to handle linear constraints in finite element (FE) analysis without penalties or the Lagrange multipliers introduced.

First, the system of linear equations corresponding to the linear constraints is solved for the leading variables in terms of the free variables and the constants. Then, the reduced system of equilibrium equations with respect to the free variables is derived from the finite-dimensional virtual work equation. Finally, the algorithm is designed.

The proposed procedure is promising in three typical cases: (1) to enforce displacement constraints in any direction; (2) to implement local refinements by allowing hanging nodes from element subdivision and (3) to treat non-matching grids of distinct parts of the problem domain. The procedure is general and suitable for 3D non-linear analyses.

The algorithm is fitted only to the Galerkin-based numerical methods.

The proposed procedure does not need Lagrange multipliers or penalties. The tangential stiffness matrix of the reduced system of equilibrium equations reserves positive definiteness and symmetry. Besides, many contemporary Galerkin-based numerical methods need to tackle the enforcement of the essential conditions, whose weak forms reduce to linear constraints. As a result, the proposed procedure is quite promising.

In this investigation, a linear encoder system based on the ultrasonic transducer has been proposed. Ultrasonic transducers are usually designed for distance measurements, such as the time of flight method and sonar system. These applications are defined as discrete-length measurement technologies. The purpose of this study is to develop a continuous displacement measurement system using ultrasonic transducers.

A modified signal processing based on heterodyne signaling is implemented in this system. In the proposed signal processing, there is an automatic gain control module, a phase-shifting module, a phase detection module, an interpolation module and especially a frequency multiplication module, which can enhance the resolution and reduce the interpolation error simultaneously.

The proposed system can generate the encoding signals and is compatible with most motion control systems. For the experimental result, the maximum measurement error and standard deviation are about −0.027 and 0.048 mm, respectively. It shows that the proposed encoder system has the potential for displacement measurement tasks.

This study reveals an ultrasonic linear encoder that is capable of generating an incremental encoding signal, accompanied by a corresponding signal processing methodology. In contrast to the conventional heterodyne signal processing approach, the proposed multiplication method effectively reduces the interpolation error that arises because of multiple reflections.

The Wiener-Hammerstein nonlinear system is made up of two dynamic linear subsystems in series with a static nonlinear subsystem, and it is widely used in electrical, mechanical, aerospace and other fields. This paper considers the parameter estimation of the Wiener-Hammerstein output error moving average (OEMA) system.

The idea of multi-population and parameter self-adaptive identification is introduced, and a multi-population self-adaptive differential evolution (MPSADE) algorithm is proposed. In order to confirm the feasibility of the above method, the differential evolution (DE), the self-adaptive differential evolution (SADE), the MPSADE and the gradient iterative (GI) algorithms are derived to identify the Wiener-Hammerstein OEMA system, respectively.

From the simulation results, the authors find that the estimation errors under the four algorithms stabilize after 120, 30, 20 and 300 iterations, respectively, and the estimation errors of the four algorithms converge to 5.0%, 3.6%, 2.7% and 7.3%, which show that all four algorithms can identify the Wiener-Hammerstein OEMA system.

Compared with DE, SADE and GI algorithm, the MPSADE algorithm not only has higher parameter estimation accuracy but also has a faster convergence speed. Finally, the input–output relationship of laser welding system is described and identified by the MPSADE algorithm. The simulation results show that the MPSADE algorithm can effectively identify parameters of the laser welding system.

This paper aims to present an unconditionally energy-stable scheme for approximating the convective heat transfer equation.

The scheme stems from the generalized positive auxiliary variable (gPAV) idea and exploits a special treatment for the convection term. The original convection term is replaced by its linear approximation plus a correction term, which is under the control of an auxiliary variable. The scheme entails the computation of two temperature fields within each time step, and the linear algebraic system resulting from the discretization involves a coefficient matrix that is updated periodically. This auxiliary variable is given by a well-defined explicit formula that guarantees the positivity of its computed value.

Compared with the semi-implicit scheme and the gPAV-based scheme without the treatment on the convection term, the current scheme can provide an expanded accuracy range and achieve more accurate simulations at large (or fairly large) time step sizes. Extensive numerical experiments have been presented to demonstrate the accuracy and stability performance of the scheme developed herein.

This study shows the unconditional discrete energy stability property of the current scheme, irrespective of the time step sizes.

This paper aims to propose a new linear parameter varying (LPV) controller for the robot tracking control problem. Using the identification of the robot dynamics in different work space points about modeling trajectory based on the least square of error algorithm, an LPV model for the robotic arm is extracted.

Parameter set mapping based on parameter component analysis results in a reduced polytopic LPV model that reduces the complexity of the implementation. An approximation of the required torque is computed based on the reduced LPV models. The state-feedback gain of each zone is computed by solving some linear matrix inequalities (LMIs) to sufficiently decrease the time derivative of a Lyapunov function. A novel smoothing method is used for the proposed controller to switch properly in the borders of the zones.

The polytopic set of the resulting gains creates the smooth switching polytopic LPV (SS-LPV) controller which is applied to the trajectory tracking problem of the six-degree-of-freedom PUMA 560 robotic arm. A sufficient condition ensures that the proposed controller stabilizes the polytopic LPV system against the torque estimation error.

Smoothing of the switching LPV controller is performed by defining some tolerances and creating some quasi-zones in the borders of the main zones leading to the compressed main zones. The proposed torque estimation is not a model-based technique; so the model variation and other disturbances cannot destroy the performance of the suggested controller. The proposed control scheme does not have any considerable computational load, because the control gains are obtained offline by solving some LMIs, and the torque computation is done online by a simple polytopic-based equation.

In this paper, a new SS-LPV controller is addressed for the trajectory tracking problem of robotic arms. Robot workspace is zoned into some main zones in such a way that the number of models in each zone is almost equal. Data obtained from the modeling trajectory is used to design the state-feedback control gain.

The purpose of this study is to propose a methodological approach for modeling catastrophic consequences caused by black swan events, based on complexity science, and framed on Feyerabend’s anarchistic theory of knowledge. An empirical application is presented to illustrate the proposed approach.

Thom’s nonlinear differential equations of morphogenesis are used to develop a theoretical model of the impact of catastrophes on international business (IB). The model is then estimated using real-world data on the performance of multinational airlines during the SARS-CoV-2 (COVID-19) pandemic.

The catastrophe model exhibits a remarkable capability to simultaneously capture complex linear and nonlinear relationships. Through empirical estimations and simulations, this approach enables the analysis of IB phenomena under normal conditions, as well as during black swan events.

To the best of the author’s knowledge, this study is the first attempt to estimate the impact of black swan events in IB using a catastrophe model grounded in complexity theory. The proposed model successfully integrates the abrupt and profound effects of catastrophes on multinational corporations, offering a critical perspective on the theoretical and practical use of complexity science in IB.

We study the informational content of factor structures in discrete triangular systems. Factor structures have been employed in a variety of settings in cross-sectional and panel data models, and in this chapter we formally quantify their identifying power in a bivariate system often employed in the treatment effects literature. Our main findings are that imposing a factor structure yields point-identification of parameters of interest, such as the coefficient associated with the endogenous regressor in the outcome equation, under weaker assumptions than usually required in these models. In particular, we show that a “non-standard” exclusion restriction that requires an explanatory variable in the outcome equation to be excluded from the treatment equation is no longer necessary for identification, even in cases where all of the regressors from the outcome equation are discrete. We also establish identification of the coefficient of the endogenous regressor in models with more general factor structures, in situations where one has access to at least two continuous measurements of the common factor.