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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.

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 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.

The global resolution of embracing dynamic and intertwined production systems has made it necessary to adopt viable systems like circular economy (CE) to ensure excellency in the business. However, in emerging countries, it is challenging to implement the CE practices due to the existing problems in the supply chain network, as well as due to the vulnerable financial condition of the business after the deadly hit of COVID-19. The main aim of this research is to determine the barriers to implementing CE considering the recent pandemic and suggest strategies to organizations to ensure CE for a cleaner environment and greener economy.

After an extensive literature review and validation from experts, 24 sub-barriers under the class of 6 main barriers are finalized by Pareto analysis, which is further analyzed via the best-worst method to determine the weight and rank of the barriers Further, fuzzy-Technique for Order of Preference by Similarity to Ideal Solution (TOPSIS) method is used to rank the proposed startegies to overcome the analysed barriers.

The results identified “unavailability of initial funding capital”, “need long time investment”, “lack of integrating production system using advance technology” and “lack of strategic planning” as the most acute sub-barriers to CE implementation. Further, fuzzy TOPSIS method is used to suggest the best strategy to mitigate the ranked barriers. The results indicated “integrated design facility to CE”, “ensuring large scale funding for CE facility” as the best strategy.

This study will motivate managers to implement CE practices to enjoy proper utilization of the resources, sustainable benefits in business, and gain competitive advantage.

Periodically, a lot of work is done on CE practices but none of them highlighted the issues in the domain of the leather products industry (LPI) and COVID-19 toward achieving sustainability in production and consumption. Thus, some significant barriers and strategies to implement CE for achieving sustainability in LPI are highlighted in this study, which is a unique contribution to the literature.

As data centres grow in size and complexity, traditional air-cooling methods are becoming less effective and more expensive. Immersion cooling, where servers are submerged in a dielectric fluid, has emerged as a promising alternative. Ensuring reliable operations in data centre applications requires the development of an effective control framework for immersion cooling systems, which necessitates the prediction of server temperature. While deep learning-based temperature prediction models have shown effectiveness, further enhancement is needed to improve their prediction accuracy. This study aims to develop a temperature prediction model using Long Short-Term Memory (LSTM) Networks based on recursive encoder-decoder architecture.

This paper explores the use of deep learning algorithms to predict the temperature of a heater in a two-phase immersion-cooled system using NOVEC 7100. The performance of recursive-long short-term memory-encoder-decoder (R-LSTM-ED), recursive-convolutional neural network-LSTM (R-CNN-LSTM) and R-LSTM approaches are compared using mean absolute error, root mean square error, mean absolute percentage error and coefficient of determination (R²) as performance metrics. The impact of window size, sampling period and noise within training data on the performance of the model is investigated.

The R-LSTM-ED consistently outperforms the R-LSTM model by 6%, 15.8% and 12.5%, and R-CNN-LSTM model by 4%, 11% and 12.3% in all forecast ranges of 10, 30 and 60 s, respectively, averaged across all the workloads considered in the study. The optimum sampling period based on the study is found to be 2 s and the window size to be 60 s. The performance of the model deteriorates significantly as the noise level reaches 10%.

The proposed models are currently trained on data collected from an experimental setup simulating data centre loads. Future research should seek to extend the applicability of the models by incorporating time series data from immersion-cooled servers.

The proposed multivariate-recursive-prediction models are trained and tested by using real Data Centre workload traces applied to the immersion-cooled system developed in the laboratory.

This study aims to discuss the numerical solutions of weakly singular Volterra and Fredholm integral equations, which are used to model the problems like heat conduction in engineering and the electrostatic potential theory, using the modified Lagrange polynomial interpolation technique combined with the biconjugate gradient stabilized method (BiCGSTAB). The framework for the existence of the unique solutions of the integral equations is provided in the context of the Banach contraction principle and Bielecki norm.

The authors have applied the modified Lagrange polynomial method to approximate the numerical solutions of the second kind of weakly singular Volterra and Fredholm integral equations.

Approaching the interpolation of the unknown function using the aforementioned method generates an algebraic system of equations that is solved by an appropriate classical technique. Furthermore, some theorems concerning the convergence of the method and error estimation are proved. Some numerical examples are provided which attest to the application, effectiveness and reliability of the method. Compared to the Fredholm integral equations of weakly singular type, the current technique works better for the Volterra integral equations of weakly singular type. Furthermore, illustrative examples and comparisons are provided to show the approach’s validity and practicality, which demonstrates that the present method works well in contrast to the referenced method. The computations were performed by MATLAB software.

The convergence of these methods is dependent on the smoothness of the solution, it is challenging to find the solution and approximate it computationally in various applications modelled by integral equations of non-smooth kernels. Traditional analytical techniques, such as projection methods, do not work well in these cases since the produced linear system is unconditioned and hard to address. Also, proving the convergence and estimating error might be difficult. They are frequently also expensive to implement.

There is a great need for fast, user-friendly numerical techniques for these types of equations. In addition, polynomials are the most frequently used mathematical tools because of their ease of expression, quick computation on modern computers and simple to define. As a result, they made substantial contributions for many years to the theories and analysis like approximation and numerical, respectively.

This work presents a useful method for handling weakly singular integral equations without involving any process of change of variables to eliminate the singularity of the solution.

To the best of the authors’ knowledge, the authors claim the originality and effectiveness of their work, highlighting its successful application in addressing weakly singular Volterra and Fredholm integral equations for the first time. Importantly, the approach acknowledges and preserves the possible singularity of the solution, a novel aspect yet to be explored by researchers in the field.

In this paper, the authors study the nonlinear matrix equation Xp=Q±A(X-1+B)-1AT, that occurs in many applications such as in filtering, network systems, optimal control and control theory.

The authors present some theoretical results for the existence of the solution of this nonlinear matrix equation. Then the authors propose two iterative schemes without inversion to find the solution to the nonlinear matrix equation based on Newton's method and fixed-point iteration. Also the authors show that the proposed iterative schemes converge to the solution of the nonlinear matrix equation, under situations.

The efficiency indices of the proposed schemes are presented, and since the initial guesses of the proposed iterative schemes have a high cost, the authors reduce their cost by changing them. Therefore, compared to the previous scheme, the proposed schemes have superior efficiency indices.

Finally, the accuracy and effectiveness of the proposed schemes in comparison to an existing scheme are demonstrated by various numerical examples. Moreover, as an application, by using the proposed schemes, the authors can get the optimal controller state feedback of $x(t+1) = A x(t) + C v(t)$.