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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.

This paper aims to overcome the lack of methodologies for optimizing the volume of bulky low-frequency inductors that the authors came across with when working on the design of hybrid active power filters. Sound work was published concerning this well-known technology, but it became evident that the mentioned optimization topic was left unaddressed.

Using the Lagrange multipliers optimization method combined with the electromagnetic laws of inductor design, it was possible to establish a new design method to determine the optimal solutions that fulfil any given scenario of specifications. In other words, it is now possible to obtain the inductor’s geometric and electric parameters that not only satisfy the system’s electromagnetic requirements but also lead to smaller, lighter or economical solutions.

A generalized set of equations was obtained to facilitate the calculations of all the inductor-building parameters. As expected, these equations take as inputs the inductor’s required inductance, its maximum current and the desired resistance, but also a customizable cost function. The later cost function will optimize the inductor’s volumes of copper and iron and can be settled, among other purposes, for minimizing the total weight, volume or cost.

All the mathematical expressions to obtain the general optimal solutions are given as well as practical graphics for the three above-mentioned optimization criteria. Using these charts, the reader will be able to obtain by simple inspection the optimal solutions for a large, generalized universe of intended specifications.

Through the scientific and reasonable evaluation of the site selection of the emergency material reserve, the optimal site selection scheme is found, which provides reference for the future emergency decision-making research.

In this paper, we have chosen three primary indicators and twelve secondary indicators to construct an assessment framework for the determination of suitable locations for storing emergency material reserves. By mean of the improved entropy weight-order relationship weight determination method, the evaluation model of kullback leibler-technique for order preference by similarity to an ideal solution (KL-TOPSIS) emergency material reserve location based on relative entropy is established. On this basis, 10 regional storage sites in Beijing are selected for evaluation.

The results show that the evaluation model of the location of emergency material reserve not only respects the objective knowledge, but also considers the subjective information of the experts, which makes the ranking result of the location of the emergency material reserve more accurate and reliable.

Firstly, the modification factor is added to the calculation formula of traditional entropy weight method to complete the improvement of entropy weight method. Secondly, the order relation analysis method is used to assign subjective weights to the indicators. The principle of minimum information entropy is introduced to determine the comprehensive weight of the index. Finally, KL distance and TOPSIS method are combined to determine the relative entropy and proximity degree of alternative solutions and positive and negative ideal solutions, and the scientific and effective of the method is proved by case study.

It is of a great significance for the health monitoring of a liquid rocket engine to build an accurate and reliable fault prediction model. The thrust of a liquid rocket engine is an important indicator for its health monitoring. By predicting the changing value of the thrust, it can be judged whether the engine will fail at a certain time. However, the thrust is affected by various factors, and it is difficult to establish an accurate mathematical model. Thus, this study uses a mixture non-parametric regression prediction model to establish the model of the thrust for the health monitoring of a liquid rocket engine.

This study analyzes the characteristics of the least squares support vector regression (LS-SVR) machine . LS-SVR is suitable to model on the small samples and high dimensional data, but the performance of LS-SVR is greatly affected by its key parameters. Thus, this study implements the advanced intelligent algorithm, the real double-chain coding target gradient quantum genetic algorithm (DCQGA), to optimize these parameters, and the regression prediction model LSSVRDCQGA is proposed. Then the proposed model is used to model the thrust of a liquid rocket engine.

The simulation results show that: the average relative error (ARE) on the test samples is 0.37% when using LS-SVR, but it is 0.3186% when using LSSVRDCQGA on the same samples.

The proposed model of LSSVRDCQGA in this study is effective to the fault prediction on the small sample and multidimensional data, and has a certain promotion.

The original contribution of this study is to establish a mixture non-parametric regression prediction model of LSSVRDCQGA and properly resolve the problem of the health monitoring of a liquid rocket engine along with modeling the thrust of the engine by using LSSVRDCQGA.

This study aims to develop an optimal tolerance allocation strategy involves integrating the unique transfer (UT) approach and the difficulty coefficient evaluation (DCE) routine in an interactive hybrid method. This method combines the strengths of both UT and DCE, ensuring simultaneous utilization for enhanced performance. The proposed tolerancing model manifests an integrated computer-aided design (CAD) tool.

By combining UT and DCE based on failure mode, effects and criticality analysis (FMECA) tool and the Ishikawa diagram, the proposed collaborative hybrid tool ensures an efficient and optimal tolerance allocation approach. The integration of these methodologies not only addresses specific transfer challenges through UT but also conducts a thorough evaluation of difficulty coefficients via DCE routine using reliability analysis tools as FMECA tool and the Ishikawa diagram. This comprehensive framework contributes to a robust and informed decision-making process in tolerance allocation, ultimately optimizing the design and manufacturing processes.

The presented methodology is implemented with the aim of generating allocated tolerances that align with specific difficulty requirements, facilitating the creation of a mechanical assembly characterized by high quality and low cost. To substantiate and validate the conceptual framework and methods, an integrated tool has been developed, featuring a graphical user interface (GUI) designed in MATLAB. This interface serves as a platform to showcase various interactive and integrated tolerance allocation approaches that adhere to both functional and manufacturing prerequisites. The proposed integrated tool, designed with a GUI in MATLAB, offers the capability to execute various examples that effectively demonstrate the benefits of the developed tolerance transfer and allocation methodology.

The originality of the proposed approach is the twining between the UT and DCE simultaneous in an integrated and concurrent tolerance transfer and allocation model. Therefore, the proposed approach is named an integrated CAD/tolerance model based on the manufacturing difficulty tool. The obtained results underscore the tangible advantages stemming from the integration of this innovative tolerance transfer and allocation approach. These benefits include a notable reduction in total cost and a concurrent enhancement in product quality.

This study aims to construct a sentiment series generation method for danmu comments based on deep learning, and explore the features of sentiment series after clustering.

This study consisted of two main parts: danmu comment sentiment series generation and clustering. In the first part, the authors proposed a sentiment classification model based on BERT fine-tuning to quantify danmu comment sentiment polarity. To smooth the sentiment series, they used methods, such as comprehensive weights. In the second part, the shaped-based distance (SBD)-K-shape method was used to cluster the actual collected data.

The filtered sentiment series or curves of the microfilms on the Bilibili website could be divided into four major categories. There is an apparently stable time interval for the first three types of sentiment curves, while the fourth type of sentiment curve shows a clear trend of fluctuation in general. In addition, it was found that “disputed points” or “highlights” are likely to appear at the beginning and the climax of films, resulting in significant changes in the sentiment curves. The clustering results show a significant difference in user participation, with the second type prevailing over others.

Their sentiment classification model based on BERT fine-tuning outperformed the traditional sentiment lexicon method, which provides a reference for using deep learning as well as transfer learning for danmu comment sentiment analysis. The BERT fine-tuning–SBD-K-shape algorithm can weaken the effect of non-regular noise and temporal phase shift of danmu text.

Multi-view fuzzy clustering algorithms are not widely used in image segmentation, and many of these algorithms are lacking in robustness. The purpose of this paper is to investigate a new algorithm that can segment the image better and retain as much detailed information about the image as possible when segmenting noisy images.

The authors present a novel multi-view fuzzy c-means (FCM) clustering algorithm that includes an automatic view-weight learning mechanism. Firstly, this algorithm introduces a view-weight factor that can automatically adjust the weight of different views, thereby allowing each view to obtain the best possible weight. Secondly, the algorithm incorporates a weighted fuzzy factor, which serves to obtain local spatial information and local grayscale information to preserve image details as much as possible. Finally, in order to weaken the effects of noise and outliers in image segmentation, this algorithm employs the kernel distance measure instead of the Euclidean distance.

The authors added different kinds of noise to images and conducted a large number of experimental tests. The results show that the proposed algorithm performs better and is more accurate than previous multi-view fuzzy clustering algorithms in solving the problem of noisy image segmentation.

Most of the existing multi-view clustering algorithms are for multi-view datasets, and the multi-view fuzzy clustering algorithms are unable to eliminate noise points and outliers when dealing with noisy images. The algorithm proposed in this paper has stronger noise immunity and can better preserve the details of the original image.

This study aims to examine the effect of governance on the consumption of modern renewable energy in the East African Community (EAC), controlling for economic growth, trade openness and foreign direct investment (FDI).

The study relied on secondary data sourced from the World Development Indicators, World Governance Indicators and the International Energy Agency (IEA) for the EAC from 1996 to 2019. A panel Cross-Sectional Augmented Distributed Lag (CS-ARDL) model and second-generation panel data models were employed in the analysis.

The findings indicate that poor governance and inadequate FDI are significantly responsible for the low level of modern renewable energy consumption (MREC) in the EAC. On the other hand, trade openness significantly enhances MREC, while GDP per capita has no significant effect on MREC.

The consumption of modern renewable energy sources (excluding the traditional use of biomass) and its determinants, as most studies focus on renewable energy consumption as a whole. The study also employed the panel CS-ARDL model and second-generation panel data models.

The paper aims to the size-dependent analysis of functionally graded materials in thermal environment based on the modified couple stress theory using finite element method.

The element formulation is developed within the framework of the penalty unsymmetric finite element method (FEM) in that the C¹ continuity requirement is satisfied in weak sense and thus, C⁰ continuous interpolation enhanced by independent nodal rotation is employed as the test function. Meanwhile, the trial function is designed based on the stress functions and the weighted residual method. Besides, the special Gauss quadrature scheme is employed for integrals of matrices in accordance with the graded variation of the material properties.

The numerical results reveal that in thermal environment, functionally graded materials exhibit better bending performance compared to homogeneous materials, Moreover, the findings also indicate that with an increase in MLSP, the natural frequencies of out-of-plane modes gradually increase, while the natural frequencies of in-plane modes show much less variation, leading to a mode switch phenomenon.

The work provides an efficient numerical tool for analyzing and designing the functionally graded structures in thermal environment in practical engineering applications.

This study aims to test the dynamic impact of public debt and economic growth on newly democratized African countries (South Africa and Namibia) and compare the findings with those of newly democratized European countries (Germany and Ukraine) during the period 1990–2022.

The methodology involves three stages: identifying the appropriate transition variable, assessing the linearity between public debt and economic growth and selecting the order m of the transition function. The linearity test helps identify the nature of relationships between public debt and economic growth. The wild cluster bootstrap-Lagrange Multiplier test is used to evaluate the model’s appropriateness. All these tests would be executed using the Lagrange Multiplier type of test.

The results signify the policy switch, as the authors find that the relationship between public debt and economic growth is characterized by two transitions that symbolize that the current stage of the relationship is beyond the U-shape; however, an S-shape. The results show that for newly democratized African countries, the threshold during the first waves was 50% of GDP, represented by a U-shape, which then transits to an inverted U-shape with a threshold of 65% of GDP. Then, for the European case, it was 60% of GDP, which is now 72% of GDP.

The findings suggest that an escalating level of public debt has a negative impact on economic growth; therefore, it is important to implement fiscal discipline, prioritize government spending and reduce reliance on debt financing. This can be achieved by focusing on revenue generation, implementing effective taxation policies, reducing wasteful expenditures and promoting investment and productivity-enhancing measures.