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This paper aims to discuss a new form of the Adomian decomposition technique for the numerical treatment of Bratu’s type one-dimensional boundary value problems (BVPs). Moreover, the author also addresses convergence and error analysis for the completeness of the proposed technique.

First, the author discusses the standard Adomian decomposition method and an algorithm based on Duan’s corollary and Rach’s rule for the fast calculation of the Adomian polynomials. Then, a new form of the Adomian decomposition technique is present for the numerical simulation of Bratu’s BVPs.

The reliability and validity of the proposed technique are examined by calculating the absolute errors of Bratu’s problem for some different values of Bratu parameter λ. Numerical simulation demonstrates that the proposed technique yields higher accuracy than the Bessel collocation and other known methods.

Unlike the other methods, the proposed technique does not need linearization, discretization or perturbation to handle the non-linear problems. So, the results obtained by the present technique are more physically realistic.

Special education is the education segment that deals with the students facing hurdles in the traditional education system. Research data have evolved in the domain of special education due to scientific advances. The present study aims to employ text mining to extract the latent patterns from the scientific data.

This study examined the 12,781 Scopus-indexed titles, abstracts and keywords published from 1987 to 2021 through an integrated text-mining and topic modeling approach. It combines dynamic topic models with highly cited reviews of this domain. It facilitates the extraction of topic clusters and communities in the topic network.

This methodology discovered children’s communication and speech using gaming techniques, mental retardation, cost effect on infant birth, involvement of special education children and their families, assistive technology information for special education, syndrome epilepsy and the impact of group study on skill development peers or self as the hottest topic of research in this domain. In addition to finding research hotspots, it further explores annual topic proportion trends, topic correlations and intertopic research areas.

The results provide a comprehensive summary of the popularity of research topics in special education in the past 34 years, and the results can provide useful insights and implications, and it could be used as a guide for contributors in special education form a structured view of past research and plan future research directions.

The purpose of this paper is to study the new (3 + 1)-dimensional integrable fourth-order nonlinear equation which is used to model the shallow water waves.

By means of the Cole–Hopf transform, the bilinear form of the studied equation is extracted. Then the ansatz function method combined with the symbolic computation is implemented to construct the breather, multiwave and the interaction wave solutions. In addition, the subequation method tis also used to search for the diverse travelling wave solutions.

The breather, multiwave and the interaction wave solutions and other wave solutions like the singular periodic wave structure and dark wave structure are obtained. To the author’s knowledge, the solutions obtained are all new and have never been reported before.

The solutions obtained in this work have never appeared in other literature and can be regarded as an extension of the solutions for the new (3 + 1)-dimensional integrable fourth-order nonlinear equation.

This study aims to assess the use of variational quantum imaginary time evolution for solving partial differential equations using real-amplitude ansätze with full circular entangling layers. A graphical mapping technique for encoding impulse functions is also proposed.

The Smoluchowski equation, including the Derjaguin–Landau–Verwey–Overbeek potential energy, is solved to simulate colloidal deposition on a planar wall. The performance of different types of entangling layers and over-parameterization is evaluated.

Colloidal transport can be modelled adequately with variational quantum simulations. Full circular entangling layers with real-amplitude ansätze lead to higher-fidelity solutions. In most cases, the proposed graphical mapping technique requires only a single bit-flip with a parametric gate. Over-parameterization is necessary to satisfy certain physical boundary conditions, and higher-order time-stepping reduces norm errors.

Variational quantum simulation can solve partial differential equations using near-term quantum devices. The proposed graphical mapping technique could potentially aid quantum simulations for certain applications.

This study shows a concrete application of variational quantum simulation methods in solving practically relevant partial differential equations. It also provides insight into the performance of different types of entangling layers and over-parameterization. The proposed graphical mapping technique could be valuable for quantum simulation implementations. The findings contribute to the growing body of research on using variational quantum simulations for solving partial differential equations.

The purpose of this paper is to find approximate solutions for a general class of fractional order boundary value problems that arise in engineering applications.

A newly developed semi-analytical scheme will be applied to find approximate solutions for fractional order boundary value problems. The technique is regarded as an extension of the well-established variation iteration method, which was originally proposed for initial value problems, to cover a class of boundary value problems.

It has been demonstrated that the method yields approximations that are extremely accurate and have uniform distributions of error throughout their domain. The numerical examples confirm the method’s validity and relatively fast convergence.

The generalized variational iteration method that is presented in this study is a novel strategy that can handle fractional boundary value problem more effectively than the classical variational iteration method, which was designed for initial value problems.

This paper aims to introduce a new fault protection scheme for microgrid DC networks with ring buses.

It is well recognized that the protection scheme in a DC ring bus microgrid becomes very complicated due to the bidirectional power flow. To provide reliable protection, the differential current signal is decomposed into several basic modes using adaptive variational mode decomposition (VMD). In this method, the mode number and the penalty factor are chosen optimally by using arithmetic optimization algorithm, yielding satisfactory decomposition results than the conventional VMD. Weighted Kurtosis index is used as the measurement index to select the sensitive mode, which is used to evaluate the discrete Teager energy (DTE) that indicates the occurrence of DC faults. For localizing cable faults, the current signals from the two ends are used on a sample-to-sample basis to formulate the state space matrix, which is solved by using generalized least squares approach. The proposed protection method is validated in MATLAB/SIMULINK by considering various test cases.

DTE is used to detect pole-pole and pole-ground fault and other disturbances such as high-impedance faults and series arc faults with a reduced detection time (10 ms) compared to some existing techniques.

Verification of this method is performed considering various test cases in MATLAB/SIMULINK platform yielding fast detection timings and accurate fault location.

Helicopter fuselage vibration prediction is important to keep a safety and comfortable flight process. The helicopter vibration mechanism model is difficult to meet of demand for accurate vibration prediction. Thus, the purpose of this paper is to develop an intelligent algorithm for accurate helicopter fuselage vibration analysis.

In this research, a novel weighted variational mode decomposition (VMD)- extreme gradient boosting (xgboost) helicopter fuselage vibration prediction model is proposed. The vibration data is decomposed and reconstructed by the signal clustering results. The vibration response is predicted by xgboost algorithm based on the reconstructed data. The information transfer order between the controllable flight data and flight attitude are analyzed.

The mean absolute percentage error (MAPE), root mean square error (RMSE) and mean absolute error (MAE) of the proposed weighted VMD-xgboost model are decreased by 6.8%, 31.5% and 32.8% compared with xgboost model. The established weighted VMD-xgboost model has the highest prediction accuracy with the lowest mean MAPE, RMSE and MAE of 4.54%, 0.0162, and 0.0131, respectively. The attitude of horizontal tail and cycle pitch are the key factors to vibration.

A novel weighted VMD-xgboost intelligent prediction methods is proposed. The prediction effect of xgboost model is highly improved by using the signal-weighted reconstruction technique. In addition, the data set used is collected from actual helicopter flight process.

The primary objective of this study is to tackle the enduring challenge of preserving feature integrity during the manipulation of geometric data in computer graphics. Our work aims to introduce and validate a variational sparse diffusion model that enhances the capability to maintain the definition of sharp features within meshes throughout complex processing tasks such as segmentation and repair.

We developed a variational sparse diffusion model that integrates a high-order L₁ regularization framework with Dirichlet boundary constraints, specifically designed to preserve edge definition. This model employs an innovative vertex updating strategy that optimizes the quality of mesh repairs. We leverage the augmented Lagrangian method to address the computational challenges inherent in this approach, enabling effective management of the trade-off between diffusion strength and feature preservation. Our methodology involves a detailed analysis of segmentation and repair processes, focusing on maintaining the acuity of features on triangulated surfaces.

Our findings indicate that the proposed variational sparse diffusion model significantly outperforms traditional smooth diffusion methods in preserving sharp features during mesh processing. The model ensures the delineation of clear boundaries in mesh segmentation and achieves high-fidelity restoration of deteriorated meshes in repair tasks. The innovative vertex updating strategy within the model contributes to enhanced mesh quality post-repair. Empirical evaluations demonstrate that our approach maintains the integrity of original, sharp features more effectively, especially in complex geometries with intricate detail.

The originality of this research lies in the novel application of a high-order L₁ regularization framework to the field of mesh processing, a method not conventionally applied in this context. The value of our work is in providing a robust solution to the problem of feature degradation during the mesh manipulation process. Our model’s unique vertex updating strategy and the use of the augmented Lagrangian method for optimization are distinctive contributions that enhance the state-of-the-art in geometry processing. The empirical success of our model in preserving features during mesh segmentation and repair presents an advancement in computer graphics, offering practical benefits to both academic research and industry applications.

In the field of heritage science, especially applied to buildings and artefacts made by organic hygroscopic materials, analyzing the microclimate has always been of extreme importance. In particular, in many cases, the knowledge of the outdoor/indoor microclimate may support the decision process in conservation and preservation matters of historic buildings. This knowledge is often gained by implementing long and time-consuming monitoring campaigns that allow collecting atmospheric and climatic data.

Sometimes the collected time series may be corrupted, incomplete and/or subjected to the sensors' errors because of the remoteness of the historic building location, the natural aging of the sensor or the lack of a continuous check of the data downloading process. For this reason, in this work, an innovative approach about reconstructing the indoor microclimate into heritage buildings, just knowing the outdoor one, is proposed. This methodology is based on using machine learning tools known as variational auto encoders (VAEs), that are able to reconstruct time series and/or to fill data gaps.

The proposed approach is implemented using data collected in Ringebu Stave Church, a Norwegian medieval wooden heritage building. Reconstructing a realistic time series, for the vast majority of the year period, of the natural internal climate of the Church has been successfully implemented.

The novelty of this work is discussed in the framework of the existing literature. The work explores the potentials of machine learning tools compared to traditional ones, providing a method that is able to reliably fill missing data in time series.

The electromechanical brake system is leading the latest development trend in railway braking technology. The tolerance stack-up generated during the assembly and production process catalyzes the slight geometric dimensioning and tolerancing between the motor stator and rotor inside the electromechanical cylinder. The tolerance leads to imprecise brake control, so it is necessary to diagnose the fault of the motor in the fully assembled electromechanical brake system. This paper aims to present improved variational mode decomposition (VMD) algorithm, which endeavors to elucidate and push the boundaries of mechanical synchronicity problems within the realm of the electromechanical brake system.

The VMD algorithm plays a pivotal role in the preliminary phase, employing mode decomposition techniques to decompose the motor speed signals. Afterward, the error energy algorithm precision is utilized to extract abnormal features, leveraging the practical intrinsic mode functions, eliminating extraneous noise and enhancing the signal’s fidelity. This refined signal then becomes the basis for fault analysis. In the analytical step, the cepstrum is employed to calculate the formant and envelope of the reconstructed signal. By scrutinizing the formant and envelope, the fault point within the electromechanical brake system is precisely identified, contributing to a sophisticated and accurate fault diagnosis.

This paper innovatively uses the VMD algorithm for the modal decomposition of electromechanical brake (EMB) motor speed signals and combines it with the error energy algorithm to achieve abnormal feature extraction. The signal is reconstructed according to the effective intrinsic mode functions (IMFS) component of removing noise, and the formant and envelope are calculated by cepstrum to locate the fault point. Experiments show that the empirical mode decomposition (EMD) algorithm can effectively decompose the original speed signal. After feature extraction, signal enhancement and fault identification, the motor mechanical fault point can be accurately located. This fault diagnosis method is an effective fault diagnosis algorithm suitable for EMB systems.

By using this improved VMD algorithm, the electromechanical brake system can precisely identify the rotational anomaly of the motor. This method can offer an online diagnosis analysis function during operation and contribute to an automated factory inspection strategy while parts are assembled. Compared with the conventional motor diagnosis method, this improved VMD algorithm can eliminate the need for additional acceleration sensors and save hardware costs. Moreover, the accumulation of online detection functions helps improve the reliability of train electromechanical braking systems.