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The purpose of this paper is to propose a compact model to represent the magnetic field outside the sources. This model provides the multipolar ordering of a spherical harmonic expansion far from the source while being valid in its close proximity.

The authors investigate equivalent surface sources that enable to compute the field very close to any chosen surface that encloses the source. Then the authors present a method to find an appropriate initial basis and its associated inner product that allow to construct multipolar harmonic bases for these equivalent sources, where any vector of order k produces a field that decreases at least as fast as the field produced by a multipole of order k. Finally, those bases are numerically implemented to demonstrate their performances, both far from the source and in its close proximity.

The charge distribution and normal dipole distribution are well-suited to construct multipolar harmonic bases of equivalent sources. These bases can be described by as few parameters as the decreasing spherical harmonic expansion. Comparison with other numerical models shows its ability to compute the field both far from the source and close to it.

A basis for normal dipole distribution has already been described in the literature. This paper presents a general method to construct a multipolar basis for equivalent sources and uses it to construct a basis for single-layer potential.

Traditional grey models are integer order whitening differential models; these models are relatively effective for the prediction of regular raw data, but the prediction error of irregular series or shock series is large, and the prediction effect is not ideal.

The new model realizes the dynamic expansion and optimization of the grey Bernoulli model. Meanwhile, it also enhances the variability and self-adaptability of the model structure. And nonlinear parameters are computed by the particle swarm optimization (PSO) algorithm.

Establishing a prediction model based on the raw data from the last six years, it is verified that the prediction performance of the new model is far superior to other mainstream grey prediction models, especially for irregular sequences and oscillating sequences. Ultimately, forecasting models are constructed to calculate various energy consumption aspects in Chongqing. The findings of this study offer a valuable reference for the government in shaping energy consumption policies and optimizing the energy structure.

It is imperative to recognize its inherent limitations. Firstly, the fractional differential order of the model is restricted to 0 < a < 2, encompassing only a three-parameter model. Future investigations could delve into the development of a multi-parameter model applicable when a = 2. Secondly, this paper exclusively focuses on the model itself, neglecting the consideration of raw data preprocessing, such as smoothing operators, buffer operators and background values. Incorporating these factors could significantly enhance the model’s effectiveness, particularly in the context of medium-term or long-term predictions.

This contribution plays a constructive role in expanding the model repertoire of the grey prediction model. The utilization of the developed model for predicting total energy consumption, coal consumption, natural gas consumption, oil consumption and other energy sources from 2021 to 2022 validates the efficacy and feasibility of the innovative model.

These findings, in turn, provide valuable guidance and decision-making support for both the Chinese Government and the Chongqing Government in optimizing energy structure and formulating effective energy policies.

This research holds significant importance in enriching the theoretical framework of the grey prediction model.

The highlights of the paper are as follows:

1. A novel grey Bernoulli prediction model is proposed to improve the model’s structure.

2. Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model.

3. The proposed model can achieve full compatibility with the traditional mainstream grey prediction models.

4. Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models.

5. The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

A novel grey Bernoulli prediction model is proposed to improve the model’s structure.

Fractional derivative, fractional accumulating generation operator and Bernoulli equation are added to the new model.

The proposed model can achieve full compatibility with the traditional mainstream grey prediction models.

Energy consumption in Chongqing verifies that the performance of the new model is much better than that of the traditional grey models.

The research provides a reference basis for the government to formulate energy consumption policies and optimize energy structure.

The main objective of the present investigation is to develop a novel efficient stochastic model for availability optimization of reverse osmosis machine system (ROMS) for water purification under the concepts of exponentially distributed decision variables and various redundancy strategies at the component level.

ROMS is a complex framework configured in a series structure using six subsystems. Initially, a state transition diagram is developed and Chapman–Kolmogorov differential-difference equations are derived using Markov birth death process. The steady-state availability of the ROMS is derived for a particular case. The impact of variation in failure and repair rates measured on availability. Furthermore, an effort is made to predict the optimal availability of the ROMS system using the metaheuristic algorithms, namely, dragonfly algorithm (DA), grasshopper optimization algorithm (GOA) and whale optimization algorithm (WOA).

It is observed that the ROMS system predicts optimal availability of 0.999926 after five iterations with a population size of 300 by the WOA. The findings of this study are significant for reliability engineers as well as for maintenance engineers to ensure the availability of ROMS for water purification.

In the present investigation, a novel stochastic model is developed for ROMS, and metaheuristics algorithms are applied to predict the optimal availability.

This study aims to design a facility network for the weavers to do direct business in the Indian handloom industry by using tourists as potential customers.

Data from 4,001 weavers of the handloom industry and 82 tourist locations of Varanasi city were collected. This data was analysed using the k-mean and elbow methods to determine the locations and the optimal number of collection centres, selling stores and warehouses to provide opportunities for the weavers to do direct business.

The study's findings showed that a greater opportunity could be provided with four optimal collection centres and selling stores, along with two warehouses in the handloom industry of Varanasi city. These results provide valuable guidance for policymakers to plan the Varanasi handloom network of facilities efficiently and effectively to improve the conditions of weavers.

Determining the optimal locations is crucial for designing a facility network. The proposed network will aid the government and policymakers in comprehending and pinpointing potential sites to establish new facilities in the handloom industry in Varanasi, a city with tourism potential.

Ultracapacitors find extensive applications in various fields because of their high energy density and long cycling periods. However, due to the movement of ions and the arrangement patterns on rough/irregular electrode surfaces during the charge and discharge process of ultracapacitors, the parameters of ultracapacitors usually change with the variation of operating conditions. The purpose of this study is to accurately and quickly identify the parameters of ultracapacitors.

A variable forgetting factor recursive least square (VFFRLS) algorithm is proposed in this paper for online identifying the equivalent series resistance and capacitance C of ultracapacitors. In this work, a real-time error-based strategy is developed to adaptively regulate the value of the forgetting factor of traditional forgetting factor recursive least square (FFRLS) algorithm. The strategy uses the square of the average time autocorrelation estimation of the prior error and the posterior error between the predicted output and the actual output as the adjustment basis of forgetting factors.

Experiments were conducted using the proposed scheme, and the results were compared with the estimation results obtained by the recursive least squares (RLS) algorithm and the traditional FFRLS algorithm. The maximum root mean square error between the estimated values and actual values for VFFRLS is 3.63%, whereas for FFRLS it is 9.61%, and for RLS it is 19.33%.

By using the proposed VFFRLS algorithm, a relatively high precision can be achieved for the online parameter estimation of ultracapacitors. Besides, the dynamic balance between parameter stability and tracking performance can be validated by dynamically adjusting the forgetting factor.

The main focus is to provide a non-similar solution for the magnetohydrodynamic (MHD) flow of Casson fluid over a curved stretching surface through the novel technique of the artificial intelligence (AI)-based Lavenberg–Marquardt scheme of an artificial neural network (ANN). The effects of joule heating, viscous dissipation and non-linear thermal radiation are discussed in relation to the thermal behavior of Casson fluid.

The non-linear coupled boundary layer equations are transformed into a non-linear dimensionless Partial Differential Equation (PDE) by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ordinary differential equations (ODEs). The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

The results indicate that the non-linear radiation parameter increases the fluid temperature. The Casson parameter reduces the fluid velocity as well as the temperature. The mean squared error (MSE), regression plot, error histogram, error analysis of skin friction, and local Nusselt number are presented. Furthermore, the regression values of skin friction and local Nusselt number are obtained as 0.99993 and 0.99997, respectively. The ANN predicted values of skin friction and the local Nusselt number show stability and convergence with high accuracy.

AI-based ANNs have not been applied to non-similar solutions of curved stretching surfaces with Casson fluid model, with viscous dissipation. Moreover, the authors of this study employed Levenberg–Marquardt supervised learning to investigate the non-similar solution of the MHD Casson fluid model over a curved stretching surface with non-linear thermal radiation and joule heating. The governing boundary layer equations are transformed into a non-linear, dimensionless PDE by using a non-similar transformation. The local non-similar technique is utilized to truncate the non-similar dimensionless system up to 2nd order, which is treated as coupled ODEs. The coupled system of ODEs is solved numerically via bvp4c. The data sets are constructed numerically and then implemented by the ANN.

Considering two types of subsidies for producers (supplier and manufacturer) and one for consumers based on product greenness and sales quantity, this study aims to formulate optimal supply chain green innovation and subsidy strategies, and to achieve this goal with the support of information systems.

This study introduces a composite green-product supply chain where suppliers focus on green innovation for component greenness and manufacturers focus on green innovation for manufacturing process greenness. Game theory modeling is applied to investigate the differences of product greenness, supply chain members’ profit and social welfare under different government subsidy strategies.

Increasing the unit greenness subsidy coefficient can boost product greenness and supply chain members’ profits, but does not always raise social welfare. When the government exclusively offers subsidies to producers, subsidies should be allocated to suppliers when there is a significant disparity in supply chain green innovation costs. Conversely, it is more beneficial to subsidize manufacturers. Consumer subsidies have the potential to enhance both environmental and economic performance in the supply chain compared with producer-exclusive subsidies, but may not always maximize social welfare when supply chain members have low unit costs associated with green innovation.

This study examines the optimal decisions for green supply chain innovation and government subsidy strategies. Supply chain members and the government can use the information system to collect and evaluate the cost of upstream and downstream green innovation, and then develop reasonable collaborative green innovation and subsidy strategies.

This paper aims to explore new variable separation solutions for a new generalized (3 + 1)-dimensional breaking soliton equation, construct novel nonlinear excitations and discuss their dynamical behaviors that may exist in many realms such as fluid dynamics, optics and telecommunication.

By means of the multilinear variable separation approach, variable separation solutions for the new generalized (3 + 1)-dimensional breaking soliton equation are derived with arbitrary low dimensional functions with respect to {y, z, t}. The asymptotic analysis is presented to represent generally the evolutions of rogue waves.

Fixing several types of explicit expressions of the arbitrary function in the potential field U, various novel nonlinear wave excitations are fabricated, such as hybrid waves of kinks and line solitons with different structures and other interesting characteristics, as well as interacting waves between rogue waves, kinks, line solitons with translation and rotation.

The paper presents that a variable separation solution with an arbitrary function of three independent variables has great potential to describe localized waves.

The roles of parameters in the chosen functions are ascertained in this study, according to which, one can understand the amplitude, shape, background and other characteristics of the localized waves.

The work provides novel localized waves that might be used to explain some nonlinear phenomena in fluids, plasma, optics and so on.

The study proposes a new generalized (3 + 1)-dimensional breaking soliton equation and derives its nonlinear variable separation solutions. It is demonstrated that a variable separation solution with an arbitrary function of three independent variables provides a treasure-house of nonlinear waves.

Indoor hallways are the most common and indispensable part of people’s daily life, commercial and industrial activities. This paper aims to achieve high-precision and dense 3D reconstruction of the narrow and long indoor hallway and proposes a 3D, dense 3D reconstruction, indoor hallway, rotating LiDAR reconstruction system based on rotating LiDAR.

This paper develops an orthogonal biaxial rotating LiDAR sensing device for low texture and narrow structures in hallways, which can capture panoramic point clouds containing rich features. A discrete interval scanning method is proposed considering the characteristics of the indoor hallway environment and rotating LiDAR. Considering the error model of LiDAR, this paper proposes a confidence-based point cloud fusion method to improve reconstruction accuracy.

In two different indoor hallway environments, the 3D reconstruction system proposed in this paper can obtain high-precision and dense reconstruction models. Meanwhile, the confidence-based point cloud fusion algorithm has been proven to improve the accuracy of 3D reconstruction.

A 3D reconstruction system was designed to obtain a high-precision and dense indoor hallway environment model. A discrete interval scanning method suitable for rotating LiDAR and hallway environments was proposed. A confidence-based point cloud fusion algorithm was designed to improve the accuracy of LiDAR 3D reconstruction. The entire system showed satisfactory performance in experiments.

The combination of improved PSO (IPSO) algorithm and artificial neural network (ANN) model for intelligent monitoring of the bearing performance of the hydrostatic turntable.

This paper proposes an artificial neural network model based on IPSO algorithm for intelligent monitoring of hydrostatic turntables.

The theoretical model proposed in this paper improves the accuracy of the working performance of the static pressure turntable and provides a new direction for intelligent monitoring of the static pressure turntable. Therefore, the theoretical research in this paper is novel.

Theoretical novelties: an ANN model based on the IPSO algorithm is designed to monitor the load-bearing performance of a static pressure turntable intelligently; this study show that the convergence accuracy and convergence speed of the IPSO-NN model have been improved by 52.55% and 10%, respectively, compared to traditional training models; and the proposed model could be used to solve the multidimensional nonlinear problem in the intelligent monitoring of hydrostatic turntables.

The peer review history for this article is available at: https://publons.com/publon/10.1108/ILT-03-2024-0081/