Research

29 pages, 11800 KiB

Open AccessArticle

Variable Selection in Data Analysis: A Synthetic Data Toolkit

by Rohan Mitra, Eyad Ali, Dara Varam, Hana Sulieman and Firuz Kamalov

Mathematics 2024, 12(4), 570; https://doi.org/10.3390/math12040570 - 14 Feb 2024

Viewed by 621

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic [...] Read more.

Variable (feature) selection plays an important role in data analysis and mathematical modeling. This paper aims to address the significant lack of formal evaluation benchmarks for feature selection algorithms (FSAs). To evaluate FSAs effectively, controlled environments are required, and the use of synthetic datasets offers significant advantages. We introduce a set of ten synthetically generated datasets with known relevance, redundancy, and irrelevance of features, derived from various mathematical, logical, and geometric sources. Additionally, eight FSAs are evaluated on these datasets based on their relevance and novelty. The paper first introduces the datasets and then provides a comprehensive experimental analysis of the performance of the selected FSAs on these datasets including testing the FSAs’ resilience on two types of induced data noise. The analysis has guided the grouping of the generated datasets into four groups of data complexity. Lastly, we provide public access to the generated datasets to facilitate bench-marking of new feature selection algorithms in the field via our Github repository. The contributions of this paper aim to foster the development of novel feature selection algorithms and advance their study. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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21 pages, 10445 KiB

Open AccessArticle

Deep Learning Method Based on Physics-Informed Neural Network for 3D Anisotropic Steady-State Heat Conduction Problems

by Zebin Xing, Heng Cheng and Jing Cheng

Mathematics 2023, 11(19), 4049; https://doi.org/10.3390/math11194049 - 24 Sep 2023

Viewed by 1167

Abstract

This paper uses the physical information neural network (PINN) model to solve a 3D anisotropic steady-state heat conduction problem based on deep learning techniques. The model embeds the problem’s governing equations and boundary conditions into the neural network and treats the neural network’s [...] Read more.

This paper uses the physical information neural network (PINN) model to solve a 3D anisotropic steady-state heat conduction problem based on deep learning techniques. The model embeds the problem’s governing equations and boundary conditions into the neural network and treats the neural network’s output as the numerical solution of the partial differential equation. Then, the network is trained using the Adam optimizer on the training set. The output progressively converges toward the accurate solution of the equation. In the first numerical example, we demonstrate the convergence of the PINN by discussing the effect of the neural network’s number of layers, each hidden layer’s number of neurons, the initial learning rate and decay rate, the size of the training set, the mini-batch size, the amount of training points on the boundary, and the training steps on the relative error of the numerical solution, respectively. The numerical solutions are presented for three different examples. Thus, the effectiveness of the method is verified. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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15 pages, 4230 KiB

Open AccessArticle

Silver Price Forecasting Using Extreme Gradient Boosting (XGBoost) Method

by Dylan Norbert Gono, Herlina Napitupulu and Firdaniza

Mathematics 2023, 11(18), 3813; https://doi.org/10.3390/math11183813 - 05 Sep 2023

Viewed by 982

Abstract

This article presents a study on forecasting silver prices using the extreme gradient boosting (XGBoost) machine learning method with hyperparameter tuning. Silver, a valuable precious metal used in various industries and medicine, experiences significant price fluctuations. XGBoost, known for its computational efficiency and [...] Read more.

This article presents a study on forecasting silver prices using the extreme gradient boosting (XGBoost) machine learning method with hyperparameter tuning. Silver, a valuable precious metal used in various industries and medicine, experiences significant price fluctuations. XGBoost, known for its computational efficiency and parallel processing capabilities, proves suitable for predicting silver prices. The research focuses on identifying optimal hyperparameter combinations to improve model performance. The study forecasts silver prices for the next six days, evaluating models based on mean absolute percentage error (MAPE) and root mean square error (RMSE). Model A (the best model based on MAPE value) suggests silver prices decline on the first and second days, rise on the third, decline again on the fourth, and stabilize with an increase on the fifth and sixth days. Model A achieves a MAPE of 5.98% and an RMSE of 1.6998, utilizing specific hyperparameters. Conversely, model B (the best model based on RMSE value) indicates a price decrease until the third day, followed by an upward trend until the sixth day. Model B achieves a MAPE of 6.06% and an RMSE of 1.6967, employing distinct hyperparameters. The study also compared the proposed models with several other ensemble models (CatBoost and random forest). The model comparison was carried out by incorporating 2 additional metrics (MAE and SI), and it was found that the proposed models exhibited the best performance. These findings provide valuable insights for forecasting silver prices using XGBoost. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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21 pages, 1330 KiB

Open AccessArticle

Application of SVM and Chi-Square Feature Selection for Sentiment Analysis of Indonesia’s National Health Insurance Mobile Application

by Ewen Hokijuliandy, Herlina Napitupulu and Firdaniza

Mathematics 2023, 11(17), 3765; https://doi.org/10.3390/math11173765 - 01 Sep 2023

Viewed by 1328

Abstract

(1) Background: sentiment analysis is a computational technique employed to discern individuals opinions, attitudes, emotions, and intentions concerning a subject by analyzing reviews. Machine learning-based sentiment analysis methods, such as Support Vector Machine (SVM) classification, have proven effective in opinion classification. Feature selection [...] Read more.

(1) Background: sentiment analysis is a computational technique employed to discern individuals opinions, attitudes, emotions, and intentions concerning a subject by analyzing reviews. Machine learning-based sentiment analysis methods, such as Support Vector Machine (SVM) classification, have proven effective in opinion classification. Feature selection methods have been employed to enhance model performance and efficiency, with the Chi-Square method being a commonly used technique; (2) Methods: this study analyzes user reviews of Indonesia’s National Health Insurance (Mobile JKN) application, evaluating model performance and identifying optimal hyperparameters using the F1-Score metric. Sentiment analysis is conducted using a combined approach of SVM classification and Chi-Square feature selection; (3) Results: the sentiment analysis of user reviews for the Mobile JKN application reveals a predominant tendency towards positive reviews. The best model performance is achieved with an F1-Score of 96.82%, employing hyperparameters where

C

is set to 10 and a “linear” kernel; (4) Conclusions: this study highlights the effectiveness of SVM classification and the significance of Chi-Square feature selection in sentiment analysis. The findings offer valuable insights into users’ sentiments regarding the Mobile JKN application, contributing to the improvement of user experience and advancing the field of sentiment analysis. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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20 pages, 4021 KiB

Open AccessArticle

Analyzing Three-Dimensional Laplace Equations Using the Dimension Coupling Method

by Fengbin Liu, Mingmei Zuo, Heng Cheng and Ji Ma

Mathematics 2023, 11(17), 3717; https://doi.org/10.3390/math11173717 - 29 Aug 2023

Viewed by 699

Abstract

Due to the low computational efficiency of the Improved Element-Free Galerkin (IEFG) method, efficiently solving three-dimensional (3D) Laplace problems using meshless methods has been a longstanding research direction. In this study, we propose the Dimension Coupling Method (DCM) as a promising alternative approach [...] Read more.

Due to the low computational efficiency of the Improved Element-Free Galerkin (IEFG) method, efficiently solving three-dimensional (3D) Laplace problems using meshless methods has been a longstanding research direction. In this study, we propose the Dimension Coupling Method (DCM) as a promising alternative approach to address this challenge. Based on the Dimensional Splitting Method (DSM), the DCM divides the 3D problem domain into a coupling of multiple two-dimensional (2D) problems which are handled via the IEFG method. We use the Finite Element Method (FEM) in the third direction to combine the 2D discretized equations, which has advantages over the Finite Difference Method (FDM) used in traditional methods. Our numerical verification demonstrates the DCM’s convergence and enhancement of computational speed without losing computational accuracy compared to the IEFG method. Therefore, this proposed method significantly reduces computational time and costs when solving 3D Laplace equations with natural or mixed boundary conditions in a dimensional splitting direction, and expands the applicability of the dimension splitting EFG method. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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17 pages, 8958 KiB

Open AccessArticle

Stress Analysis of the Radius and Ulna in Tennis at Different Flexion Angles of the Elbow

by Yan Chen, Qiang Du, Xiyang Yin, Renjie Fu and Yiyun Zhu

Mathematics 2023, 11(16), 3524; https://doi.org/10.3390/math11163524 - 15 Aug 2023

Viewed by 974

Abstract

In this paper, based on the finite element method, the stresses of the radius and ulna are analyzed at different flexion angles of the elbow when playing tennis. The finite element model is presented for the elbow position with flexion angles of 0°, [...] Read more.

In this paper, based on the finite element method, the stresses of the radius and ulna are analyzed at different flexion angles of the elbow when playing tennis. The finite element model is presented for the elbow position with flexion angles of 0°, 25°, 60°, and 80° according to the normal human arm bone. In this model, the whole arm with metacarpals, radius, ulna, humerus and scapula is considered. The calculation is simplified by setting the scapula and metacarpals as rigid bodies and using Tie binding constraints between the humerus and the radius and ulna. This model is discretized using the 10-node second-order tetrahedral element (C3D10). This model contains 109,765 nodes and 68,075 elements. The hitting forces applied to the metacarpal bone are 100 N and 300 N, respectively. The numerical results show that the highest principal stresses are at the points of 1/4 of the radius, the elbow joint, and the points of 1/10 of the ulna. The results of the maximum principal stress show that the external pressures are more pronounced as the elbow flexion angle increases and that the magnitude of the hitting force does not affect the principal stress distribution pattern. Elbow injuries to the radius can be reduced by using a stroke with less elbow flexion, and it is advisable to wear a reinforced arm cuff on the dorsal 1/4 of the hand, a radial/dorsal hand wrist, and an elbow guard to prevent radial ulnar injuries. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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16 pages, 7923 KiB

Open AccessArticle

The Evolution of Probability Density Function for Power System Excited by Fractional Gaussian Noise

by Hufei Li and Shaojuan Ma

Mathematics 2023, 11(13), 2854; https://doi.org/10.3390/math11132854 - 26 Jun 2023

Viewed by 607

Abstract

This article is devoted to investigating the evolution of the probability density function for power system excited by fractional stochastic noise. First, the single-machine-infinite-bus (SMIB) power system model excited by fractional Gaussian noise (FGN) is established. Second, we derive the Fokker–Planck–Kolmogorov (FPK) equation [...] Read more.

This article is devoted to investigating the evolution of the probability density function for power system excited by fractional stochastic noise. First, the single-machine-infinite-bus (SMIB) power system model excited by fractional Gaussian noise (FGN) is established. Second, we derive the Fokker–Planck–Kolmogorov (FPK) equation for the proposed model and solve the FPK equation using the finite difference method. Finally, the numerical results verify that the addition of FGN would influence dynamical stability of the SMIB power system under certain conditions. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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21 pages, 70163 KiB

Open AccessArticle

A Numerical Study of Heat Performance of Multi-PCM Brick in a Heat Storage Building

by Nadezhda S. Bondareva and Mikhail A. Sheremet

Mathematics 2023, 11(13), 2825; https://doi.org/10.3390/math11132825 - 23 Jun 2023

Cited by 1 | Viewed by 811

Abstract

Modern technologies of thermal power engineering make it possible to design and build systems using renewable energy sources. Often, energy accumulation and storage require the development and adaptation of appropriate systems, the simplest of which are passive systems based on phase-change materials. In [...] Read more.

Modern technologies of thermal power engineering make it possible to design and build systems using renewable energy sources. Often, energy accumulation and storage require the development and adaptation of appropriate systems, the simplest of which are passive systems based on phase-change materials. In this study, a numerical analysis of heat transfer in a brick wall containing several materials with different melting temperatures is carried out. The unsteady two-dimensional conjugate problem of phase transitions is considered, taking into account natural convection in the melt, which has been solved using the developed in-house finite difference technique. A numerical experiment has been carried out for a brick block with several rectangular inserts filled with PCMs under various external thermal conditions. As a result of the numerical analysis, it has been shown that the relative arrangement of materials with different melting points has a significant impact on the heat transfer and heat exchange between the environment and the room. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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26 pages, 10699 KiB

Open AccessArticle

A Semantic Representation Method of Building Codes Applied to Compliance Checking

by Yuchao Li, Mingsong Yang, Qin Zhao, Zongjian Li, Zhaoxi Ma, Yunhe Liu and Xinhong Hei

Mathematics 2023, 11(11), 2552; https://doi.org/10.3390/math11112552 - 01 Jun 2023

Viewed by 1163

Abstract

Compliance checking is a very important step in engineering construction. With the development of information technology, automated compliance checking (ACC) has been paid more and more attention by researchers. One of the most important steps in automated compliance checking is the representation of [...] Read more.

Compliance checking is a very important step in engineering construction. With the development of information technology, automated compliance checking (ACC) has been paid more and more attention by researchers. One of the most important steps in automated compliance checking is the representation of the code information. However, the relationship constraint is often ignored in the code information and spatial geometric relationship is challenging to represent. The general code representation method does not have enough ability to identify the situation that does not meet the checking conditions because it is easy to cause semantic ambiguity in the checking results. This paper proposes a code representation method, and the building code information is represented in five parts. Relationships in the engineering domain and spatial relationships can be represented in constraint mode; different spatial relationship constraint-checking methods are also explicated. Constraint subject and constraint item can distinguish checking conditions and requirements, which supports semantic checking results. The mapping between the building information ontology and the code concepts is established, which can be used to automatically generate reasoning rules for compliance checking. Finally, the proposed method is verified by the representation of the China Metro Design Code and the application of the actual Metro model. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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29 pages, 8015 KiB

Open AccessArticle

Station Layout Optimization and Route Selection of Urban Rail Transit Planning: A Case Study of Shanghai Pudong International Airport

by Pei Yin and Miaojuan Peng

Mathematics 2023, 11(6), 1539; https://doi.org/10.3390/math11061539 - 22 Mar 2023

Cited by 2 | Viewed by 1409

Abstract

In this paper, a cost-oriented optimization model of station spacing is presented to analyze the influencing factors of station spacing and layout near Shanghai Pudong International Airport. The Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm is used to cluster and [...] Read more.

In this paper, a cost-oriented optimization model of station spacing is presented to analyze the influencing factors of station spacing and layout near Shanghai Pudong International Airport. The Hierarchical Density-Based Spatial Clustering of Applications with Noise (HDBSCAN) algorithm is used to cluster and analyze the high population density, and optimize the station layout in the southwest of Pudong International Airport. A spatial analysis of the land use and geological conditions in Pudong New Area is given. Combining the optimal station spacing, ideal location and spatial analysis, five routing schemes to Pudong International Airport are proposed. The DBSCAN and K-means algorithms are used to analyze the “PDIA-SL” dataset. The results show that the space complexity of the HDBSCAN is O(825), and the silhouette coefficient is 0.6043, which has obvious advantages over the results of DBSCAN and K-means. This paper combines urban rail transit planning with the HDBSCAN algorithm to present some suggestions and specific route plans for local governments to scientifically plan rail transit lines. Meanwhile, the research method of station layout, which integrates station spacing, ideal location and spatial analysis optimization, is pioneering and can provide a reference for developing rail transit in metropolises. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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18 pages, 12286 KiB

Open AccessArticle

Mining Significant Utility Discriminative Patterns in Quantitative Databases

by Huijun Tang, Jufeng Wang and Le Wang

Mathematics 2023, 11(4), 950; https://doi.org/10.3390/math11040950 - 13 Feb 2023

Viewed by 893

Abstract

Drawing a discriminative pattern in quantitative datasets is often represented to return a high utility pattern (HUP). The traditional methods output patterns with a utility above a pre-given threshold. Nevertheless, the current user-centered algorithm requires outputting the results in a timely manner to [...] Read more.

Drawing a discriminative pattern in quantitative datasets is often represented to return a high utility pattern (HUP). The traditional methods output patterns with a utility above a pre-given threshold. Nevertheless, the current user-centered algorithm requires outputting the results in a timely manner to strengthen the interaction between the mining system and users. Pattern sampling can return results with a probability guarantee in a short time, and it could be a candidate technology to mine such discriminative patterns. In this paper, a novel approach named HUPSampler is proposed to sample one potential HUP, which is extracted with probability significance according to its utility in the database. HUPSampler introduces an interval constraint on the length of HUP and randomly extracts an integer k according to the utility proportion firstly; then, the HUPs could be obtained efficiently from a random tree by using a pattern growth way, and finally, it returns a HUP of length k randomly. The experimental study shows that HUPSampler is efficient in regard to memory usage, runtime, and utility distribution. In addition, case studies show that HUPSampler can be significantly used in analyzing the COVID-19 epidemic by identifying critical locations. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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19 pages, 4101 KiB

Open AccessArticle

The Improved Element-Free Galerkin Method for 3D Steady Convection-Diffusion-Reaction Problems with Variable Coefficients

by Heng Cheng, Zebin Xing and Yan Liu

Mathematics 2023, 11(3), 770; https://doi.org/10.3390/math11030770 - 03 Feb 2023

Cited by 5 | Viewed by 1008

Abstract

In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape [...] Read more.

In order to obtain the numerical results of 3D convection-diffusion-reaction problems with variable coefficients efficiently, we select the improved element-free Galerkin (IEFG) method instead of the traditional element-free Galerkin (EFG) method by using the improved moving least-squares (MLS) approximation to obtain the shape function. For the governing equation of 3D convection-diffusion-reaction problems, we can derive the corresponding equivalent functional; then, the essential boundary conditions are imposed by applying the penalty method; thus, the equivalent integral weak form is obtained. By introducing the IMLS approximation, we can derive the final solved linear equations of the convection-diffusion-reaction problem. In numerical examples, the scale parameter and the penalty factor of the IEFG method for such problems are discussed, the convergence is proved numerically, and the calculation efficiency of the IEFG method are verified by four numerical examples. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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19 pages, 7706 KiB

Open AccessArticle

Multi-Lane Traffic Load Clustering Model for Long-Span Bridge Based on Parameter Correlation

by Yue Zhao, Xuelian Guo, Botong Su, Yamin Sun and Yiyun Zhu

Mathematics 2023, 11(2), 274; https://doi.org/10.3390/math11020274 - 05 Jan 2023

Cited by 3 | Viewed by 998

Abstract

Traffic loads are the primary external loads on bridges during their service life. However, an accurate analysis of the long-term effect of the operating traffic load is difficult because of the diversity of traffic flow in terms of vehicle type and intensity. This [...] Read more.

Traffic loads are the primary external loads on bridges during their service life. However, an accurate analysis of the long-term effect of the operating traffic load is difficult because of the diversity of traffic flow in terms of vehicle type and intensity. This study established a traffic load simulation method for long-span bridges based on high authenticity traffic monitoring data, and an improved k-means clustering algorithm and Correlated variables Sampling based on Sobol sequence and Copula function (CSSC) sampling method. The monitoring traffic data collected through a weigh-in-motion (WIM) system was processed to generate a multi-lane stochastic traffic flow. The dynamic response of a prototype suspension bridge under a traffic load was analyzed. The results show that the traffic load can be divided into clusters with identical distribution characteristics using a clustering algorithm. Combined with CSSC sampling, the generated traffic flow can effectively represent daily traffic and vehicle characteristics, which improves the accuracy of the assessment of the loads long-term effect. The dynamic response of the bridge to different traffic flows varied significantly. The maximum and minimum vertical displacement of the main girder was 0.404 m and 0.27 m, respectively. The maximum and minimum bending stresses of the short suspender were 50.676 MPa and 28.206 MPa, respectively. The maximum equivalent bending stress and axial stress were 16.068 MPa and 10.542 MPa, respectively, whereas the minimum values were 9.429 MPa and 8.679 MPa, respectively. These differences directly influence the short and long-term evaluation of bridge components. For an accurate evaluation of the bridge operation performance, the traffic flow density must be considered. Full article

(This article belongs to the Special Issue Numerical Computation, Data Analysis and Software in Mathematics and Engineering, 2nd Edition)

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