• Title/Summary/Keyword: Mathematics error

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An optimized ANFIS model for predicting pile pullout resistance

  • Yuwei Zhao;Mesut Gor;Daria K. Voronkova;Hamed Gholizadeh Touchaei;Hossein Moayedi;Binh Nguyen Le
    • Steel and Composite Structures
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    • v.48 no.2
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    • pp.179-190
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    • 2023
  • Many recent attempts have sought accurate prediction of pile pullout resistance (Pul) using classical machine learning models. This study offers an improved methodology for this objective. Adaptive neuro-fuzzy inference system (ANFIS), as a popular predictor, is trained by a capable metaheuristic strategy, namely equilibrium optimizer (EO) to predict the Pul. The used data is collected from laboratory investigations in previous literature. First, two optimal configurations of EO-ANFIS are selected after sensitivity analysis. They are next evaluated and compared with classical ANFIS and two neural-based models using well-accepted accuracy indicators. The results of all five models were in good agreement with laboratory Puls (all correlations > 0.99). However, it was shown that both EO-ANFISs not only outperform neural benchmarks but also enjoy a higher accuracy compared to the classical version. Therefore, utilizing the EO is recommended for optimizing this predictive tool. Furthermore, a comparison between the selected EO-ANFISs, where one employs a larger population, revealed that the model with the population size of 75 is more efficient than 300. In this relation, root mean square error and the optimization time for the EO-ANFIS (75) were 19.6272 and 1715.8 seconds, respectively, while these values were 23.4038 and 9298.7 seconds for EO-ANFIS (300).

Computational intelligence models for predicting the frictional resistance of driven pile foundations in cold regions

  • Shiguan Chen;Huimei Zhang;Kseniya I. Zykova;Hamed Gholizadeh Touchaei;Chao Yuan;Hossein Moayedi;Binh Nguyen Le
    • Computers and Concrete
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    • v.32 no.2
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    • pp.217-232
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    • 2023
  • Numerous studies have been performed on the behavior of pile foundations in cold regions. This study first attempted to employ artificial neural networks (ANN) to predict pile-bearing capacity focusing on pile data recorded primarily on cold regions. As the ANN technique has disadvantages such as finding global minima or slower convergence rates, this study in the second phase deals with the development of an ANN-based predictive model improved with an Elephant herding optimizer (EHO), Dragonfly Algorithm (DA), Genetic Algorithm (GA), and Evolution Strategy (ES) methods for predicting the piles' bearing capacity. The network inputs included the pile geometrical features, pile area (m2), pile length (m), internal friction angle along the pile body and pile tip (Ø°), and effective vertical stress. The MLP model pile's output was the ultimate bearing capacity. A sensitivity analysis was performed to determine the optimum parameters to select the best predictive model. A trial-and-error technique was also used to find the optimum network architecture and the number of hidden nodes. According to the results, there is a good consistency between the pile-bearing DA-MLP-predicted capacities and the measured bearing capacities. Based on the R2 and determination coefficient as 0.90364 and 0.8643 for testing and training datasets, respectively, it is suggested that the DA-MLP model can be effectively implemented with higher reliability, efficiency, and practicability to predict the bearing capacity of piles.

Development of a Hydrograph Triggered by Earth-Dam-Break for Compiling a Flood Hazard Map (홍수위험지도 작성을 위한 댐 붕괴 지점에서의 유량곡선 산정)

  • Lee, Khil-Ha;Kim, Sung-Wook;Yu, Soonyoung;Kim, Sang-Hyun;Cho, Jinwoo;Kim, Jin-Man
    • The Journal of Engineering Geology
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    • v.23 no.4
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    • pp.381-387
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    • 2013
  • In compiling flood hazard maps for the case of dam-failure, a scenario-based numerical modeling approach is commonly used, involving the modeling of important parameters that capture peak discharge, such as breach formation and progress. In this study, an earth-dam-break model is constructed assuming an identical mechanism and hydraulic process for all dam-break processes. A focus of the analysis is estimation of the hydrograph at the outlet as a function of time. The constructed hydrograph then serves as an upper boundary condition in running the flood routing model downstream, although flood routing is not considered here. Validation was performed using the record of the Tangjishan dam-break in China. The results were satisfactory, with a coefficient of determination of 0.974, Nash-Sutcliffe Coefficient of Efficiency (NSC) of 0.94, and Root Mean Square Error (RMSE) of $610m^3/sec$. The proposed model will contribute to assessments of potential flood hazards caused by dam-break.

Application of Self-Adaptive Meta-Heuristic Optimization Algorithm for Muskingum Flood Routing (Muskingum 홍수추적을 위한 자가적응형 메타 휴리스틱 알고리즘의 적용)

  • Lee, Eui Hoon
    • Journal of the Korea Academia-Industrial cooperation Society
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    • v.21 no.7
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    • pp.29-37
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    • 2020
  • In the past, meta-heuristic optimization algorithms were developed to solve the problems caused by complex nonlinearities occurring in natural phenomena, and various studies have been conducted to examine the applicability of the developed algorithms. The self-adaptive vision correction algorithm (SAVCA) showed excellent performance in mathematics problems, but it did not apply to complex engineering problems. Therefore, it is necessary to review the application process of the SAVCA. The SAVCA, which was recently developed and showed excellent performance, was applied to the advanced Muskingum flood routing model (ANLMM-L) to examine the application and application process. First, initial solutions were generated by the SAVCA, and the fitness was then calculated by ANLMM-L. The new value selected by a local and global search was put into the SAVCA. A new solution was generated, and ANLMM-L was applied again to calculate the fitness. The final calculation was conducted by comparing and improving the results of the new solution and existing solutions. The sum of squares (SSQ) was used to calculate the error between the observed and calculated runoff, and the applied results were compared with the current models. SAVCA, which showed excellent performance in the Muskingum flood routing model, is expected to show excellent performance in a range of engineering problems.

Empirical Mode Decomposition using the Second Derivative (이차 미분을 이용한 경험적 모드분해법)

  • Park, Min-Su;Kim, Donghoh;Oh, Hee-Seok
    • The Korean Journal of Applied Statistics
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    • v.26 no.2
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    • pp.335-347
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    • 2013
  • There are various types of real world signals. For example, an electrocardiogram(ECG) represents myocardium activities (contraction and relaxation) according to the beating of the heart. ECG can be expressed as the fluctuation of ampere ratings over time. A signal is a composite of various types of signals. An orchestra (which boasts a beautiful melody) consists of a variety of instruments with a unique frequency; subsequently, each sound is combined to form a perfect harmony. Various research on how to to decompose mixed stationary signals have been conducted. In the case of non-stationary signals, there is a limitation to use methodologies for stationary signals. Huang et al. (1998) proposed empirical mode decomposition(EMD) to deal with non-stationarity. EMD provides a data-driven approach to decompose a signal into intrinsic mode functions according to local oscillation through the identification of local extrema. However, due to the repeating process in the construction of envelopes, EMD algorithm is not efficient and not robust to a noise, and its computational complexity tends to increase as the size of a signal grows. In this research, we propose a new method to extract a local oscillation embedded in a signal by utilizing the second derivative.

A Study on the Development of Mathematical-Ethical Linkage·Convergence Class Materials according to the Theme-Based Design Model (주제기반 설계 모형에 따른 수학-윤리 연계·융합 수업 자료 개발 연구)

  • Lee, Dong Gun;Kwon, Hye Joo
    • Communications of Mathematical Education
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    • v.36 no.2
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    • pp.253-286
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    • 2022
  • This study is a study in which four teachers from the same school who participated in a teacher learning community program at the school field developed interdisciplinary linkage and convergence data using Plato as a collaborative circle in ethics and mathematics subjects. In particular, this study aimed to develop practical and shareable lesson materials. The data development procedure was developed according to the following four procedures. 'Development of data development plan, data development, verification of development data, and development of final data that reflects the verification opinions' At this time, in the data development stage, a theme-based design model was applied and developed. In addition, the development data were verified by conducting CVR verification for field teachers to focus on the validity and class applicability, and the final data were presented after the development data being revised to reflect the verification results. This study not only introduced the developed data, but also described the procedure of the data development process and the trial and error and concerns of the developers in the process to provide information on the nature of basic research to other field researchers who attempt data development.

A Study on the Development of Mathematical-Informatics Linkage·Convergence Class Materials according to the Theme-Based Design Model (주제기반 설계 모형에 따른 수학-정보 연계·융합 수업 자료 개발 연구)

  • Lee, Dong Gun;Kim, Han Su
    • Communications of Mathematical Education
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    • v.37 no.3
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    • pp.517-544
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    • 2023
  • This study presents the process and outcomes of developing mathematical-informatics linkage·convergence class materials, based on previous research findings that indicate a lack of such materials in high schools despite the increasing need for development of interdisciplinary linkage·convergence class materials In particular, this research provides insights into the discussions of six teachers who participated in the same professional learning community program, aiming to create materials that are suitable for linkage·convergence class materials and highly practical for classroom implementation. Following the material development process, a theme-based design model was applied to create the materials. In alignment with prior research and consensus among teacher learning community members, mathematics and informatics teachers developed instructional materials that can be utilized together during a 100-minute block lesson. The developed materials utilize societal issue contexts to establish links between the two subjects, enabling students to engage in problem-solving through mathematical modeling and coding. To increase the validity and practicality of the developed resources during their field application, CVR verification was conducted involving field teachers. Incorporating the results of the CVR verification, the finalized instructional materials were presented in the form of a teaching guide. Furthermore, we aimed to provide insights into the trial-and-error experiences and deliberations of the developers throughout the material development process, with the intention of offering valuable information that can serve as a foundation for conducting related research by field researchers. These research findings hold value as empirical evidence that can explore the applicability of teaching material development models in fields. The accumulation of such materials is expected to facilitate a cyclical relationship between theoretical teaching models and practical classroom applications.

A Study of the Representation in the Elementary Mathematical Problem-Solving Process (초등 수학 문제해결 과정에 사용되는 표현 방법에 대한 연구)

  • Kim, Yu-Jung;Paik, Seok-Yoon
    • Journal of Elementary Mathematics Education in Korea
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    • v.9 no.2
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    • pp.85-110
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    • 2005
  • The purpose of this study is to examine the characteristics of visual representation used in problem solving process and examine the representation types the students used to successfully solve the problem and focus on systematizing the visual representation method using the condition students suggest in the problems. To achieve the goal of this study, following questions have been raised. (1) what characteristic does the representation the elementary school students used in the process of solving a math problem possess? (2) what types of representation did students use in order to successfully solve elementary math problem? 240 4th graders attending J Elementary School located in Seoul participated in this study. Qualitative methodology was used for data analysis, and the analysis suggested representation method the students use in problem solving process and then suggested the representation that can successfully solve five different problems. The results of the study as follow. First, the students are not familiar with representing with various methods in the problem solving process. Students tend to solve the problem using equations rather than drawing a diagram when they can not find a word that gives a hint to draw a diagram. The method students used to restate the problem was mostly rewriting the problem, and they could not utilize a table that is essential in solving the problem. Thus, various errors were found. Students did not simplify the complicated problem to find the pattern to solve the problem. Second, the image and strategy created as the problem was read and the affected greatly in solving the problem. The first image created as the problem was read made students to draw different diagram and make them choose different strategies. The study showed the importance of first image by most of the students who do not pass the trial and error step and use the strategy they chose first. Third, the students who successfully solved the problems do not solely depend on the equation but put them in the form which information are decoded. They do not write difficult equation that they can not solve, but put them into a simplified equation that know to solve the problem. On fraction problems, they draw a diagram to solve the problem without calculation, Fourth, the students who. successfully solved the problem drew clear diagram that can be understood with intuition. By representing visually, unnecessary information were omitted and used simple image were drawn using symbol or lines, and to clarify the relationship between the information, numeric explanation was added. In addition, they restricted use of complicated motion line and dividing line, proper noun in the word problems were not changed into abbreviation or symbols to clearly restate the problem. Adding additional information was useful source in solving the problem.

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