The paper presents the comparative study on numerical methods of Euler method,Improved Euler method and fourth-order Runge-Kutta method for solving the engineering problems and applications.The three proposed methods ...The paper presents the comparative study on numerical methods of Euler method,Improved Euler method and fourth-order Runge-Kutta method for solving the engineering problems and applications.The three proposed methods are quite efficient and practically well suited for solving the unknown engineering problems.This paper aims to enhance the teaching and learning quality of teachers and students for various levels.At each point of the interval,the value of y is calculated and compared with its exact value at that point.The next interesting point is the observation of error from those methods.Error in the value of y is the difference between calculated and exact value.A mathematical equation which relates various functions with its derivatives is known as a differential equation.It is a popular field of mathematics because of its application to real-world problems.To calculate the exact values,the approximate values and the errors,the numerical tool such as MATLAB is appropriate for observing the results.This paper mainly concentrates on identifying the method which provides more accurate results.Then the analytical results and calculates their corresponding error were compared in details.The minimum error directly reflected to realize the best method from different numerical methods.According to the analyses from those three approaches,we observed that only the error is nominal for the fourth-order Runge-Kutta method.展开更多
Algorithms are the primary component of Artificial Intelligence(AI).The algorithm is the process in AI that imitates the human mind to solve problems.Currently evaluating the performance of AI is achieved by evaluatin...Algorithms are the primary component of Artificial Intelligence(AI).The algorithm is the process in AI that imitates the human mind to solve problems.Currently evaluating the performance of AI is achieved by evaluating AI algorithms by metric scores on data sets.However the evaluation of algorithms in AI is challenging because the evaluation of the same type of algorithm has many data sets and evaluation metrics.Different algorithms may have individual strengths and weaknesses in evaluation metric scores on separate data sets,lacking the credibility and validity of the evaluation.Moreover,evaluation of algorithms requires repeated experiments on different data sets,reducing the attention of researchers to the research of the algorithms itself.Crucially,this approach to evaluating comparative metric scores does not take into account the algorithm’s ability to solve problems.And the classical algorithm evaluation of time and space complexity is not suitable for evaluating AI algorithms.Because classical algorithms input is infinite numbers,whereas AI algorithms input is a data set,which is limited and multifarious.According to the AI algorithm evaluation without response to the problem solving capability,this paper summarizes the features of AI algorithm evaluation and proposes an AI evaluation method that incorporates the problem-solving capabilities of algorithms.展开更多
For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint ...For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.展开更多
In the process of promoting the new curriculum reform, the new education concept guides the new teaching reform. For the important basic subject of primary school mathematics, teachers need to examine the teaching met...In the process of promoting the new curriculum reform, the new education concept guides the new teaching reform. For the important basic subject of primary school mathematics, teachers need to examine the teaching methods and teaching content, reconstruct the teaching mode according to the new curriculum standards and students reality, especially pay attention to the diversified research of problem solving methods, so as to tap students learning potential and enlighten their wisdom, promote the improvement of mathematics learning level. Specifically, in the teaching process, teachers should change their teaching concepts in time, encourage students to think actively, focus on consolidating basic knowledge, guide students to use flexibly, actively guide innovative research, cultivate students divergent thinking, carry out group cooperative learning, achieve the collision of students thinking, and pay attention to the application of life practice to ensure the effect of thinking expansion training.展开更多
Quality function deployment （QFD） is a quality system, that can help to design novel products that meet customers＇ needs. Theory of inventive problem solving （TRIZ） is a very powerful tool in helping to solve dif...Quality function deployment （QFD） is a quality system, that can help to design novel products that meet customers＇ needs. Theory of inventive problem solving （TRIZ） is a very powerful tool in helping to solve difficult technical problems encountered in the design process. Introducing QFD and TRIZ into the conceptual design of the pumping unit combines advantages of these two theories, therefore meeting different demands of different users. It can tell us “What should we do it” with QFD and “How should we do it” with TRIZ. The conceptual design method, which is based on QFD and TRIZ, is introduced andused to analyze and evaluate the conceptual design project of a pumping unit.展开更多
Genetic algorithm(GA)is a heuristic and random search technique for mimicking na-ture.This paper presents the basic principle and principal character of GA,and the defini-tion and function of the genetic operators.On ...Genetic algorithm(GA)is a heuristic and random search technique for mimicking na-ture.This paper presents the basic principle and principal character of GA,and the defini-tion and function of the genetic operators.On the basis of these,the paper proposes a newmethod of solving the Job-Shop group scheduling problem by use of GA,and discusses thecoded representation method of the feasible solution and the particular limitation to the ge-netic operators.展开更多
间接边界积分方程法IBIEM(indirect boundary integral equation method)求解波动问题时控制方程基本解构造依赖经验判断和试算,导致宽频散射求解不够稳定。本文通过粒子群优化-人工神经网络建立IBIEM控制方程基本解构造模型,以数据驱...间接边界积分方程法IBIEM(indirect boundary integral equation method)求解波动问题时控制方程基本解构造依赖经验判断和试算,导致宽频散射求解不够稳定。本文通过粒子群优化-人工神经网络建立IBIEM控制方程基本解构造模型,以数据驱动代替经验判断,处理基本解构造过程中的不确定性。以二维峡谷对平面SH波散射IBIEM模拟为例验证所建模型的可靠性。结果表明,所建IBIEM控制方程基本解构造模型可对虚拟波源位置和数量的最优设置进行有效预测,兼顾计算效率和精度,大幅提高IBIEM求解波动问题时的稳定性和高效性;虚拟波源位置和数量最优设置方案受入射波频率和场地几何条件影响显著,且表现出非单调变化特征,依据经验设置基本解可靠性较差,以数据驱动的预测模型具有明显优势。本文所建方法可为IBIEM求解其他类型场地地震波动问题提供参考。展开更多
为了得到一种普遍适用于医疗器械行业的标准化且有效的产品质量问题解决方法,本文结合医疗器械行业的特点和相关法律法规要求,对被国际汽车行业广泛采用来解决产品质量问题的8D问题解决方法(Eight Disciplines Problem Solving,缩写:8D...为了得到一种普遍适用于医疗器械行业的标准化且有效的产品质量问题解决方法,本文结合医疗器械行业的特点和相关法律法规要求,对被国际汽车行业广泛采用来解决产品质量问题的8D问题解决方法(Eight Disciplines Problem Solving,缩写:8D)在医疗器械行业的适用性进行了研究,并对传统8D问题解决方法进行了改善,着重突出变更管理,得到了一种适用于医疗器械行业的8D问题解决方法。展开更多
文摘The paper presents the comparative study on numerical methods of Euler method,Improved Euler method and fourth-order Runge-Kutta method for solving the engineering problems and applications.The three proposed methods are quite efficient and practically well suited for solving the unknown engineering problems.This paper aims to enhance the teaching and learning quality of teachers and students for various levels.At each point of the interval,the value of y is calculated and compared with its exact value at that point.The next interesting point is the observation of error from those methods.Error in the value of y is the difference between calculated and exact value.A mathematical equation which relates various functions with its derivatives is known as a differential equation.It is a popular field of mathematics because of its application to real-world problems.To calculate the exact values,the approximate values and the errors,the numerical tool such as MATLAB is appropriate for observing the results.This paper mainly concentrates on identifying the method which provides more accurate results.Then the analytical results and calculates their corresponding error were compared in details.The minimum error directly reflected to realize the best method from different numerical methods.According to the analyses from those three approaches,we observed that only the error is nominal for the fourth-order Runge-Kutta method.
基金funded by the General Program of the National Natural Science Foundation of China grant number[62277022].
文摘Algorithms are the primary component of Artificial Intelligence(AI).The algorithm is the process in AI that imitates the human mind to solve problems.Currently evaluating the performance of AI is achieved by evaluating AI algorithms by metric scores on data sets.However the evaluation of algorithms in AI is challenging because the evaluation of the same type of algorithm has many data sets and evaluation metrics.Different algorithms may have individual strengths and weaknesses in evaluation metric scores on separate data sets,lacking the credibility and validity of the evaluation.Moreover,evaluation of algorithms requires repeated experiments on different data sets,reducing the attention of researchers to the research of the algorithms itself.Crucially,this approach to evaluating comparative metric scores does not take into account the algorithm’s ability to solve problems.And the classical algorithm evaluation of time and space complexity is not suitable for evaluating AI algorithms.Because classical algorithms input is infinite numbers,whereas AI algorithms input is a data set,which is limited and multifarious.According to the AI algorithm evaluation without response to the problem solving capability,this paper summarizes the features of AI algorithm evaluation and proposes an AI evaluation method that incorporates the problem-solving capabilities of algorithms.
文摘For the 2-D wave inverse problems introduced from geophysical exploration, in this paper, the author presents integration-characteristic method to solve the velocity parameter, and then applies it to common shotpoint model data, in noise-free case. The accuracy is quite good.
文摘In the process of promoting the new curriculum reform, the new education concept guides the new teaching reform. For the important basic subject of primary school mathematics, teachers need to examine the teaching methods and teaching content, reconstruct the teaching mode according to the new curriculum standards and students reality, especially pay attention to the diversified research of problem solving methods, so as to tap students learning potential and enlighten their wisdom, promote the improvement of mathematics learning level. Specifically, in the teaching process, teachers should change their teaching concepts in time, encourage students to think actively, focus on consolidating basic knowledge, guide students to use flexibly, actively guide innovative research, cultivate students divergent thinking, carry out group cooperative learning, achieve the collision of students thinking, and pay attention to the application of life practice to ensure the effect of thinking expansion training.
文摘Quality function deployment （QFD） is a quality system, that can help to design novel products that meet customers＇ needs. Theory of inventive problem solving （TRIZ） is a very powerful tool in helping to solve difficult technical problems encountered in the design process. Introducing QFD and TRIZ into the conceptual design of the pumping unit combines advantages of these two theories, therefore meeting different demands of different users. It can tell us “What should we do it” with QFD and “How should we do it” with TRIZ. The conceptual design method, which is based on QFD and TRIZ, is introduced andused to analyze and evaluate the conceptual design project of a pumping unit.
基金Supported by the High Technology Research and Development Programme of China.
文摘Genetic algorithm(GA)is a heuristic and random search technique for mimicking na-ture.This paper presents the basic principle and principal character of GA,and the defini-tion and function of the genetic operators.On the basis of these,the paper proposes a newmethod of solving the Job-Shop group scheduling problem by use of GA,and discusses thecoded representation method of the feasible solution and the particular limitation to the ge-netic operators.
文摘间接边界积分方程法IBIEM(indirect boundary integral equation method)求解波动问题时控制方程基本解构造依赖经验判断和试算,导致宽频散射求解不够稳定。本文通过粒子群优化-人工神经网络建立IBIEM控制方程基本解构造模型,以数据驱动代替经验判断,处理基本解构造过程中的不确定性。以二维峡谷对平面SH波散射IBIEM模拟为例验证所建模型的可靠性。结果表明,所建IBIEM控制方程基本解构造模型可对虚拟波源位置和数量的最优设置进行有效预测,兼顾计算效率和精度,大幅提高IBIEM求解波动问题时的稳定性和高效性;虚拟波源位置和数量最优设置方案受入射波频率和场地几何条件影响显著,且表现出非单调变化特征,依据经验设置基本解可靠性较差,以数据驱动的预测模型具有明显优势。本文所建方法可为IBIEM求解其他类型场地地震波动问题提供参考。
文摘为了得到一种普遍适用于医疗器械行业的标准化且有效的产品质量问题解决方法,本文结合医疗器械行业的特点和相关法律法规要求,对被国际汽车行业广泛采用来解决产品质量问题的8D问题解决方法(Eight Disciplines Problem Solving,缩写:8D)在医疗器械行业的适用性进行了研究,并对传统8D问题解决方法进行了改善,着重突出变更管理,得到了一种适用于医疗器械行业的8D问题解决方法。
