The geometry of an inductively coupled plasma (ICP) etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these pa...The geometry of an inductively coupled plasma (ICP) etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these parameters were determined by the "trial and error" method, resulting in wastes of time and funds. In this paper, a new approach of regression orthogonal design with plasma simulation experiments is proposed to investigate the sensitivity of the structural parameters on the uniformity of plasma characteristics. The tool for simulating plasma is CFD-ACE+, which is commercial multi-physical modeling software that has been proven to be accurate for plasma simulation. The simulated experimental results are analyzed to get a regression equation on three structural parameters. Through this equation, engineers can compute the uniformity of the electron number density rapidly without modeling by CFD-ACE+. An optimization performed at the end produces good results.展开更多
Although friction characteristics of fault gouge are important to understand reactivation of fault,behavior of earthquake,and mechanism of slope failure,analysis results of fault gouge have low accuracy mostly than th...Although friction characteristics of fault gouge are important to understand reactivation of fault,behavior of earthquake,and mechanism of slope failure,analysis results of fault gouge have low accuracy mostly than those of soils or rocks due to its high heterogeneity and low strength.Therefore,to improve the accuracy of analysis results,we conducted simple regression analysis and structural equation model analysis and selected major influential factors of friction characteristics among many factors,and then we deduced advanced regression model with the highest coefficient of determination(R^(2)) via multiple regression analysis.Whereas most coefficients of determination in simple regression analysis are below0.3-0.4,coefficient of determination in multiple regression analysis is remarkably large as 0.657.展开更多
Damage detection in structures is performed via vibra-tion based structural identification. Modal information, such as fre-quencies and mode shapes, are widely used for structural dama-ge detection to indicate the hea...Damage detection in structures is performed via vibra-tion based structural identification. Modal information, such as fre-quencies and mode shapes, are widely used for structural dama-ge detection to indicate the health conditions of civil structures.The deep learning algorithm that works on a multiple layer neuralnetwork model termed as deep autoencoder is proposed to learnthe relationship between the modal information and structural stiff-ness parameters. This is achieved via dimension reduction of themodal information feature and a non-linear regression against thestructural stiffness parameters. Numerical tests on a symmetri-cal steel frame model are conducted to generate the data for thetraining and validation, and to demonstrate the efficiency of theproposed approach for vibration based structural damage detec-tion.展开更多
Purpose: General linear modeling (GLM) is usually applied to investigate factors associated with the domains of Quality of Life (QOL). A summation score in a specific sub-domain is regressed by a statistical model inc...Purpose: General linear modeling (GLM) is usually applied to investigate factors associated with the domains of Quality of Life (QOL). A summation score in a specific sub-domain is regressed by a statistical model including factors that are associated with the sub-domain. However, using the summation score ignores the influence of individual questions. Structural equation modeling (SEM) can account for the influence of each question’s score by compositing a latent variable from each question of a sub-domain. The objective of this study is to determine whether a conventional approach such as GLM, with its use of the summation score, is valid from the standpoint of the SEM approach. Method: We used the Japanese version of the Maugeri Foundation Respiratory Failure Questionnaire, a QOL measure, on 94 patients with heart failure. The daily activity sub-domain of the questionnaire was selected together with its four accompanying factors, namely, living together, occupation, gender, and the New York Heart Association’s cardiac function scale (NYHA). The association level between individual factors and the daily activity sub-domain was estimated using SEM?and GLM, respectively. The standard partial regression coefficients of GLM and standardized path coefficients of SEM were compared. If?these coefficients were similar (absolute value of the difference -0.06 and -0.07 for the GLM and SEM. Likewise, the estimates of occupation, gender, and NYHA were -0.18 and -0.20, -0.08 and -0.08, 0.51 and 0.54, respectively. The absolute values of the difference for each factor were 0.01, 0.02, 0.00, and 0.03, respectively. All differences were less than 0.05. This means that these two approaches lead to similar conclusions. Conclusion: GLM is a valid method for exploring association factors with a domain in QOL.展开更多
Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of i...Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">0</span></sub><span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family:""><span style="font-family:Verdana;">β</span><span style="font-family:Verdana;"><sub>3 </sub></span></em><span style="font-family:Verdana;">= 3.6</span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Five (5) </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">levels of</span><span style="white-space:nowrap;font-family:Verdana;"> </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">mulicollinearity </span></span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">with seven</span><span style="font-family:""> </span><span style="font-family:Verdana;">(7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I</span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;">) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.展开更多
A short review is given of standard regression analysis. It is shown that the results presented by program packages are not always reliable. Here is presented a general framework for linear regression that includes mo...A short review is given of standard regression analysis. It is shown that the results presented by program packages are not always reliable. Here is presented a general framework for linear regression that includes most linear regression methods based on linear algebra. The H-principle of mathematical modelling is presented. It uses the analogy between the modelling task and measurement situation in quantum mechanics. The principle states that the modelling task should be carried out in steps where at each step an optimal balance should be determined between the value of the objective function, the fit, and the associated precision. H-methods are different methods to carry out the modelling task based on recommendations of the H-principle. They have been applied to different types of data. In general, they provide better predictions than linear regression methods in the literature.展开更多
In order to establish the baseline finite element model for structural health monitoring,a new method of model updating was proposed after analyzing the uncertainties of measured data and the error of finite element m...In order to establish the baseline finite element model for structural health monitoring,a new method of model updating was proposed after analyzing the uncertainties of measured data and the error of finite element model.In the new method,the finite element model was replaced by the multi-output support vector regression machine(MSVR).The interval variables of the measured frequency were sampled by Latin hypercube sampling method.The samples of frequency were regarded as the inputs of the trained MSVR.The outputs of MSVR were the target values of design parameters.The steel structure of National Aquatic Center for Beijing Olympic Games was introduced as a case for finite element model updating.The results show that the proposed method can avoid solving the problem of complicated calculation.Both the estimated values and associated uncertainties of the structure parameters can be obtained by the method.The static and dynamic characteristics of the updated finite element model are in good agreement with the measured data.展开更多
With the development of the times,the role of human capital in economic growth has been highlighted.However,in the current academic world,the research on the topic of demographic structure and human capital accumulati...With the development of the times,the role of human capital in economic growth has been highlighted.However,in the current academic world,the research on the topic of demographic structure and human capital accumulation is not closely integrated.China is now in a period of economic transformation and upgrading,and it is urgent to change the traditional economic growth model,increase human capital investment,and cultivate new growth momentum.Therefore,this paper examines the impact of China’s population structure on human capital accumulation by constructing a mathematical model based on relevant panel data of 31 provinces(municipalities and autonomous regions)from 2001 to 2020.The empirical results show that human capital accumulation in China has a certain lagging effect,while population age and urban-rural structure enhance human capital accumulation in both quantitative and qualitative terms,respectively.In addition,industrial transformation,economic growth level,and per capita income all have significant positive effects.The effect of education,on the other hand,is not significant,while the interaction between urbanization and industrial structure may hurt it.Based on this,this paper proposes targeted countermeasures and suggestions in terms of fully developing the population quality dividend,fully tapping the talent knowledge dividend,continuously improving the health dividend,and continually tapping the aging dividend.展开更多
Understanding the interaction between canopy structure and the parameters of interception loss is essential in predicting the variations in partitioning rainfall and water resources as affected by changes in canopy st...Understanding the interaction between canopy structure and the parameters of interception loss is essential in predicting the variations in partitioning rainfall and water resources as affected by changes in canopy structure and in implementing water-based management in semiarid forest plantations.In this study,seasonal variations in rainfall interception loss and canopy storage capacity as driven by canopy structure were predicted and the linkages were tested using seasonal filed measurements.The study was conducted in nine 50 m×50 m Robinia pseudoacacia plots in the semiarid region of China’s Loess Plateau.Gross rain-fall,throughfall and stemflow were measured in seasons with and without leaves in 2015 and 2016.Results show that measured average interception loss for the nine plots were 17.9% and 9.4% of gross rainfall during periods with leaves (the growing season) and without leaves, respectively. Average canopy storage capacity estimated using an indirect method was 1.3 mm in the growing season and 0.2 mm in the leafless season. Correlations of relative interception loss and canopy storage capacity to canopy variables were highest for leaf/wood area index (LAI/WAI) and canopy cover, fol-lowed by bark area, basal area, tree height and stand density. Combined canopy cover, leaf/wood area index and bark area multiple regression models of interception loss and canopy storage capacity were established for the growing season and in the leafless season in 2015. It explained 97% and 96% of the variations in relative interception loss during seasons with and without leaves, respectively. It also explained 98% and 99% of the variations in canopy storage capacity during seasons with and without leaves, respectively. The empiri-cal regression models were validated using field data col-lected in 2016. The models satisfactorily predicted relative interception loss and canopy storage capacity during seasons with and without leaves. This study provides greater under-standing about the effects of changes in tree canopy structure (e.g., dieback or mortality) on hydrological processes.展开更多
基金supported by Important National Science & Technology Specific Projects of China (No.2) (Nos.2009ZX02001,2011ZX02403)
文摘The geometry of an inductively coupled plasma (ICP) etcher is usually considered to be an important factor for determining both plasma and process uniformity over a large wafer. During the past few decades, these parameters were determined by the "trial and error" method, resulting in wastes of time and funds. In this paper, a new approach of regression orthogonal design with plasma simulation experiments is proposed to investigate the sensitivity of the structural parameters on the uniformity of plasma characteristics. The tool for simulating plasma is CFD-ACE+, which is commercial multi-physical modeling software that has been proven to be accurate for plasma simulation. The simulated experimental results are analyzed to get a regression equation on three structural parameters. Through this equation, engineers can compute the uniformity of the electron number density rapidly without modeling by CFD-ACE+. An optimization performed at the end produces good results.
基金supported by Postdoctoral Fellowship Program funded by the Ministry of Education of the Republic of Korea through the Chungbuk National University in 2020。
文摘Although friction characteristics of fault gouge are important to understand reactivation of fault,behavior of earthquake,and mechanism of slope failure,analysis results of fault gouge have low accuracy mostly than those of soils or rocks due to its high heterogeneity and low strength.Therefore,to improve the accuracy of analysis results,we conducted simple regression analysis and structural equation model analysis and selected major influential factors of friction characteristics among many factors,and then we deduced advanced regression model with the highest coefficient of determination(R^(2)) via multiple regression analysis.Whereas most coefficients of determination in simple regression analysis are below0.3-0.4,coefficient of determination in multiple regression analysis is remarkably large as 0.657.
文摘Damage detection in structures is performed via vibra-tion based structural identification. Modal information, such as fre-quencies and mode shapes, are widely used for structural dama-ge detection to indicate the health conditions of civil structures.The deep learning algorithm that works on a multiple layer neuralnetwork model termed as deep autoencoder is proposed to learnthe relationship between the modal information and structural stiff-ness parameters. This is achieved via dimension reduction of themodal information feature and a non-linear regression against thestructural stiffness parameters. Numerical tests on a symmetri-cal steel frame model are conducted to generate the data for thetraining and validation, and to demonstrate the efficiency of theproposed approach for vibration based structural damage detec-tion.
文摘Purpose: General linear modeling (GLM) is usually applied to investigate factors associated with the domains of Quality of Life (QOL). A summation score in a specific sub-domain is regressed by a statistical model including factors that are associated with the sub-domain. However, using the summation score ignores the influence of individual questions. Structural equation modeling (SEM) can account for the influence of each question’s score by compositing a latent variable from each question of a sub-domain. The objective of this study is to determine whether a conventional approach such as GLM, with its use of the summation score, is valid from the standpoint of the SEM approach. Method: We used the Japanese version of the Maugeri Foundation Respiratory Failure Questionnaire, a QOL measure, on 94 patients with heart failure. The daily activity sub-domain of the questionnaire was selected together with its four accompanying factors, namely, living together, occupation, gender, and the New York Heart Association’s cardiac function scale (NYHA). The association level between individual factors and the daily activity sub-domain was estimated using SEM?and GLM, respectively. The standard partial regression coefficients of GLM and standardized path coefficients of SEM were compared. If?these coefficients were similar (absolute value of the difference -0.06 and -0.07 for the GLM and SEM. Likewise, the estimates of occupation, gender, and NYHA were -0.18 and -0.20, -0.08 and -0.08, 0.51 and 0.54, respectively. The absolute values of the difference for each factor were 0.01, 0.02, 0.00, and 0.03, respectively. All differences were less than 0.05. This means that these two approaches lead to similar conclusions. Conclusion: GLM is a valid method for exploring association factors with a domain in QOL.
文摘Heteroscedasticity and multicollinearity are serious problems when they exist in econometrics data. These problems exist as a result of violating the assumptions of equal variance between the error terms and that of independence between the explanatory variables of the model. With these assumption violations, Ordinary Least Square Estimator</span><span style="font-family:""> </span><span style="font-family:""><span style="font-family:Verdana;">(OLS) will not give best linear unbiased, efficient and consistent estimator. In practice, there are several structures of heteroscedasticity and several methods of heteroscedasticity detection. For better estimation result, best heteroscedasticity detection methods must be determined for any structure of heteroscedasticity in the presence of multicollinearity between the explanatory variables of the model. In this paper we examine the effects of multicollinearity on type I error rates of some methods of heteroscedasticity detection in linear regression model in other to determine the best method of heteroscedasticity detection to use when both problems exist in the model. Nine heteroscedasticity detection methods were considered with seven heteroscedasticity structures. Simulation study was done via a Monte Carlo experiment on a multiple linear regression model with 3 explanatory variables. This experiment was conducted 1000 times with linear model parameters of </span><span style="white-space:nowrap;"><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">0</span></sub><span style="font-family:Verdana;"> = 4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">1</span></sub><span style="font-family:Verdana;"> = 0.4 , </span><em><span style="font-family:Verdana;">β</span></em><sub><span style="font-family:Verdana;">2</span></sub><span style="font-family:Verdana;">= 1.5</span></span></span><span style="font-family:""><span style="font-family:Verdana;"> and </span><em style="font-family:""><span style="font-family:Verdana;">β</span><span style="font-family:Verdana;"><sub>3 </sub></span></em><span style="font-family:Verdana;">= 3.6</span><span style="font-family:Verdana;">. </span><span style="font-family:Verdana;">Five (5) </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">levels of</span><span style="white-space:nowrap;font-family:Verdana;"> </span><span style="font-family:Verdana;"></span><span style="font-family:Verdana;">mulicollinearity </span></span><span style="font-family:Verdana;">are </span><span style="font-family:Verdana;">with seven</span><span style="font-family:""> </span><span style="font-family:Verdana;">(7) different sample sizes. The method’s performances were compared with the aids of set confidence interval (C.I</span><span style="font-family:Verdana;">.</span><span style="font-family:Verdana;">) criterion. Results showed that whenever multicollinearity exists in the model with any forms of heteroscedasticity structures, Breusch-Godfrey (BG) test is the best method to determine the existence of heteroscedasticity at all chosen levels of significance.
文摘A short review is given of standard regression analysis. It is shown that the results presented by program packages are not always reliable. Here is presented a general framework for linear regression that includes most linear regression methods based on linear algebra. The H-principle of mathematical modelling is presented. It uses the analogy between the modelling task and measurement situation in quantum mechanics. The principle states that the modelling task should be carried out in steps where at each step an optimal balance should be determined between the value of the objective function, the fit, and the associated precision. H-methods are different methods to carry out the modelling task based on recommendations of the H-principle. They have been applied to different types of data. In general, they provide better predictions than linear regression methods in the literature.
基金Project(50678052) supported by the National Natural Science Foundation of China
文摘In order to establish the baseline finite element model for structural health monitoring,a new method of model updating was proposed after analyzing the uncertainties of measured data and the error of finite element model.In the new method,the finite element model was replaced by the multi-output support vector regression machine(MSVR).The interval variables of the measured frequency were sampled by Latin hypercube sampling method.The samples of frequency were regarded as the inputs of the trained MSVR.The outputs of MSVR were the target values of design parameters.The steel structure of National Aquatic Center for Beijing Olympic Games was introduced as a case for finite element model updating.The results show that the proposed method can avoid solving the problem of complicated calculation.Both the estimated values and associated uncertainties of the structure parameters can be obtained by the method.The static and dynamic characteristics of the updated finite element model are in good agreement with the measured data.
文摘With the development of the times,the role of human capital in economic growth has been highlighted.However,in the current academic world,the research on the topic of demographic structure and human capital accumulation is not closely integrated.China is now in a period of economic transformation and upgrading,and it is urgent to change the traditional economic growth model,increase human capital investment,and cultivate new growth momentum.Therefore,this paper examines the impact of China’s population structure on human capital accumulation by constructing a mathematical model based on relevant panel data of 31 provinces(municipalities and autonomous regions)from 2001 to 2020.The empirical results show that human capital accumulation in China has a certain lagging effect,while population age and urban-rural structure enhance human capital accumulation in both quantitative and qualitative terms,respectively.In addition,industrial transformation,economic growth level,and per capita income all have significant positive effects.The effect of education,on the other hand,is not significant,while the interaction between urbanization and industrial structure may hurt it.Based on this,this paper proposes targeted countermeasures and suggestions in terms of fully developing the population quality dividend,fully tapping the talent knowledge dividend,continuously improving the health dividend,and continually tapping the aging dividend.
基金This study is supported by National Key Research and Development Program(2016YFC0501603).
文摘Understanding the interaction between canopy structure and the parameters of interception loss is essential in predicting the variations in partitioning rainfall and water resources as affected by changes in canopy structure and in implementing water-based management in semiarid forest plantations.In this study,seasonal variations in rainfall interception loss and canopy storage capacity as driven by canopy structure were predicted and the linkages were tested using seasonal filed measurements.The study was conducted in nine 50 m×50 m Robinia pseudoacacia plots in the semiarid region of China’s Loess Plateau.Gross rain-fall,throughfall and stemflow were measured in seasons with and without leaves in 2015 and 2016.Results show that measured average interception loss for the nine plots were 17.9% and 9.4% of gross rainfall during periods with leaves (the growing season) and without leaves, respectively. Average canopy storage capacity estimated using an indirect method was 1.3 mm in the growing season and 0.2 mm in the leafless season. Correlations of relative interception loss and canopy storage capacity to canopy variables were highest for leaf/wood area index (LAI/WAI) and canopy cover, fol-lowed by bark area, basal area, tree height and stand density. Combined canopy cover, leaf/wood area index and bark area multiple regression models of interception loss and canopy storage capacity were established for the growing season and in the leafless season in 2015. It explained 97% and 96% of the variations in relative interception loss during seasons with and without leaves, respectively. It also explained 98% and 99% of the variations in canopy storage capacity during seasons with and without leaves, respectively. The empiri-cal regression models were validated using field data col-lected in 2016. The models satisfactorily predicted relative interception loss and canopy storage capacity during seasons with and without leaves. This study provides greater under-standing about the effects of changes in tree canopy structure (e.g., dieback or mortality) on hydrological processes.