As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for...As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for most of actual conditions, the independent variable generally takes the real value, while both parameter and dependent variable take the Fuzzy value. This paper propounded a method for the latter and its relevant Fuzzy regreession model. In addition the Fuzzy observation, matrix distribution and the rational estimation of modeling parameter have also been discussed. Furthermore, the Max min estimation of modeling parameter and its corresponding calculating sequence have also been offered to and the calculating example shows the method is feasible.展开更多
In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperature...In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series ¶llel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.展开更多
A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kin...A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.展开更多
The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When thi...The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.展开更多
In this article, to improve the doubly robust estimator, the nonlinear regression models with missing responses are studied. Based on the covariate balancing propensity score (CBPS), estimators for the regression coef...In this article, to improve the doubly robust estimator, the nonlinear regression models with missing responses are studied. Based on the covariate balancing propensity score (CBPS), estimators for the regression coefficients and the population mean are obtained. It is proved that the proposed estimators are asymptotically normal. In simulation studies, the proposed estimators show improved performance relative to usual augmented inverse probability weighted estimators.展开更多
Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （K...Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.展开更多
This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence re...This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.展开更多
Assume that in the nonlinear regression model, independent variable sequence {xi, i ≥ 1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The co...Assume that in the nonlinear regression model, independent variable sequence {xi, i ≥ 1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The condition is essential for proving the consistency and asymptotic normality of the estimator.展开更多
In order to reduce the influence of outliers on the parameter estimate of the attenuation formula for the blasting vibration velocity,a fuzzy nonlinear regression method of Sadov’s vibration formula was proposed on t...In order to reduce the influence of outliers on the parameter estimate of the attenuation formula for the blasting vibration velocity,a fuzzy nonlinear regression method of Sadov’s vibration formula was proposed on the basis of the fuzziness of blasting engineering,and the algorithm was described in details as well.In accordance with an engineering case,the vibration attenuation formula was regressed by the fuzzy nonlinear regression method and the nonlinear least square method,respectively.The calculation results showed that the fuzzy nonlinear regression method is more suitable to the field test data.It differs from the nonlinear least square method because the weight of residual square in the objective function can be adjusted according to the membership of each data.And the deviation calculation of least square estimate of parameters in the nonlinear regression model verified the rationality of using the membership to assign the weight of residual square.The fuzzy nonlinear regression method provides a calculation basis for estimating Sadov’s vibration formula’s parameters more accurately.展开更多
This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on th...This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].展开更多
The effects of centering response and explanatory variables as a way of simplifying fitted linear models in the presence of correlation are reviewed and extended to include nonlinear models, common in many biological ...The effects of centering response and explanatory variables as a way of simplifying fitted linear models in the presence of correlation are reviewed and extended to include nonlinear models, common in many biological and economic applications. In a nonlinear model, the use of a local approximation can modify the effect of centering. Even in the presence of uncorrelated explanatory variables, centering may affect linear approximations and related test statistics. An approach to assessing this effect in relation to intrinsic curvature is developed and applied. Mis-specification bias of linear versus nonlinear models also reflects this centering effect.展开更多
Total organic carbon(TOC)content is a crucial evaluation parameter in the process of shale gas exploration and development.Marine-continental transitional shale is characterized by strong heterogeneity and thin single...Total organic carbon(TOC)content is a crucial evaluation parameter in the process of shale gas exploration and development.Marine-continental transitional shale is characterized by strong heterogeneity and thin single-layer thickness.The discrete TOC data measured by experimental methods are unable to accurately reflect the reservoir characteristics of marine-continental transitional shale.In this paper,a multivariate nonlinear regression prediction model(R-MNR)was established,and the model was applied to predict the TOC content of shale for the first time.TheΔlgR model,multiple linear regression model(MLR),BP neural network model(BP model),and R-MNR model were built to predict the TOC of shale in Benxi Formation.The coefficient of determination(R2),mean-absolute-percentage-error(MAPE),root-mean-square-error(RMSE),and the number of input layer parameters(NILP)were employed to assess the efficacy of the model through the analytic hierarchy process(AHP)method.The total weight of R-MNR is 0.361,and that of BP model is 0.336.The weights of the two traditional models are 0.104 and 0.199,respectively.The results indicate that the R-MNR is comparable to the BP model in terms of prediction accuracy,and both models are significantly more accurate than the traditional prediction model.The R-MNR is capable of obtaining a clear TOC prediction formula,which is convenient for verification and promotion.During the training process of the R-MNR,the influence of each parameter and coupling relationship on the prediction results is elucidated,which enables researchers to gain a deeper understanding of the geophysical significance and geological process of the model.The result of this study suggests that the R-MNR can be employed to predict the TOC content of marine-continental transitional shale effectively in the future.展开更多
Triaxial tests,a staple in rock engineering,are labor-intensive,sample-demanding,and costly,making their optimization highly advantageous.These tests are essential for characterizing rock strength,and by adopting a fa...Triaxial tests,a staple in rock engineering,are labor-intensive,sample-demanding,and costly,making their optimization highly advantageous.These tests are essential for characterizing rock strength,and by adopting a failure criterion,they allow for the derivation of criterion parameters through regression,facilitating their integration into modeling programs.In this study,we introduce the application of an underutilized statistical technique—orthogonal regression—well-suited for analyzing triaxial test data.Additionally,we present an innovation in this technique by minimizing the Euclidean distance while incorporating orthogonality between vectors as a constraint,for the case of orthogonal linear regression.Also,we consider the Modified Least Squares method.We exemplify this approach by developing the necessary equations to apply the Mohr-Coulomb,Murrell,Hoek-Brown,andÚcar criteria,and implement these equations in both spreadsheet calculations and R scripts.Finally,we demonstrate the technique's application using five datasets of varied lithologies from specialized literature,showcasing its versatility and effectiveness.展开更多
In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed fi...In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.展开更多
In the recent era,piled raft foundation(PRF)has been considered an emergent technology for offshore and onshore structures.In previous studies,there is a lack of illustration regarding the load sharing and interaction...In the recent era,piled raft foundation(PRF)has been considered an emergent technology for offshore and onshore structures.In previous studies,there is a lack of illustration regarding the load sharing and interaction behavior which are considered the main intents in the present study.Finite element(FE)models are prepared with various design variables in a double-layer soil system,and the load sharing and interaction factors of piled rafts are estimated.The obtained results are then checked statistically with nonlinear multiple regression(NMR)and artificial neural network(ANN)modeling,and some prediction models are proposed.ANN models are prepared with Levenberg-Marquardt(LM)algorithm for load sharing and interaction factors through backpropagation technique.The factor of safety(FS)of PRF is also estimated using the proposed NMR and ANN models,which can be used for developing the design strategy of PRF.展开更多
A kinetic nonlinear regression model for multi-component assay of esters was proposed based on their different alkaline-catalysed hydrolysis rate. The reaction rate was determined by monitoring the conductance change ...A kinetic nonlinear regression model for multi-component assay of esters was proposed based on their different alkaline-catalysed hydrolysis rate. The reaction rate was determined by monitoring the conductance change in solution with a liquid-purpose surface acoustic wave impedance sensor(SAW). The model was tested theoretically and experimentally with the mixture of methyl acetate and n-propyl acetate. The experimental detection limit of methyl acetate and n-propyl acetate (within 10 min) was 0.5 mu mol/L and 1.0 mu mol/L respectively and the recovery of the sensor system ranged from 93% to 106% (n=6).展开更多
In this paper,we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed.We propose a correspondent mini-max problem for nonlinear regression and give ...In this paper,we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed.We propose a correspondent mini-max problem for nonlinear regression and give a numerical algorithm.Such an algorithm can be applied in regression and machine learning problems,and yields better results than traditional least squares and machine learning methods.展开更多
Moistube irrigation is a new micro-irrigation technology.Accurately estimating its wetting pattern dimensions presents a challenge.Therefore,it is necessary to develop models for efficient assessment of the wetting tr...Moistube irrigation is a new micro-irrigation technology.Accurately estimating its wetting pattern dimensions presents a challenge.Therefore,it is necessary to develop models for efficient assessment of the wetting transport pattern in order to design a cost-effective moistube irrigation system.To achieve this goal,this study developed a multivariate nonlinear regression model and compared it with a dimensional model.HYDRUS-2D was used to perform numerical simulations of 56 irrigation scenarios with different factors.The experiments showed that the shape of the wetting soil body approximated a cylinder and was mainly affected by soil texture,pressure head,and matric potential.A multivariate nonlinear model using a power function relationship between wetting size and irrigation time was developed,with a determination coefficient greater than 0.99.The model was validated for cases with six soil texture types,with mean average absolute errors of 0.43-0.90 cm,root mean square errors of 0.51-0.95 cm,and mean deviation percentage values of 3.23%-6.27%.The multivariate nonlinear regression model outperformed the dimensional model.It can therefore provide a scientific foundation for the development of moistube irrigation systems.展开更多
In oil and gas exploration,elucidating the complex interdependencies among geological variables is paramount.Our study introduces the application of sophisticated regression analysis method at the forefront,aiming not...In oil and gas exploration,elucidating the complex interdependencies among geological variables is paramount.Our study introduces the application of sophisticated regression analysis method at the forefront,aiming not just at predicting geophysical logging curve values but also innovatively mitigate hydrocarbon depletion observed in geochemical logging.Through a rigorous assessment,we explore the efficacy of eight regression models,bifurcated into linear and nonlinear groups,to accommodate the multifaceted nature of geological datasets.Our linear model suite encompasses the Standard Equation,Ridge Regression,Least Absolute Shrinkage and Selection Operator,and Elastic Net,each presenting distinct advantages.The Standard Equation serves as a foundational benchmark,whereas Ridge Regression implements penalty terms to counteract overfitting,thus bolstering model robustness in the presence of multicollinearity.The Least Absolute Shrinkage and Selection Operator for variable selection functions to streamline models,enhancing their interpretability,while Elastic Net amalgamates the merits of Ridge Regression and Least Absolute Shrinkage and Selection Operator,offering a harmonized solution to model complexity and comprehensibility.On the nonlinear front,Gradient Descent,Kernel Ridge Regression,Support Vector Regression,and Piecewise Function-Fitting methods introduce innovative approaches.Gradient Descent assures computational efficiency in optimizing solutions,Kernel Ridge Regression leverages the kernel trick to navigate nonlinear patterns,and Support Vector Regression is proficient in forecasting extremities,pivotal for exploration risk assessment.The Piecewise Function-Fitting approach,tailored for geological data,facilitates adaptable modeling of variable interrelations,accommodating abrupt data trend shifts.Our analysis identifies Ridge Regression,particularly when augmented by Piecewise Function-Fitting,as superior in recouping hydrocarbon losses,and underscoring its utility in resource quantification refinement.Meanwhile,Kernel Ridge Regression emerges as a noteworthy strategy in ameliorating porosity-logging curve prediction for well A,evidencing its aptness for intricate geological structures.This research attests to the scientific ascendancy and broad-spectrum relevance of these regression techniques over conventional methods while heralding new horizons for their deployment in the oil and gas sector.The insights garnered from these advanced modeling strategies are set to transform geological and engineering practices in hydrocarbon prediction,evaluation,and recovery.展开更多
In this work, we seek the relationship between the order of the polynomial model and the number of knots and intervals that we need to fit the splines regression model. Regression models (polynomial and spline regress...In this work, we seek the relationship between the order of the polynomial model and the number of knots and intervals that we need to fit the splines regression model. Regression models (polynomial and spline regression models) are presented and discussed in detail in order to discover the relation. Intrinsically, both models are dependent on the linear regression model. Spline is designed to draw curves to balance the goodness of fit and minimize the mean square error of the regression model. In the splines model, the curve at any point depends only on the observations at that point and some specified neighboring points. Using the boundaries of the intervals of the splines, we fit a smooth cubic interpolation function that goes through (n + 1) data points. On the other hand, polynomial regression is a useful technique when the pattern of the data indicates a nonlinear relationship between the dependent and independent variables. Moreover, higher-degree polynomials can capture more intricate patterns, but it can also lead to overfitting. A simulation study is implemented to illustrate the performance of splines and spline segments based on the degree of the polynomial model. For each model, we compute the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to compare the optimal polynomial order for fitting the data with the number of knots and intervals for the splines model. Both AIC and BIC can help to identify the model that best balances fit and complexity, aiming to prevent overfitting by penalizing the use of excessive parameters. We compare the results that we got from applying the polynomial regression model with the splines model results in terms of point estimates, the mean sum of squared errors, and the fitted regression line. We can say that order five of the polynomial model may be used to estimate splines with five segments.展开更多
文摘As far as the nonlinear regression method is concerned, the condition when both independent and dependent variable take the Fuzzy value, while the parameter, θ∈ΘR m the real value, have been discussed in . But for most of actual conditions, the independent variable generally takes the real value, while both parameter and dependent variable take the Fuzzy value. This paper propounded a method for the latter and its relevant Fuzzy regreession model. In addition the Fuzzy observation, matrix distribution and the rational estimation of modeling parameter have also been discussed. Furthermore, the Max min estimation of modeling parameter and its corresponding calculating sequence have also been offered to and the calculating example shows the method is feasible.
基金Project(51275414)supported by the National Natural Science Foundation of ChinaProject(2015JM5204)supported by the Natural Science Foundation of Shaanxi Province,China+1 种基金Project(Z2015064)supported by the Graduate Starting Seed Fund of the Northwestern Polytechnical University,ChinaProject(130-QP-2015)supported by the Research Fund of the State Key Laboratory of Solidification Processing(NWPU),China
文摘In order to study the work-ability and establish the optimum hot formation processing parameters for industrial 1060 pure aluminum, the compressive deformation behavior of pure aluminum was investigated at temperatures of 523?823 K and strain rates of 0.005?10 s?1 on a Gleeble?1500 thermo-simulation machine. The influence rule of processing parameters (strain, strain rate and temperature) on flow stress of pure aluminum was investigated. Nine analysis factors consisting of material parameters and according weights were optimized. Then, the constitutive equations of multilevel series rules, multilevel parallel rules and multilevel series ¶llel rules were established. The correlation coefficients (R) are 0.992, 0.988 and 0.990, respectively, and the average absolute relative errors (AAREs) are 6.77%, 8.70% and 7.63%, respectively, which proves that the constitutive equations of multilevel series rules can predict the flow stress of pure aluminum with good correlation and precision.
文摘A geometric framework is proposed for semiparametric nonlinear regression models based on the concept of least favorable curve, introduced by Severini and Wong (1992). The authors use this framework to drive three kinds of improved approximate confidence regions for the parameter and parameter subset in terms of curvatures. The results obtained by Hamilton et al. (1982), Hamilton (1986) and Wei (1994) are extended to semiparametric nonlinear regression models.
文摘The purpose of this paper is to study the theory of conservative estimating functions in nonlinear regression model with aggregated data. In this model, a quasi-score function with aggregated data is defined. When this function happens to be conservative, it is projection of the true score function onto a class of estimation functions. By constructing, the potential function for the projected score with aggregated data is obtained, which have some properties of log-likelihood function.
文摘In this article, to improve the doubly robust estimator, the nonlinear regression models with missing responses are studied. Based on the covariate balancing propensity score (CBPS), estimators for the regression coefficients and the population mean are obtained. It is proved that the proposed estimators are asymptotically normal. In simulation studies, the proposed estimators show improved performance relative to usual augmented inverse probability weighted estimators.
文摘Chaos theory has taught us that a system which has both nonlinearity and random input will most likely produce irregular data. If random errors are irregular data, then random error process will raise nonlinearity （Kantz and Schreiber （1997））. Tsai （1986） introduced a composite test for autocorrelation and heteroscedasticity in linear models with AR（1） errors. Liu （2003） introduced a composite test for correlation and heteroscedasticity in nonlinear models with DBL（p, 0, 1） errors. Therefore, the important problems in regression model axe detections of bilinearity, correlation and heteroscedasticity. In this article, the authors discuss more general case of nonlinear models with DBL（p, q, 1） random errors by score test. Several statistics for the test of bilinearity, correlation, and heteroscedasticity are obtained, and expressed in simple matrix formulas. The results of regression models with linear errors are extended to those with bilinear errors. The simulation study is carried out to investigate the powers of the test statistics. All results of this article extend and develop results of Tsai （1986）, Wei, et al （1995）, and Liu, et al （2003）.
文摘This paper constructs a set of confidence regions of parameters in terms of statistical curvatures for AR(q) nonlinear regression models. The geometric frameworks are proposed for the model. Then several confidence regions for parameters and parameter subsets in terms of statistical curvatures are given based on the likelihood ratio statistics and score statistics. Several previous results, such as [1] and [2] are extended to AR(q) nonlinear regression models.
文摘Assume that in the nonlinear regression model, independent variable sequence {xi, i ≥ 1} is a known constant-vector sequence. This article proposes a condition on {xi}, which can be tested and verified easily. The condition is essential for proving the consistency and asymptotic normality of the estimator.
基金Supported by the National Natural Science Foundation of China(10272109)。
文摘In order to reduce the influence of outliers on the parameter estimate of the attenuation formula for the blasting vibration velocity,a fuzzy nonlinear regression method of Sadov’s vibration formula was proposed on the basis of the fuzziness of blasting engineering,and the algorithm was described in details as well.In accordance with an engineering case,the vibration attenuation formula was regressed by the fuzzy nonlinear regression method and the nonlinear least square method,respectively.The calculation results showed that the fuzzy nonlinear regression method is more suitable to the field test data.It differs from the nonlinear least square method because the weight of residual square in the objective function can be adjusted according to the membership of each data.And the deviation calculation of least square estimate of parameters in the nonlinear regression model verified the rationality of using the membership to assign the weight of residual square.The fuzzy nonlinear regression method provides a calculation basis for estimating Sadov’s vibration formula’s parameters more accurately.
基金Supported by the NSSFC(02BTJ001) Supported by the NSSFC(04BTJ002) Supported by the Grant for Post-Doctorial Fellows in Southeast University
文摘This paper is devoted to a study of geometric properties of AR(q) nonlinear regression models. We present geometric frameworks for regression parameter space and autoregression parameter space respectively based on the weighted inner product by fisher information matrix. Several geometric properties related to statistical curvatures are given for the models. The results of this paper extended the work of Bates & Watts(1980,1988)[1.2] and Seber & Wild (1989)[3].
文摘The effects of centering response and explanatory variables as a way of simplifying fitted linear models in the presence of correlation are reviewed and extended to include nonlinear models, common in many biological and economic applications. In a nonlinear model, the use of a local approximation can modify the effect of centering. Even in the presence of uncorrelated explanatory variables, centering may affect linear approximations and related test statistics. An approach to assessing this effect in relation to intrinsic curvature is developed and applied. Mis-specification bias of linear versus nonlinear models also reflects this centering effect.
基金funded by the National Natural Science Foundation of China(Grant No.42372194)the Natural Science Foundation of Shanxi Province,China(No.20210302123165),the Chinese Postdoctoral Science Foundation(No.2024T170634)the Open Fund Project of Provincial Center of Technology Innovation for Coal Measure Gas Co-production(ZZGSSASMCYJ2024-0306).
文摘Total organic carbon(TOC)content is a crucial evaluation parameter in the process of shale gas exploration and development.Marine-continental transitional shale is characterized by strong heterogeneity and thin single-layer thickness.The discrete TOC data measured by experimental methods are unable to accurately reflect the reservoir characteristics of marine-continental transitional shale.In this paper,a multivariate nonlinear regression prediction model(R-MNR)was established,and the model was applied to predict the TOC content of shale for the first time.TheΔlgR model,multiple linear regression model(MLR),BP neural network model(BP model),and R-MNR model were built to predict the TOC of shale in Benxi Formation.The coefficient of determination(R2),mean-absolute-percentage-error(MAPE),root-mean-square-error(RMSE),and the number of input layer parameters(NILP)were employed to assess the efficacy of the model through the analytic hierarchy process(AHP)method.The total weight of R-MNR is 0.361,and that of BP model is 0.336.The weights of the two traditional models are 0.104 and 0.199,respectively.The results indicate that the R-MNR is comparable to the BP model in terms of prediction accuracy,and both models are significantly more accurate than the traditional prediction model.The R-MNR is capable of obtaining a clear TOC prediction formula,which is convenient for verification and promotion.During the training process of the R-MNR,the influence of each parameter and coupling relationship on the prediction results is elucidated,which enables researchers to gain a deeper understanding of the geophysical significance and geological process of the model.The result of this study suggests that the R-MNR can be employed to predict the TOC content of marine-continental transitional shale effectively in the future.
文摘Triaxial tests,a staple in rock engineering,are labor-intensive,sample-demanding,and costly,making their optimization highly advantageous.These tests are essential for characterizing rock strength,and by adopting a failure criterion,they allow for the derivation of criterion parameters through regression,facilitating their integration into modeling programs.In this study,we introduce the application of an underutilized statistical technique—orthogonal regression—well-suited for analyzing triaxial test data.Additionally,we present an innovation in this technique by minimizing the Euclidean distance while incorporating orthogonality between vectors as a constraint,for the case of orthogonal linear regression.Also,we consider the Modified Least Squares method.We exemplify this approach by developing the necessary equations to apply the Mohr-Coulomb,Murrell,Hoek-Brown,andÚcar criteria,and implement these equations in both spreadsheet calculations and R scripts.Finally,we demonstrate the technique's application using five datasets of varied lithologies from specialized literature,showcasing its versatility and effectiveness.
基金National Natural Science Foundation of China(Grant Nos.11901006 and 11601008)Natural Science Foundation of Anhui Province(Grant No.1908085QA06)。
文摘In this paper,we propose a new numerical scheme for the coupled Stokes-Darcy model with the Beavers-Joseph-Saffman interface condition.We use the weak Galerkin method to discretize the Stokes equation and the mixed finite element method to discretize the Darcy equation.A discrete inf-sup condition is proved and the optimal error estimates are also derived.Numerical experiments validate the theoretical analysis.
文摘In the recent era,piled raft foundation(PRF)has been considered an emergent technology for offshore and onshore structures.In previous studies,there is a lack of illustration regarding the load sharing and interaction behavior which are considered the main intents in the present study.Finite element(FE)models are prepared with various design variables in a double-layer soil system,and the load sharing and interaction factors of piled rafts are estimated.The obtained results are then checked statistically with nonlinear multiple regression(NMR)and artificial neural network(ANN)modeling,and some prediction models are proposed.ANN models are prepared with Levenberg-Marquardt(LM)algorithm for load sharing and interaction factors through backpropagation technique.The factor of safety(FS)of PRF is also estimated using the proposed NMR and ANN models,which can be used for developing the design strategy of PRF.
基金Project supported by the National Natural Science Foundation of China and the State Education Commission of China.
文摘A kinetic nonlinear regression model for multi-component assay of esters was proposed based on their different alkaline-catalysed hydrolysis rate. The reaction rate was determined by monitoring the conductance change in solution with a liquid-purpose surface acoustic wave impedance sensor(SAW). The model was tested theoretically and experimentally with the mixture of methyl acetate and n-propyl acetate. The experimental detection limit of methyl acetate and n-propyl acetate (within 10 min) was 0.5 mu mol/L and 1.0 mu mol/L respectively and the recovery of the sensor system ranged from 93% to 106% (n=6).
文摘In this paper,we consider a class of nonlinear regression problems without the assumption of being independent and identically distributed.We propose a correspondent mini-max problem for nonlinear regression and give a numerical algorithm.Such an algorithm can be applied in regression and machine learning problems,and yields better results than traditional least squares and machine learning methods.
基金supported by the National Natural Science Foundation of China(Grant No.51969013)the Natural Science Foundation of Gansu Province(Grant No.21JR7RA225).
文摘Moistube irrigation is a new micro-irrigation technology.Accurately estimating its wetting pattern dimensions presents a challenge.Therefore,it is necessary to develop models for efficient assessment of the wetting transport pattern in order to design a cost-effective moistube irrigation system.To achieve this goal,this study developed a multivariate nonlinear regression model and compared it with a dimensional model.HYDRUS-2D was used to perform numerical simulations of 56 irrigation scenarios with different factors.The experiments showed that the shape of the wetting soil body approximated a cylinder and was mainly affected by soil texture,pressure head,and matric potential.A multivariate nonlinear model using a power function relationship between wetting size and irrigation time was developed,with a determination coefficient greater than 0.99.The model was validated for cases with six soil texture types,with mean average absolute errors of 0.43-0.90 cm,root mean square errors of 0.51-0.95 cm,and mean deviation percentage values of 3.23%-6.27%.The multivariate nonlinear regression model outperformed the dimensional model.It can therefore provide a scientific foundation for the development of moistube irrigation systems.
文摘In oil and gas exploration,elucidating the complex interdependencies among geological variables is paramount.Our study introduces the application of sophisticated regression analysis method at the forefront,aiming not just at predicting geophysical logging curve values but also innovatively mitigate hydrocarbon depletion observed in geochemical logging.Through a rigorous assessment,we explore the efficacy of eight regression models,bifurcated into linear and nonlinear groups,to accommodate the multifaceted nature of geological datasets.Our linear model suite encompasses the Standard Equation,Ridge Regression,Least Absolute Shrinkage and Selection Operator,and Elastic Net,each presenting distinct advantages.The Standard Equation serves as a foundational benchmark,whereas Ridge Regression implements penalty terms to counteract overfitting,thus bolstering model robustness in the presence of multicollinearity.The Least Absolute Shrinkage and Selection Operator for variable selection functions to streamline models,enhancing their interpretability,while Elastic Net amalgamates the merits of Ridge Regression and Least Absolute Shrinkage and Selection Operator,offering a harmonized solution to model complexity and comprehensibility.On the nonlinear front,Gradient Descent,Kernel Ridge Regression,Support Vector Regression,and Piecewise Function-Fitting methods introduce innovative approaches.Gradient Descent assures computational efficiency in optimizing solutions,Kernel Ridge Regression leverages the kernel trick to navigate nonlinear patterns,and Support Vector Regression is proficient in forecasting extremities,pivotal for exploration risk assessment.The Piecewise Function-Fitting approach,tailored for geological data,facilitates adaptable modeling of variable interrelations,accommodating abrupt data trend shifts.Our analysis identifies Ridge Regression,particularly when augmented by Piecewise Function-Fitting,as superior in recouping hydrocarbon losses,and underscoring its utility in resource quantification refinement.Meanwhile,Kernel Ridge Regression emerges as a noteworthy strategy in ameliorating porosity-logging curve prediction for well A,evidencing its aptness for intricate geological structures.This research attests to the scientific ascendancy and broad-spectrum relevance of these regression techniques over conventional methods while heralding new horizons for their deployment in the oil and gas sector.The insights garnered from these advanced modeling strategies are set to transform geological and engineering practices in hydrocarbon prediction,evaluation,and recovery.
文摘In this work, we seek the relationship between the order of the polynomial model and the number of knots and intervals that we need to fit the splines regression model. Regression models (polynomial and spline regression models) are presented and discussed in detail in order to discover the relation. Intrinsically, both models are dependent on the linear regression model. Spline is designed to draw curves to balance the goodness of fit and minimize the mean square error of the regression model. In the splines model, the curve at any point depends only on the observations at that point and some specified neighboring points. Using the boundaries of the intervals of the splines, we fit a smooth cubic interpolation function that goes through (n + 1) data points. On the other hand, polynomial regression is a useful technique when the pattern of the data indicates a nonlinear relationship between the dependent and independent variables. Moreover, higher-degree polynomials can capture more intricate patterns, but it can also lead to overfitting. A simulation study is implemented to illustrate the performance of splines and spline segments based on the degree of the polynomial model. For each model, we compute the Akaike Information Criterion (AIC) and Bayesian Information Criterion (BIC) to compare the optimal polynomial order for fitting the data with the number of knots and intervals for the splines model. Both AIC and BIC can help to identify the model that best balances fit and complexity, aiming to prevent overfitting by penalizing the use of excessive parameters. We compare the results that we got from applying the polynomial regression model with the splines model results in terms of point estimates, the mean sum of squared errors, and the fitted regression line. We can say that order five of the polynomial model may be used to estimate splines with five segments.
