Chloride ion transport in reclaimed soil solutions filled with fly ash （FA） was investigated by measuring the hydraulic parameters （i,e. water retention curves and hydraulic conductivity） of three substrates, name...Chloride ion transport in reclaimed soil solutions filled with fly ash （FA） was investigated by measuring the hydraulic parameters （i,e. water retention curves and hydraulic conductivity） of three substrates, namely GSL, GFA, and CFA. Similar simulations were carried out under certain weather conditions. The different boundary conditions of chloride transport were also discussed from FA texture, cover soil thickness, groundwater table level, and initial chloride concentration. Furthermore, the sensitivities of chloride ions to these effect factors were analyzed. The results show that the different top soil thickness and initial chloride concentration have no effect on salinity of topsoil solution in the monitoring points, but they can clearly change the chloride concentration of FA layers. The sensibilities from top soil thickness and initial chloride content are exceedingly weak to the salinity balance based on two dimensions of the time and concentration. While the different FA texture and groundwater table not only affect the salinity equilibrium process of the whole reclaimed soil profile, but also change its balance state. Generally, coarse FA particles and high groundwater table can defer the salinity balance process of the reclaimed soil solution, and they also increase the chloride concentration of FA layer solutions, and even topsoil ones.展开更多
As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely use...As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.展开更多
This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>...This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (<em>i.e.</em>, model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2<sup>nd</sup>-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1<sup>st</sup>-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2<sup>nd</sup>-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (<em>N</em>2/2 + 3 <em>N</em>/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2<sup>nd</sup>-LASS requires very little additional effort beyond the construction of the 1<sup>st</sup>-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1<sup>st</sup>-LASS and 2<sup>nd</sup>-LASS requires the same computational solvers as needed for solving (<em>i.e.</em>, “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1<sup>st</sup>-LASS and the 2<sup>nd</sup>-LASS. Since neither the 1<sup>st</sup>-LASS nor the 2<sup>nd</sup>-LASS involves any differentials of the operators underlying the original system, the 1<sup>st</sup>-LASS is designated as a “<u>first-level</u>” (as opposed to a “first-order”) adjoint sensitivity system, while the 2<sup>nd</sup>-LASS is designated as a “<u>second-level</u>” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2<sup>nd</sup>-LASS that involve the imprecisely known boundary parameters. Notably, the 2<sup>nd</sup>-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.展开更多
This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the...This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the n<sup>th</sup>-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the n<sup>th</sup>-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the n<sup>th</sup>-FASAM-N methodology becomes identical to the extant n<sup>th</sup> CASAM-N (“n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.展开更多
基金Supported by the National Natural Science Foundation of China （51274013） the International Cooperation Projects of Anhui, China （10080703026） Acknowledgements We thank the work group of soil information systems and solute transport models from Osnabrueck University of Applied Sciences, Germany for providing us their experimental work.
文摘Chloride ion transport in reclaimed soil solutions filled with fly ash （FA） was investigated by measuring the hydraulic parameters （i,e. water retention curves and hydraulic conductivity） of three substrates, namely GSL, GFA, and CFA. Similar simulations were carried out under certain weather conditions. The different boundary conditions of chloride transport were also discussed from FA texture, cover soil thickness, groundwater table level, and initial chloride concentration. Furthermore, the sensitivities of chloride ions to these effect factors were analyzed. The results show that the different top soil thickness and initial chloride concentration have no effect on salinity of topsoil solution in the monitoring points, but they can clearly change the chloride concentration of FA layers. The sensibilities from top soil thickness and initial chloride content are exceedingly weak to the salinity balance based on two dimensions of the time and concentration. While the different FA texture and groundwater table not only affect the salinity equilibrium process of the whole reclaimed soil profile, but also change its balance state. Generally, coarse FA particles and high groundwater table can defer the salinity balance process of the reclaimed soil solution, and they also increase the chloride concentration of FA layer solutions, and even topsoil ones.
基金supported by National Key Basic Research Program (973 Program, Grant No. 2011CB706804)National Natural Science Foundation of China (Grant No. 50805093)Science & Technology Commission of Shanghai Municipality, China (Grant No. 09QH1401500)
文摘As one of the bases of gradient-based optimization algorithms, sensitivity analysis is usually required to calculate the derivatives of the system response with respect to the machining parameters. The most widely used approaches for sensitivity analysis are based on time-consuming numerical methods, such as finite difference methods. This paper presents a semi-analytical method for calculation of the sensitivity of the stability boundary in milling. After transforming the delay-differential equation with time-periodic coefficients governing the dynamic milling process into the integral form, the Floquet transition matrix is constructed by using the numerical integration method. Then, the analytical expressions of derivatives of the Floquet transition matrix with respect to the machining parameters are obtained. Thereafter, the classical analytical expression of the sensitivity of matrix eigenvalues is employed to calculate the sensitivity of the stability lobe diagram. The two-degree-of-freedom milling example illustrates the accuracy and efficiency of the proposed method. Compared with the existing methods, the unique merit of the proposed method is that it can be used for analytically computing the sensitivity of the stability boundary in milling, without employing any finite difference methods. Therefore, the high accuracy and high efficiency are both achieved. The proposed method can serve as an effective tool for machining parameter optimization and uncertainty analysis in high-speed milling.
文摘This work presents the “Second-Order Comprehensive Adjoint Sensitivity Analysis Methodology (2<sup>nd</sup>-CASAM)” for the efficient and exact computation of 1<sup>st</sup>- and 2<sup>nd</sup>-order response sensitivities to uncertain parameters and domain boundaries of linear systems. The model’s response (<em>i.e.</em>, model result of interest) is a generic nonlinear function of the model’s forward and adjoint state functions, and also depends on the imprecisely known boundaries and model parameters. In the practically important particular case when the response is a scalar-valued functional of the forward and adjoint state functions characterizing a model comprising N parameters, the 2<sup>nd</sup>-CASAM requires a single large-scale computation using the First-Level Adjoint Sensitivity System (1<sup>st</sup>-LASS) for obtaining all of the first-order response sensitivities, and at most N large-scale computations using the Second-Level Adjoint Sensitivity System (2<sup>nd</sup>-LASS) for obtaining exactly all of the second-order response sensitivities. In contradistinction, forward other methods would require (<em>N</em>2/2 + 3 <em>N</em>/2) large-scale computations for obtaining all of the first- and second-order sensitivities. This work also shows that constructing and solving the 2<sup>nd</sup>-LASS requires very little additional effort beyond the construction of the 1<sup>st</sup>-LASS needed for computing the first-order sensitivities. Solving the equations underlying the 1<sup>st</sup>-LASS and 2<sup>nd</sup>-LASS requires the same computational solvers as needed for solving (<em>i.e.</em>, “inverting”) either the forward or the adjoint linear operators underlying the initial model. Therefore, the same computer software and “solvers” used for solving the original system of equations can also be used for solving the 1<sup>st</sup>-LASS and the 2<sup>nd</sup>-LASS. Since neither the 1<sup>st</sup>-LASS nor the 2<sup>nd</sup>-LASS involves any differentials of the operators underlying the original system, the 1<sup>st</sup>-LASS is designated as a “<u>first-level</u>” (as opposed to a “first-order”) adjoint sensitivity system, while the 2<sup>nd</sup>-LASS is designated as a “<u>second-level</u>” (rather than a “second-order”) adjoint sensitivity system. Mixed second-order response sensitivities involving boundary parameters may arise from all source terms of the 2<sup>nd</sup>-LASS that involve the imprecisely known boundary parameters. Notably, the 2<sup>nd</sup>-LASS encompasses an automatic, inherent, and independent “solution verification” mechanism of the correctness and accuracy of the 2nd-level adjoint functions needed for the efficient and exact computation of the second-order sensitivities.
文摘This work presents the “n<sup>th</sup>-Order Feature Adjoint Sensitivity Analysis Methodology for Nonlinear Systems” (abbreviated as “n<sup>th</sup>-FASAM-N”), which will be shown to be the most efficient methodology for computing exact expressions of sensitivities, of any order, of model responses with respect to features of model parameters and, subsequently, with respect to the model’s uncertain parameters, boundaries, and internal interfaces. The unparalleled efficiency and accuracy of the n<sup>th</sup>-FASAM-N methodology stems from the maximal reduction of the number of adjoint computations (which are considered to be “large-scale” computations) for computing high-order sensitivities. When applying the n<sup>th</sup>-FASAM-N methodology to compute the second- and higher-order sensitivities, the number of large-scale computations is proportional to the number of “model features” as opposed to being proportional to the number of model parameters (which are considerably more than the number of features).When a model has no “feature” functions of parameters, but only comprises primary parameters, the n<sup>th</sup>-FASAM-N methodology becomes identical to the extant n<sup>th</sup> CASAM-N (“n<sup>th</sup>-Order Comprehensive Adjoint Sensitivity Analysis Methodology for Nonlinear Systems”) methodology. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N methodologies are formulated in linearly increasing higher-dimensional Hilbert spaces as opposed to exponentially increasing parameter-dimensional spaces thus overcoming the curse of dimensionality in sensitivity analysis of nonlinear systems. Both the n<sup>th</sup>-FASAM-N and the n<sup>th</sup>-CASAM-N are incomparably more efficient and more accurate than any other methods (statistical, finite differences, etc.) for computing exact expressions of response sensitivities of any order with respect to the model’s features and/or primary uncertain parameters, boundaries, and internal interfaces.
