Journal of Environmental Science Health Part a, Dec 15, 2008
A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis ... more A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis with a single set of coefficients. The model is predicated on the assumption that two types of adsorption sites are present on the sorbent. At the first type of sites, solutes are irreversibly adsorbed in an amount related to the highest concentration at which the sorbent was exposed. Adsorption at the other sites is completely reversible and non‐hysteretic. The total adsorption is the sum of the two. However, when the equilibrium concentration is decreased, only the reversible component desorbs. Experimental protocol and mathematical techniques are presented for calibrating and verifying the model. The model is capable of predicting continuous flow column behavior based upon batch isotherm data.
Journal of Environmental Science and Health . Part A: Environmental Science and Engineering, 1988
A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis ... more A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis with a single set of coefficients. The model is predicated on the assumption that two types of adsorption sites are present on the sorbent. At the first type of sites, solutes are irreversibly adsorbed in an amount related to the highest concentration at which the sorbent was exposed. Adsorption at the other sites is completely reversible and non‐hysteretic. The total adsorption is the sum of the two. However, when the equilibrium concentration is decreased, only the reversible component desorbs. Experimental protocol and mathematical techniques are presented for calibrating and verifying the model. The model is capable of predicting continuous flow column behavior based upon batch isotherm data.
Nonlinear response results of a gravity-load carrying column member subjected to close-standoff b... more Nonlinear response results of a gravity-load carrying column member subjected to close-standoff blast loading of varying size are used to apply Multivariable Polynomial Regression (MPR) aiming to parameterize and optimize blast-resistant design. The MPR approach combines the advantages of other modeling approaches, such as multilinear regression and artificial neural networks in that it produces simple, transparent models as in the former method, but can accurately capture complex behavior as with the latter. The modeling approach is intriguing in regard to the following: (a) the method accounts for multidimensional interaction of design variables geometrically visualized by a response surface in three-dimensional space, where the axes are the governing parameters; (b) the response surface is mathematically expressed by a polynomial function with polynomial terms found by statistical best-fit criteria. These terms visualize the multivariable interactions and prioritize the design wh...
IEEE/IAFE 1996 Conference on Computational Intelligence for Financial Engineering (CIFEr), 1996
ABSTRACT A new class of models is proposed for use in economic correlation and forecasting. The n... more ABSTRACT A new class of models is proposed for use in economic correlation and forecasting. The new model, termed the multivariable polynomial regression (MPR) model, is essentially a multiple regression model with polynomial and cross-product (interaction) terms. For example, if Y is a function of Q, R, and S, terms can be included such as QR2S or Q3S. MPR models can be fitted using conventional multiple regression software, although an automated program facilitates the analysis. Only terms which are statistically significant are retained in the model. MPR models are likely to be applicable to low-to-moderate dimensionality problems as are encountered in economics. If the number of independent variables is not too great, MPR models compare favorably to artificial neural network (ANN) models: MPR models can provide a better fit with fewer coefficients; as a result there is less overfitting of “memorizing” of data; the fitting procedure converges absolutely; MPR models result in a simple explicit equation for prediction or analysis; standard statistical tests can be applied to all coefficients and forecast predictions. The technique was applied to correlation of the performance of retail stores to a set of thirteen potential causative variables. An MPR model was developed which was able to explain 82% of the variation in the gross margin of the stores under study
... Assuming an homogeneous initial concentration distribution (Co), and zero surface concentrati... more ... Assuming an homogeneous initial concentration distribution (Co), and zero surface concentration, the Fickian model for semiinfinite plate can be presented as (Batchelor, 1990): C(x,t) = Co • erf (1) where C(x,t) is the concentration ...
A formulation to calculate the mean cell residence time (MCRT or sludge age) of unsteady-state ac... more A formulation to calculate the mean cell residence time (MCRT or sludge age) of unsteady-state activated sludge systems is presented. The formulation was studied by applying it to data generated by computer simulation and to data obtained from an actual wastewater treatment plant. The computer simulation study allowed the effects of step and pulse changes in biochemical oxygen demand (BOD) loading, and step changes in a control variable, waste sludge flow rate, to be studied independently of each other and of other disturbances. The unsteady-state MCRT formulation (herein called the dynamic sludge age, or DSA) was found to be an improvement over the traditional steady-state calculation, both for process control, and for research into activated sludge dynamics.
Journal of Environmental Science Health Part a, Dec 15, 2008
A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis ... more A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis with a single set of coefficients. The model is predicated on the assumption that two types of adsorption sites are present on the sorbent. At the first type of sites, solutes are irreversibly adsorbed in an amount related to the highest concentration at which the sorbent was exposed. Adsorption at the other sites is completely reversible and non‐hysteretic. The total adsorption is the sum of the two. However, when the equilibrium concentration is decreased, only the reversible component desorbs. Experimental protocol and mathematical techniques are presented for calibrating and verifying the model. The model is capable of predicting continuous flow column behavior based upon batch isotherm data.
Journal of Environmental Science and Health . Part A: Environmental Science and Engineering, 1988
A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis ... more A model is proposed which is capable of describing non‐linear irreversible adsorption hysteresis with a single set of coefficients. The model is predicated on the assumption that two types of adsorption sites are present on the sorbent. At the first type of sites, solutes are irreversibly adsorbed in an amount related to the highest concentration at which the sorbent was exposed. Adsorption at the other sites is completely reversible and non‐hysteretic. The total adsorption is the sum of the two. However, when the equilibrium concentration is decreased, only the reversible component desorbs. Experimental protocol and mathematical techniques are presented for calibrating and verifying the model. The model is capable of predicting continuous flow column behavior based upon batch isotherm data.
Nonlinear response results of a gravity-load carrying column member subjected to close-standoff b... more Nonlinear response results of a gravity-load carrying column member subjected to close-standoff blast loading of varying size are used to apply Multivariable Polynomial Regression (MPR) aiming to parameterize and optimize blast-resistant design. The MPR approach combines the advantages of other modeling approaches, such as multilinear regression and artificial neural networks in that it produces simple, transparent models as in the former method, but can accurately capture complex behavior as with the latter. The modeling approach is intriguing in regard to the following: (a) the method accounts for multidimensional interaction of design variables geometrically visualized by a response surface in three-dimensional space, where the axes are the governing parameters; (b) the response surface is mathematically expressed by a polynomial function with polynomial terms found by statistical best-fit criteria. These terms visualize the multivariable interactions and prioritize the design wh...
IEEE/IAFE 1996 Conference on Computational Intelligence for Financial Engineering (CIFEr), 1996
ABSTRACT A new class of models is proposed for use in economic correlation and forecasting. The n... more ABSTRACT A new class of models is proposed for use in economic correlation and forecasting. The new model, termed the multivariable polynomial regression (MPR) model, is essentially a multiple regression model with polynomial and cross-product (interaction) terms. For example, if Y is a function of Q, R, and S, terms can be included such as QR2S or Q3S. MPR models can be fitted using conventional multiple regression software, although an automated program facilitates the analysis. Only terms which are statistically significant are retained in the model. MPR models are likely to be applicable to low-to-moderate dimensionality problems as are encountered in economics. If the number of independent variables is not too great, MPR models compare favorably to artificial neural network (ANN) models: MPR models can provide a better fit with fewer coefficients; as a result there is less overfitting of “memorizing” of data; the fitting procedure converges absolutely; MPR models result in a simple explicit equation for prediction or analysis; standard statistical tests can be applied to all coefficients and forecast predictions. The technique was applied to correlation of the performance of retail stores to a set of thirteen potential causative variables. An MPR model was developed which was able to explain 82% of the variation in the gross margin of the stores under study
... Assuming an homogeneous initial concentration distribution (Co), and zero surface concentrati... more ... Assuming an homogeneous initial concentration distribution (Co), and zero surface concentration, the Fickian model for semiinfinite plate can be presented as (Batchelor, 1990): C(x,t) = Co • erf (1) where C(x,t) is the concentration ...
A formulation to calculate the mean cell residence time (MCRT or sludge age) of unsteady-state ac... more A formulation to calculate the mean cell residence time (MCRT or sludge age) of unsteady-state activated sludge systems is presented. The formulation was studied by applying it to data generated by computer simulation and to data obtained from an actual wastewater treatment plant. The computer simulation study allowed the effects of step and pulse changes in biochemical oxygen demand (BOD) loading, and step changes in a control variable, waste sludge flow rate, to be studied independently of each other and of other disturbances. The unsteady-state MCRT formulation (herein called the dynamic sludge age, or DSA) was found to be an improvement over the traditional steady-state calculation, both for process control, and for research into activated sludge dynamics.
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