Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple...Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative method to CEMS, which use gas analyzers, they can provide cost savings and substantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.展开更多
An improved parallel multiple-precision Taylor(PMT) scheme is developed to obtain clean numerical simulation(CNS) solutions of chaotic ordinary differential equations(ODEs). The new version program is about 500 times ...An improved parallel multiple-precision Taylor(PMT) scheme is developed to obtain clean numerical simulation(CNS) solutions of chaotic ordinary differential equations(ODEs). The new version program is about 500 times faster than the reported solvers developed in the MATHEMATICA, and also 2–3 times faster than the older version(PMT-1.0) of the scheme. This solver has the ability to yield longer solutions of Lorenz equations [up to5000 TU(time unit)]. The PMT-1.1 scheme is applied to a selection of chaotic systems including the Chen, Rossler,coupled Lorenz and Lu¨ systems. The Tc-M and Tc-K diagrams for these chaotic systems are presented and used to analyze the computation parameters for long-term solutions. The reliable computation times of these chaotic equations are obtained for single- and double-precision computation.展开更多
In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution o...In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.展开更多
文摘Predictive Emission Monitoring Systems (PEMS) offer a cost-effective and environmentally friendly alternative to Continuous Emission Monitoring Systems (CEMS) for monitoring pollution from industrial sources. Multiple regression is one of the fundamental statistical techniques to describe the relationship between dependent and independent variables. This model can be effectively used to develop a PEMS, to estimate the amount of pollution emitted by industrial sources, where the fuel composition and other process-related parameters are available. It often makes them sufficient to predict the emission discharge with acceptable accuracy. In cases where PEMS are accepted as an alternative method to CEMS, which use gas analyzers, they can provide cost savings and substantial benefits for ongoing system support and maintenance. The described mathematical concept is based on the matrix algebra representation in multiple regression involving multiple precision arithmetic techniques. Challenging numerical examples for statistical big data analysis, are investigated. Numerical examples illustrate computational accuracy and efficiency of statistical analysis due to increasing the precision level. The programming language C++ is used for mathematical model implementation. The data for research and development, including the dependent fuel and independent NOx emissions data, were obtained from CEMS software installed on a petrochemical plant.
基金supported by the National Basic Research Program of China(2011CB309704)the National Natural Science Foundation of China(41375112)
文摘An improved parallel multiple-precision Taylor(PMT) scheme is developed to obtain clean numerical simulation(CNS) solutions of chaotic ordinary differential equations(ODEs). The new version program is about 500 times faster than the reported solvers developed in the MATHEMATICA, and also 2–3 times faster than the older version(PMT-1.0) of the scheme. This solver has the ability to yield longer solutions of Lorenz equations [up to5000 TU(time unit)]. The PMT-1.1 scheme is applied to a selection of chaotic systems including the Chen, Rossler,coupled Lorenz and Lu¨ systems. The Tc-M and Tc-K diagrams for these chaotic systems are presented and used to analyze the computation parameters for long-term solutions. The reliable computation times of these chaotic equations are obtained for single- and double-precision computation.
文摘In order to find stable, accurate, and computationally efficient methods for performing the inverse Laplace transform, a new double transformation approach is proposed. To validate and improve the inversion solution obtained using the Gaver-Stehfest algorithm, direct Laplace transforms are taken of the numerically inverted transforms to compare with the original function. The numerical direct Laplace transform is implemented with a composite Simpson’s rule. Challenging numerical examples involving periodic and oscillatory functions, are investigated. The numerical examples illustrate the computational accuracy and efficiency of the direct Laplace transform and its inverse due to increasing the precision level and the number of terms included in the expansion. It is found that the number of expansion terms and the precision level selected must be in a harmonious balance in order for correct and stable results to be obtained.
