To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, th...To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.展开更多
Two universal spectral ranges(4550-4100 cm^(-1) and 6190-5510 cm^(-1))for construction of quantitative models of homologous analogs of cephalosporins were proposed by evaluating theperformance of five spectral ranges ...Two universal spectral ranges(4550-4100 cm^(-1) and 6190-5510 cm^(-1))for construction of quantitative models of homologous analogs of cephalosporins were proposed by evaluating theperformance of five spectral ranges and their combinations,using three data sets of cephalos-porins for injection,ie.,cefuroxime sodium,cetriaxone sodium and cefoperazone sodium.Subsequently,the proposed ranges were validated by using eight calibration sets of otherhomologous analogs of cephalosporins for injection,namely cefmenoxime hydrochloride,ceftezole sodium,cefmetazole,cefoxitin sodium,cefotaxime sodium,cefradine,cephazolin sodium and ceftizoxime sodium.All the constructed quantitative models for the eight kinds of cephalosporinsusing these universal ranges could fulill the requirements for quick quantification.After that,competitive adaptive reweighted sampling(CARS)algorithm and infrared(IR)-near infrared(NIR)two-dimensional(2D)correlation spectral analysis were used to determine the scientific basis of these two spectral ranges as the universal regions for the construction of quantitativemodels of cephalosporins.The CAR.S algorithm demonstrated that the ranges of 4550-4100 cm^(-1) and 6190-5510 cm^(-1) included some key wavenumbers which could be attributed to content changes of cephalosporins.The IR-NIR 2D spectral analysis showed that certain wavenumbersin these two regions have strong correlations to the structures of those cephalosporins that wereeasy to degrade.展开更多
基金National Hi-Tech Research and Development Program of China (863 Program) Under Grant No. 2006AA04Z416Nation Natural Science Foundation of China Under Grant No. 50725828
文摘To overcome excessive computation errors and convergence failures encountered in an iterative calculation of the reliability index using the response surface method （RSM） for some nonlinear limit state functions, this study investigates an essential factor based on chaotic dynamics theory. The bifurcation diagrams of the reliability index are presented for some typical nonlinear limit state functions, and the computation results from the mapping functions due to the RSM iterations show the complicated dynamic phenomena such as the periodic oscillation, as well as bifurcation and chaos. From the numerical examples, it is concluded that the parameter of selection range fplays an important role in the convergence of the RSM iteration, and an improved RSM iterative algorithm is proposed with regard to the incorporation of the iterative sequential function of selection rangef The proposed method is shown to be efficient and to yield accurate results.
基金supported by grant from the National Department Public Benefit Research Foundation(General Administration of Quality Supervision,inspection and Quarantine of the People's Republicof China)(Grant No.2012104008)At the sametime,the authors would like to thank Prof Yi zeng Liang(Central South University,PR China)for freely providing us with CARS program。
文摘Two universal spectral ranges(4550-4100 cm^(-1) and 6190-5510 cm^(-1))for construction of quantitative models of homologous analogs of cephalosporins were proposed by evaluating theperformance of five spectral ranges and their combinations,using three data sets of cephalos-porins for injection,ie.,cefuroxime sodium,cetriaxone sodium and cefoperazone sodium.Subsequently,the proposed ranges were validated by using eight calibration sets of otherhomologous analogs of cephalosporins for injection,namely cefmenoxime hydrochloride,ceftezole sodium,cefmetazole,cefoxitin sodium,cefotaxime sodium,cefradine,cephazolin sodium and ceftizoxime sodium.All the constructed quantitative models for the eight kinds of cephalosporinsusing these universal ranges could fulill the requirements for quick quantification.After that,competitive adaptive reweighted sampling(CARS)algorithm and infrared(IR)-near infrared(NIR)two-dimensional(2D)correlation spectral analysis were used to determine the scientific basis of these two spectral ranges as the universal regions for the construction of quantitativemodels of cephalosporins.The CAR.S algorithm demonstrated that the ranges of 4550-4100 cm^(-1) and 6190-5510 cm^(-1) included some key wavenumbers which could be attributed to content changes of cephalosporins.The IR-NIR 2D spectral analysis showed that certain wavenumbersin these two regions have strong correlations to the structures of those cephalosporins that wereeasy to degrade.
