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
Particle filtering （PF） is being applied successfully in nonlinear and/or non-Gaussian system failure prognosis. However, for failure prediction of many complex systems whose dynamic state evolution models involve t...Particle filtering （PF） is being applied successfully in nonlinear and/or non-Gaussian system failure prognosis. However, for failure prediction of many complex systems whose dynamic state evolution models involve time-varying parameters, the tradi- tional PF-based prognosis framework will probably generate serious deviations in results since it implements prediction through iterative calculation using the state models. To address the problem, this paper develops a novel integrated PF-LSSVR frame- work based on PF and least squares support vector regression （LSSVR） for nonlinear system failure prognosis. This approach employs LSSVR for long-term observation series prediction and applies PF-based dual estimation to collaboratively estimate the values of system states and parameters of the corresponding future time instances. Meantime, the propagation of prediction un- certainty is emphatically taken into account. Therefore, PF-LSSVR avoids over-dependency on system state models in prediction phase. With a two-sided failure definition, the probability distribution of system remaining useful life （RUL） is accessed and the corresponding methods of calculating performance evaluation metrics are put forward. The PF-LSSVR framework is applied to a three-vessel water tank system failure prognosis and it has much higher prediction accuracy and confidence level than traditional PF-based framework.展开更多
I. INSTRUCTIONThe study of the acoustic nonlinearity parameter B/A in the biological medium has been of the basic importance and has been treated as the frontier in the field of biomedical acoustics since 1980 when th...I. INSTRUCTIONThe study of the acoustic nonlinearity parameter B/A in the biological medium has been of the basic importance and has been treated as the frontier in the field of biomedical acoustics since 1980 when the nonlinear acoustic effects were found in that area. In those years, the measurement of B/A shows that B/A value varies with the physical,展开更多
Understanding language competition and extinction is an interdisciplinary challenge, and math models provide a tool for interpreting linguistic census data and possibly predict the language shift trend at the populati...Understanding language competition and extinction is an interdisciplinary challenge, and math models provide a tool for interpreting linguistic census data and possibly predict the language shift trend at the population scale. In this study, new data from previously examined areas were modeled, specifically Catalan and Spanish in Catalonia, Spanish and English in Houston, Texas, Dutch and French in Brussels, Euskera and Spanish in Spain and French and English in Canada. Three mathematical models of the language competition have been validated. The first is the Abrams-Strogatz model, which treats populations as having two monolingual groups. The second is the Castelló model, which considers bilingual speakers. The third is the Mira model, which considers language competition when the two languages have high similarities. It was found that the some of the data matched Abrams-Strogatz original model, but some divergences could still be addressed. It was also found that the Mira model needs some improvement in how it treats the differences between languages.展开更多
The system error of guidance instruments together with that of orbit tracking is considered and a mathematical model for estimating both of them is established. A thorough investigation of the accurate calculation of ...The system error of guidance instruments together with that of orbit tracking is considered and a mathematical model for estimating both of them is established. A thorough investigation of the accurate calculation of circumstance function and the effects of the system error model is made. Finally, the estimator of the two kinds of errors is presented based on nonlinear regression model and the accuracy of the presented estimator is given. Theoretical analysis and simulation results confirm the validity and effectiveness of this method.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Aeronautical Science Foundation of China (20100751010, 2010ZD11007)
文摘Particle filtering （PF） is being applied successfully in nonlinear and/or non-Gaussian system failure prognosis. However, for failure prediction of many complex systems whose dynamic state evolution models involve time-varying parameters, the tradi- tional PF-based prognosis framework will probably generate serious deviations in results since it implements prediction through iterative calculation using the state models. To address the problem, this paper develops a novel integrated PF-LSSVR frame- work based on PF and least squares support vector regression （LSSVR） for nonlinear system failure prognosis. This approach employs LSSVR for long-term observation series prediction and applies PF-based dual estimation to collaboratively estimate the values of system states and parameters of the corresponding future time instances. Meantime, the propagation of prediction un- certainty is emphatically taken into account. Therefore, PF-LSSVR avoids over-dependency on system state models in prediction phase. With a two-sided failure definition, the probability distribution of system remaining useful life （RUL） is accessed and the corresponding methods of calculating performance evaluation metrics are put forward. The PF-LSSVR framework is applied to a three-vessel water tank system failure prognosis and it has much higher prediction accuracy and confidence level than traditional PF-based framework.
基金Project supported by the National Natural Science Foundation of China.
文摘I. INSTRUCTIONThe study of the acoustic nonlinearity parameter B/A in the biological medium has been of the basic importance and has been treated as the frontier in the field of biomedical acoustics since 1980 when the nonlinear acoustic effects were found in that area. In those years, the measurement of B/A shows that B/A value varies with the physical,
文摘Understanding language competition and extinction is an interdisciplinary challenge, and math models provide a tool for interpreting linguistic census data and possibly predict the language shift trend at the population scale. In this study, new data from previously examined areas were modeled, specifically Catalan and Spanish in Catalonia, Spanish and English in Houston, Texas, Dutch and French in Brussels, Euskera and Spanish in Spain and French and English in Canada. Three mathematical models of the language competition have been validated. The first is the Abrams-Strogatz model, which treats populations as having two monolingual groups. The second is the Castelló model, which considers bilingual speakers. The third is the Mira model, which considers language competition when the two languages have high similarities. It was found that the some of the data matched Abrams-Strogatz original model, but some divergences could still be addressed. It was also found that the Mira model needs some improvement in how it treats the differences between languages.
文摘The system error of guidance instruments together with that of orbit tracking is considered and a mathematical model for estimating both of them is established. A thorough investigation of the accurate calculation of circumstance function and the effects of the system error model is made. Finally, the estimator of the two kinds of errors is presented based on nonlinear regression model and the accuracy of the presented estimator is given. Theoretical analysis and simulation results confirm the validity and effectiveness of this method.
