Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying...Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.展开更多
The problem of distributed detection fusion using multiple sensors for remote underwater target detection is studied. Considering that multiple access channel （MAC） schemes are able to offer high efficiency in bandw...The problem of distributed detection fusion using multiple sensors for remote underwater target detection is studied. Considering that multiple access channel （MAC） schemes are able to offer high efficiency in bandwidth usage and consume less energy than the parallel access channel （PAC）, the MAC scheme is introduced into the underwater target detection field. The model of underwater distributed detection fusion based on MAC schemes is established. A new method for detection fusion of MAC based on deflection coefficient maximization （DCM） and Neyman-Pearson （NP） rule is proposed. Under the power constraint of local sensors, this paper uses the DCM theory to derive the optimal weight coefficients and offsets. The closed-form expressions of detection probability and false alarm probability for fusion systems are obtained. The optimal detection performance of fusion systems is analyzed and deeply researched. Both the theory analysis and simulation experiments indicate that the proposed method could improve the detection performance and decrease the error probability effectively under power constraints of local sensors and low signal to noise ratio.展开更多
基金Supported by the National Natural Science Foundation of China(51276017)
文摘Based on the differential equation of the deflection curve for the beam,the equation of the deflection curve for the simple beamis obtained by integral. The equation of the deflection curve for the simple beamcarrying the linear load is generalized,and then it is expanded into the corresponding Fourier series.With the obtained summation results of the infinite series,it is found that they are related to Bernoulli num-bers and π. The recurrent formula of Bernoulli numbers is presented. The relationships among the coefficients of the beam,Bernoulli numbers and Euler numbers are found,and the relative mathematical formulas are presented.
基金supported by the National Natural Science Foundation of China (60972152)Northwestern Polytechnical University Foun dations for Fundamental Research (JC201027 JC20100223)
文摘The problem of distributed detection fusion using multiple sensors for remote underwater target detection is studied. Considering that multiple access channel （MAC） schemes are able to offer high efficiency in bandwidth usage and consume less energy than the parallel access channel （PAC）, the MAC scheme is introduced into the underwater target detection field. The model of underwater distributed detection fusion based on MAC schemes is established. A new method for detection fusion of MAC based on deflection coefficient maximization （DCM） and Neyman-Pearson （NP） rule is proposed. Under the power constraint of local sensors, this paper uses the DCM theory to derive the optimal weight coefficients and offsets. The closed-form expressions of detection probability and false alarm probability for fusion systems are obtained. The optimal detection performance of fusion systems is analyzed and deeply researched. Both the theory analysis and simulation experiments indicate that the proposed method could improve the detection performance and decrease the error probability effectively under power constraints of local sensors and low signal to noise ratio.
