Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability ...Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.展开更多
In the methods of image thresholding segmentation, such methods based on two-dimensional （2D） histogram and optimal objective functions are important. However, when they are used for infrared image segmentation, the...In the methods of image thresholding segmentation, such methods based on two-dimensional （2D） histogram and optimal objective functions are important. However, when they are used for infrared image segmentation, they are weak in suppressing background noises and worse in segmenting targets with non-uniform gray level. The concept of 2D histogram shape modification is proposed, which is realized by target information prior restraint after enhancing target information using plateau histogram equalization. The formula of 2D minimum Renyi entropy is deduced for image segmentation, then the shape-modified 2D histogram is combined wfth four optimal objective functions （i.e., maximum between-class variance, maximum entropy, maximum correlation and minimum Renyi entropy） respectively for the appli- cation of infrared image segmentation. Simultaneously, F-measure is introduced to evaluate the segmentation effects objectively. The experimental results show that F-measure is an effective evaluation index for image segmentation since its value is fully consistent with the subjective evaluation, and after 2D histogram shape modification, the methods of optimal objective functions can overcome their original forms＇ deficiency and their segmentation effects are more or less improvements, where the best one is the maximum entropy method based on 2D histogram shape modification.展开更多
Knowledge of the phase space density distribution in details is useful to understand subsequent evolution of the charged particle beam in a transport line.This makes the beam tomography very useful in the application ...Knowledge of the phase space density distribution in details is useful to understand subsequent evolution of the charged particle beam in a transport line.This makes the beam tomography very useful in the application for beam diagnostics.This application is not limited by the beam energy,as opposed to the emittance scanner.This paper presented the simulations and measurements we undertook in TRIUMF beam-lines to validate the maximum entropy(MENT)technique for the tomographic reconstruction of beam density distribution in the 2-dimensional transverse phase space.Beam profiles were taken with a single wire scanner while changing an upstream quadrupole’s strength.Moreover,the phase space plots were directly measured with emittance scanner.A close comparison was made on the resulting phase space density distribution and the emittance value at the same location of the beam-line.They show good agreement.展开更多
基金Project(50978112) supported by the National Natural Science Foundation of China
文摘Routine reliability index method, first order second moment (FOSM), may not ensure convergence of iteration when the performance function is strongly nonlinear. A modified method was proposed to calculate reliability index based on maximum entropy (MaxEnt) principle. To achieve this goal, the complicated iteration of first order second moment (FOSM) method was replaced by the calculation of entropy density function. Local convergence of Newton iteration method utilized to calculate entropy density function was proved, which ensured the convergence of iteration when calculating reliability index. To promote calculation efficiency, Newton down-hill algorithm was incorporated into calculating entropy density function and Monte Carlo simulations (MCS) were performed to assess the efficiency of the presented method. Two numerical examples were presented to verify the validation of the presented method. Moreover, the execution and advantages of the presented method were explained. From Example 1, after seven times iteration, the proposed method is capable of calculating the reliability index when the performance function is strongly nonlinear and at the same time the proposed method can preserve the calculation accuracy; From Example 2, the reliability indices calculated using the proposed method, FOSM and MCS are 3.823 9, 3.813 0 and 3.827 6, respectively, and the according iteration times are 5, 36 and 10 6 , which shows that the presented method can improve calculation accuracy without increasing computational cost for the performance function of which the reliability index can be calculated using first order second moment (FOSM) method.
基金supported by the China Postdoctoral Science Foundation(20100471451)the Science and Technology Foundation of State Key Laboratory of Underwater Measurement&Control Technology(9140C2603051003)
文摘In the methods of image thresholding segmentation, such methods based on two-dimensional （2D） histogram and optimal objective functions are important. However, when they are used for infrared image segmentation, they are weak in suppressing background noises and worse in segmenting targets with non-uniform gray level. The concept of 2D histogram shape modification is proposed, which is realized by target information prior restraint after enhancing target information using plateau histogram equalization. The formula of 2D minimum Renyi entropy is deduced for image segmentation, then the shape-modified 2D histogram is combined wfth four optimal objective functions （i.e., maximum between-class variance, maximum entropy, maximum correlation and minimum Renyi entropy） respectively for the appli- cation of infrared image segmentation. Simultaneously, F-measure is introduced to evaluate the segmentation effects objectively. The experimental results show that F-measure is an effective evaluation index for image segmentation since its value is fully consistent with the subjective evaluation, and after 2D histogram shape modification, the methods of optimal objective functions can overcome their original forms＇ deficiency and their segmentation effects are more or less improvements, where the best one is the maximum entropy method based on 2D histogram shape modification.
文摘Knowledge of the phase space density distribution in details is useful to understand subsequent evolution of the charged particle beam in a transport line.This makes the beam tomography very useful in the application for beam diagnostics.This application is not limited by the beam energy,as opposed to the emittance scanner.This paper presented the simulations and measurements we undertook in TRIUMF beam-lines to validate the maximum entropy(MENT)technique for the tomographic reconstruction of beam density distribution in the 2-dimensional transverse phase space.Beam profiles were taken with a single wire scanner while changing an upstream quadrupole’s strength.Moreover,the phase space plots were directly measured with emittance scanner.A close comparison was made on the resulting phase space density distribution and the emittance value at the same location of the beam-line.They show good agreement.
