From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The inv...From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The investigations reveal that the angular spreading of the wave energy is consistent with cos2s(θ/2) proposed by Longuet-Higgins et al. (1963, Ocean Wad Spectra,11~136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole results. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al. (1975, Journal of Physical Oceanography, 5, 750~760)and Hasselmann et al. (1980, Journal of physical Oceanography, 10, 1264~1280) in the field, and the relationship between the four nondimensional parameters sm, fo, b1 and b2, determining the directional width, and (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al. (1985, Philosophical Transaction of Royal Society of London, A315, 509~562) when applied to field waves.展开更多
The fatigue lives of materials and structures at different strain levels show het- eroscedasticity. In addition when the number of test specimens is insufficient, the fatigue strength coefficient and fatigue ductility...The fatigue lives of materials and structures at different strain levels show het- eroscedasticity. In addition when the number of test specimens is insufficient, the fatigue strength coefficient and fatigue ductility coefficient of the fitting parameters in the total strain life equa- tion may not have definite physical significance. In this work, a maximum likelihood method for estimating probabilistic strain amplitude fatigue life curves is presented based on the fatigue lives at different strain levels. The proposed method is based on the general basic assumption that the logarithm of fatigue life at an arbitrary strain level is normally distributed. The rela- tionship among the parameters of total strain life equation, monotonic ultimate tensile stress and percentage reduction of area is adopted. The presented approach is finally illustrated by two applications. It is shown that probabilistic strain amplitude-fatigue life curves can be eas- ily estimated based on the maximum likelihood method. The results show that fatigue lives at different strain levels have heteroscedasticity and the values of fatigue strength coefficient and fatigue ductility coefficient obtained by the proposed method are close to those of the true tensile fracture stress and true tensile fracture strain.展开更多
The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In or...The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.展开更多
Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical s...Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.展开更多
This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both ...This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.展开更多
By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of ...By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.展开更多
From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of swell in deep water are systematically investigated with maximum likelihood method. It is shown that the ...From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of swell in deep water are systematically investigated with maximum likelihood method. It is shown that the directional spreading of swell, qualitatively similar to that of developing wind wave which is narrowest in the region of Peak frequency and bxoadens with increasing or decreasing frequency, can be effectively described by cos2s(θ/2) introduced by Longuet-Higgins et al. (1963,Ocean Wave Spectra, 111~136). It is intriguing that bimodal distribution found in our experiments appers at the forward face instead of the rear face of a frequency spectrum in the cases of nonlinearity being very weak. Parameterized by nonlinearity, formulations which can be applied to swell as well as wind wave are proposed. It is concluded that nonlinear interaction plays a central role in controlling the development of directional angular spreading even for the swell.展开更多
In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum like...In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.展开更多
Directing at evaluation for qualifying rate in weaponry test,this article discusses firstly how field test information is flooded with lots of prior information.Then a fast Bayesian evaluation algorithm is presented b...Directing at evaluation for qualifying rate in weaponry test,this article discusses firstly how field test information is flooded with lots of prior information.Then a fast Bayesian evaluation algorithm is presented based on the elaborate analysis of prior information reliability and the second category of maximum likelihood.The example demonstrates that the algorithm presented in this article is better and more robust compared with classical evaluation algorithm for safe-or-failure test and normal Bayesian method,which can make the best of prior information.展开更多
Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear mode...Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.展开更多
文摘From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of wind-generated waves in deep water are systematically determined by using maximum likehood method.The investigations reveal that the angular spreading of the wave energy is consistent with cos2s(θ/2) proposed by Longuet-Higgins et al. (1963, Ocean Wad Spectra,11~136), if the bimodal distributions of wave energy are not taken into account. Bimodality occurring on higher frequency than peak frequency is too rare to affect our whole results. Surprisingly, a much broader directional spreading than that of the field, which is interpreted by the strongly nonlinear energy transfer because of the very young waves in laboratory, is found. The parameter s depends on frequency in the same way as observed by Mitsuyasu et al. (1975, Journal of Physical Oceanography, 5, 750~760)and Hasselmann et al. (1980, Journal of physical Oceanography, 10, 1264~1280) in the field, and the relationship between the four nondimensional parameters sm, fo, b1 and b2, determining the directional width, and (corresponding to the inverse of wave age) are given respectively. The observed distributions are found to agree well with the suggestion of Donelan et al. (1985, Philosophical Transaction of Royal Society of London, A315, 509~562) when applied to field waves.
基金supported by the National Natural Science Foundation of China(No.51475022)
文摘The fatigue lives of materials and structures at different strain levels show het- eroscedasticity. In addition when the number of test specimens is insufficient, the fatigue strength coefficient and fatigue ductility coefficient of the fitting parameters in the total strain life equa- tion may not have definite physical significance. In this work, a maximum likelihood method for estimating probabilistic strain amplitude fatigue life curves is presented based on the fatigue lives at different strain levels. The proposed method is based on the general basic assumption that the logarithm of fatigue life at an arbitrary strain level is normally distributed. The rela- tionship among the parameters of total strain life equation, monotonic ultimate tensile stress and percentage reduction of area is adopted. The presented approach is finally illustrated by two applications. It is shown that probabilistic strain amplitude-fatigue life curves can be eas- ily estimated based on the maximum likelihood method. The results show that fatigue lives at different strain levels have heteroscedasticity and the values of fatigue strength coefficient and fatigue ductility coefficient obtained by the proposed method are close to those of the true tensile fracture stress and true tensile fracture strain.
基金supported by the National Natural science Foundation of China (No. 42127807)the Sichuan Science and Technology Program (No. 2020YJ0334)the Sichuan Science and Technology Breeding Program (No. 2022041)。
文摘The neutron spectrum unfolding by Bonner sphere spectrometer(BSS) is considered a complex multidimensional model,which requires complex mathematical methods to solve the first kind of Fredholm integral equation. In order to solve the problem of the maximum likelihood expectation maximization(MLEM) algorithm which is easy to suffer the pitfalls of local optima and the particle swarm optimization(PSO) algorithm which is easy to get unreasonable flight direction and step length of particles, which leads to the invalid iteration and affect efficiency and accuracy, an improved PSO-MLEM algorithm, combined of PSO and MLEM algorithm, is proposed for neutron spectrum unfolding. The dynamic acceleration factor is used to balance the ability of global and local search, and improves the convergence speed and accuracy of the algorithm. Firstly, the Monte Carlo method was used to simulated the BSS to obtain the response function and count rates of BSS. In the simulation of count rate, four reference spectra from the IAEA Technical Report Series No. 403 were used as input parameters of the Monte Carlo method. The PSO-MLEM algorithm was used to unfold the neutron spectrum of the simulated data and was verified by the difference of the unfolded spectrum to the reference spectrum. Finally, the 252Cf neutron source was measured by BSS, and the PSO-MLEM algorithm was used to unfold the experimental neutron spectrum.Compared with maximum entropy deconvolution(MAXED), PSO and MLEM algorithm, the PSO-MLEM algorithm has fewer parameters and automatically adjusts the dynamic acceleration factor to solve the problem of local optima. The convergence speed of the PSO-MLEM algorithm is 1.4 times and 3.1 times that of the MLEM and PSO algorithms. Compared with PSO, MLEM and MAXED, the correlation coefficients of PSO-MLEM algorithm are increased by 33.1%, 33.5% and 1.9%, and the relative mean errors are decreased by 98.2%, 97.8% and 67.4%.
文摘Iteration methods and their convergences of the maximum likelihoodestimator are discussed in this paper.We study Gauss-Newton method and give a set ofsufficient conditions for the convergence of asymptotic numerical stability.The modifiedGauss-Newton method is also studied and the sufficient conditions of the convergence arepresented.Two numerical examples are given to illustrate our results.
基金supported by the National Science Foundations (DMS0504783 DMS0604207)National Science Fund for Distinguished Young Scholars of China (70825005)
文摘This paper deals with the problems of consistency and strong consistency of the maximum likelihood estimators of the mean and variance of the drift fractional Brownian motions observed at discrete time instants. Both the central limit theorem and the Berry-Ess′een bounds for these estimators are obtained by using the Stein’s method via Malliavin calculus.
文摘By taking the subsequence out of the input-output sequence of a system polluted by white noise, an independent observation sequence and its probability density are obtained and then a maximum likelihood estimation of the identification parameters is given. In order to decrease the asymptotic error, a corrector of maximum likelihood (CML) estimation with its recursive algorithm is given. It has been proved that the corrector has smaller asymptotic error than the least square methods. A simulation example shows that the corrector of maximum likelihood estimation is of higher approximating precision to the true parameters than the least square methods.
文摘From measurements by a circular array consisting of 18 wave gauges in a large wave tank, directional spectra of swell in deep water are systematically investigated with maximum likelihood method. It is shown that the directional spreading of swell, qualitatively similar to that of developing wind wave which is narrowest in the region of Peak frequency and bxoadens with increasing or decreasing frequency, can be effectively described by cos2s(θ/2) introduced by Longuet-Higgins et al. (1963,Ocean Wave Spectra, 111~136). It is intriguing that bimodal distribution found in our experiments appers at the forward face instead of the rear face of a frequency spectrum in the cases of nonlinearity being very weak. Parameterized by nonlinearity, formulations which can be applied to swell as well as wind wave are proposed. It is concluded that nonlinear interaction plays a central role in controlling the development of directional angular spreading even for the swell.
文摘In this article, we consider a new life test scheme called a progressively first-failure censoring scheme introduced by Wu and Kus [1]. Based on this type of censoring, the maximum likelihood, approximate maximum likelihood and the least squares method estimators for the unknown parameters of the inverse Weibull distribution are derived. A comparison between these estimators is provided by using extensive simulation and two criteria, namely, absolute bias and mean squared error. It is concluded that the estimators based on the least squares method are superior compared to the maximum likelihood and the approximate maximum likelihood estimators. Real life data example is provided to illustrate our proposed estimators.
基金the National Defense Research Foundation of China(No.4010203010401)
文摘Directing at evaluation for qualifying rate in weaponry test,this article discusses firstly how field test information is flooded with lots of prior information.Then a fast Bayesian evaluation algorithm is presented based on the elaborate analysis of prior information reliability and the second category of maximum likelihood.The example demonstrates that the algorithm presented in this article is better and more robust compared with classical evaluation algorithm for safe-or-failure test and normal Bayesian method,which can make the best of prior information.
文摘Compositional data, such as relative information, is a crucial aspect of machine learning and other related fields. It is typically recorded as closed data or sums to a constant, like 100%. The statistical linear model is the most used technique for identifying hidden relationships between underlying random variables of interest. However, data quality is a significant challenge in machine learning, especially when missing data is present. The linear regression model is a commonly used statistical modeling technique used in various applications to find relationships between variables of interest. When estimating linear regression parameters which are useful for things like future prediction and partial effects analysis of independent variables, maximum likelihood estimation (MLE) is the method of choice. However, many datasets contain missing observations, which can lead to costly and time-consuming data recovery. To address this issue, the expectation-maximization (EM) algorithm has been suggested as a solution for situations including missing data. The EM algorithm repeatedly finds the best estimates of parameters in statistical models that depend on variables or data that have not been observed. This is called maximum likelihood or maximum a posteriori (MAP). Using the present estimate as input, the expectation (E) step constructs a log-likelihood function. Finding the parameters that maximize the anticipated log-likelihood, as determined in the E step, is the job of the maximization (M) phase. This study looked at how well the EM algorithm worked on a made-up compositional dataset with missing observations. It used both the robust least square version and ordinary least square regression techniques. The efficacy of the EM algorithm was compared with two alternative imputation techniques, k-Nearest Neighbor (k-NN) and mean imputation (), in terms of Aitchison distances and covariance.
