A new anaerobic reactor, Jet-loop anaerobic fluidized bed (JLAFB), was designed for treating high-sulfate wastewater. The treatment characteristics, including the effect of influent COD/SO42 ratio and alkalinity and...A new anaerobic reactor, Jet-loop anaerobic fluidized bed (JLAFB), was designed for treating high-sulfate wastewater. The treatment characteristics, including the effect of influent COD/SO42 ratio and alkalinity and sulfide inhibition in reactors, were discussed for a JLAFB and a general anaerobic fiuidized bed (AFB) reactor used as sulfate-reducing phase and methane-producing phase, respectively, in two-phase anaerobic digestion process. The formation of granules in the two reactors was also examined. The results indicated that COD and sulfate removal had different demand of influent COD/SO4^2- ratios. When total COD removal was up to 85%, the ratio was only required up to 1.2, whereas, total sulfate removal up to 95% required it exceeding 3.0. The alkalinity in the two reactors increased linearly with the growth of influent alkalinity. Moreover, the change of influent alkalinity had no significant effect on pH and volatile fatty acids (VFA) in the two reactors. Influent alkalinity kept at 400-500 mg/L could meet the requirement of the treating process. The JLAFB reactor had great advantage in avoiding sulfide and free-H2S accumulation and toxicity inhibition on microorganisms. When sulfate loading rate was up to 8. 1 kg/(m^3.d), the sulfide and free-H2S concentrations in JLAFB reactor were 58.6 and 49.7 mg/L, respectively. Furthermore, the granules, with offwhite color, ellipse shape and diameters of 1.0-3.0 mm, could be developed in JLAFB reactor. In granules, different groups of bacteria were distributed in different layers, and some inorganic metal compounds such as Fe, Ca, Mg etc. were found.展开更多
为提高非线性退化轨迹拟合的精度,针对多阶段退化中的非线性规律建立Wiener过程模型,考虑变点的连续性与部件个体的差异性,给出基于非线性复杂退化的可靠性评估方法。结合幂律函数推导出非线性多阶段Wiener过程模型,得到模型参数的极大...为提高非线性退化轨迹拟合的精度,针对多阶段退化中的非线性规律建立Wiener过程模型,考虑变点的连续性与部件个体的差异性,给出基于非线性复杂退化的可靠性评估方法。结合幂律函数推导出非线性多阶段Wiener过程模型,得到模型参数的极大似然估计量;通过最小均方误差原则给出变点以及幂参数的初值确定方法;根据SIC(schwarz information criterion)方法得到模型变点的精确值,并检验其准确性;结合不同部件之间的差异性,得到变点的连续分布;推导出非线性Wiener过程连续时段内的可靠度函数估计;利用本模型对高压脉冲电容器电容相对变化量的退化数据建模,与线性建模结果对比,验证多阶段Wiener过程模型在可靠性评估方面的有效性与可行性,估计结果更接近真实值。展开更多
In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence's C-R increments fo...In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence's C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen's law of iterated logarithm for a Wiener process.展开更多
In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of i...In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.展开更多
Standing on a different view point from Anderson, we prove that the extended Wiener process defined by Anderson satisfies the definition of the Wiener process in standard analysis, for example the Wiener process at ti...Standing on a different view point from Anderson, we prove that the extended Wiener process defined by Anderson satisfies the definition of the Wiener process in standard analysis, for example the Wiener process at time t obeys the normal distribution N(0,t) by showing the central limit theorem. The essential theory used in the proof is the extended convolution property in nonstandard analysis which is shown by Kanagawa, Nishiyama and Tchizawa (2018). When processing the extension by non-standardization, we have already pointed out that it is needed to proceed the second extension for the convolution, not only to do the first extension for the delta function. In Section 2, we shall introduce again the extended convolution as preliminaries described in our previous paper. In Section 3, we shall provide the extended stochastic process using a hyper number N, and it satisfies the conditions being Wiener process. In Section 4, we shall give a new proof for the non-differentiability in the Wiener process.展开更多
A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-...A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.展开更多
An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degra...An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.展开更多
Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the fail...Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold(RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization(EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.展开更多
Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degrad...Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item's individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.展开更多
为探究城市轨道交通(简称:城轨)车辆轮对的轮径值退化规律,有效评估轮对可靠性,提出基于Wiener过程的城轨车辆轮对可靠性评估方法。选取轮径值作为性能退化指标,建立基于Wiener过程的城轨车辆轮对退化模型。通过计算轮对剩余寿命,选择...为探究城市轨道交通(简称:城轨)车辆轮对的轮径值退化规律,有效评估轮对可靠性,提出基于Wiener过程的城轨车辆轮对可靠性评估方法。选取轮径值作为性能退化指标,建立基于Wiener过程的城轨车辆轮对退化模型。通过计算轮对剩余寿命,选择精度最高的退化模型进行可靠性评估。针对退化模型参数后验分布计算公式较为复杂的问题,采用马尔可夫链蒙特卡洛(MCMC,Markov Chain Monte Carlo)方法进行求解。基于广州地铁8号线列车轮对实测数据进行实例验证,结果表明,城轨车辆应保证轮对可靠度不低于0.9,且在镟修后运行至27.51万km时,应检查轮对退化情况,以保障车辆的运行安全。展开更多
Rolling bearing is the key part of mechanical system.Accurate prediction of bearing life can reduce maintenance costs,improve availability,and prevent catastrophic consequences,aiming at solving the problem of the non...Rolling bearing is the key part of mechanical system.Accurate prediction of bearing life can reduce maintenance costs,improve availability,and prevent catastrophic consequences,aiming at solving the problem of the nonlinear,random and small sample problems faced by rolling bearings in actual operating conditions.In this work,the nonlinearWiener process with random effect and unbiased estimation of unknown parameters is used to predict the remaining useful life of rolling bearings.Firstly,random effects and nonlinear parameters are added to the traditional Wiener process,and a parameter unbiased estimation method is used to estimate the positional parameters of the constructed Wiener model.Finally,the model is validated using a common set of bearing datasets.Experimental results show that compared with the traditional maximum likelihood function estimation method,the parameter unbiased estimation method can effectively improve the accuracy and stability of the parameter estimation results.The model has a good fitting effect,which can accurately predict the remaining useful life of rolling bearing.展开更多
A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but ...A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but they could be included in the model without major difficulties. Based on the opinion proposed by Abgrall that “a two phase system, uniform in velocity and pressure at t=0 will be uniform on the same variable during its temporal evolution", a simple accurate and fully Eulerian numerical method was presented for the simulation of multiphase compressible flows in hydrodynamic regime. The numerical method relies on Godunov-type scheme, with HLLC and Lax-Friedrichs type approximate Riemann solvers for the resolution of conservation equations, and nonconservative equation. Speed relaxation and pressure relaxation processes were introduced to account for the interaction between the phases. Test problem was presented in one space dimension which illustrated that our scheme is accurate, stable and oscillation free.展开更多
Assume that D is a nuclear space and D' its strong topological dual space. Let {B_t}t∈(0,∞) be a Wiener D'-process. In this paper, the real-valued and D'-valued weak stochastic integral with respect to {...Assume that D is a nuclear space and D' its strong topological dual space. Let {B_t}t∈(0,∞) be a Wiener D'-process. In this paper, the real-valued and D'-valued weak stochastic integral with respect to {B_t} are established.AMS Subject Classification. 60H05.展开更多
基金Project supported by the National Natural Science Foundation of China(No. 50278036)the Natural Science Foundation of Guangdong Province (No. 04105951)
文摘A new anaerobic reactor, Jet-loop anaerobic fluidized bed (JLAFB), was designed for treating high-sulfate wastewater. The treatment characteristics, including the effect of influent COD/SO42 ratio and alkalinity and sulfide inhibition in reactors, were discussed for a JLAFB and a general anaerobic fiuidized bed (AFB) reactor used as sulfate-reducing phase and methane-producing phase, respectively, in two-phase anaerobic digestion process. The formation of granules in the two reactors was also examined. The results indicated that COD and sulfate removal had different demand of influent COD/SO4^2- ratios. When total COD removal was up to 85%, the ratio was only required up to 1.2, whereas, total sulfate removal up to 95% required it exceeding 3.0. The alkalinity in the two reactors increased linearly with the growth of influent alkalinity. Moreover, the change of influent alkalinity had no significant effect on pH and volatile fatty acids (VFA) in the two reactors. Influent alkalinity kept at 400-500 mg/L could meet the requirement of the treating process. The JLAFB reactor had great advantage in avoiding sulfide and free-H2S accumulation and toxicity inhibition on microorganisms. When sulfate loading rate was up to 8. 1 kg/(m^3.d), the sulfide and free-H2S concentrations in JLAFB reactor were 58.6 and 49.7 mg/L, respectively. Furthermore, the granules, with offwhite color, ellipse shape and diameters of 1.0-3.0 mm, could be developed in JLAFB reactor. In granules, different groups of bacteria were distributed in different layers, and some inorganic metal compounds such as Fe, Ca, Mg etc. were found.
文摘为提高非线性退化轨迹拟合的精度,针对多阶段退化中的非线性规律建立Wiener过程模型,考虑变点的连续性与部件个体的差异性,给出基于非线性复杂退化的可靠性评估方法。结合幂律函数推导出非线性多阶段Wiener过程模型,得到模型参数的极大似然估计量;通过最小均方误差原则给出变点以及幂参数的初值确定方法;根据SIC(schwarz information criterion)方法得到模型变点的精确值,并检验其准确性;结合不同部件之间的差异性,得到变点的连续分布;推导出非线性Wiener过程连续时段内的可靠度函数估计;利用本模型对高压脉冲电容器电容相对变化量的退化数据建模,与线性建模结果对比,验证多阶段Wiener过程模型在可靠性评估方面的有效性与可行性,估计结果更接近真实值。
基金supported by the National Natural Science Foundation of China(Grant No51079043)the Special Fund for Public Welfare Industry of Ministry of Water Resources of China(Grants No200901064 and 201001020)the Research Innovation Program for College Graduates of Jiangsu Province(Grant No CXZZ11_0450)
基金Supported by the Natural Science Foundation of Hubei Province of China(2011CDB229)
文摘In this paper, with the aid of large deviation formulas established in strong topology of functional space generated by HSlder norm, we discuss the functional sample path properties of subsequence's C-R increments for a Wiener process in HSlder norm. The obtained results, generalize the corresponding results of Chen and the classic Strassen's law of iterated logarithm for a Wiener process.
基金Supported by the National Natural Science Foundation of ChinaZhejiang Province Natural Science Fund
文摘In this paper, we consider a general form of the increments for a two-parameter Wiener process. Both the Csorgo-Revesz's increments and a class of the lag increments are the special cases of this general form of increments. Our results imply the theorem that have been given by Csorgo and Revesz (1978), and some of their conditions are removed.
文摘Standing on a different view point from Anderson, we prove that the extended Wiener process defined by Anderson satisfies the definition of the Wiener process in standard analysis, for example the Wiener process at time t obeys the normal distribution N(0,t) by showing the central limit theorem. The essential theory used in the proof is the extended convolution property in nonstandard analysis which is shown by Kanagawa, Nishiyama and Tchizawa (2018). When processing the extension by non-standardization, we have already pointed out that it is needed to proceed the second extension for the convolution, not only to do the first extension for the delta function. In Section 2, we shall introduce again the extended convolution as preliminaries described in our previous paper. In Section 3, we shall provide the extended stochastic process using a hyper number N, and it satisfies the conditions being Wiener process. In Section 4, we shall give a new proof for the non-differentiability in the Wiener process.
文摘A general form of the increments of two-parameter fractional Wiener process is given. The results of Csoergo-Révész increments are a special case,and it also implies the results of the increments of the two-parameter Wiener process.
基金Project(60904002)supported by the National Natural Science Foundation of China
文摘An adaptive method of residual life estimation for deteriorated products with two performance characteristics (PCs) was proposed, which was sharply different from existing work that only utilized one-dimensional degradation data. Once new degradation information was available, the residual life of the product being monitored could be estimated in an adaptive manner. Here, it was assumed that the degradation of each PC over time was governed by a Wiener degradation process and the dependency between them was characterized by the Frank copula function. A bivariate Wiener process model with measurement errors was used to model the degradation measurements. A two-stage method and the Markov chain Monte Carlo (MCMC) method were combined to estimate the unknown parameters in sequence. Results from a numerical example about fatigue cracks show that the proposed method is valid as the relative error is small.
基金Projects(51475462,61174030,61473094,61374126)supported by the National Natural Science Foundation of China
文摘Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold(RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization(EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.
基金Projects(51475462,61374138,61370031)supported by the National Natural Science Foundation of China
文摘Real time remaining useful life(RUL) prediction based on condition monitoring is an essential part in condition based maintenance(CBM). In the current methods about the real time RUL prediction of the nonlinear degradation process, the measurement error is not considered and forecasting uncertainty is large. Therefore, an approximate analytical RUL distribution in a closed-form of a nonlinear Wiener based degradation process with measurement errors was proposed. The maximum likelihood estimation approach was used to estimate the unknown fixed parameters in the proposed model. When the newly observed data are available, the random parameter is updated by the Bayesian method to make the estimation adapt to the item's individual characteristic and reduce the uncertainty of the estimation. The simulation results show that considering measurement errors in the degradation process can significantly improve the accuracy of real time RUL prediction.
文摘为探究城市轨道交通(简称:城轨)车辆轮对的轮径值退化规律,有效评估轮对可靠性,提出基于Wiener过程的城轨车辆轮对可靠性评估方法。选取轮径值作为性能退化指标,建立基于Wiener过程的城轨车辆轮对退化模型。通过计算轮对剩余寿命,选择精度最高的退化模型进行可靠性评估。针对退化模型参数后验分布计算公式较为复杂的问题,采用马尔可夫链蒙特卡洛(MCMC,Markov Chain Monte Carlo)方法进行求解。基于广州地铁8号线列车轮对实测数据进行实例验证,结果表明,城轨车辆应保证轮对可靠度不低于0.9,且在镟修后运行至27.51万km时,应检查轮对退化情况,以保障车辆的运行安全。
基金National Natural Science Foundation of China (51965052,51865045)Scientific Research Project of Higher Education Institutions of Inner Mongolia Autonomous Region (NJZY22114).
文摘Rolling bearing is the key part of mechanical system.Accurate prediction of bearing life can reduce maintenance costs,improve availability,and prevent catastrophic consequences,aiming at solving the problem of the nonlinear,random and small sample problems faced by rolling bearings in actual operating conditions.In this work,the nonlinearWiener process with random effect and unbiased estimation of unknown parameters is used to predict the remaining useful life of rolling bearings.Firstly,random effects and nonlinear parameters are added to the traditional Wiener process,and a parameter unbiased estimation method is used to estimate the positional parameters of the constructed Wiener model.Finally,the model is validated using a common set of bearing datasets.Experimental results show that compared with the traditional maximum likelihood function estimation method,the parameter unbiased estimation method can effectively improve the accuracy and stability of the parameter estimation results.The model has a good fitting effect,which can accurately predict the remaining useful life of rolling bearing.
文摘A numerical method for two-phase flow with hydrodynamics behavior was considered. The nonconservative hyperbolic governing equations proposed by Saurel and Gallout were adopted. Dissipative effects were neglected but they could be included in the model without major difficulties. Based on the opinion proposed by Abgrall that “a two phase system, uniform in velocity and pressure at t=0 will be uniform on the same variable during its temporal evolution", a simple accurate and fully Eulerian numerical method was presented for the simulation of multiphase compressible flows in hydrodynamic regime. The numerical method relies on Godunov-type scheme, with HLLC and Lax-Friedrichs type approximate Riemann solvers for the resolution of conservation equations, and nonconservative equation. Speed relaxation and pressure relaxation processes were introduced to account for the interaction between the phases. Test problem was presented in one space dimension which illustrated that our scheme is accurate, stable and oscillation free.
文摘Assume that D is a nuclear space and D' its strong topological dual space. Let {B_t}t∈(0,∞) be a Wiener D'-process. In this paper, the real-valued and D'-valued weak stochastic integral with respect to {B_t} are established.AMS Subject Classification. 60H05.