Two-dimensional(2D)supports confined single-atom catalysts(2D SACs)with unique geometric and electronic structures have been attractive candidates in different catalytic applications,such as energy conversion and stor...Two-dimensional(2D)supports confined single-atom catalysts(2D SACs)with unique geometric and electronic structures have been attractive candidates in different catalytic applications,such as energy conversion and storage,value-added chemical synthesis and environmental remediation.However,their environmental appli-cations lack of a comprehensive summary and in-depth discussion.In this review,recent progresses in synthesis routes and advanced characterization techniques for 2D SACs are introduced,and a comprehensive discussion on their applications in environmental remediation is presented.Generally,2D SACs can be effective in catalytic elimination of aqueous and gaseous pollutants via radical or non-radical routes and transformation of toxic pollutants into less poisonous species or highly value-added products,opening a new horizon for the contami-nant treatment.In addition,in-depth reaction mechanisms and potential pathways are systematically discussed,and the relationship between the structure-performance is highlighted.Finally,several critical challenges within this field are presented,and possible directions for further explorations of 2D SACs in environmental remediation are suggested.Although the research of 2D SACs in the environmental application is still in its infancy,this review will provide a timely summary on the emerging field,and would stimulate tremendous interest for designing more attractive 2D SACs and promoting their wide applications.展开更多
Based on the two-dimensional (2D) system theory, an integrated predictive iterative learning control (2D-IPILC) strategy for batch processes is presented. First, the output response and the error transition model ...Based on the two-dimensional (2D) system theory, an integrated predictive iterative learning control (2D-IPILC) strategy for batch processes is presented. First, the output response and the error transition model predictions along the batch index can be calculated analytically due to the 2D Roesser model of the batch process. Then, an integrated framework of combining iterative learning control (ILC) and model predictive control (MPC) is formed reasonably. The output of feedforward ILC is estimated on the basis of the predefined process 2D model. By min- imizing a quadratic objective function, the feedback MPC is introduced to obtain better control performance for tracking problem of batch processes. Simulations on a typical batch reactor demonstrate that the satisfactory tracking performance as well as faster convergence speed can be achieved than traditional proportion type (P- t-we) ILC despite the model error and disturbances.展开更多
The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To prov...The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.展开更多
The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because ...The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.展开更多
The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to con...The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.展开更多
We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correl...We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.展开更多
This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is ...This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.展开更多
In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend t...In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.展开更多
The mass of the embedded systems are driven by second batteries, not by wired power supply. So saving energy is one of the main design goals for embedded system. In this paper we present a new technique for modelling ...The mass of the embedded systems are driven by second batteries, not by wired power supply. So saving energy is one of the main design goals for embedded system. In this paper we present a new technique for modelling and solving the dynamic power management (DPM) problem for embedded systems with complex behavioural characteristics. First we model a power-managed embedded computing system as a controllable Flow Chart. Then we use the Poisson process for optimisation, and give the power management algorithm by the help of Dynamic Voltage Scaling (DVS) technology. At last we built the experi- mental model using the PXA 255 Processors. The experimental results showed that the proposed technique can achieve more than 12% power saving compared to other existing DPM techniques.展开更多
New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aimin...New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process(NHPP) corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.展开更多
D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated si...D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization methods)have been proposed successively,but most are limited to numerical simulations.This study focused on the applicability of different inversion methods for NMR logging data of various acquisition sequences,from which the optimal inversion method was selected based on the comparative analysis.First,the two-dimensional NMR logging principle was studied.Then,these inversion methods were studied in detail,and the precision and computational efficiency of CPMG and diffusion editing(DE)sequences obtained from oil-water and gas-water models were compared,respectively.The inversion results and calculation time of truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization were compared and analyzed through numerical simulations.The inversion method was optimized to process SP mode logging data from the MR Scanner instrument.The results showed that the TIST-regularization and LM-norm smoothing methods were more accurate for the CPMG and DE sequence echo trains of the oil-water and gas-water models.However,the LM-norm smoothing method was less time-consuming,making it more suitable for logging data processing.A case study in well A25 showed that the processing results by the LM-norm smoothing method were consistent with GEOLOG software.This demonstrates that the LM-norm smoothing method is applicable in practical NMR logging processing.展开更多
Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most ...Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.展开更多
The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of ...The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.展开更多
In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting ...In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.展开更多
Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam (IPIB) generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the...Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam (IPIB) generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the ablation process of the target during a pulse time has been simulated. We have come to the conclusion that the melting and evaporating process begin from the surface and the target is ablated layer by layer when the target is irradiated by the IPIB. Meanwhile, we also obtained the result that the average ablation velocity in target central region is about 10 m/s, which is far less than the ejection velocity of the plume plasma formed by irradiation. Different effects have been compared to the different ratio of the ions and different energy density of IPIB while the target is irradiated by pulsed beams.展开更多
River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal pro...River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.展开更多
基金This work was financially supported by the National Natural Science Foundation of China(51602133,51876093)China MOST(2018YFE0183600).
文摘Two-dimensional(2D)supports confined single-atom catalysts(2D SACs)with unique geometric and electronic structures have been attractive candidates in different catalytic applications,such as energy conversion and storage,value-added chemical synthesis and environmental remediation.However,their environmental appli-cations lack of a comprehensive summary and in-depth discussion.In this review,recent progresses in synthesis routes and advanced characterization techniques for 2D SACs are introduced,and a comprehensive discussion on their applications in environmental remediation is presented.Generally,2D SACs can be effective in catalytic elimination of aqueous and gaseous pollutants via radical or non-radical routes and transformation of toxic pollutants into less poisonous species or highly value-added products,opening a new horizon for the contami-nant treatment.In addition,in-depth reaction mechanisms and potential pathways are systematically discussed,and the relationship between the structure-performance is highlighted.Finally,several critical challenges within this field are presented,and possible directions for further explorations of 2D SACs in environmental remediation are suggested.Although the research of 2D SACs in the environmental application is still in its infancy,this review will provide a timely summary on the emerging field,and would stimulate tremendous interest for designing more attractive 2D SACs and promoting their wide applications.
基金Supported in part by the State Key Development Program for Basic Research of China(2012CB720505)the National Natural Science Foundation of China(61174105,60874049)
文摘Based on the two-dimensional (2D) system theory, an integrated predictive iterative learning control (2D-IPILC) strategy for batch processes is presented. First, the output response and the error transition model predictions along the batch index can be calculated analytically due to the 2D Roesser model of the batch process. Then, an integrated framework of combining iterative learning control (ILC) and model predictive control (MPC) is formed reasonably. The output of feedforward ILC is estimated on the basis of the predefined process 2D model. By min- imizing a quadratic objective function, the feedback MPC is introduced to obtain better control performance for tracking problem of batch processes. Simulations on a typical batch reactor demonstrate that the satisfactory tracking performance as well as faster convergence speed can be achieved than traditional proportion type (P- t-we) ILC despite the model error and disturbances.
文摘The Inspection Paradox refers to the fact that in a Renewal Process, the length of the interarrival period which contains a fixed time is stochastically larger than the length of a typical interarrival period. To provide a more complete understanding of this phenomenon, conditioning arguments are used to obtain the distributions and moments of the lengths of the interarrival periods other than the one containing this fixed time for the case of the time-homogeneous Poisson Process. Distributions of the waiting times for events that occur both before and after this fixed time are derived. This provides a fairly complete probabilistic analysis of the Inspection Paradox.
文摘The delayed S-shaped software reliability growth model (SRGM) is one of the non-homogeneous Poisson process (NHPP) models which have been proposed for software reliability assessment. The model is distinctive because it has a mean value function that reflects the delay in failure reporting: there is a delay between failure detection and reporting time. The model captures error detection, isolation, and removal processes, thus is appropriate for software reliability analysis. Predictive analysis in software testing is useful in modifying, debugging, and determining when to terminate software development testing processes. However, Bayesian predictive analyses on the delayed S-shaped model have not been extensively explored. This paper uses the delayed S-shaped SRGM to address four issues in one-sample prediction associated with the software development testing process. Bayesian approach based on non-informative priors was used to derive explicit solutions for the four issues, and the developed methodologies were illustrated using real data.
基金Characteristic Innovation Projects of Ordinary Universities of Guangdong Province,China(No.2022KTSCX150)Zhaoqing Education Development Institute Project,China(No.ZQJYY2021144)Zhaoqing College Quality Project and Teaching Reform Project,China(Nos.zlgc202003 and zlgc202112)。
文摘The paper discusses the statistical inference problem of the compound Poisson vector process(CPVP)in the domain of attraction of normal law but with infinite covariance matrix.The empirical likelihood(EL)method to construct confidence regions for the mean vector has been proposed.It is a generalization from the finite second-order moments to the infinite second-order moments in the domain of attraction of normal law.The log-empirical likelihood ratio statistic for the average number of the CPVP converges to F distribution in distribution when the population is in the domain of attraction of normal law but has infinite covariance matrix.Some simulation results are proposed to illustrate the method of the paper.
文摘We investigate the approximating capability of Markov modulated Poisson processes (MMPP) for modeling multifractal Internet traffic. The choice of MMPP is motivated by its ability to capture the variability and correlation in moderate time scales while being analytically tractable. Important statistics of traffic burstiness are described and a customized moment-based fitting procedure of MMPP to traffic traces is presented. Our methodology of doing this is to examine whether the MMPP can be used to predict the performance of a queue to which MMPP sample paths and measured traffic traces are fed for comparison respectively, in addition to the goodness-of-fit test of MMPP. Numerical results and simulations show that the fitted MMPP can approximate multifractal traffic quite well, i.e. accurately predict the queueing performance.
基金This work was supported in part by the National Natural Science Foundation of China (10071058, 70273029) the Ministry of Education of China.
文摘This article considers a risk model as in Yuen et al. (2002). Under this model the two claim number processes are correlated. Claim occurrence of both classes relate to Poisson and Erlang processes. The formulae is derived for the distribution of the surplus immediately before ruin, for the distribution of the surplus immediately after ruin and the joint distribution of the surplus immediately before and after ruin. The asymptotic property of these ruin functions is also investigated.
基金supported by National Natural Science Foundation of China (10901054)
文摘In this paper, we first prove that one-parameter standard α-stable sub-Gaussian processes can be approximated by processes constructed by integrals based on the Poisson process with random intensity. Then we extend this result to the two-parameter processes. At last, we consider the approximation of the subordinated fractional Brownian motion.
基金Project (No. 2003AA1Z2120) supported by the Hi-Tech Researchand Development Program (863) of China
文摘The mass of the embedded systems are driven by second batteries, not by wired power supply. So saving energy is one of the main design goals for embedded system. In this paper we present a new technique for modelling and solving the dynamic power management (DPM) problem for embedded systems with complex behavioural characteristics. First we model a power-managed embedded computing system as a controllable Flow Chart. Then we use the Poisson process for optimisation, and give the power management algorithm by the help of Dynamic Voltage Scaling (DVS) technology. At last we built the experi- mental model using the PXA 255 Processors. The experimental results showed that the proposed technique can achieve more than 12% power saving compared to other existing DPM techniques.
基金supported by Sustentation Program of National Ministries and Commissions of China (Grant No. 51319030302 and Grant No. 9140A19030506KG0166)
文摘New armament systems are subjected to the method for dealing with multi-stage system reliability-growth statistical problems of diverse population in order to improve reliability before starting mass production. Aiming at the test process which is high expense and small sample-size in the development of complex system, the specific methods are studied on how to process the statistical information of Bayesian reliability growth regarding diverse populations. Firstly, according to the characteristics of reliability growth during product development, the Bayesian method is used to integrate the testing information of multi-stage and the order relations of distribution parameters. And then a Gamma-Beta prior distribution is proposed based on non-homogeneous Poisson process(NHPP) corresponding to the reliability growth process. The posterior distribution of reliability parameters is obtained regarding different stages of product, and the reliability parameters are evaluated based on the posterior distribution. Finally, Bayesian approach proposed in this paper for multi-stage reliability growth test is applied to the test process which is small sample-size in the astronautics filed. The results of a numerical example show that the presented model can make use of the diverse information synthetically, and pave the way for the application of the Bayesian model for multi-stage reliability growth test evaluation with small sample-size. The method is useful for evaluating multi-stage system reliability and making reliability growth plan rationally.
基金sponsored by the National Natural Science Foundation of China(Nos.42174149,41774144)the National Major Projects(No.2016ZX05014-001).
文摘D-T_(2)two-dimensional nuclear magnetic resonance(2D NMR)logging technology can distinguish pore fluid types intuitively,and it is widely used in oil and gas exploration.Many 2D NMR inversion methods(e.g.,truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization methods)have been proposed successively,but most are limited to numerical simulations.This study focused on the applicability of different inversion methods for NMR logging data of various acquisition sequences,from which the optimal inversion method was selected based on the comparative analysis.First,the two-dimensional NMR logging principle was studied.Then,these inversion methods were studied in detail,and the precision and computational efficiency of CPMG and diffusion editing(DE)sequences obtained from oil-water and gas-water models were compared,respectively.The inversion results and calculation time of truncated singular value decomposition(TSVD),Butler-Reds-Dawson(BRD),LM-norm smoothing,and TIST-L1 regularization were compared and analyzed through numerical simulations.The inversion method was optimized to process SP mode logging data from the MR Scanner instrument.The results showed that the TIST-regularization and LM-norm smoothing methods were more accurate for the CPMG and DE sequence echo trains of the oil-water and gas-water models.However,the LM-norm smoothing method was less time-consuming,making it more suitable for logging data processing.A case study in well A25 showed that the processing results by the LM-norm smoothing method were consistent with GEOLOG software.This demonstrates that the LM-norm smoothing method is applicable in practical NMR logging processing.
基金supported by the National Natural Science Foundation of China (71671090)the Fundamental Research Funds for the Central Universities (NP2020022)the Qinglan Project of Excellent Youth or Middle-Aged Academic Leaders in Jiangsu Province。
文摘Due to the randomness and time dependence of the factors affecting software reliability, most software reliability models are treated as stochastic processes, and the non-homogeneous Poisson process(NHPP) is the most used one.However, the failure behavior of software does not follow the NHPP in a statistically rigorous manner, and the pure random method might be not enough to describe the software failure behavior. To solve these problems, this paper proposes a new integrated approach that combines stochastic process and grey system theory to describe the failure behavior of software. A grey NHPP software reliability model is put forward in a discrete form, and a grey-based approach for estimating software reliability under the NHPP is proposed as a nonlinear multi-objective programming problem. Finally, four grey NHPP software reliability models are applied to four real datasets, the dynamic R-square and predictive relative error are calculated. Comparing with the original single NHPP software reliability model, it is found that the modeling using the integrated approach has a higher prediction accuracy of software reliability. Therefore, there is the characteristics of grey uncertain information in the NHPP software reliability models, and exploiting the latent grey uncertain information might lead to more accurate software reliability estimation.
文摘The Goel-Okumoto software reliability model, also known as the Exponential Nonhomogeneous Poisson Process,is one of the earliest software reliability models to be proposed. From literature, it is evident that most of the study that has been done on the Goel-Okumoto software reliability model is parameter estimation using the MLE method and model fit. It is widely known that predictive analysis is very useful for modifying, debugging and determining when to terminate software development testing process. However, there is a conspicuous absence of literature on both the classical and Bayesian predictive analyses on the model. This paper presents some results about predictive analyses for the Goel-Okumoto software reliability model. Driven by the requirement of highly reliable software used in computers embedded in automotive, mechanical and safety control systems, industrial and quality process control, real-time sensor networks, aircrafts, nuclear reactors among others, we address four issues in single-sample prediction associated closely with software development process. We have adopted Bayesian methods based on non-informative priors to develop explicit solutions to these problems. An example with real data in the form of time between software failures will be used to illustrate the developed methodologies.
基金supported by the National Natural Science Foundation of China(11571262,11731012 and 11971361)。
文摘In this article,we study the hitting probabilities of weighted Poisson processes and their subordinated versions with different intensities.Furthermore,we simulate and analyze the asymptotic properties of the hitting probabilities in different weights and give an example in the case of subordination.
文摘Two-dimensional numerical research has been carried out on the ablation effects of titanium target irradiated by intense pulsed ion beam (IPIB) generated by TEMP Ⅱ accelerator. Temporal and spatial evolution of the ablation process of the target during a pulse time has been simulated. We have come to the conclusion that the melting and evaporating process begin from the surface and the target is ablated layer by layer when the target is irradiated by the IPIB. Meanwhile, we also obtained the result that the average ablation velocity in target central region is about 10 m/s, which is far less than the ejection velocity of the plume plasma formed by irradiation. Different effects have been compared to the different ratio of the ions and different energy density of IPIB while the target is irradiated by pulsed beams.
基金supported by the National Natural Science Foundation of China(Grant No.50579030)
文摘River ice is a natural phenomenon in cold regions, influenced by meteorology, geomorphology, and hydraulic conditions. River ice processes involve complex interactions between hydrodynamic, mechanical, and thermal processes, and they are also influenced by weather and hydrologic conditions. Because natural rivers are serpentine, with bends, narrows, and straight reaches, the commonly-used one-dimensional river ice models and two-dimensional models based on the rectangular Cartesian coordinates are incapable of simulating the physical phenomena accurately. In order to accurately simulate the complicated river geometry and overcome the difficulties of numerical simulation resulting from both complex boundaries and differences between length and width scales, a two-dimensional river ice numerical model based on a boundary-fitted coordinate transformation method was developed. The presented model considers the influence of the frazil ice accumulation under ice cover and the shape of the leading edge of ice cover during the freezing process. The model is capable of determining the velocity field, the distribution of water temperature, the concentration distribution of frazil ice, the transport of floating ice, the progression, stability, and thawing of ice cover, and the transport, accumulation, and erosion of ice under ice cover. A MacCormack scheme was used to solve the equations numerically. The model was validated with field observations from the Hequ Reach of the Yellow River. Comparison of simulation results with field data indicates that the model is capable of simulating the river ice process with high accuracy.