The feature on the posterior conditional probability of finite state Markov channel

The feature of finite state Markov channel probability distribution is discussed on condition that original I/O are known. The probability is called posterior condition probability. It is also proved by Bayes formula that posterior condition probability forms stationary Markov sequence if channel input is independently and identically distributed. On the contrary, Markov property of posterior condition probability isn’t kept if the input isn’t independently and identically distributed and a numerical example is utilized to explain this case. The properties of posterior condition probability will aid the study of the numerical calculated recurrence formula of finite state Markov channel capacity.

Conditional Probability Approach for Fault Detection in Photovoltaic Energy Farms

Detection of electric faults in photovoltaic (PV) farms enhances a sustainable service continuity of farm energy generation. In this paper, a probabilisticfunction is introduced to detect the faults in the PV farms. The conditional probability functions are adopted to detect different fault conditions such as internalstring faults, string-to-string faults, and string-to-negative terminal faults. As thediodes are important to make the PV farms in-service safely during the faults,the distribution currents of these faults are evaluated with different concepts ofdiode consideration as well as without considering any diode installation. Thispart of the study enhances the diode utilization in the PV farms concerning theprotection point of view. The PV string currents are used as inputs to the conditional probability detection algorithms. However, the setting of the fault detectiontechnique is not portable for the other PV systems due to broad ranges of PV system ratings. To accordingly generalize the proposed fault detection algorithm, thePV string currents are first normalized to the total array current for universallyapplying the detection function at different PV string ratings. The limiting faultresistances are evaluated to show the sensitivity of the proposed fault detector.The results ensure the application of the proposed probabilistic detection functionfor PV farms.

Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

A Hierarchy of Compatibility and Comeasurability Levels in Quantum Logics with Unique Conditional Probabilities

In the quantum mechanical Hilbert space formalism, the probabilistic interpretation is a later ad-hoc add-on, more or less enforced by the experimental evidence, but not motivated by the mathematical model itself. A model involving a clear probabilistic interpretation from the very beginning is provided by the quantum logics with unique conditional probabilities. It includes the projection lattices in von Neumann algebras and here probability conditionalization becomes identical with the state transition of the Lueders-von Neumann measurement process. This motivates the definition of a hierarchy of five compatibility and comeasurability levels in the abstract setting of the quantum logics with unique conditional probabilities. Their meanings are： the absence of quantum interference or influence, the existence of a joint distribution, simultaneous measurability, and the independence of the final state after two successive measurements from the sequential order of these two measurements. A further level means that two elements of the quantum logic （events） belong to the same Boolean subalgebra. In the general case, the five compatibility and comeasurability levels appear to differ, but they all coincide in the common Hilbert space formalism of quantum mechanics, in von Neumann algebras, and in some other cases.

Nonparametric inferences for kurtosis and conditional kurtosis

Under the assumption of strictly stationary process, this paper proposes a nonparametric model to test the kurtosis and conditional kurtosis for risk time series. We apply this method to the daily returns of S＆P500 index and the Shanghai Composite Index, and simulate GARCH data for verifying the efficiency of the presented model. Our results indicate that the risk series distribution is heavily tailed, but the historical information can make its future distribution light-tailed. However the far future distribution＇s tails are little affected by the historical data.

Study on the Recurrence Probability of Strong Earthquakes of Faults

Based on the physical model of Brownian passage time,the probabilities of recurrence of strong earthquakes on the major active faults in China are calculated in different predictive time spans,based mainly on the analysis of the earthquake preparation process before a strong earthquake occurs. Furthermore,the seismic risks on active faults are studied. The results show that the earthquake probabilities on the Xianshuihe fault,the Altyn Tagh fault,the east Kunlun fault and Xiaojiang fault are significantly greater than other faults in the Chinese mainland,which indicates that the level of stress accumulation on these faults are higher than on other faults. Therefore,these faults may have a seismic risk for strong earthquake in future.

Propagation characteristics from meteorological drought to agricultural drought over the Heihe River Basin, Northwest China

In the context of global warming,drought events occur frequently.In order to better understanding the process and mechanism of drought occurrence and evolution,scholars have dedicated much attention on drought propagation,mainly focusing on drought propagation time and propagation probability.However,there are relatively few studies on the sensitivities of drought propagation to seasons and drought levels.Therefore,we took the Heihe River Basin(HRB)of Northwest China as the case study area to quantify the propagation time and propagation probability from meteorological drought to agricultural drought during the period of 1981–2020,and subsequently explore their sensitivities to seasons(irrigation and non-irrigation seasons)and drought levels.The correlation coefficient method and Copula-based interval conditional probability model were employed to determine the drought propagation time and propagation probability.The results determined the average drought propagation time as 8 months in the whole basin,which was reduced by 2 months(i.e.,6 months)on average during the irrigation season and prolonged by 2 months(i.e.,10 months)during the non-irrigation season.Propagation probability was sensitive to both seasons and drought levels,and the sensitivities had noticeable spatial differences in the whole basin.The propagation probability of agricultural drought at different levels generally increased with the meteorological drought levels for the upstream,midstream,and southern downstream regions of the HRB.Lesser agricultural droughts were more likely to be triggered during the irrigation season,while severer agricultural droughts were occurred mostly during the non-irrigation season.The research results are helpful to understand the characteristics of drought propagation and provide a scientific basis for the prevention and control of droughts.This study is of great significance for the rational planning of local water resources and maintaining good ecological environment in the HRB.

A cloud Bayesian network approach to situation assessment of scouting underwater targets with fixed-wing patrol aircraft

The battlefield situation changes rapidly because underwater targets'are concealment and the sea environment is uncertain.So,a great number of situation information greatly increase,which need to be dealt with in the course of scouting underwater targets.Situation assessment in sea battlefield with a lot of uncertain information is studied,and a new situation assessment method of scouting underwater targets with fixed-wing patrol aircraft is proposed based on the cloud Bayesian network,which overcomes the deficiency of the single cloud model in reasoning ability and the defect of Bayesian network in knowledge representation.Moreover,in the method,the cloud model knowledge deal with the input data of Bayesian network reasoning,and the advantages in knowledge representation of cloud theory and reasoning of Bayesian network are applied;also,the fuzziness and stochasticity of cloud theory in knowledge expression,the reasoning ability of Bayesian network,are combined.Then,the situation assessment model of scouting underwater targets with fixed-wing patrol aircraft is established.Hence,the directed acyclic graph of Bayesian network structure is constructed and the assessment index is determined.Next,the cloud model is used to deal with Bayesian network,and the discrete Bayesian network is obtained.Moreover,after CPT of each node and the transformation between certainty degree and probability are accomplished;the final situation level is obtained through a probability synthesis formula.Therefore,the target type and the operational intention of the other side are deduced to form the battlefield situation.Finally,simulations are carried out,and the rationality and validity of the proposed method are testified by simulation results.By this method,the battlefield situation can be gained.And this method has a wider application range,especially for large sample data processing,and it has better practicability.

Reliability Risk Evaluation Method for Complex Mechanical System Based on Optimal Bayesian Network

In order to reduce the calculation of the failure probability in the complex mechanical system reliability risk evaluation,and to implement importance analysis of system components effectively,the system fault tree was converted into five different Bayesian network models. The Bayesian network with the minimum conditional probability table specification and the highest computation efficiency was selected as the optimal network. The two heuristics were used to optimize the Bayesian network. The fault diagnosis and causal reasoning of the system were implemented by using the selected Bayesian network. The calculation methods of Fussel-Vesely( FV),risk reduction worth( RRW),Birnbaum measure( BM) and risk achievement worth( RAW) importances were presented. A certain engine was taken as an application example to illustrate the proposed method. The results show that not only the correlation of the relevant variables in the system can be accurately expressed and the calculation complexity can be reduced,but also the relatively weak link in the system can be located accurately.

NEW METHOD TO OBTAIN THE POWER SPECTRA OF HIDDEN VARIABLES AND ITS APPLICATION TO OCEAN DATA

A novel method is proposed to obtain the power spectra of hidden variables in a chaotic time series. By embedding the data in phase space , and recording the conditional probability density of points that the trajectory encounters as it evolves in the reconstructed phase space, it is possible to recover the power spectra of hidden variables in chaotic time series through a spectral analysis over the conditional probability density time series. The method is robust in the application to Lorenz system, 4 dimension Rssler system and rigid body motion by linear feedback system (LFRBM). Applying the method to the time series of sea surface temperature (SST) of the South China Sea, we obtained the power spectra of the wind speed (WS) from SST data. Furthermore, the results showed that there exists an important nonlinear interaction between the SST and the WS.

Statistical Mechanics Model of Liquid Binary Alloy（Ⅱ）─Parameters of Liquid Binary Alloy

Some parameters of liquid binary alloy were investigated , and the calculation formulae were proposed.According to the formulae for calculating coordination number, the accordination numbers of Cu-Zr , Fe-B, Ni-B, Co-P, Fe-P systems were calculated, the results agree well with those in literature and in experiments ofthis study.

Application of Brownian model in the north- western Beijing, China

The mathematic theory of Brownian passage-time model and its difference from other recurrence models such as Poisson, lognormal, gamma and Weibull, were introduced. We assessed and analyzed the earthquake probabilities of the major faults with the elapsed time much greater than the recurrence interval in the northwest region of Bei- jing (China) in 100-year by using both Brownian passage-time model and Poisson model, and concluded that the calculated results obtained from Brownian passage-time model is more reasonable.

Identification of Major Sources of PM2.5 in St. Louis Missouri USA

The objective of this study is to examine the use of the conditional probability function(CPF) and nonparametric regression(NPR) to identify the relationship between wind direction and concentration of PM2.5(particulate matter with aerodynamic diameter less than or equal to 2.5 μm). Twenty four-hour integrated PM2.5 mass and species concentrations were measured at the St. Louis-Midwest Supersite in East St. Louis,Illinois,USA in the periods of 22-28 June 2001,7-13 November 2001,and 19-25 March 2002. Wind directions were measured on site. The concentrations of 15 elements and ions,i.e. Al,As,Cd,Cr,Cu,Fe,Mn,Ni,Pb,Se,Zn,OC,EC,SO4,and NO3 were calculated using the CPF and NPR. The comparison between the results obtained from the CPF and NPR demonstrated that they both agreed well with the locations of the known local point sources. The CPF was simpler and easier to calculate than NPR. In contrast,NPR provided PM2.5 concentrations but with some uncertainties. This study indicates that both methods can be utilized to promote the source apportionment study of ambient PM2.5.

A LIMIT THEOREM FOR INTERACTING MEASURE-VALUED BRANCHING PROCESSES

It is well known that Fleming-Viot superprocesses can be obtained from the Dawson-Watanabe superprocesses by conditioning the latter to have constant total mass. The same question is investigated for measure-valued branching processes with interacting intensity independent of the geographical position. It is showed that a sequence of conditioned probability laws of this kind of interacting measure-valued branching processes also approximates to the probability law of Fleming-Viot superprocesses.

DIAGNOSIS AND IDENTIFICATION OF DYNAMIC CORRELATION FACTORS BETWEEN WEST-PACIFIC SUBTROPICAL HIGH AND EAST ASIA MONSOON SYSTEM INDEXES

Based on the daily reanalysis data of NCEP / NCAR and by using the method of phase space reconstruction, the point conditional probability density of the subtropical high ridge index are determined and then used, together with their power spectra, to seek the correlation between them and individual monsoon-affecting factors and their power spectra. Through diagnosis, six indexes are discovered that have the most important effects on the subtropical high index. The results of the diagnosis indicate that the technique can identify the factors which are dynamically correlated. It can offer the basis in determining and choosing dynamic conceptual factors.

Uncertainty Modeling Based on Bayesian Network in Ontology Mapping

How to deal with uncertainty is crucial in exact concept mapping between ontologies. This paper presents a new framework on modeling uncertainty in ontologies based on bayesian networks （BN）. In our approach, ontology Web language （OWL） is extended to add probabilistie markups for attaching probability information, the source and target ontol ogies （expressed by patulous OWL） are translated into hayesian networks （BNs）, the mapping between the two ontologies can be digged out by constructing the conditional probability tables （CPTs） of the BN using a improved algorithm named I-IPFP based on iterative proportional fitting procedure （IPFP）. The basic idea of this framework and algorithm are validated by positive results from computer experiments.

Improved stress release model: Application to the study of earthquake prediction in Taiwan Region

Stress release model used to be applied to seismicity study of large historical earthquakes in a space of large scale. In this paper, we improve the stress release model, and discuss whether the stress release model is still applicable or not in the case of smaller spatio-temporal scale and weaker earthquakes. As an example of testing the model, we have analyzed the M greater than or equal 6 earthquakes in recent about 100 years. The result shows that the stress release model is still applicable. The earthquake conditional probability intensity in Taiwan Region is calculated with the improved stress release model. We see that accuracy of earthquake occurrence time predicted by the improved stress release model is higher than that by Poisson model in the test of retrospect earthquake prediction.

Long－ and intermediate－termseismic poten－tial of Fen－Wei seismic belt：active fault data application

Recurrence model for strong earthquakes on Fen Wei seismic belt is proposed on the basis of the collection and analysis of fault slip rate, paleoearthquake sequence, maximum displacement of each event etc. on 21 fault segments of the belt, which are active since late Late Pleistocene. And the long and intermediate term seismic potential of the belt has been evaluated through four approaches.

Conditional Probability on the Kpka's D-posets

Kopka＇s D-poset is a very important notion in quantum structures. In this paper the conditional probability on the Kopka＇s D-posets is studied. The notion of conditional probability is introduced and the basic properties of conditional probability are proved.

A Framework for Modern Risk-Informed Root Cause Analysis Process

The paper discusses the framework for a risk-informed root cause analysis process.Such process enables scaling of the analysis performed based on the risk associated with the undesired event or condition,thereby creating tiers of analysis where the greater the risk,the more sophisticated the analysis.In a risk-informed root cause analysis process,a situation is normally not analyzed at a level less than what actually occurred.However,a situation may be investigated as though the consequence were greater than actually happened,especially if only slight differences in circumstances could result in a significantly higher consequence.While operational events or safety issues are normally expected to result only with negligible or marginal actual consequences,many of those would actually have certain potential to develop or propagate into catastrophic events.This potential can be expressed qualitatively or quantitatively.Risk-informing of root cause analysis relies on mapping the event or safety issue into a risk matrix which,traditionally,is a two-dimensional probability-consequence matrix.A new concept employed in the risk matrix for root cause analysis is that,while the probability reflects the observed or expected range of values(retaining,thus,its“traditional”meaning),the consequence reflects not only the observed or materialized impact(such as failure of equipment)but,also,its potential to propagate or develop into highly undesirable final state.The paper presents main elements of risk-informed root cause analysis process and discusses qualitative and quantitative aspects and approaches to determination of risk significance of operational events or safety issues.