On the Application of Mixed Models of Probability and Convex Set for Time-Variant Reliability Analysis

In time-variant reliability problems,there are a lot of uncertain variables from different sources.Therefore,it is important to consider these uncertainties in engineering.In addition,time-variant reliability problems typically involve a complexmultilevel nested optimization problem,which can result in an enormous amount of computation.To this end,this paper studies the time-variant reliability evaluation of structures with stochastic and bounded uncertainties using a mixed probability and convex set model.In this method,the stochastic process of a limit-state function with mixed uncertain parameters is first discretized and then converted into a timeindependent reliability problem.Further,to solve the double nested optimization problem in hybrid reliability calculation,an efficient iterative scheme is designed in standard uncertainty space to determine the most probable point(MPP).The limit state function is linearized at these points,and an innovative random variable is defined to solve the equivalent static reliability analysis model.The effectiveness of the proposed method is verified by two benchmark numerical examples and a practical engineering problem.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.

Developing theory of probability density function for stochastic modeling of turbulent gas-particle flows

Turbulent gas-particle flows are studied by a kinetic description using a prob- ability density function （PDF）. Unlike other investigators deriving the particle Reynolds stress equations using the PDF equations, the particle PDF transport equations are di- rectly solved either using a finite-difference method for two-dimensional （2D） problems or using a Monte-Carlo （MC） method for three-dimensional （3D） problems. The proposed differential stress model together with the PDF （DSM-PDF） is used to simulate turbulent swirling gas-particle flows. The simulation results are compared with the experimental results and the second-order moment （SOM） two-phase modeling results. All of these simulation results are in agreement with the experimental results, implying that the PDF approach validates the SOM two-phase turbulence modeling. The PDF model with the SOM-MC method is used to simulate evaporating gas-droplet flows, and the simulation results are in good agreement with the experimental results.

Probability Prediction Model for Landslide Occurrences in Xi'an, Shaanxi Province, China

Landslides are increasing since the 1980s in Xi'an, Shaanxi Province, China. This is due to the increase of the frequency and intensity of precipitation caused by complex geological structures, the presence of steep landforms, seasonal heavy rainfall, and the intensifcation of human activities. In this study, we propose a landslide prediction model based on the analysis of intraday rainfall(IR) and antecedent effective rainfall(AER). Primarily, the number of days and degressive index of the antecedent effective rainfall which affected landslide occurrences in the areas around Qin Mountains, Li Mountains and Loess Tableland was established. Secondly, the antecedent effective rainfall and intraday rainfall were calculated from weather data which were used to construct critical thresholds for the 10%, 50% and 90% probabilities for future landslide occurrences in Qin Mountain, Li Mountain and Loess Tableland. Finally, the regions corresponding to different warning levels were identified based on the relationship between precipitation and the threshold, that is; "A" region is safe, "B" region is on watch alert, "C" region is on warning alert and "D" region is on severe warning alert. Using this model, a warning program is proposed which can predict rainfall-induced landslides by means of real-time rain gauge data and real-time geo-hazard alert and disaster response programs. Sixteen rain gauges were installed in the Xi'an region by keeping in accordance with the regional geology and landslide risks. Based on the data from gauges, this model accurately achieves the objectives of conducting real-time monitoring as well as providing early warnings of landslides in the Xi'an region.

Probability-based analytical model for predicting the post-earthquake residual deformation of SDOF systems

A probability-based analytical model for predicting the seismic residual deformation of bilinear single-degreeof-freedom(SDOF)systems with a kinematic/Takeda hysteretic model is proposed based on a statistical analysis of the nonlinear time history response,and the proposed model explicitly incorporates the influence of record-to-record variability.In addition,the influence of primary parameters such as the natural vibration period,relative yield force coefficient,stiffness ratio and peak ground acceleration(PGA)on the seismic residual/maximum deformation ratio(dR/dm)are investigated.The results show that significant dispersion of the dR/dm ratio is observed for SDOF systems under different seismic ground motion records,and the dispersion degree is influenced by the model parameters and record-to-record variability.The statistical distribution of the dR/dm results of SDOF systems can be described by a lognormal distribution.Finally,a case study for seismic residual deformation and reparability assessment of the bridge structure designed with a single pier is carried out to illustrate the detailed analytical procedure of the probability-based analytical model proposed in this study.

A Danger Estimation System for Infants Based on a Foreground Dynamic Probability Model

This study presents a danger estimation system to prevent accidents among infants. A video camera positioned above the infant＇s crib captures video. The proposed system can monitor the behavior of infants aged zero to six months. If there is a change in behavior or any other unusual occurrence, the system alerts the person responsible to attend to the baby immediately. The proposed system operates in three phases, which are foreground color model （FC model） construction, infant detection, and degree of danger analysis. During FC model construction, the foreground color histogram is created iteratively; the background image does not have to be constructed first. A motion-history image （MHI） is also obtained based on the motion of the infant. The color and motion information supplied by the FC model and the MHI are combined to detect the infant, who is regarded as the foreground object in the input frame. Moreover, six features of infant behavior are extracted from the detected infant to measure the degree of danger faced by the infant, and the result is used to warn the baby-sitter if needed. Experimental results show that the proposed method is robust and efficient.

The efficiency and accuracy of probability diagram, spatial statistic and fractal methods in the identification of shear zone gold mineralization: a case study of the Saqqez gold ore district,NW Iran

In this study,geochemical anomaly separation was carried out with methods based on the distribution model,which includes probability diagram(MPD),fractal(concentration-area technique),and U-statistic methods.The main objective is to evaluate the efficiency and accuracy of the methods in separation of anomalies on the shear zone gold mineralization.For this purpose,samples were taken from the secondary lithogeochemical environment(stream sediment samples)on the gold mineralization in Saqqez,NW of Iran.Interpretation of the histograms and diagrams showed that the MPD is capable of identifying two phases of mineralization.The fractal method could separate only one phase of change based on the fractal dimension with high concentration areas of the Au element.The spatial analysis showed two mixed subpopulations after U=0 and another subpopulation with very high U values.The MPD analysis followed spatial analysis,which shows the detail of the variations.Six mineralized zones detected from local geochemical exploration results were used for validating the methods mentioned above.The MPD method was able to identify the anomalous areas higher than 90%,whereas the two other methods identified 60%(maximum)of the anomalous areas.The raw data without any estimation for the concentration was used by the MPD method using aminimum of calculations to determine the threshold values.Therefore,the MPD method is more robust than the other methods.The spatial analysis identified the detail soft hegeological and mineralization events that were affected in the study area.MPD is recommended as the best,and the spatial U-analysis is the next reliable method to be used.The fractal method could show more detail of the events and variations in the area with asymmetrical grid net and a higher density of sampling or at the detailed exploration stage.

A New Probability of Detection Model for Updating Crack Distribution of Offshore Structures

There exists model uncertainty of probability of detection for inspecting ship structures with nondestructive inspection techniques. Based on a comparison of several existing probability of detection (POD) models, a new probability of detection model is proposed for the updating of crack size distribution. Furthermore, the theoretical derivation shows that most existing probability of detection models are special cases of the new probability of detection model. The least square method is adopted for determining the values of parameters in the new POD model. This new model is also compared with other existing probability of detection models. The results indicate that the new probability of detection model can fit the inspection data better. This new probability of detection model is then applied to the analysis of the problem of crack size updating for offshore structures. The Bayesian updating method is used to analyze the effect of probability of detection models on the posterior distribution of a crack size. The results show that different probabilities of detection models generate different posterior distributions of a crack size for offshore structures.

Auxiliary error and probability density function based neuro-fuzzy model and its application in batch processes

This paper focuses on resolving the identification problem of a neuro-fuzzy model(NFM) applied in batch processes. A hybrid learning algorithm is introduced to identify the proposed NFM with the idea of auxiliary error model and the identification principle based on the probability density function(PDF). The main contribution is that the NFM parameter updating approach is transformed into the shape control for the PDF of modeling error. More specifically, a virtual adaptive control system is constructed with the aid of the auxiliary error model and then the PDF shape control idea is used to tune NFM parameters so that the PDF of modeling error is controlled to follow a targeted PDF, which is in Gaussian or uniform distribution. Examples are used to validate the applicability of the proposed method and comparisons are made with the minimum mean square error based approaches.

Research on the Applications of Probability Model and Matrix Transformation in Data Analysis and Management under the Environment of Information Time

In this paper, we research the probability theory and matrix transformation based technique to manage the data for processing and analysis. Clustering analysis research has a long history, over the decades, the importance and the cross characteristics with other research direction to get the affirmation of the people. The probability theory and linear algebra act as the powerful tool for analyzing and mining data. The experimental result illustrates the effectiveness. In the near future, we plan to conduct more theoretical analysis on the topic.

The estimation of yearly probability gain for seismic statistical model

Based on the calculation method of information gain in the stochastic process presented by Vere-Jones, the rela tion between information gain and probability gain is studied, which is very common in earthquake prediction, and the yearly probability gain for seismic statistical model is proposed. The method is applied to the non stationary Poisson model with whole-process exponential increase and stress release model. In addition, the prediction method of stress release model is obtained based on the inverse function simulation method of stochastic variable.

Passengers gathering-scattering analysis at the corners of subway stations

During both daily operation and emergency evacuation,the corners of walking facilities in subway stations play an important role in efficient circulation.However,the effectiveness of the corner is difficult to assess.In this paper,a method of passenger gathering and scattering analysis based on queueing models was proposed to investigate the corner performance in subway stations.Firstly,we constructed a set of state spaces of passenger flow according to passenger density and proposed the state transition model of passenger flow.Moreover,the model of passenger flow blocking and unblocking probability were also presented.Then,to illustrate the validity of the method and model,several passenger gathering-scattering scenarios and were simulated to verify the influence of passenger distribution and facility width on passenger walking,and the blocking probability,throughput,and expected time were also analyzed under various widths of the target corridor and arrival rates.Results showed that the proposed model can reproduce the trend of walking parameters changing and the self-organizing phenomenon of'faster is lower'.With the increase of arrival rates of passengers,walking speeds of passengers decrease and the expected walking time is prolonged,and the blocking probability sharply increased when the arrival rate exceeded 7 peds/s.In addition,with change of width of the target facility,efficiency of capacity of walking circulation facility fluctuated.With the width of the target corridor enlarged by 10%,the steady state of passenger flow was less crowded.Therefore,corridor width is critical to the circulation efficiency of passengers in subway stations.The conclusions will help to develop reasonable passenger flow control plans to ease the jam and keep passengers walking safely.

Feature study for improving Chinese overlapping ambiguity resolution based on SVM

In order to improve Chinese overlapping ambiguity resolution based on a support vector machine, statistical features are studied for representing the feature vectors. First, four statistical parameters-mutual information, accessor variety, two-character word frequency and single-character word frequency are used to describe the feature vectors respectively. Then other parameters are tried to add as complementary features to the parameters which obtain the best results for further improving the classification performance. Experimental results show that features represented by mutual information, single-character word frequency and accessor variety can obtain an optimum result of 94. 39%. Compared with a commonly used word probability model, the accuracy has been improved by 6. 62%. Such comparative results confirm that the classification performance can be improved by feature selection and representation.

Advances in statistical mechanics of rock masses and its engineering applications

To efficiently link the continuum mechanics for rocks with the structural statistics of rock masses,a theoretical and methodological system called the statistical mechanics of rock masses(SMRM)was developed in the past three decades.In SMRM,equivalent continuum models of stressestrain relationship,strength and failure probability for jointed rock masses were established,which were based on the geometric probability models characterising the rock mass structure.This follows the statistical physics,the continuum mechanics,the fracture mechanics and the weakest link hypothesis.A general constitutive model and complete stressestrain models under compressive and shear conditions were also developed as the derivatives of the SMRM theory.An SMRM calculation system was then developed to provide fast and precise solutions for parameter estimations of rock masses,such as full-direction rock quality designation(RQD),elastic modulus,Coulomb compressive strength,rock mass quality rating,and Poisson’s ratio and shear strength.The constitutive equations involved in SMRM were integrated into a FLAC3D based numerical module to apply for engineering rock masses.It is also capable of analysing the complete deformation of rock masses and active reinforcement of engineering rock masses.Examples of engineering applications of SMRM were presented,including a rock mass at QBT hydropower station in northwestern China,a dam slope of Zongo II hydropower station in D.R.Congo,an open-pit mine in Dexing,China,an underground powerhouse of Jinping I hydropower station in southwestern China,and a typical circular tunnel in Lanzhou-Chongqing railway,China.These applications verified the reliability of the SMRM and demonstrated its applicability to broad engineering issues associated with jointed rock masses.

Role of street patterns in zone-based traffic safety analysis

Although extensive analyses of road segments and intersections located in urban road networks have examined the role of many factors that contribute to the frequency and severity of crashes, the explicit relationship between street pattern characteristics and traffic safety remains underexplored. Based on a zone-based Hong Kong database, the Space Syntax was used to quantify the topological characteristics of street patterns and investigate the role of street patterns and zone-related factors in zone-based traffic safety analysis. A joint probability model was adopted to analyze crash frequency and severity in an integrated modeling framework and the maximum likelihood estimation method was used to estimate the parameters. In addition to the characteristics of street patterns, speed, road geometry, land-use patterns, and temporal factors were considered. The vehicle hours was also included as an exposure proxy in the model to make crash frequency predictions. The results indicate that the joint probability model can reveal the relationship between zone-based traffic safety and various other factors, and that street pattern characteristics play an important role in crash frequency prediction.

Visual SLAM in dynamic environments based on object detection

A great number of visual simultaneous localization and mapping(VSLAM)systems need to assume static features in the environment.However,moving objects can vastly impair the performance of a VSLAM system which relies on the static-world assumption.To cope with this challenging topic,a real-time and robust VSLAM system based on ORB-SLAM2 for dynamic environments was proposed.To reduce the influence of dynamic content,we incorporate the deep-learning-based object detection method in the visual odometry,then the dynamic object probability model is added to raise the efficiency of object detection deep neural network and enhance the real-time performance of our system.Experiment with both on the TUM and KITTI benchmark dataset,as well as in a real-world environment,the results clarify that our method can significantly reduce the tracking error or drift,enhance the robustness,accuracy and stability of the VSLAM system in dynamic scenes.

Superposition model for analyzing the dynamic ground subsidence in mining area of thick loose layer

The dynamic ground subsidence due to underground mining is a complicated time-dependent and rate- dependent process. Based. on the theory of rock rheology and probability integral method, this study developed the superposltlOn model for the prediction and analysis of the ground dynamic subsidence in mining area of thick !oose layer. The model consists of two parts （the prediction of overlying bedrock and the prediction of thick loose layer）. The overlying bedrock is regarded as visco-elastic beam, of which the dynamic subsidence is predicted by the Kelvin visco-elastic rheological model. The thick loose layer is regarded as random medium, and the ground dynamic subsidence, is predicted by the probability integral model. At last, the two prediction models are vertically stacked in the same coordinate system, and the bedrock dynamic subsidence is regarded as a variable mining thickness input into the prediction model of ground dynamic subsidence. The prediction results obtained were compared w^th actual movement and deformation data from Zhao I and Zhao II mine, central China. The agreement of the prediction results with the. field measurements.show that the superposition model （SM） is more satisfactory and the formulae obtained are more effective than the classical single probability Integral model（SPIM）, and thus can be effectively used for predicting the ground dynamic subsidence in mining area of thick loose layer.

Probabilistic Approach of Coastal Defense Against Typhoon Attacks for Nuclear Power Plant

With the global warming and sea level rising, it is widely recognized that there is an increasing tendency of typhoon occurrence frequency and intensity. The defenses code against typhoon attacks for nuclear power plant should be calibrated because of the increasing threat of typhoon disaster and severe consequences. This paper discusses the probabilistic approach of definitions about ＂probable maximum typhoon＂ and ＂probable maximum storm surge＂ in nuclear safety regulations of China and has made some design code calibrations by use of a newly proposed Double Layer Nested Mtdti-objective Probability Model （DLNMPM）.

Assessment of immunization procedures for foot-and-mouth disease in large-scale pig farms in China based on actual data and dynamics

Foot-and-mouth disease(FMD)is an acute,highly infectious and pathogenic animal disease.In recent years,with the rapid development of the swine breeding industry in China,pig farms have shown a trend of larger-scale development.Large-scale pig farms employ standardized management,a high level of automation,and a strict_system.However,these farms have a large trading volume,and increased transmission intensity of FMD is noted inside the farm.At present,the main control measure against FMD is pig vaccination.However,a standard for immunization procedures is not available,and currently adopted immunization procedures have not been effectively and systematically evaluated.Taking a typical large-scale pig farm in China as the research subject and considering the breeding pattern,piggery structure,age structure and immunization procedures,an individual-based state probability model is established to evaluate the effectiveness of the immune procedure.Based on numerical simulation,it is concluded that the optimal immunization program involves primary immunization at 40 days of age and secondary immunization at 80 days of age for commercial pigs.Breeding boars and breeding sows are immunized 4 times a year,and reserve pigs are immunized at 169 and 259 days of age.According to the theoretical analysis,the average control reproduction number of individuals under the optimal immunization procedure in the farm is 0.4927.In the absence of immunization,the average is 1.7498,indicating that the epidemic cannot be controlled without immunization procedures.

Existence and Uniqueness of Positive Solutions for a System of Multi-order Fractional Differential Equations

In this paper, we study a class of ruin problems, in which premiums and claims are dependent. Under the assumption that premium income is a stochastic process, we raise the model that premiums and claims are dependent, give its numerical characteristics and the ruin probability of the individual risk model in the surplus process. In addition, we promote the number of insurance policies to a Poisson process with parameter λ, using martingale methods to obtain the upper bound of the ultimate ruin probability.