High-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer based on probability density evolution method

This paper proposed an efficient research method for high-dimensional uncertainty quantification of projectile motion in the barrel of a truck-mounted howitzer.Firstly,the dynamic model of projectile motion is established considering the flexible deformation of the barrel and the interaction between the projectile and the barrel.Subsequently,the accuracy of the dynamic model is verified based on the external ballistic projectile attitude test platform.Furthermore,the probability density evolution method(PDEM)is developed to high-dimensional uncertainty quantification of projectile motion.The engineering example highlights the results of the proposed method are consistent with the results obtained by the Monte Carlo Simulation(MCS).Finally,the influence of parameter uncertainty on the projectile disturbance at muzzle under different working conditions is analyzed.The results show that the disturbance of the pitch angular,pitch angular velocity and pitch angular of velocity decreases with the increase of launching angle,and the random parameter ranges of both the projectile and coupling model have similar influence on the disturbance of projectile angular motion at muzzle.

A model for extracting large deformation mining subsidence using D-InSAR technique and probability integral method

Due to the difficulties in obtaining large deformation mining subsidence using differential Interferometric Synthetic Aperture Radar （D-InSAR） alone, a new algorithm was proposed to extract large deformation mining subsidence using D-InSAR technique and probability integral method. The details of the algorithm are as follows：the control points set, containing correct phase unwrapping points on the subsidence basin edge generated by D-InSAR and several observation points （near the maximum subsidence and inflection points）, was established at first; genetic algorithm （GA） was then used to optimize the parameters of probability integral method; at last, the surface subsidence was deduced according to the optimum parameters. The results of the experiment in Huaibei mining area, China, show that the presented method can generate the correct mining subsidence basin with a few surface observations, and the relative error of maximum subsidence point is about 8.3%, which is much better than that of conventional D-InSAR （relative error is 68.0%）.

Study of probability integration method parameter inversion by the genetic algorithm

In order to obtain accurate probability integration method(PIM) parameters for surface movement of multi-panel mining, a genetic algorithm(GA) was used to optimize the parameters. As the measured surface movement is affected by more than one mining panel, traditional PIM parameter inversion model is difficult to ensure the reliability of the results due to the complexity of rock movement. With crossover,mutation and selection operators, GA can perform a global optimization search and has high computation efficiency. Compared with the pattern search algorithm, the fitness function can avoid falling into local minima traps. GA reduces the risk of local minima traps which improves the accuracy and reliability with the mutation mechanism. Application at Xuehu colliery shows that GA can be used to inverse the PIM parameters for multi-panel surface movement observation, and reliable results can be obtained. The research provides a new way for back-analysis of PIM parameters for mining subsidence under complex conditions.

Nonlinear finite-element-based structural system failure probability analysis methodology for gravity dams considering correlated failure modes

The structural system failure probability(SFP) is a valuable tool for evaluating the global safety level of concrete gravity dams.Traditional methods for estimating the failure probabilities are based on defined mathematical descriptions,namely,limit state functions of failure modes.Several problems are to be solved in the use of traditional methods for gravity dams.One is how to define the limit state function really reflecting the mechanical mechanism of the failure mode;another is how to understand the relationship among failure modes and enable the probability of the whole structure to be determined.Performing SFP analysis for a gravity dam system is a challenging task.This work proposes a novel nonlinear finite-element-based SFP analysis method for gravity dams.Firstly,reasonable nonlinear constitutive modes for dam concrete,concrete/rock interface and rock foundation are respectively introduced according to corresponding mechanical mechanisms.Meanwhile the response surface(RS) method is used to model limit state functions of main failure modes through the Monte Carlo(MC) simulation results of the dam-interface-foundation interaction finite element(FE) analysis.Secondly,a numerical SFP method is studied to compute the probabilities of several failure modes efficiently by simple matrix integration operations.Then,the nonlinear FE-based SFP analysis methodology for gravity dams considering correlated failure modes with the additional sensitivity analysis is proposed.Finally,a comprehensive computational platform for interfacing the proposed method with the open source FE code Code Aster is developed via a freely available MATLAB software tool(FERUM).This methodology is demonstrated by a case study of an existing gravity dam analysis,in which the dominant failure modes are identified,and the corresponding performance functions are established.Then,the dam failure probability of the structural system is obtained by the proposed method considering the correlation relationship of main failure modes on the basis of the mechanical mechanism analysis with the MC-FE simulations.

Numerical method of slope failure probability based on Bishop model

Based on Bishop's model and by applying the first and second order mean deviations method, an approximative solution method for the first and second order partial derivatives of functional function was deduced according to numerical analysis theory. After complicated multi-independent variables implicit functional function was simplified to be a single independent variable implicit function and rule of calculating derivative for composite function was combined with principle of the mean deviations method, an approximative solution format of implicit functional function was established through Taylor expansion series and iterative solution approach of reliability degree index was given synchronously. An engineering example was analyzed by the method. The result shows its absolute error is only 0.78% as compared with accurate solution.

A Fast Product of Conditional Reduction Method for System Failure Probability Sensitivity Evaluation

Systemreliability sensitivity analysis becomes difficult due to involving the issues of the correlation between failure modes whether using analytic method or numerical simulation methods.A fast conditional reduction method based on conditional probability theory is proposed to solve the sensitivity analysis based on the approximate analytic method.The relevant concepts are introduced to characterize the correlation between failure modes by the reliability index and correlation coefficient,and conditional normal fractile the for the multi-dimensional conditional failure analysis is proposed based on the two-dimensional normal distribution function.Thus the calculation of system failure probability can be represented as a summation of conditional probability terms,which is convenient to be computed by iterative solving sequentially.Further the system sensitivity solution is transformed into the derivation process of the failure probability correlation coefficient of each failure mode.Numerical examples results show that it is feasible to apply the idea of failure mode relevancy to failure probability sensitivity analysis,and it can avoid multi-dimension integral calculation and reduce complexity and difficulty.Compared with the product of conditional marginalmethod,a wider value range of correlation coefficient for reliability analysis is confirmed and an acceptable accuracy can be obtained with less computational cost.

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.

Application of probability integral method in ground deformation prediction

In order to study the law of mining subsidence and ground movement, to provide the basis of coal mining under building, railway and water, we used the probability integration method to make comprehensive evaluation of ground stability. Take Yingcheng Coal Mine of Jiutai as an example. Mining-induced movement and horizontal movement are analyzed on the basis of the measurement data. The resuhs of prediction can pro- vide reference and basis for prevention of coal mining subsidence and future restoration and treatment.

A CALCULATING METHOD OF THE KILL PROBABILITY ATTACK AREA FOR AAM

This paper provides a calculating method which can be used in calculation of the kill probability attack area for every AAM. At first, attack area of AAM and kill probability of every characteristic point are obtained by combining trajectory calculation with kill probability calculation. Then, coordinates of a fire point relative to standard kill probability value in terms of standardization method are found. At last, equivalent kill probability curve equations are formulated by means of curve fitting method.

A probability-consistent method based on practical ground surface motion

In this paper, a new method for seismic hazard analysis, the probability-consistent method based on practical ground surface motion is proposed. Time histories on ground surface in the method correspond to earthquakes occurring at potential sources around sites. So of the envelope parameter, response spectrum, peak ground acceleration are of physical sense. Neglecting the response of site soil layers, the method is the same as routine probability-consistent method. The natural seismic acceleration time histories can be used for input wave directly. Generating ground motion is an approximation under lack of data of strong motion. Along with accumulating of the strong motion data around sites, we can describe the seismic environment more objectively.

Probabilistic Response and Short-Term Extreme Load Estimation of Offshore Monopile Wind Turbine Towers by Probability Density Evolution Method

A new analysis framework based on probability density evolution method(PDEM)and its Chebyshev collocation solution are introduced to predict the dynamic response and short-term extreme load of offshore wind turbine(OWT)towers subjected to random sea state.With regard to the stochastic responses,random function method is employed to generate samples of sea elevation,the probability density evolution equation(PDEE)is solved to calculate time-variant probability density functions of structural responses.For the probabilistic load estimation,a FAST model of NREL 5MW offshore turbine is established to obtain samples of bending moment at the tower base.The equivalent extreme event theory is used to construct a virtual stochastic process(VSP)to assess the short-term extreme load.The results indicate that the proposed approach can predict time-variant probability density functions of the structural responses,and shows good agreement with Monte Carlo simulations.Additionally,the predicted short-term extreme load can capture the fluctuation at the tail of the extreme value distribution,thus is more rational than results from the typical distribution models.Overall,the proposed method shows good adaptation,precision and efficiency for the dynamic response analysis and load estimation of OWT towers.

Study on the offset of inflection point about probability function method

In this paper, rock mass is regarded as anisotropic clastic units and the partial differential equation of subsidence has been testified. The solution about homogeneous anisotropy has been obtained. The existence of inflection point offset in subsidence formula has been proved. Lastly, the relevant influence factors about the offset of inflection point have been simply discussed.

Monte Carlo method for evaluation of surface emission rate measurement uncertainty

The aim of this study is to evaluate the uncertainty of 2πα and 2πβ surface emission rates using the windowless multiwire proportional counter method.This study used the Monte Carlo method (MCM) to validate the conventional Guide to the Expression of Uncertainty in Measurement (GUM) method.A dead time measurement model for the two-source method was established based on the characteristics of a single-channel measurement system,and the voltage threshold correction factor measurement function was indirectly obtained by fitting the threshold correction curve.The uncertainty in the surface emission rate was calculated using the GUM method and the law of propagation of uncertainty.The MCM provided clear definitions for each input quantity and its uncertainty distribution,and the simulation training was realized with a complete and complex mathematical model.The results of the surface emission rate uncertainty evaluation for four radioactive plane sources using both methods showed the uncertainty’s consistency E_(n)<0.070 for the comparison of each source,and the uncertainty results of the GUM were all lower than those of the MCM.However,the MCM has a more objective evaluation process and can serve as a validation tool for GUM results.

Research on the Application of PBL+SPOC Blended Teaching Model in Probability and Statistics Course

To cultivate talents with an exploratory spirit and practical skills in the era of information technology,it is imperative to reform teaching methods and approaches.In the teaching process of the Probability and Statistics course,an application-oriented blended teaching model combining problem-based learning and small private online course was explored.By organizing and implementing online and offline teaching activities based on problem-based learning,a multidimensional process-oriented learning assessment system was established.Practice has shown that this model can effectively enhance classroom teaching effectiveness,benefiting the improvement of students’overall skills and mathematical literacy.

基于概率的震级完备度方法评估云南地震台网的监测能力

为了科学评估云南地震台网的监测能力,分析云南地区的地震监测能力时空分布特征,采用基于概率的震级完备度(PMC)方法,利用2009-2023年云南地震台网地震目录、震相和台站信息等数据,计算了云南地震台网在云南地区的平均地震监测能力和在不同深度的监测能力,得到滇中、滇西局部地区的基于概率的完备性震级M_(P)=1.5,云南全境基本都能监测到2.5级地震。评估了研究时段内云南地震台网台站监测能力的演变,发现部分台站的监测能力持续下降。但自2018年增加20个台站后,云南2.0及2.5级地震的监测范围有一定的扩大,但微震监测能力提升不明显,可能是因为2018年以来云南一直处于小震弱活动状态。最后,对应用PMC方法规划提升台网监测能力进行了展望。

Monte Carlo numerical simulation and its application in probability analysis of long span bridges

To get the probability of long span bridges under the influence of external random factors, the Monte Carlo method using Latin hypercube sampling is applied. Combined with the condition assessment system on Runyang Suspension Bridge, which is the longest suspension bridge in China, the structural probabilities in normal and damaged situations are calculated with the external random factors considered including environmental temperature, wind load, load of vehicles, etc. The main assessment items contain the maximal vertical displacement of girder, the maximal stress of cables, the maximal horizontal displacement of towers etc. Finally, the probabilities and their cumulative distribution functions are provided. The analysis results can be plotted on line in a clear and vivid way, so the efficiency of assessment is increased and the decision-making of maintenance is more objective and accurate.

Recovering implied risk-neutral probability density function using SVR

Using support vector regression （SVR）, a novel non-parametric method for recovering implied risk-neutral probability density function （IRNPDF） is investigated by solving linear operator equations. First, the SVR principle for function approximation is introduced, and an SVR method for solving linear operator equations with knowing some values of the right-hand function and without knowing its form is depicted. Then, the principle for solving the IRNPDF based on SVR and the method for constructing cross-kernel functions are proposed. Finally, an empirical example is given to verify the validity of the method. The results show that the proposed method can overcome the shortcomings of the traditional parametric methods, which have strict restrictions on the option exercise price; meanwhile, it requires less data than other non-parametric methods, and it is a promising method for the recover of IRNPDF.

A Numerical Method for Calculating Transmission Coefficients Across Arbitrary Potential Barriers with High Accuracy

We report a new method for calculating transmission coefficients across arbitrary potential barriers based on the Runge-Kutta method. A numerical solution of the Schrodinger equation is calculated using the Runge-Kutta method,and a new model is established to analyze the numerical results to find the transmission coefficient. This technique is applied to various cases, such as parabolic potential barrier and double-barrier structures. Transmission probability with high precision is obtained and discussed. The tunnelling current density through a MOS structure is also explored and the result coincides with the Fowler-Nordheim model,which indicates the applicability of our method.

A new method of formation evaluation for fractured and caved carbonate reservoirs:A case study from the Lundong area,Tarim Basin,China

The carbonate reservoirs in the Tarim Basin are characterized by low matrix-porosity,heterogeneity and anisotropy,which make it difficult to predict and evaluate these reservoirs.The reservoir formations in Lundong area experienced a series of diagenesis and tectonic evolution stages.And secondary storage spaces such as fractures and dissolution caves were developed while nearly all the primary pores have disappeared.Based on a summary of different types of storage spaces and their responses in conventional logs,FMI and full waveform sonic logs which are sensitive to different reservoirs,the comprehensive probability index （CPI） method is applied to evaluating the reservoirs and a standard of reservoir classification is established.By comparing the evaluation results with actual welllogging results,the method has proven to be practical for formation evaluation of carbonate reservoirs,especially for the fractured carbonate reservoirs.In reservoir fluid identification,the multivariate stepwise discriminant analysis （MSDA） method is introduced.Combining the CPI method and MSDA method,comprehensive formation evaluation has been performed for fractured and caved carbonate reservoirs in the Tarim Basin.Additionally,on the basis of secondary pore inversion results,another new method of formation evaluation is also proposed in the discussion part of this paper.Through detailed application result analysis,the method shows a promising capability for formation evaluation of complex carbonate reservoirs dominated by various secondary pores such as holes,caves,and cracks.