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.

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.

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.

SVM model for estimating the parameters of the probability-integral method of predicting mining subsidence

A new mathematical model to estimate the parameters of the probability-integral method for mining subsidence prediction is proposed.Based on least squares support vector machine(LS-SVM) theory, it is capable of improving the precision and reliability of mining subsidence prediction.Many of the geological and mining factors involved are related in a nonlinear way.The new model is based on statistical theory(SLT) and empirical risk minimization(ERM) principles.Typical data collected from observation stations were used for the learning and training samples.The calculated results from the LS-SVM model were compared with the prediction results of a back propagation neural network(BPNN) model.The results show that the parameters were more precisely predicted by the LS-SVM model than by the BPNN model.The LS-SVM model was faster in computation and had better generalized performance.It provides a highly effective method for calculating the predicting parameters of the probability-integral method.

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 results of prediction can provide reference and basis for prevention of coal mining subsidence and future restoration and treatment.

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.

Probability Density Analysis of Nonlinear Random Ship Rolling

Ship rolling in random waves is a complicated nonlinear motion that contributes substantially to ship instability and capsizing.The finite element method(FEM)is employed in this paper to solve the Fokker Planck(FP)equations numerically for homoclinic and heteroclinic ship rolling under random waves described as periodic and Gaussian white noise excitations.The transient joint probability density functions(PDFs)and marginal PDFs of the rolling responses are also obtained.The effects of stimulation strength on ship rolling are further investigated from a probabilistic standpoint.The homoclinic ship rolling has two rolling states,the connection between the two peaks of the PDF is observed when the periodic excitation amplitude or the noise intensity is large,and the PDF is remarkably distributed in phase space.These phenomena increase the possibility of a random jump in ship motion states and the uncertainty of ship rolling,and the ship may lose stability due to unforeseeable facts or conditions.Meanwhile,only one rolling state is observed when the ship is in heteroclinic rolling.As the periodic excitation amplitude grows,the PDF concentration increases and drifts away from the beginning location,suggesting that the ship rolling substantially changes in a cycle and its stability is low.The PDF becomes increasingly uniform and covers a large region as the noise intensity increases,reducing the certainty of ship rolling and navigation safety.The current numerical solutions and analyses may be applied to evaluate the stability of a rolling ship in irregular waves and capsize mechanisms.

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.

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.

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 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.

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.

覆岩导水裂隙带发育高度动态演化规律研究

为了研究覆岩导水裂隙带发育高度动态演化规律,以小保当矿区2^(-2)煤层为研究对象,通过理论分析、相似模拟实验及实例验证的方法,对导水裂隙带动态发育高度进行研究;借助概率积分法预计其上部岩层移动变形的理论公式,给出了1种基于覆岩曲率变形的导水裂隙带动态发育高度预计方法。研究表明:导水裂隙带上部岩层下沉系数是1个与挠度及下部自由空间高度相关的分段函数,上部岩层曲率变形大小是决定导水裂隙带发育高度的关键因素;导水裂隙带发育高度与工作面推进长度相关;理论预计小保当矿区2^(-2)煤层导水裂隙带发育高度为160.8 m,相似模拟实验发育高度为155 m,现场实测发育高度为152.01~175.57 m。

基于F-J-M法的桥梁温度与地震作用效应组合研究

目前铁路桥梁设计逐渐由容许应力法向极限状态法转变,而《铁路桥涵设计规范(极限状态法)》(Q/CR 9300—2018)并未提及地震作用与温度等可变作用的联合作用,给高寒高烈度区桥梁结构抗震设计带来了较大困难。为了推进桥梁以更经济的抗力方式抵御外荷载作用,通过目标可靠度指标确定其最优地震设计状况荷载组合分项系数,从而对现行桥梁设计规范抗震设计进行优化。建立了高寒地区某桥温度作用效应概率模型,使用Ferry Borges荷载组合理论探究地震和环境温度作用的效应分布特征,并基于JC法和多灾害荷载系数设计法(MH-LRFD)建立地震、温度作用荷载系数的表达式。依托某桥梁工程实例分别探究了地震、温度以及两者共同作用下的桥梁的失效概率。研究结果表明:环境温度引起的桥梁温度内力响应、主要构件材料特性变异均能显著影响桥梁的失效概率;对于高寒大温差地区,现行规范忽略环境温度效应将显著低估桥梁在地震作用下的失效概率。本文提出的F-J-M(Ferry Borges+JC+MH-LRFD)方法计算地震、温度作用组合系数,可为高寒地区桥梁抗震设计提供必要理论依据。

鹤壁九矿工作面开采对副井井筒采动影响分析

煤矿副井是地下开采活动的重要通道,肩负着矿井的人员提升、物料运输和通风等重要功能,在井筒保护煤柱开采中对井筒稳定性的研究至关重要。以鹤壁九矿新副井保护煤柱内工作面开采为研究对象,利用概率积分法计算井筒移动变形规律,并以此为基础,通过Drucker-Prager准则对井筒全段岩层的破坏情况进行判定,以此来评价开采方案对新副井的采动影响,可为煤矿的生产规划提供依据,为类似条件矿井井筒保护煤柱开采提供理论指导。

基于蒙特卡罗方法的煤矿爆破作业风险评估

为量化分析煤矿爆破作业各作业步骤造成的风险以及全面客观地对其进行风险评估,借助蒙特卡罗方法建立煤矿爆破作业步骤风险评估模型,对作业流程的行为风险后果值进行累积概率分布,最终依据蒙特卡罗方法模拟的均值结果和作业流程总体风险结果判定各作业步骤的风险大小和风险等级,并提出控制此类不安全行为发生的措施。结果表明:爆破作业流程风险大小顺序依次为清退物品入库、装药、连线、警戒、起爆后安全检查、领取并检查爆破物品、起爆、运送爆破物品、接受爆破任务、作业前安全检查、起爆前安全检查、封孔。

Stein方法在求解随机变量线性组合概率分布中的应用

给出一种基于改进后的Stein方程求解随机变量线性组合概率分布的证明方法.基于随机变量Z_(r)和Z_(r)的线性组合H=m^(-1 )Z_r+n^(-1),利用伽马分布Γ(r,1)的Stein特征,求得关于H的Stein方程;加入二次可微函数,并采用改进后的Stein方程,求得H_(+)和H_(-)概率密度函数及显示公式.

一种基于AK-MCS-K的失效概率函数估计方法

针对可靠性优化设计中失效概率函数求解复杂、计算量大等问题,提出一种求解失效概率函数的高效方法。所提方法的基本思路是利用自主学习Kriging方法构造输入变量全空间在失效边界处的局部代理模型,进而通过该局部代理模型结合Monte Carlo模拟法计算在指定分布参数样本下结构的失效概率,然后基于Kriging方法拟合分布参数样本点与对应结构失效概率之间的函数关系,最终建立用Kriging模型表达的失效概率函数的隐式函数。为了检验所提方法的精度和效率,给出了两个算例,对比了所提方法与已有的求解失效概率函数方法的计算结果。算例结果表明,所提方法适用于求解复杂的功能函数问题,并在满足精度要求的基础上显著降低了计算量。

基于直接概率积分法的列车-轨道-桥梁系统随机分析

由于施工和制造误差使得铁路工程结构参数不可避免地具有不确定性,同时作为系统主要自激励的轨道不平顺亦具有明显的随机性和时变性,因此,探明不确定因子对列车和轨道-桥梁结构动态性能的影响非常重要。为了高效地完成列车-轨道-桥梁系统随机性能分析,建立列车-轨道-桥梁空间振动分析模型,采用轨道不平顺概率模型和谱表达-随机函数的方式在有限随机变量空间中实现轨道不平顺随机过程的高效模拟。引入概率密度积分方程和直接概率积分法发展了列车-轨道-桥梁系统随机动力方程和相应的计算求解策略。基于MATLAB实现了列车-轨道-桥梁随机振动的直接概率积分法分析程序,计算了全概率不平顺激励和参数随机条件下车-轨-桥系统振动响应的均值、标准差和时变的概率密度信息。研究结果表明:与概率密度演化分析方法相比,直接概率积分法可较好地反映行车过程中系统响应的概率密度特征,然而其在系统响应随机后处理时更为高效,其效率可提高1~2个数量级。此外,考虑轨道不平顺全概率激励更能准确地反映行车过程系统响应的概率特征,平均概率谱可能使得计算结果偏于保守;行车速度对于列车和桥梁动态行为的影响是显著的,随着行车速度的增加系统响应的范围逐渐变大。研究结果进一步拓展了列车-轨道-桥梁随机系统的分析方法,可以高效地用于系统状态评估和设计优化。