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.

An equivalent target plate damage probability calculation mathematics model and damage evaluation method

Aiming at the requirement of damage testing and evaluation of equivalent target plate based on the explosion of intelligent ammunition, this paper proposes a novel method for damage testing and evaluation method of circumferential equivalent target plate. Leveraging the dispersion characteristics parameters of fragment, we establish a calculation model of the fragment power situation and the damage calculation model under the condition of fragment ultimate penetration equivalent target plate. The damage model of equivalent target plate involves the fragment dispersion density, the local perforation damage criterion, the tearing damage model, and the damage probability. We use the camera to obtain the image of the equivalent target plate with fragment perforation, and research the algorithm of fragment distribution position recognition and fragment perforation area calculation method on the equivalent target plate by image processing technology. Based on the obtained parameters of the breakdown position and perforation area of fragments on equivalent target plate, we apply to damage calculation model of equivalent target plate, and calculate the damage probability of each equivalent target plate, and use the combined probabilistic damage calculation method to obtain the damage evaluation results of the circumferential equivalent target plate in an intelligent ammunition explosion experiment. Through an experimental testing, we verify the feasibility and rationality of the proposed damage evaluation method by comparison, the calculation results can reflect the actual damage effect of the equivalent target plate.

Insight Into the Separation-of-Variable Methods for the Closed-Form Solutions of Free Vibration of Rectangular Thin Plates

The separation-of-variable(SOV)methods,such as the improved SOV method,the variational SOV method,and the extended SOV method,have been proposed by the present authors and coworkers to obtain the closed-form analytical solutions for free vibration and eigenbuckling of rectangular plates and circular cylindrical shells.By taking the free vibration of rectangular thin plates as an example,this work presents the theoretical framework of the SOV methods in an instructive way,and the bisection–based solution procedures for a group of nonlinear eigenvalue equations.Besides,the explicit equations of nodal lines of the SOV methods are presented,and the relations of nodal line patterns and frequency orders are investigated.It is concluded that the highly accurate SOV methods have the same accuracy for all frequencies,the mode shapes about repeated frequencies can also be precisely captured,and the SOV methods do not have the problem of missing roots as well.

Structural Modal Parameter Recognition and Related Damage Identification Methods under Environmental Excitations: A Review

Modal parameters can accurately characterize the structural dynamic properties and assess the physical state of the structure.Therefore,it is particularly significant to identify the structural modal parameters according to the monitoring data information in the structural health monitoring(SHM)system,so as to provide a scientific basis for structural damage identification and dynamic model modification.In view of this,this paper reviews methods for identifying structural modal parameters under environmental excitation and briefly describes how to identify structural damages based on the derived modal parameters.The paper primarily introduces data-driven modal parameter recognition methods(e.g.,time-domain,frequency-domain,and time-frequency-domain methods,etc.),briefly describes damage identification methods based on the variations of modal parameters(e.g.,natural frequency,modal shapes,and curvature modal shapes,etc.)and modal validation methods(e.g.,Stability Diagram and Modal Assurance Criterion,etc.).The current status of the application of artificial intelligence(AI)methods in the direction of modal parameter recognition and damage identification is further discussed.Based on the pre-vious analysis,the main development trends of structural modal parameter recognition and damage identification methods are given to provide scientific references for the optimized design and functional upgrading of SHM systems.

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%）.

Probability evaluation method for cable safety of long-span cable-stayed bridges

A method of cable safety analysis is proposed for safety evaluation of long-span cable-stayed bridges. The Daniels＇ effect and the probability of broken wires in the cable are introduced to develop the cable strength model and the reliability assessment technique for long-span cable-stayed bridges based on the safety factors analysis of stay cables in service. As an application of the proposed model, the cable safety reliability of the cable No. 25 of Zhaobaoshan cable-stayed bridge in China is calculated. The effects of various parameters on the estimated cable safety reliability are investigated. The results indicate that the proposed method can be used to assess the safety level of stay cables in cable-stayed bridges effectively. The Daniels＇ effect should be taken into account for assessment, and the probability of broken wires can be used to simulate the deterioration of stay cables in service.

AN IMPROVED FOSM METHOD FOR CALCULATING FAILURE PROBABILITY OF WELDED PIPES WITH FLAWS

The R F first order second moment method will produce more error for calculating the reliability of welded engineering pipe structures when the failure function is seriously nonlinear and the random variables don′t serve as normal distribution. In order to increase the computing accuracy of reliability, an improved FOSM method is used for calculating the failure probability of welded pipes with flaws in this paper. Because of solving the problems of the linear expansion of failure function at the failure point and constructing equivalent normal variables, the new algorithm can greatly improve the calculating accuracy of probability of the welded pipes with cracks. The examples show that this method is simple, efficient and accurate for reliability safety assessment of the welded pipes with cracks. It can save more time than the Monte Carlo method does, so that the improved FOSM method is recommended for engineering reliability safety assessment of the welded pipes with flaws.

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.

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.

Evaluation of the effect of geometrical parameters on stope probability of failure in the open stoping method using numerical modeling

Stress-induced failure is among the most common causes of instability in Canadian deep underground mines.Open stoping is the most widely practiced underground excavation method in these mines,and creates large stopes which are subjected to stress-induced failure.The probability of failure(POF)depends on many factors,of which the geometry of an open stope is especially important.In this study,a methodology is proposed to assess the effect of stope geometrical parameters on the POF,using numerical modelling.Different ranges for each input parameter are defined according to previous surveys on open stope geometry in a number of Canadian underground mines.A Monte-Carlo simulation technique is combined with the finite difference code FLAC3D,to generate model realizations containing stopes with different geometrical features.The probability of failure(POF)for different categories of stope geometry,is calculated by considering two modes of failure;relaxation-related gravity driven(tensile)failure and rock mass brittle failure.The individual and interactive effects of stope geometrical parameters on the POF,are analyzed using a general multi-level factorial design.Finally,mathematical optimization techniques are employed to estimate the most stable stope conditions,by determining the optimal ranges for each stope’s geometrical parameter.

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.

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.

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.

Probability Density Function Method for Observing Reconstructed Attractor Structure

Probability density function (PDF) method is proposed for analysing the structure of the reconstructed attractor in computing the correlation dimensions of RR intervals of ten normal old men. PDF contains important information about the spatial distribution of the phase points in the reconstructed attractor. To the best of our knowledge, it is the first time that the PDF method is put forward for the analysis of the reconstructed attractor structure. Numerical simulations demonstrate that the cardiac systems of healthy old men are about 6-6.5 dimensional complex dynamical systems. It is found that PDF is not symmetrically distributed when time delay is small, while PDF satisfies Gaussian distribution when time delay is big enough. A cluster effect mechanism is presented to explain this phenomenon. By studying the shape of PDFs, that the roles played by time delay are more important than embedding dimension in the reconstruction is clearly indicated. Results have demonstrated that the PDF method represents a promising numerical approach for the observation of the reconstructed attractor structure and may provide more information and new diagnostic potential of the analyzed cardiac system.

An Improved Method for Estimating the Transition Probability Using Diameter Growth in Even-aged Forest Stands

The method of Zeng et al. (1991) employed diameter growth to estimate the transition probability of the matrix model in uneven-aged forest stands. In this paper the Weibull distribution for even-aged forest stands instead of uniform distribution chosen by Zeng is used. By comparing the results of the improved method with those of the original method of Zeng, it turns out that the improved method of Zeng given in this paper is more efficient.

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 small signal stability analysis of power system with wind power and photovoltaic power based on probability collocation method

Recently, with increasing improvements in the penetration of wind power and photovoltaic power in the world, probabilistic small signal stability analysis(PSSSA) of a power system consisting of multiple types of renewable energy has become a key problem. To address this problem, this study proposes a probabilistic collocation method(PCM)-based PSSSA for a power system consisting of wind farms and photovoltaic farms. Compared with the conventional Monte Carlo method, the proposed method meets the accuracy and precision requirements and greatly reduces the computation; therefore, it is suitable for the PSSSA of this power system. Case studies are conducted based on a 4-machine 2-area and New England systems, respectively. The simulation results show that, by reducing synchronous generator output to improve the penetration of renewable energy, the probabilistic small signal stability(PSSS) of the system is enhanced. Conversely, by removing part of the synchronous generators to improve the penetration of renewable energy, the PSSS of the system may be either enhanced or deteriorated.

Application of Risk Probability Evaluation Method to Offshore Platform Construction

Offshore project risk concerns many influence factors with complex relationship, and traditional methods cannot be used for the evaluation on risk probability. To deal with this problem, a new method was developed by the combination of improved technique for order preference by similarity ideal solution method, analytical hierarchy process method and the network response surface method. The risk probability was calculated by adopting network response surface analysis based on the state variable of a known event and its degree of membership.This quantification method was applied to an offshore platform project, Bonan oil and gas field project in Bohai Bay in June 2004.There were 7 sub-projects and each includes 4 risk factors.The values of 28 risk factors, ranging from 10^-6 to 10^-4, were achieved. This precision conforms to the international principle of as low as reasonably practically.The evaluation indicates that the values of comprehensive level of construction group and ability of technical personnel on the spot are relatively high among all risk factors, so these two factors should be paid more attention to in offshore platform construction.