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%）.

SIMULATION OF SOLUTE TRANSPORT IN FRACTURED NETWORK WITH A PROBABILITY METHOD

The simulation of solute transport in fractured rock mass has Finite Element Method（FEM） and Finite Analysis Method（FAM）, etc. been conducted with the Finite Difference Method（FDM）, However, groundwater flow and solute transport is very complex in fractured network compared to the rocks matrix because water flow and tracer particles have different selections of pathways when they travel to the fractured intersections. It is difficult for traditional method to simulate the law of solute transport in fractured network. Hence a new simulation method, the probability method, is developed. In the method, transfer probabilities for fractured network are calculated using the flux of input and output from fractured intersection points, and travel times of tracer particles are determined with random numbers, dispersion parameter and velocity. Furthermore, corresponding computing program is developed using the FORTRAN language. The comparison between simulated and experimental results shows that the probability method is of considerable reliability and is an effective method to simulate solute transport in fractured network, and the case study of the Jinping I-Hydropower Station displays its wide application prospect.

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.

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 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.

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.

A novel refined dynamic model of high-speed maglev train-bridge coupled system for random vibration and running safety assessment

Running safety assessment and tracking irregularity parametric sensitivity analysis of high-speed maglev train-bridge system are of great concern,especially need perfect refinement models in which all properties can be well characterized based on various stochastic excitations.A three-dimensional refined spatial random vibration analysis model of high-speed maglev train-bridge coupled system is established in this paper,in which multi-source uncertainty excitation can be considered simultaneously,and the probability density evolution method(PDEM)is adopted to reveal the system-specific uncertainty dynamic characteristic.The motion equation of the maglev vehicle model is composed of multi-rigid bodies with a total 210-degrees of freedom for each vehicle,and a refined electromagnetic force-air gap model is used to account for the interaction and coupling effect between the moving train and track beam bridges,which are directly established by using finite element method.The model is proven to be applicable by comparing with Monte Carlo simulation.By applying the proposed stochastic framework to the high maglev line,the random dynamic responses of maglev vehicles running on the bridges are studied for running safety and stability assessment.Moreover,the effects of track irregularity wavelength range under different amplitude and running speeds on the coupled system are investigated.The results show that the augmentation of train speed will move backward the sensitive wavelength interval,and track irregularity amplitude influences the response remarkably in the sensitive interval.

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.

A method to calculate displacement factors using SVM

In order to improve the precision of mining subsidence prediction, a mathematical model using Support Vector Machine （SVM） was established to calculate the displacement factor. The study is based on a comprehensive analysis of factors affecting the displacement factor, such as mechanical properties of the cover rock, the ratio of mining depth to seam thickness, dip angle of the coal seam and the thickness of loose layer. Data of 63 typical observation stations were used as a training and testing sample set. A SVM regression model of the displacement factor and the factors affecting it was established with a kernel function, an insensitive loss factor and a properly selected penalty factor. Given an accurate calculation algorithm for testing and analysis, the results show that an SVM regression model can calcu- late displacement factor precisely and reliable precision can be obtained which meets engineering requirements. The experimental results show that the method to calculation of the displacement factor, based on the SVM method, is feasible. The many factors affecting the displacement factor can be consid- ered with this method. The research provides an efficient and accurate approach for the calculation of displacement in mining subsidence orediction.

Joint probability density function of the stochastic responses of nonlinear structures

The joint probability density fimction （PDF） of different structural responses is a very important topic in the stochastic response analysis of nonlinear structures. In this paper, the probability density evolution method, which is successfully developed to capture the instantaneous PDF of an arbitrary single response of interest, is extended to evaluate the joint PDF of any two responses. A two-dimensional partial differential equation in terms of the joint PDF is established. The strategy of selecting representative points via the number theoretical method and sieved by a hyper-ellipsoid is outlined. A two-dimensional difference scheme is developed. The free vibration of an SDOF system is examined to verify the proposed method, and a flame structure exhibiting hysteresis subjected to stochastic ground motion is investigated. It is pointed out that the correlation of different responses results from the fact that randomness of different responses comes from the same set of basic random parameters involved. In other words, the essence of the probabilistic correlation is a physical correlation.

Evaluation of the Method Based on Restriction Fragment Length Polymorphism Analysis as Simple Analysis Method of Lactic Acid Bacteria in Foods

Lactic acid bacteria have not only been used to produce various kinds of fermented food, but also used as probiotic products. As lactic acid bacterial group was consisted from diverse genera, a simple inspection method by which numbers and contained microorganisms could be automatically analyzed without any preliminary information was required to use them more effectively. In this manuscript, lactic acid bacterial groups in commercial products of kimuchi, komekouji-miso, and yoghurt were identified and enumerated by our newly developed method [1]-[3], to evaluate whether the method could be used as an inspection method of various food samples. In kimuchi, numerically dominant bacteria were Lactobacillus sakei, and L. casei (1.4 × 104 MPN g-1) and Leuconostoc spp. (l.4 × 104 MPN). In kouji-miso, numerically dominant bacteria was Bacillus spp. (3 × 103 MPN), which mainly included B. subtilis group and B. cereus group. Lactic acid bacteria such as Lactobacillus spp., or Lactococcus spp., included in the komekouji-miso, could be enumerated after 3 days incubation (1.24 × 104 MPN), but not detected after 7 days incubation. In yoghurt A and C, Lactococcus lactis was detected as numerically dominant lactic acid bacteria (3.0 × 105 MPN). In yoghurt B, Lactobacillus spp., or Lactococcus spp., was detected not only by a culturebased method but also by an unculture-based method, although there was a difference between the both estimated numbers. The present results suggested that the method might become useful as a simple inspection method of food microorganisms, because time and labor of the analysis could be reduced by using an unculture-based method and MCE-202 MultiNA. In this study, Bifidobacteriium spp. was not detected in B and C yoghurt, in spite of indicating their existence, and numbers of lactic acid bacteria were lower than the level of the daily product regulation, because 16S rDNA of Bifidobacteriium spp. might not be amplified by the used PCR condition. The PCR condition must be changed so as to amplify Bifidobacterium spp., before the method will be used as an inspection method for lactic acid bacteria.

Identification and Enumeration Method of Both Eukaryotic and Prokaryotic Microorganisms in Food Sample

The method to analyze both eukaryotic and prokaryotic microorganisms without preliminary microbial information of sample seemed to be useful not only for research and investigation of microorganisms but also for industry using microorganisms. In the present manuscript, preparation of a new DNA primers, new reference database for 18S rDNA for our newly developed method [1]- [3], and analyses of eukaryotic and prokaryotic microorganisms in fermentation products were presented. In komekouji, Aspergillus spp., was enumerated to be 46.5 × 106 MPN g-1, and Penicillium spp., was enumerated to be 1.5 × 106 MPN g-1. In dry yeast, Saccharomyces group, were enumerated to be 8600 × 106 MPN g-1. In komekouji-miso, no eukaryotic microorganism was detected, while the other Bacillus spp., was numerically dominant (21.5 × 106 MPN g-1) as prokaryotic microorganisms, followed by B. subtilis group (4.65 × 106 MPN g-1), and the other Firmicutes (3.7 × 106 MPN g-1). The komekouji-miso included lower number of Actinobacteria (0.15 × 106 MPN g-1), Burkhokderia sp. (1.5 × 106 MPN g-1), and the other α,β,γ-proteobacteria (0.12 × 106 MPN g-1). In sake-kasu, both prokaryote and eukaryote were not detected by the method. Present results indicated that using both universal primers for eukaryotic and prokaryotic microorganisms, each groups of prokaryotic and eukaryotic microorganisms were enumerated without any preliminary information nor setting up standard curve, which were required for real time PCR.

A New Evaluation Method for Antibiotic-Resistant Bacterial Groups in Environment

In the present manuscript it was presented whether spreading of antibiotic resistant bacterial groups in environment could be monitored by our newly developed method by enumerating antibiotic resistant bacterial groups in various biological wastes and composts. Although the numbers were not so high, diverse kinds of colistin resistant bacteria (25 mg·L-1) were included in row cattle feces (1.78 × 104 MPN g-1) and cattle feces manure (>3.84 × 104 MPN g-1). Compost originated from leftover food (>44.8 × 104 MPN g-1) and shochu lee (>320 × 104 MPN g-1) included higher numbers of chlortetracycline resistant Pseudomonas sp., (25 mg·L-1), and row cattle feces included higher numbers of chlortetracycline resistant Enterobacteriacea (15.7 × 104 MPN g-1), which mostly consisted from Pantoea sp. or Xenorhobdus doucetiae. Numbers of multi drug resistant bacteria, resistant to 25 mg·L-1 of ciprofloxacin, streptomycin, chloramphenicol, and ampicillin, were the highest in row cattle feces (>143.6 × 104 MPN g-1), followed by cattle feces manure (4.19 × 104 MPN g-1), and shochu lee (0.36 × 104 MPN g-1), which included diverse kinds of bacterial group. The present results indicated that higher numbers of multi drug resistant bacteria were typically found in row cattle feces, and the method was found suitable to enumerate and identify them. These results suggested that the method might become their environmental risk evaluation method.

Characterization of Complex Fracture System in Volume Fracturing of Shale Gas Reservoir

After volume fracturing of horizontal wells in shale gas reservoir, an extremely complex fracture system is formed. The space area of the fracture system is the reservoir reconstruction volume of shale gas reservoir. The geometric parameters such as crack length, crack width, crack height, and characteristic parameters such as crack permeability and fracture conductivity proposed for a single crack in conventional fracturing are insufficient to describe and characterize the complex network fracture system after volume fracturing. In this paper, the discrete fracture modeling method is used to establish the volume fracturing network fracture model of horizontal wells in shale gas reservoir by using the random modeling method within the determined reservoir space. The model is random and selective, and can fully provide different forms of volume fracturing fracture expansion, such as conventional fracture morphology, line network model and arbitrarily distributed network fractures. The research results provide a theoretical basis for the development plan and stimulation plan of shale gas reservoir, and have important reference value and significance for other unconventional gas reservoir fracturing.

Typhoon hazard assessment at the site-specific scale based on the probability density evolution method and its application on the southeast coast of China

Herein, a typhoon hazard assessment method at the site-specific scale is proposed. This method integrates the nonlinear threedimensional wind field model and the probability density evolution method. At the site-specific scale, the track of a typhoon near the engineering site is approximated via a straight line. The wind field model is utilized to calculate the wind speed at the surface given the gradient wind field at the top of the boundary layer. A comparison between the simulated and observed wind histories for Typhoon Hagupit that made landfall in Guangdong Province demonstrates the fidelity of the wind field model. The probability density evolution method is utilized to calculate the propagation of the randomness from the basic random variables toward the extremities of the typhoon surface wind. To model the probability distribution of the basic random variables, several candidate distributions are considered to fit the observations. Akaike information criterion and Anderson-Darling distance are used for selecting the preferred probability distribution model. The adequacy of the probability density evolution method in assessing typhoon hazards is verified by comparing the results with those generated by Monte Carlo simulations. The typhoon wind hazards estimated by the present study are compared with those proposed by other studies and the design code, and the differences are analyzed and discussed. The results of the proposed method provide the reasonable probabilistic model for the assessment of the structural reliability and the improvement of community resilience in the typhoon-prone areas.

Reliability Design for Impact Vibration of Hydraulic Pressure Pipeline Systems

The research of reliability design for impact vibration of hydraulic pressure pipeline systems is still in the primary stage,and the research of quantitative reliability of hydraulic components and system is still incomplete.On the condition of having obtained the numerical characteristics of basic random parameters,several techniques and methods including the probability statistical theory,hydraulic technique and stochastic perturbation method are employed to carry out the reliability design for impact vibration of the hydraulic pressure system.Considering the instantaneous pressure pulse of hydraulic impact in pipeline,the reliability analysis model of hydraulic pipeline system is established,and the reliability-based optimization design method is presented.The proposed method can reflect the inherent reliability of hydraulic pipe system exactly,and the desired result is obtained.The reliability design of hydraulic pipeline system is achieved by computer programs and the reliability design information of hydraulic pipeline system is obtained.This research proposes a reliability design method,which can solve the problem of the reliability-based optimization design for the hydraulic pressure system with impact vibration practically and effectively,and enhance the quantitative research on the reliability design of hydraulic pipeline system.The proposed method has generality for the reliability optimization design of hydraulic pipeline system.

Extreme value distribution and reliability of nonlinear stochastic structures

A new approach to evaluate the extreme value distribution （EVD） of the response and reliability of general multi-DOF nonlinear stochastic structures is proposed. The approach is based on the recently developed probability density evolution method, which enables the instantaneous probability density functions of the stochastic responses to be captured. In the proposed method, a virtual stochastic process is first constructed to satisfy the condition that the extreme value of the response equals the value of the constructed process at a certain instant of time. The probability density evolution method is then applied to evaluate the instantaneous probability density function of the response, yielding the EVD. The reliability is therefore available through a simple integration over the safe domain. A numerical algorithm is developed using the Number Theoretical Method to select the discretized representative points. Further, a hyper-ball is imposed to sieve the points from the preceding point set in the hypercube. In the numerical examples, the EVD of random variables is evaluated and compared with the analytical solution. A frame structure is analyzed to capture the EVD of the response and the dynamic reliability. The investigations indicate that the proposed approach provides reasonable accuracy and efficiency.

Probabilistic model and analysis of coupled train-ballasted track-subgrade system with uncertain structural parameters

Random dynamic responses caused by the uncertainty of structural parameters of the coupled train-ballasted track-subgrade system under train loading can pose safety concerns to the train operation.This paper introduced a computational model for analyzing probabilistic dynamic responses of three-dimensional(3D)coupled train-ballasted track-subgrade system(TBTSS),where the coupling effects of uncertain rail irregularities,stiffness and damping properties of ballast and subgrade layers were simultaneously considered.The number theoretical method(NTM)was employed to design discrete points for the multi-dimensional stochastic parameters.The time-histories of stochastic dynamic vibrations of the TBSS with systematically uncertain structural parameters were calculated accurately and efficiently by employing the probability density evolution method(PDEM).The model-predicted results were consistent with those by the Monte Carlo simulation method.A sensitivity study was performed to assess the relative importance of those uncertain structural parameters,based on which a case study was presented to explore the stochastic probability evolution mechanism of such train-ballasted track-subgrade system.