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.

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.

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.

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.

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.

Orthogonal expansion of ground motion and PDEM-based seismic response analysis of nonlinear structures

This paper introduces an orthogonal expansion method for general stochastic processes. In the method, a normalized orthogonal function of time variable t is first introduced to carry out the decomposition of a stochastic process and then a correlated matrix decomposition technique, which transforms a correlated random vector into a vector of standard uncorrelated random variables, is used to complete a double orthogonal decomposition of the stochastic processes. Considering the relationship between the Hartley transform and Fourier transform of a real-valued function, it is suggested that the first orthogonal expansion in the above process is carried out using the Hartley basis function instead of the trigonometric basis function in practical applications. The seismic ground motion is investigated using the above method. In order to capture the main probabilistic characteristics of the seismic ground motion, it is proposed to directly carry out the orthogonal expansion of the seismic displacements. The case study shows that the proposed method is feasible to represent the seismic ground motion with only a few random variables. In the second part of the paper, the probability density evolution method （PDEM） is employed to study the stochastic response of nonlinear structures subjected to earthquake excitations. In the PDEM, a completely uncoupled one-dimensional partial differential equation, the generalized density evolution equation, plays a central role in governing the stochastic seismic responses of the nonlinear structure. The solution to this equation will yield the instantaneous probability density function of the responses. Computational algorithms to solve the probability density evolution equation are described. An example, which deals with a nonlinear frame structure subjected to stochastic ground motions, is illustrated to validate the above approach.

Serviceability evaluation of water supply networks under seismic loads utilizing their operational physical mechanism

The serviceability of water supply networks(WSNs)under seismic loads has significant importance for estimating the probable losses and the impact of diminished functionality on affected communities.The innovation presented in this paper is suggesting a new strategy to evaluate the seismic serviceability of WSNs,utilizing their operational physical mechanism.On one hand,this method can obtain the seismic serviceability of each node as well as entire WSNs.On the other hand,this method can dynamically reflect the propagation of randomness from ground motions to WSNs.First,a finite element model is established to capture the seismic response of buried pipe networks,and a leakage model is suggested to obtain the leakage area of WSNs.Second,the transient flow analysis of WSNs with or without leakage is derived to obtain dynamic water flow and pressure.Third,the seismic serviceability of WSNs is analyzed based on the probability density evolution method(PDEM).Finally,the seismic serviceability of a real WSN in Mianzhu city is assessed to illustrate the method.The case study shows that randomness from the ground motions can obviously affect the leakage state and the probability density of the nodal head during earthquakes.

Dimension-reduction of FPK equation via equivalent drift coefficient

The Fokker–Planck–Kolmogorov（FPK） equation plays an essential role in nonlinear stochastic dynamics. However, neither analytical nor numerical solution is available as yet to FPK equations for high-dimensional systems. In the present paper, the dimension reduction of FPK equation for systems excited by additive white noise is studied. In the proposed method, probability density evolution method（PDEM）, in which a decoupled generalized density evolution equation is solved, is employed to reproduce the equivalent flux of probability for the marginalized FPK equation. A further step of constructing an equivalent coefficient finally completes the dimension-reduction of FPK equation. Examples are illustrated to verify the proposed method.

A Simple Evaluation System for Microbial Property in Soil and Manure

Analyses of microbial properties in soil and manure had always included the problem that there was no available standard method to evaluate microbial property. The one of the major problems was the vast diversity and the enormous population of soil microorganisms [1], the other was an existence of numerically dominant unculturable microorganisms which comprise 99% of soil habitat [2]. We evaluated whether our newly developed method, by which taxonomies and their number of each bacterial groups were estimated, could be used as evaluation method of microbial properties of soils and manures. In the forest soil, β-Proteobacteria, which included Burkholderia sp., Ralstonia sp., and Alcaligenes sp., was numerically dominant bacteria (3.64 × 106 MPN g-1 dry soil), followed by γ-Proteobacteria (1.32 × 106 MPN), δ-Proteobacteria (0.006 × 106 MPN), and the other gram negative bacteria (0.006 × 106 MPN). In the commercial manure, Actinobacteria, which included Streptoverticillium salmonis, Mycrococcus sp., Streptomyces bikiniensis, and Microbacterium ulmi, was numerically dominant bacterial group (30.8 × 106 MPN), followed by α-Proteobacteria (26.0 × 106 MPN), β-Proteobacteria (17.1 × 106 MPN), δ-Proteobacteria (11.2 × 106 MPN), the other Firmicutes (1.71 × 106 MPN), γ-Proteobacteria (0.5 × 106 MPN), and the other gram negative bacteria (0.05 × 106 MPN). In the upland field, the other Firmicutes, which included Paenibacillus sp., was numerically dominant bacteria (4.41 × 106 MPN), followed by Actinobacteria (2.14 × 106 MPN), Bacillus sp. (2.14 × 106 MPN), and γ-Proteobacteria (0.35 × 106 MPN). Although the precision of the affiliations became lower because of higher diversity of samples and the number of some Antinobacteria and Firmicutes might be underestimated by the used PCR condition, the method was found suitable as a candidate of a new evaluation system of soil and manure.

Probabilistic method for the size design of energy piles considering the uncertainty in soil parameters

Energy piles have attracted increasing attention as profitable solutions for the utilization of shallow geothermal energy.Although various complex geotechnical design models of energy piles have been proposed,a simplified sizing method that considers the uncertainty propagation in the soil is required.In this study,a Monte Carlo Simulation-based method was proposed for the size design of energy piles considering the uncertainty of parameters in the soil,such as thermal conductivity and friction angle.The small-sample analysis method of Markov chain Monte Carlo simulation combined with the Bayesian theoretical framework was developed to generate equiv-alent samples.Subsequently,the thermal response function and thermomechanical load transfer methods were employed to address the failure probability of the energy pile in the serviceability limit state and ultimate limit state.In addition,a case study was presented to illustrate the implementation of the proposed probabilistic sizing method.The analysis results of the case study confirm the necessity of modeling the soil uncertainty in the energy pile size design.

Parametric and Non-Parametric Survival Analysis of Patients with Acute Myeloid Leukemia (AML)

Background: Acute Myeloid leukemia (AML) is the most prominent acute leukemia in adults. In the United States, we experience over 20,000 cases per year. Over the past decade, improvements in the diagnosis of subtypes of AML and advances in therapeutic approaches have improved the outlook for patients with AML. However, despite these advancements, the survival rate among patients who are less than 65 years of age is only 40 percent. Purpose: The purpose of the paper is to study if there exists any significant difference in the survival probabilities of male and female AML patients. Also, we want to investigate if there is any parametric probability distribution that best fits the male and female patient survival and compare the survival probabilities with the non-parametric Kaplan-Meier (KM) method. Methods: We used both parametric and non-parametric statistical methods to perform the survival analysis to assess the survival probabilities of 2015 patients diagnosed with AML. Results: We found evidence of a statistically significant difference between the mean survival time of male and female patients diagnosed with AML. We performed parametric survival analysis and found a Generalized Extreme Value (GEV) distribution best fitting the data of the survival time for male and female patients. We then estimated the survival probabilities and compared them with the frequently used non-parametric Kaplan-Meier (KM) survival method. Conclusion: The comparison between the survival probability estimates of the two methods revealed a better survival probability estimate by the parametric method than the Kaplan-Meier. We also compared the median survival time of male and female patients individually with descriptive, parametric, and non-parametric methods of analysis. The parametric survival analysis is more robust and efficient because it is based on a well-defined parametric probabilistic distribution, hence preferred over the non-parametric Kaplan-Meier estimate. This study offers therapeutic significance for further enhancement to treat patients with Acute Myeloid Leukemia.