Predicting the probability distribution of Martian rocks mechanical property based on microscale rock mechanical experiments and accurate grain-based modeling

The exploration of Mars would heavily rely on Martian rocks mechanics and engineering technology.As the mechanical property of Martian rocks is uncertain,it is of utmost importance to predict the probability distribution of Martian rocks mechanical property for the success of Mars exploration.In this paper,a fast and accurate probability distribution method for predicting the macroscale elastic modulus of Martian rocks was proposed by integrating the microscale rock mechanical experiments(micro-RME),accurate grain-based modeling(AGBM)and upscaling methods based on reliability principles.Firstly,the microstructure of NWA12564 Martian sample and elastic modulus of each mineral were obtained by micro-RME with TESCAN integrated mineral analyzer(TIMA)and nanoindentation.The best probability distribution function of the minerals was determined by Kolmogorov-Smirnov(K-S)test.Secondly,based on best distribution function of each mineral,the Monte Carlo simulations(MCS)and upscaling methods were implemented to obtain the probability distribution of upscaled elastic modulus.Thirdly,the correlation between the upscaled elastic modulus and macroscale elastic modulus obtained by AGBM was established.The accurate probability distribution of the macroscale elastic modulus was obtained by this correlation relationship.The proposed method can predict the probability distribution of Martian rocks mechanical property with any size and shape samples.

The Cox-Aalen Models as Framework for Construction of Bivariate Probability Distributions, Universal Representation

Starting with the Aalen （1989） version of Cox （1972） ＇regression model＇ we show the method for construction of ＂any＂ joint survival function given marginal survival functions. Basically, however, we restrict ourselves to model positive stochastic dependences only with the general assumption that the underlying two marginal random variables are centered on the set of nonnegative real values. With only these assumptions we obtain nice general characterization of bivariate probability distributions that may play similar role as the copula methodology. Examples of reliability and biomedical applications are given.

Two Probability Plots of the Three-Parameter Lognormal Distribution

The two-parameter lognormal distribution is a variant of the normal distribution and the three-parameter lognormal distribution is an extension of the two-parameter lognormal distribution by introducing a location parameter. The Q-Q plot of the three-parameter lognormal distribution is widely used. To obtain the Q-Q plot one needs to iteratively try different values of the shape parameter and subjectively judge the linearity of the Q-Q plot. In this paper,a mathematical method was proposed to determine the value of the shape parameter so as to simplify the generation of the Q-Q plot. Then a new probability plot was proposed,which was more easily obtained and provided more accurate parameter estimates than the Q-Q plot. These are illustrated by three realworld examples.

Probability Distribution Characteristics of Strong Nonlinear Waves Under Typhoon Conditions in the Northern South China Sea

The generation and propagation mechanism of strong nonlinear waves in the South China Sea is an essential research area. In this study, the third-generation wave model WAVEWATCH Ⅲ is employed to simulate wave fields under extreme sea states. The model, integrating the ST6 source term, is validated against observed data, demonstrating its credibility. The spatial distribution of the occurrence probability of strong nonlinear waves during typhoons is shown, and the waves in the straits and the northeastern part of the South China Sea show strong nonlinear characteristics. The high-order spectral model HOS-ocean is employed to simulate the random wave surface series beneath five different platform areas. The waves during the typhoon exhibit strong nonlinear characteristics, and freak waves exist. The space-varying probability model is established to describe the short-term probability distribution of nonlinear wave series. The exceedance probability distributions of the wave surface beneath different platform areas are compared and analyzed. The results show that with an increase in the platform area, the probability of a strong nonlinear wave beneath the platform increases.

A Novel Statistical Delay Model Based on the Birnbaum-Saunders Distribution for RLC Interconnects in 90nm Technologies

For performance optimization such as placement,interconnect synthesis,and routing, an efficient and accurate interconnect delay metric is critical,even in design tools development like design for yield （DFY） and design for manufacture （DFM）. In the nanometer regime, the recently proposed delay models for RLC interconnects based on statistical probability density function （PDF）interpretation such as PRIMO,H-gamma,WED and RLD bridge the gap between accuracy and efficiency. However, these models always require table look-up when operating. In this paper, a novel delay model based on the Birnbaum-Saunders distribution （BSD） is presented. BSD can accomplish interconnect delay estimation fast and accurately without table look-up operations. Furthermore, it only needs the first two moments to match. Experimental results in 90nm technology show that BSD is robust, easy to implement,efficient,and accurate.

Slant Range Distribution Characteristics of Submarine Launch Mobile Mine

With the bias between the predetermined planting location and the fact mine position,slant range of SLMM(submarine launch mobile mine)appears randomly scattered.The normal distribution model of slant range was proposed by the distribution theory of multivariate random variables,and the simplified model based on key parameters was present,and the laws of slant range distribution parameters such as mean and variance were given,which were affected by key parameters.The conclusions ensure that slant range of SLMM can be controlled when laying mines and provide the basis for tactical decision-making.

Fluctuation-Model-Based Discrete Probability Estimation for Small Samples

A robust method is proposed for estimating discrete probability functions for small samples. The proposed approach introduces and minimizes a parameterized objective function that is analogous to free energy functions in statistical physics. A key feature of the method is a model of the parameter that controls the trade-off between likelihood and robustness in response to the degree of fluctuation. The method thus does not require the value of the parameter to be manually selected. It is proved that the estimator approaches the maximum likelihood estimator at the asymptotic limit. The effectiveness of the method in terms of robustness is demonstrated by experimental studies on point estimation for probability distributions with various entropies.

Single Server Queueing Models and Birth-Death Process

A transition diagram is used to describe the behavior of systems. Birth-death equations were derived from transition diagram depicting the state of the birth-death processes. Queue models and characteristics of queue models are also derivable from birth-death processes. These queue models consist of mathematical formulas and relationships that can be used to determine the operating characteristics （performance measures） for a waiting line. Schematic and transition diagrams of different single server queue models were shown. Relationships between birth-death processes, waiting lines （queues） and transition diagrams were given. While M/M/I/K queue model states was limited by K customers and had （K＋I） states, M/M/1/1 queue model had only two states. M/G/1/∝/∝ and M/M/1/∝/∝ shared similar characteristics. Many ideal queuing situations employ M/M/1 queueing model.

On the Relationship between Statistical and Phenomenological Models of the Thermodynamic Systems

The paper deals with the performing of a critical analysis of the problems arising in matching the classical models of the statistical and phenomenological thermodynamics. The performed analysis shows that some concepts of the statistical and phenomenological methods of describing the classical systems do not quite correlate with each other. Particularly, in these methods various caloric ideal gas equations of state are employed, while the possibility existing in the thermodynamic cyclic processes to obtain the same distributions both due to a change of the particle concentration and owing to a change of temperature is not allowed for in the statistical methods. The above-mentioned difference of the equations of state is cleared away when using in the statistical functions corresponding to the canonical Gibbs equations instead of the Planck’s constant a new scale factor that depends on the parameters of a system and coincides with the Planck’s constant in going of the system to the degenerate state. Under such an approach, the statistical entropy is transformed into one of the forms of heat capacity. In its turn, the agreement of the methods under consideration in the question as to the dependence of the molecular distributions on the concentration of particles, apparently, will call for further refinement of the physical model of ideal gas and the techniques for its statistical description.

Locally and globally uniform approximations for ruin probabilities of a nonstandard bidimensional risk model with subexponential claims

Consider a nonstandard continuous-time bidimensional risk model with constant force of interest,in which the two classes of claims with subexponential distributions satisfy a general dependence structure and each pair of the claim-inter-arrival times is arbitrarily dependent.Under some mild conditions,we achieve a locally uniform approximation of the finite-time ruin probability for all time horizon within a finite interval.If we further assume that each pair of the claim-inter-arrival times is negative quadrant dependent and the two classes of claims are consistently-varying-tailed,it shows that the above obtained approximation is also globally uniform for all time horizon within an infinite interval.

Near-surface velocity model construction based on a Monte-Carlo scheme

In tomographic statics seismic data processing, it 1s crucial to cletermme an optimum base for a near-surface model. In this paper, we consider near-surface model base determination as a global optimum problem. Given information from uphole shooting and the first-arrival times from a surface seismic survey, we present a near-surface velocity model construction method based on a Monte-Carlo sampling scheme using a layered equivalent medium assumption. Compared with traditional least-squares first-arrival tomography, this scheme can delineate a clearer, weathering-layer base, resulting in a better implementation of damming correction. Examples using synthetic and field data are used to demonstrate the effectiveness of the proposed scheme.

Establishment Method of a Mixture Model and Its Practical Application for Transmission Gears in an Engineering Vehicle

Highly versatile machines, such as wheel loaders, forklifts, and mining haulers, are subject to many kinds of working conditions, as well as indefinite factors that lead to the complexity of the load. The load probability distribution function （PDF） of transmission gears has many distributions centers; thus, its PDF cannot be well represented by just a single-peak function. For the purpose of representing the distribution characteristics of the complicated phenomenon accurately, this paper proposes a novel method to establish a mixture model. Based on linear regression models and correlation coefficients, the proposed method can be used to automatically select the best-fitting function in the mixture model. Coefficient of determination, the mean square error, and the maximum deviation are chosen and then used as judging criteria to describe the fitting precision between the theoretical distribution and the corresponding histogram of the available load data. The applicability of this modeling method is illustrated by the field testing data of a wheel loader. Meanwhile, the load spectra based on the mixture model are compiled. The comparison results show that the mixture model is more suitable for the description of the load-distribution characteristics. The proposed research improves the flexibility and intelligence of modeling, reduces the statistical error and enhances the fitting accuracy, and the load spectra complied by this method can better reflect the actual load characteristic of the gear component.

Coupling effects of influence factors on probability of corrosion initiation time of reinforced concrete

The coupling model of major influence factors such state affecting the chloride diffusion process in concrete is as environmental relative humidity, load-induced crack and stress discussed. The probability distributions of the critical chloride concentration Cc, the chloride diffusion coefficient D, and the surface chloride concentration Cs were determined based on the collected natural exposure data. And the estimation of probability of corrosion initiation considering the coupling effects of influence factors is presented. It is found that the relative humidity and curing time are the most effective factors affecting the probability of corrosion initiation before and after 10 years of exposure time. At the same exposure time, the influence of load-induced crack and stress state on the probability of corrosion initiation is obvious, in which the effect of crack is the most one

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 time fractional model to represent rainfall process

This paper deals with a stochastic representation of the rainfall process. The analysis of a rainfall time series shows that cumulative representation of a rainfall time series can be modeled as a non-Gaussian random walk with a log-normal jump distribution and a time-waiting distribution following a tempered a-stable probability law. Based on the random walk model, a fractional Fokker-Planck equation （FFPE） with tempered a-stable waiting times was obtained. Through the comparison of observed data and simulated results from the random walk model and FFPE model with tempered a-stable waiting times, it can be concluded that the behavior of the rainfall process is globally reproduced, and the FFPE model with tempered a-stable waiting times is more efficient in reproducing the observed behavior.

Lithium-ion cell inconsistency analysis based on three-parameter Weibull probability model

The inconsistency of lithium-ion cells degrades battery performance,lifetime and even safety.The complexity of the cell reaction mechanism causes an irregular asymmetrical distribution of various cell parameters,such as capacity and internal resistance,among others.In this study,the Newman electrochemical model was used to simulate the 1 C discharge curves of 100 LiMn2 O4 pouch cells with parameter variations typically produced in manufacturing processes,and the three-parameter Weibull probability model was used to analyze the dispersion and symmetry of the resulting discharge voltage distributions.The results showed that the dispersion of the voltage distribution was related to the rate of decrease in the discharge voltage,and the symmetry was related to the change in the rate of voltage decrease.The effect of the cells’capacity dominated the voltage distribution thermodynamically during discharge,and the phase transformation process significantly skewed the voltage distribution.The effects of the ohmic drop and polarization voltage on the voltage distribution were primarily kinetic.The presence of current returned the right-skewed voltage distribution caused by phase transformation to a more symmetrical distribution.Thus,the Weibull parameters elucidated the electrochemical behavior during the discharge process,and this method can guide the prediction and control of cell inconsistency,as well as detection and control strategies for cell management systems.

A Study of Wind Statistics Through Auto-Regressive and Moving-Average (ARMA) Modeling

Statistical properties of winds near the Taichung Harbour are investigated. The 26 years'incomplete data of wind speeds, measured on an hourly basis, are used as reference. The possibility of imputation using simulated results of the Auto-Regressive (AR), Moving-Average (MA), and/ or Auto-Regressive and Moving-Average (ARMA) models is studied. Predictions of the 25-year extreme wind speeds based upon the augmented data are compared with the original series. Based upon the results, predictions of the 50- and 100-year extreme wind speeds are then made.

Ruin Probability and Joint Distributions of Some Actuarial Random Vectors in the Compound Pascal Model

The compound negative binomial model, introduced in this paper, is a discrete time version. We discuss the Markov properties of the surplus process, and study the ruin probability and the joint distributions of actuarial random vectors in this model. By the strong Markov property and the mass function of a defective renewal sequence, we obtain the explicit expressions of the ruin probability, the finite-horizon ruin probability, the joint distributions of T, U（T - 1）, ｜U（T）｜ and inf U（n） （i.e., the time of ruin, the surplus immediately before ruin, the deficit at ruin and maximal deficit from ruin to recovery） and the distributions of some actuarial random vectors.

MULTI-DIMENSIONAL MARKOV CHAIN–BASED ANALYSIS OF CONFLICT PROBABILITY FOR SPECTRUM RESOURCE SHARING

In this paper, we consider the optimal problem of channels sharing with het-erogeneous traffic （real-time service and non-real-time service） to reduce the data conflict probability of users. Moreover, a multi-dimensional Markov chain model is developed to analyze the performance of the proposed scheme. Meanwhile, performance metrics are derived. Numerical results show that the proposed scheme can effectively reduce the forced termination probability, blocking probability and spectrum utilization.

Transitions in a genotype selection model driven by coloured noises

This paper investigates a genotype selection model subjected to both a multiplicative coloured noise and an additive coloured noise with different correlation time τ1 and τ2 by means of the numerical technique. By directly simulating the Langevin Equation, the following results are obtained. （1） The multiplicative coloured noise dominates, however, the effect of the additive coloured noise is not neglected in the practical gene selection process. The selection rate μ decides that the selection is propitious to gene A haploid or gene B haploid. （2） The additive coloured noise intensity and the correlation time τ2 play opposite roles. It is noted that α and τ2 can not separate the single peak, while can make the peak disappear and ^-2 can make the peak be sharp. （3） The multiplicative coloured noise intensity D and the correlation time τ1 can induce phase transition, at the same time they play opposite roles and the reentrance phenomenon appears. In this case, it is easy to select one type haploid from the group with increasing D and decreasing τ1.