Non-Stationary Random Process for Large-Scale Failure and Recovery of Power Distribution

This work applies non-stationary random processes to resilience of power distribution under severe weather. Power distribution, the edge of the energy infrastructure, is susceptible to external hazards from severe weather. Large-scale power failures often occur, resulting in millions of people without electricity for days. However, the problem of large-scale power failure, recovery and resilience has not been formulated rigorously nor studied systematically. This work studies the resilience of power distribution from three aspects. First, we derive non-stationary random processes to model large-scale failures and recoveries. Transient Little’s Law then provides a simple approximation of the entire life cycle of failure and recovery through a queue at the network-level. Second, we define time-varying resilience based on the non-stationary model. The resilience metric characterizes the ability of power distribution to remain operational and recover rapidly upon failures. Third, we apply the non-stationary model and the resilience metric to large-scale power failures caused by Hurricane Ike. We use the real data from the electric grid to learn time-varying model parameters and the resilience metric. Our results show non-stationary evolution of failure rates and recovery times, and how the network resilience deviates from that of normal operation during the hurricane.

The study of lithographic variation in resistive random access memory

Reducing the process variation is a significant concern for resistive random access memory(RRAM).Due to its ultrahigh integration density,RRAM arrays are prone to lithographic variation during the lithography process,introducing electrical variation among different RRAM devices.In this work,an optical physical verification methodology for the RRAM array is developed,and the effects of different layout parameters on important electrical characteristics are systematically investigated.The results indicate that the RRAM devices can be categorized into three clusters according to their locations and lithography environments.The read resistance is more sensitive to the locations in the array(~30%)than SET/RESET voltage(<10%).The increase in the RRAM device length and the application of the optical proximity correction technique can help to reduce the variation to less than 10%,whereas it reduces RRAM read resistance by 4×,resulting in a higher power and area consumption.As such,we provide design guidelines to minimize the electrical variation of RRAM arrays due to the lithography process.

MOMENTS OF CONTINUOUS-STATE BRANCHING PROCESSES IN LéVY RANDOM ENVIRONMENTS

For continuous-state branching processes in Levy random environments, the recursion of n-moments and the equivalent condition for the existence of general f-moments are established, where f is a positive continuous function satisfying some standard conditions.

MOMENTS AND LARGE DEVIATIONS FOR SUPERCRITICAL BRANCHING PROCESSES WITH IMMIGRATION IN RANDOM ENVIRONMENTS

Let(Z_(n))be a branching process with immigration in a random environmentξ,whereξis an independent and identically distributed sequence of random variables.We show asymptotic properties for all the moments of Z_(n) and describe the decay rates of the n-step transition probabilities.As applications,a large deviation principle for the sequence log Z_(n) is established,and related large deviations are also studied.

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS-THE EXISTENCE AND UNIQUENESS

The concepts of Markov process in random environment,q-matrix in random environment,and q-process in random environment are introduced.The minimal q-process in random environment is constructed and the necessary and sufficient conditions for the uniqueness of q-process in random environment are given.

THE CONSTRUCTION OF DENUMERABLE q-PROCESSES IN RANDOM ENVIRONMENTS SATISFYING (F) OR (B)

This article is a continuation of[9].Based on the discussion of random Kolmogorov forward(backward)equations,for any given q-matrix in random environment, Q(θ)=(q(θ;x,y),x,y∈X),an infinite class of q-processes in random environments satisfying the random Kolmogorov forward(backward)equation is constructed.Moreover, under some conditions,all the q-processes in random environments satisfying the random Kolmogorov forward(backward)equation are constructed.

ON DESIGN METHOD OF THE PRECISION CAM PROFILE WITH RANDOM PROCESSING ERRORS

Based on probability and statistic, a design method of precision cam profile concerning the influence of random processing errors is advanced. Combining the design with the process, which can be used to predict that cam profiles will be successfully processed or not in the design stage, design of the cam can be done by balancing the economization and reliability. In addition, an fuzzy deduction method based on Bayers formula is advanced to estimate processing reasonable of the designed precision cam profile, and it take few samples.

Remaining useful life estimation based on Wiener degradation processes with random failure threshold

Remaining useful life(RUL) estimation based on condition monitoring data is central to condition based maintenance(CBM). In the current methods about the Wiener process based RUL estimation, the randomness of the failure threshold has not been studied thoroughly. In this work, by using the truncated normal distribution to model random failure threshold(RFT), an analytical and closed-form RUL distribution based on the current observed data was derived considering the posterior distribution of the drift parameter. Then, the Bayesian method was used to update the prior estimation of failure threshold. To solve the uncertainty of the censored in situ data of failure threshold, the expectation maximization(EM) algorithm is used to calculate the posteriori estimation of failure threshold. Numerical examples show that considering the randomness of the failure threshold and updating the prior information of RFT could improve the accuracy of real time RUL estimation.

A Novel 2-D Signal Processing Scheme for Quasi-Random Step Frequency Signal

Due to the heavy congestion in HF bands, HF radars are restricted to operating within narrow frequency bands. To improve the system bandwidth and avoid heavy interference bands, a quasi-random step frequency signal with discontinuous bands is presented. A novel two-dimensional signal processing scheme for this signal is proposed on the basis of delicate signal analysis. Simulation results demonstrate that the scheme could successfully realize the resolutions by decoupling the range-Doppler ambiguity, and effectively suppress the maximal sidelobe. Moreover, the scheme is simple and has good numerical stability.

Laplace Transformation and Ergodic Potential Kernel for q-Process in Random Environment

This paper introduces some concepts such as q-process in random environment, Laplace transformation, ergodic potential kernel, error function and some basic lemmas.We study the continuity and Laplace transformation of random transition function. Finally, we give the sufficient condition for the existence of ergodic potential kernel for homogeneous q-processes in random environments.

THE ERGODICITY FOR BI-IMMIGRATION BIRTH AND DEATH PROCESSES IN RANDOM ENVIRONMENT

在随机的环境的在随机的环境的双性人移民出生和双性人移民出生和死亡过程的概念被介绍。为在有出生率&#955; 【 死亡率&#956; 的随机的环境 Q (&#952; )的任何双性人移民出生和死亡矩阵，下列结果被证明，( 1 )在随机的环境有唯一的q过程， p (&#952;~*( 0 )； t )=( p (&#952;~*( 0 )； t ，我， j )，我， j &#8805; 0 ) ，它是各态历经的，也就是说 lim_(t&#8594;&#8734;) p (&#952;~*(0 ) ；t，我， j )=&#960; (&#952;~*(0 ) ； j )&#8805; 0 不取决于 i &#8805; 0 并且 &#8721;_(j &#8805; 0 )&#960; (&#952;~*(0 ) ； j )= 1 )(2 ) 在随机的环境有双性人移民出生和死亡过程(X~*={ X_t， t &#8805; 0 } ， &#958;~*={&#958;_t， t &#8712; (有随机的转变矩阵 P 的 -&#8734;,&#8734;)})(&#952;~*(0 ) ； t ) 以便 X~* 是一个严格地静止的过程。

Limit theorems for supremum of Gaussian processes over a random interval

Let {X(t), t ≥ 0} be a centered stationary Gaussian process with correlation r(t)such that 1-r(t) is asymptotic to a regularly varying function. With T being a nonnegative random variable and independent of X(t), the exact asymptotics of P(sup_(t∈[0,T])X(t) > x) is considered, as x →∞.

Application of Random Process in Soil Profile Modeling

When using the random process in soil profile modeling, the stationary and ergodicity of thesoil properties in the profile must be tested. This paper describes a procedure for stationary and ergodicity testing. Numerical examples were given for demonstration. A log-cosine function is suggested to simulate the correlation function, which has been proved to be good for soil profile modeling.

FRACTAL PROPERTIES OF POLAR SETS OF RANDOM STRING PROCESSES

This paper studies fractal properties of polar sets for random string processes. We give upper and lower bounds of the hitting probabilities on compact sets and prove some sufficient conditions and necessary conditions for compact sets to be polar for the random string process. Moreover, we also determine the smallest Hausdorff dimensions of non-polar sets by constructing a Cantor-type set to connect its Hausdorff dimension and capacity.

Simulation of non-stationary ground motion processes(I)

This paper presents a spectral representation method for simulation of non-stationary ground motion processes on the basis of Priestley′s evolutionary spectral theory. Following this method, sample processes can be generated using a cosine series formula. It is shown that, these sample processes accurately reflect the prescribed characteris- tics of the evolutionary power spectral density function when the number of the terms in the cosine series is large enough; and the ensemble expected value and the ensemble autocorrelation function approach the corresponding target functions, respectively, as the sample size increases; and these sample processes are asymptotically normal as the number of the terms in the series tends to infinity. Finally, a few special cases of the formula are discussed, one of which is non-stationary white noise process, and other one is reduced to the formula for simulation of sta- tionary stochastic processes.

Simulation of non-stationary ground motion processes (II)

This paper proposes a method for simulation of non-stationary ground motion processes having the identical statis-tical feature, time-dependent power spectrum, with a given ground motion record, on the basis of review of simu-lation of non-stationary ground motion processes. The method has the following advantages: the sample processes are non-stationary both in amplitude and frequency, and both the amplitude and frequency non-stationarity depend on the target power spectrum; the power spectrum of any sample process does not necessarily accord with the tar-get power spectrum, but statistically, it strictly accords with the target power spectrum. Finally, the method is veri-fied by simulation of one acceleration record in Landers earthquake.

Representation Theorems for Fuzzy Random Sets and Fuzzy Stochastic Processes

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LIMIT THEOREMS FOR A GALTON-WATSON PROCESS IN THE I.I.D. RANDOM ENVIRONMENT

In this article,we obtain the central limit theorem and the law of the iterated logarithm for Galton-Watson processes in i.i.d.random environments.

Definition of Laplace Transforms for Distribution of the First Passage of Zero Level of the Semi-Markov Random Process with Positive Tendency and Negative Jump

One of the important problems of stochastic process theory is to define the Laplace transforms for the distribution of semi-markov random processes. With this purpose, we will investigate the semimarkov random processes with positive tendency and negative jump in this article. The first passage of the zero level of the process will be included as a random variable. The Laplace transforms for the distribution of this random variable is defined. The parameters of the distribution will be calculated on the basis of the final results.

THE STATIONARY DISTRIBUTION OF A CONTINUOUS－TIME RANDOM GRAPH PROCESS WITH INTERACTING EDGES

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