一些组合恒等式的概率方法证明

本文通过Stirling数等特殊组合数的概率表示,结合着已有的基本恒等式,演化得到了若干新的关于常见组合变量的恒等式及递推关系,同时对一些已有的组合恒等式及递推关系给出了新的概率的证明。     

Probabilistic Distribution of the Maximum Wave Heigh

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio. The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height. Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the variable cannot be easily defined. In this study, however, it can be derived from the relationship between the maximum and significant waves in a nonbreaking environment. Some examples are shown to validate the derived probability density function for the wave ratio parameter. By introducing the wave height ratio into reliability analysis of caisson breakwater, the maximum wave height can be used as an independent and primary random variable, which means that the risk of caisson failure during its lifetime can be evaluated realistically.     

Probabilistic distribution of the maximum wave height

A new method of treating maximum wave height as a random variable in reliability analysis of breakwater caissons is proposed. The maximum wave height is expressed as the significant wave height multiplied by the so-called wave height ratio.The proposed wave height ratio is a type of transfer function from the significant wave height to the maximum wave height.Under the condition of a breaking wave, the ratio is intrinsically nonlinear. Therefore, the probability density function for the     

Probabilistic downtime estimation for sequential marine operations

A marine project consists of series of operations, with each operation subject to a predefined operational limit and duration. If actual weather conditions exceed the operational limit, the operation cannot be executed and hence downtime occurs. An accurate assessment of uncertainties and the expected downtime during a marine project is important in the tender and execution phase. This paper proposes a new probabilistic model for downtime estimation. It utilizes linked Markov chains that use actual metocean conditions to produce binary workability sequences for each operation. Synthetic time-series can be generated based on the statistics of the past observations and more project simulations are realizable, reducing the simulation uncertainty. The capabilities and limitations of the proposed approach are illustrated in a case study for a hypothetical project in the Tasman Sea.     

Beam noise characteristics

Beam-noise spectrum levels were measured with high-resolution horizontal arrays of 22 to 100 wavelengths long at frequencies between 50 and 320 Hz in the Mediterranean Sea. Results indicate that the low-frequency noise field has two major components one of which is due to the dynamic and temporally variable distant shipping. Beam noise level differences of 10 to 20 dB were observed between the resolved distant shipping and the uncorrelated background noise. The measured distributions of beam-noise-intensity fluctuations were found to be non-Gaussian. The beam-noise-intensity distribution was found to depend on aperture length, frequency, bandwidth, integration time, and steering angle. The shapes of the beam-noise-intensity cumulative distribution functions were variable and qualitatively described by nonhomogeneous compound Poisson process as shown with a simulation of the shipping-induced noise field. Temporal characteristics of beam-noise-intensity fluctuations were found to have noise level fades at 30% probability below the median noise level with durations of 1 h for observations over 10 h.     

z变换整周模糊度概率特性影响分析

为了评估整周模糊度求解精度,首先介绍了整周模糊度概率特性的基本理论和z变换的基本思想。对直接归整法和序贯归整法整周模糊度概率特性进行了分析,探讨z变换对序贯归整法整周模糊度概率特性的影响。给出了一个基线解算实例。得出了z变换优化整周模糊度概率特性的结论。     

A Probabilistic Model for Fatigue Crack Propagation Analysis

A simple probabilistic model for predicting crack growth behavior under random loading is pre-sented.In the model,the parameters c and m in the Paris-Erdogan Equation are taken as random variables,and their stochastic characteristic values are obtained through fatigue crack propagation tests on an offshorestructural steel under constant amplitude loading.Furthermore,by using the Monte Carlo simulation tech-nique,the fatigue crack propagation life to reach a given crack length is predicted.The tests are conducted toverify the applicability of the theoretical prediction of the fatigue crack propagation.     

渤海海域地震海啸灾害概率性风险评估

渤海作为我国地震活动性最为活跃的近海,其地震海啸风险不可忽视。本文应用概率性海啸风险评估方法对渤海周边区域的海啸风险进行评估。根据历史地震目录建立了渤海区域的震级-频率关系,基于蒙特卡洛算法随机生成了一套10万年的地震目录,最终通过对地震事件的海啸数值模拟及最大波幅的统计分析给出了环渤海区域典型重现期的最大波幅分布以及重点城市的海啸波幅曲线。评估结果表明,渤海地区海啸风险主要集中在渤海湾和莱州湾周边,波幅可达到1~3 m,辽东湾地区海啸风险较低。     

Deep-ocean vertical noise directionality

The structure of beam noise measured at the output of a vertical array in a range dependent ocean basin was investigated using the modified wide-angle parabolic equation (PE). Noise sources were distributed throughout the basin, and the field due to each noise source at an array located in the midbasin was calculated. The response of the array to the superposition of the noise sources was found by beamforming. An efficient and direct approach that superimposes the noise sources on the PE field as the field is marched toward the array was developed. Downslope calculations of the midbasin vertical directionality were made between 50 and 400 Hz with this technique. Use of a geoacoustic model shows that the bottom behaves as a low-pass filter     

Fuzzy Probabilistic Analysis of Seismic Stability of Coastal Embankment

The stability of slope is affected by a number of factors, some of which have not only random property but also fuzzy characteristic. Therefore, the analysis of slope stability is really an uncertain problem. The customary safety factor does not in reality reflect stability scientifically, quantitatively and practically. In order to obtain more practical results, the slope stability is treated as a fuzzy random event for the evaluation of its fuzzy probability. Finally, the seismic stability of an existing coastal embankment is analyzed by means of the suggested fuzzy probabilistic method. It may be seen that the results of analysis can more fully represent the numerical assessment of the degree of slope seismic stability.     

Stirling数的概率表示的新应用

运用两类Stirling数的概率表示得到两类Stirling数的一些特殊值,证明并得到了一些有关两类Stirling数的新的递推公式和恒等式,从而丰富发展了孙平、王天明关于“Stirling数的概率表示和应用”中的内容。     

Probabilistic Analysis for Seismic Stability of Beach Earth Embankment

The current safety factor method for evaluating earth embankment stability is not very rational since the assessment of slope stability is really an uncertainty problem. In order to consider the random property of this problem, the probabilistic analysis is introduced herein. Finally, the stability of a real beach earth embankment is analysed by means of the suggested probabilitic approach. It may be seen that the results of analysis can represent the numerical assessment of the degree of seismic stability.     

Probabilistic prediction of capsize applied to small high-speed craft

The prediction of capsize of small high-speed craft is highly complex. In this paper, risk analysis is applied to predict the probability of capsize of two types of high-speed craft due to dangerous wave events in the estuary of the Bonny River in the Niger Delta region of Nigeria. Fibreglass reinforced plastic (FRP) hull craft, widely used for transportation, were considered for the prediction. The probability of the craft encountering a dangerous wave situation at a random position at sea and the probability of capsize were calculated using published wave statistics and computer-based analytical models. Results obtained compared favourably with similar analyses carried out by previous investigators for other regions. Various rational and practical ways of reducing the probability of capsize to an acceptable level are presented. From the prediction it was established that human error was a predominant factor in the capsize of vessels.     

A Probabilistic Method for Motion Analysis of Caisson Breakwaters

1 .IntroductionInrecent years ,especiallyfrom1994 when aninternational conference on breakwater design washeldinJapan,muchresearchonthe dynamic analysis of caisson breakwaters has been done ,and manyimportant progresses have been made .Oumeraci and Korten…     

Red noise and regime shifts

The analysis of interdecadal physical and biological variability is made challenging by the relative shortness of available time series. It has been suggested that rapid temporal changes of the most energetic empirical orthogonal function of North Pacific sea surface temperature (sometimes called the Pacific Decadal Oscillation or PDO) represents a “regime shift” between states with otherwise stable statistics. Using random independent time series generated to have the same frequency content as the PDO, we show that a composite analysis of climatic records recently used to identify regime shifts is likely to find them in Gaussian, red noise with stationary statistics. Detection of a shift by this procedure is not evidence of nonlinear processes leading to bi-stable behavior or any other meaningful regime shift.     

Ship sources of ambient noise

The rapid increase in world shipping results in an increase in low-frequency ambient noise at an average rate of about 1/2 dB per year. During the past 10 years there has been a virtual revolution in the sizes and speeds of merchant ships, resulting in significant increases in the noise radiated by the average ship. This trend is continuing. In this paper, the trends in world merchant shipping will be presented, including important changes in propulsion plants as well as in numbers and sizes of ships. The need for radiated noise measurements of these new ship types will be stressed. Ambient noise is also dependent on the geographical distribution of shipping. The LRAPP-sponsored program to establish standard shipping distributions for the Northern Hemisphere will be discussed, and the reliability of current information will be assessed.     

Depth dependence of ambient noise

Omnidirectional measurements of ambient noise versus depth in the Caribbean, Mediterranean, Arctic, Pacific, and Atlantic areas are presented. The shapes of the vertical ambient noise profiles spanning the water column at frequencies from 25 to 500 Hz are shown to be heavily influenced by passing ships. The qualitative features of average noise profiles measured by mid-water hydrophones can be explained with the aid of a straightforward model, and it is concluded that low-frequency omnidirectional ambient noise depth dependence is predictable. The sensitivity of the vertical noise profile to passing ships, coupled with noise predictability suggests that surveillance could be effected by a vertical string of hydrophones without coherent processing in areas of relatively light shipping.     

Ambient noise data logger buoy

A buoy for measuring wind speed and the ambient noise sound pressure level from 10 to 1500 Hz with 1-Hz resolution is described. The measurement buoy was deployed in a remote fjord in southeastern Alaska from October to December, 1989. The results from the data collected show that, for a wind speed of 5 kn, the measured ambient noise level at 900 Hz lies well below the Knudsen curve for open-ocean, wind-generated noise. As the wind speed increases from 5 to 10 kn, the measured ambient noise level approaches the Knudsen curve, increasing at 4 dB/kn compared to 1 dB/kn for the Knudsen curve. Above 10 kn, the measured ambient noise level matches the Knudsen curve