Joint probability distribution of winds and waves from wave simulation of 20 years (1989-2008) in Bohai Bay

The joint probability distribution of wind speed and significant wave height in the Bohai Bay was investigated by comparing the Gurnbel logistic model, the Gumbel-Hougaard （GH） copula function, and the Clayton copula function. Twenty years of wind data from 1989 to 2008 were collected from the European Centre for Medium-Range Weather Forecasts （ECMWF） database and the blended wind data of the Quick Scatterometer （QSCAT） satellite data set and re-analysis data from the United States National Centers for Environmental Prediction （NCEP）. Several typhoons were taken into account and merged with the background wind fields from the ECMWF or QSCAT/NCEP database. The 20-year data of significant wave height were calculated with the unstructured-grid version of the third-generation wind wave model Simulating WAves Nearshore （SWAN） under extreme wind process conditions. The Gumbel distribution was used for univariate and marginal distributions. The distribution parameters were estimated with the method of L-moments. Based on the marginal distributions, the joint probability distributions, the associated return periods, and the conditional probability distributions were obtained. The GH copula function was found to be optimal according to the ordinary least squares （OLS） test. The results show that wind waves are the prevailing type of wave in the Bohai Bay.

Uncertainty and joint probability of sea ice loads

Ice load is one of the most important factors for design of marine stuctures in cold sea area.The designcriteria of ice loads for marine structures consist of two parts: level ice thickness and crushing strength. Due to thestrong randomness of the affecting factors on ice thickness and crushing strength, such as ice temperature,air temperature, water temperature,salinity,wind field, numerical simulation method method can not produce satisfactory results. Thispaper proposes a method of uncertainty analysis and joint probabilistic prediction of level ice thickness and crushingstrength instead of traditional ice load criteria for marine structures.

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.

The joint long-term distribution of design environmental factors for offshore structures Multivariate probabilities and simulating method

With the development of ocean engineering, it is one of the most important factors which determine the structural safety, cost and suitable forms of engineerings to select the ocean environmental design criteria. Owing to the complexity , variation and randomness of ocean environmental conditions, the commonly used methods for determining design criteria cannot consider the joint occurring probabilities of several environmental factors ,therefore, lead to overestimate design criteria of them and result in an unnecessary overspend invest in engineering. On the basis of the measured and hindcasting data and the multi-demension joint probability theory, this paper presented the study of the joint loads of wind , wave and current on the offshore structures and its responsible joint probability level with the application of random simulation techniques, and presented the joint design criteria of environmental loads for the realistic design of engineerings.

Heterogeneous sensors data fusion method based on peak picking in probability density space

The multi-sensor multi-target localization and data fusion problem is discussed, and a new data fusion method called joint probability density matrix （JPDM） has been proposed, which can associate with and fuse measurements from spatially distributed heterogeneous sensors to produce good estimates of the targets. Based on probabilistic grids representation, the uncertainty regions of all the measurements are numerically combined in a general framework. The NP-hard multi-sensor data fusion problem has been converted to a peak picking problem in the grids map. Unlike most of the existing data fusion methods, the JPDM method does not need association processing, and will not lead to combinatorial explosion. Its convergence to the CRB with a diminishing grid size has been proved. Simulation results are presented to illustrate the effectiveness of the proposed technique.

Multi-hazard joint probability distribution model for wind speed,wind direction and rain intensity

Multiple disasters such as strong wind and torrential rain pose great threats to civil infrastructures.However,most existing studies ignored the dependence structure between them,as well as the effect of wind direction.From the dimension of the engineering sector,this paper introduces the vine copula to model the joint probability distribution(JPD)of wind speed,wind direction and rain intensity based on the field data in Yangjiang,China during 1971–2020.First,the profiles of wind and rain in the studied area are statistically analyzed,and the original rainfall amounts are converted into short-term rain intensity.Then,the marginal distributions of individual variables and their pairwise dependence structures are built,followed by the development of the trivariate joint distribution model.The results show that the constructed vine copula-based model can well characterize the dependence structure between wind speed,wind direction and rain intensity.Meanwhile,the JPD characteristics of wind speed and rain intensity show significant variations depending on wind direction,thus the effect of wind direction cannot be neglected.The proposed JPD model will be conducive for reasonable and precise performance assessment of structures subjected to multiple hazards of wind and rain actions.

Role of street patterns in zone-based traffic safety analysis

Although extensive analyses of road segments and intersections located in urban road networks have examined the role of many factors that contribute to the frequency and severity of crashes, the explicit relationship between street pattern characteristics and traffic safety remains underexplored. Based on a zone-based Hong Kong database, the Space Syntax was used to quantify the topological characteristics of street patterns and investigate the role of street patterns and zone-related factors in zone-based traffic safety analysis. A joint probability model was adopted to analyze crash frequency and severity in an integrated modeling framework and the maximum likelihood estimation method was used to estimate the parameters. In addition to the characteristics of street patterns, speed, road geometry, land-use patterns, and temporal factors were considered. The vehicle hours was also included as an exposure proxy in the model to make crash frequency predictions. The results indicate that the joint probability model can reveal the relationship between zone-based traffic safety and various other factors, and that street pattern characteristics play an important role in crash frequency prediction.

System Analysis of Disaster Prevention Design Criteria for Coastal and Estuarine Cities

In China, estuarine and coastal cities are mostly regional economic development centers. The disasters by combined effect of upper reach flood, storm surge and typhoon waves are primary obstacles to the economic development of such cities. Thus the risk analysis and system analysis of flood-storm surge-wave disaster, economic loss and flood-storm surge control measures play a very important role in the sustainable development of coastal cities. There are three types of coastal cities for consideration. The first type of city is like Tianjin. The most significant damage is from the upper reach flood. The effect of storm surge is negligible, because in the estuary of the Haihe River, tidal locks are built. The Grey Markov Model (GMM) is used to forecast the flood peak level GMM combines the Grey system and the Markov theory into a high-precision model The predicted flood peak levels are close to the measured data. A synthetic model is established for economic assessment, risk analysis and flood-control benefit estimation As a new contribution, a stochastic simulation technique is used to compute risk probability. At the same time, consideration is given to the effect of correlation between variables on risk probability. The second type of city is like Shanghai, where sometimes the combined effect of river flood peak and set storm surge is the most severe disaster. The water level of a 1000 yr. return period of the Huangpu river is used as the design criterion. The simulated combined water level of flood peak, storm surge and maximum astronomical tidal level of a 400 yr. return period is close to the conventional design water level of a return period of 1000 years. The third type of city is Like Qingdao, where the combined effect of the maximum astronomical tide, storm surge and waves bring about the most significant damage. With the stochastic simulation technique, different combinations of storm surge and waves at the 1% and 2% joint probability level are simulated for disaster prevention.

Sand particle lift-off velocity measurements and numerical simulation of mass flux distributions in a wind tunnel

Lift-off velocity of saltating sand particles in wind-blown sand located at 1.0 mm above the sand bed surface was measured using a phase Doppler particle analyzer in a wind tunnel. The results show that the probability distribution of lift-off velocity can be expressed as a lognormal function, while that of lift-off angle follows an exponential function. The probability distribution of lift-off angle conditioned for each lift-off velocity also follows an exponential function, with a slope that becomes steeper with increasing lift-off velocity. This implies that the probability distribution of lift-off velocity is strongly dependent on the lift-off angle. However, these lift-off parameters are generally treated as an independent joint probability distribution in the literature. Numerical simulations were carried out to investigate the effects of conditional versus independent joint probability distributions on the vertical sand mass flux distribution. The simulation results derived from the conditional joint probability distribution agree much better with experimental data than those from the independent ones. Thus, it is better to describe the lift-off velocity of saltating sand particles using the conditional joint probability distribution. These results improve our understanding of saltation processes in wind-blown sand.

New model for deducing directional extrema based on multivariate extremum statistical theory

The parameters of principal and directional extrema in a marine environment are important in marine engineering design, especially for appropriate construction of oceanic platforms and other structures. When designing wave walls and break water structures, the orientation of the breakwater or seawall depends mainly on the direction of the strongest waves. However, the strength of the breakwater and the elevation of the seawall depend on the magnitude of the biggest wave height of the strongest waves. Thus, identification of directional extrema plays an important role in the design of wave factors. When calculating the directional extremum, different materials may require different specific computational methods, yet few theoretical studies have been conducted in this field of research. Based on multivariate extremnm statistical theory, this paper utilizes a discrete random variable to build a joint probability model compounded by a discrete random variable and a multivariate continuous random variable. Furthermore, this paper provides the first investigation on the theories and methodologies to deduce wave directional extrema. The results provide tools for both creating the calculation method of the directional extremum value and providing the rational directional extremum parameters for marine engineering design.

Estimating Design Loads with Environmental Contour Approach Using Copulas for an Offshore Jacket Platform

Jacket-type offshore platforms are widely used for oil, gas field, and energy development in shallow water. The design of a jacket structure is highly dependent on target environmental variables. This study focuses on a strategy to estimate design loads for offshore jacket structures based on an environmental contour approach. In addition to the popular conditional distribution model, various classes of bivariate copulas are adopted to construct joint distributions of environmental variables. Analytical formulations of environmental contours based on various models are presented and discussed in this study. The design loads are examined by dynamic response analysis of jacket platform. Results suggest that the conditional model is not recommended for use in estimating design loads in sampling locations due to poor fitting results. Independent copula produces conservative design loads and the extreme response obtained using the conditional model are smaller than those determined by copulas. The suitability of a model for contour construction varies with the origin of wave data. This study provides a reference for the design load estimation of jacket structures and offers an alternative procedure to determine the design criteria for offshore structures.

Effect of Sea Level Variation on Calculation of Design Water Level

The long-term variation and seasonal variation of sea level have a notable effect on the calculation of engineering water level. Stich an effect is first analyzed in this paper. The maximal amplitude of inter-annual anomaly of monthly mean sea level along the China coast is larger than 60 cm. Both the storm surge disaster and cold wave disaster are seasonal disasters in various regions, so the water level corresponding to the 1% of the cumulative frequency in the cumulative frequency curve of hourly water level data for different seasons in various sea areas is different from design water level., for example, the difference between them reaches maximum in June, July and August for northern sea area, and maximum in September, October and November for Southern China Sea, The hourly water level data of 19 gauge stations along the China coast are analyzed. Firstly, the annual mean sea level for every station is obtained; secondly, linear changing rates of annual mean sea level are obtained with the stochastic dynamic method; thirdly, the astronomical tide and storm surge tide are obtained by subtracting the linear fitting part from the original hourly data, finally, two distributions corresponding to the astronomical tide and wind tide are obtain ed according to whether the astronomical tide and storm tide are correlative or not. So the two check water levels are obtained with the joint probability method, The maximal difference between the two water levels of 100 years' recurrence is more than 30 cm. Both of the two check water levels have disadvantages in the use of observation data, so the mean value is suggested to be taken as the final check water level. A comparison between the two check-water levels indicates that the effect of sea level variation upon design water level and check water level is larger than 80 cm at some stations.

Multi-target pig tracking algorithm based on joint probability data association and particle filter

In order to evaluate the health status of pigs in time,monitor accurately the disease dynamics of live pigs,and reduce the morbidity and mortality of pigs in the existing large-scale farming model,pig detection and tracking technology based on machine vision are used to monitor the behavior of pigs.However,it is challenging to efficiently detect and track pigs with noise caused by occlusion and interaction between targets.In view of the actual breeding conditions of pigs and the limitations of existing behavior monitoring technology of an individual pig,this study proposed a method that used color feature,target centroid and the minimum circumscribed rectangle length-width ratio as the features to build a multi-target tracking algorithm,which based on joint probability data association and particle filter.Experimental results show the proposed algorithm can quickly and accurately track pigs in the video,and it is able to cope with partial occlusions and recover the tracks after temporary loss.

On the Exceedance Probabilities of Extreme Drift Motions of An Offshore Structure

The response statistics of a compliant offshore structure excited by slowly varying wave drift forces is calculated by use of a numerical path integral solution method. The path integral solution is based on the Ganss-Legendre interpolation scheme, and the values of the response probability density are obtained at the Gauss quadrature points in sub-intervals. It is demonstrated that a distinct advantage of the path integral solution is that the joint probability density of the response displacement and velocity is one of the by products of the calculations. This makes it possible to calculate the mean level up-crossing rates, which provides estimates of the exceedance probabilities of specified response levels for given time periods.

Ecological risk assessment of heavy metals in surface seawater and sediment near the outlet of a zinc factory in Huludao City, Liaoning Province, China

At present, the methods widely applied to assess ecological risk of heavy metals are essentially single-point estimates in which exposure and toxicity data cannot be fully used and probabilities of adverse biological effects cannot be achieved. In this study, based on investigation of concentrations of six heavy metals(As, Hg, Pb, Cd, Cu, and Zn) in the surface seawater and sediment near the outlet of a zinc factory, located in Huludao City, Liaoning Province, China, a tiered approach consisting of several probabilistic options was used to refi ne ecological risk assessment for the individuals. A mixture of various heavy metals was detected in the surface seawater, and potential ecological risk index(PERI) was adopted to assess the potential ecological risk of heavy metals in the surface sediment. The results from all levels of aquatic ecological risk assessment in the tiered framework, ranging from comparison of single effects and exposure values to the use of distribution-based Hazard Quotient obtained through Monte Carlo simulation, are consistent with each other. Briefl y, aquatic Zn and Cu posed a clear ecological risk, while Cd, Pb, Hg, and As in the water column posed potential risk. As expected, combined ecological risk of heavy metal mixture in the surface seawater was proved signifi cantly higher than the risk caused by any individual heavy metal, calculated using the concept of total equivalent concentration. According to PERI, the severity of pollution by the six heavy metals in the surface sediment decreased in the following sequence: Cd>Hg>As>Pb>Cu>Zn, and the total heavy metals in the sediment posed a very high risk to the marine environment. This study provides a useful mathematical framework for ecological risk assessment of heavy metals.

Method for extracting geometrical characteristics of joint probability density based on contour lines

This paper presents a method for extracting geometrical features of the joint probability density function(PDF)of two-dimensional systems based on its contour lines,with particular interests given to the number and position of peaks and craters.In order to detect those two types of structures,a series of horizontal planes are applied to truncate the joint PDF with contour lines generated.Starting with the analysis of contour lines in a single plane,shape characteristics of the peak and the crater can be reflected on the contour lines in the aspects of gradient direction and inclusion relationship.Aided by the properties of PDF,the information about gradient direction and inclusion relationship of contour lines can be obtained simultaneously if the contour tree is built.According to the contour tree,the contour lines can be classified as two groups.Then the corresponding relation between contour lines in different planes is discussed.Based on the corresponding relation,clustering analysis about contour lines belonging to the same group but having different heights is performed.Two sets of contour lines are finally obtained as the simplest expression of geometrical characteristics of a joint PDF.They can be used to obtain the number and position of each peak and crater.Three oscillators of different types are chosen to test this method,which shows that this method can pave the way for numerical calculation about the stochastic P-bifurcation of multi-dimensional systems.

Seismic reliability analysis of large electric power systems

Based on the De.Morgan laws and Boolean simplification, a recursive decomposition method is introduced in this paper to identify the main exclusive safe paths and failed paths of a network. The reliability or the reliability bound of a network can be conveniently expressed as the summation of the joint probabilities of these paths. Under the multivariate normal distribution assumption, a conditioned reliability index method is developed to evaluate joint probabilities of various exclusive safe paths and failed paths, and, finally, the seismic reliability or the reliability bound of an electric power system. Examples given in the paper show that the method is very simple and provides accurate results in the seismic reliability analysis.

Selection of Environmental Conditions for Nearshore Structure Design

Different from the traditional one dimensional extreme value statistical method, practical design criteria for nearshore structure design are presented based on joint probability theory in this paper. The proposed procedure considers the combined effect of tide level, huge waves and wind affecting coastal structures. The Importance Sampling Procedure (ISP) is utilized to solve the joint distribution of non Gaussian correlated multivariate distributions. The calculation results show that the ISP is a simulating technique with the advantages of efficiency and high convergency. Finally the environmental conditions are given using this technique for near shore structure design in the Qingdao area.

Cosine Moments and Their Application to ∑ Relationships

Recent advances In the theory of ∑ relationships lead to the Investigation of moments needed to derive the relavant joint probability densities. These together with the linear theory of relationships, make possible the calcualtion of therelationships from ∑1 to ∑2 one by one. The superior performance ofour new ∑4 and ∑r relationships, for example, with respect to the older ∑1 and ∑3 formulas strongly suggests a deeper study of the pertinent moments. In this paper a new concept, the cosine moment, is introduced which, together with a certain integral theorem, permits the derivation of the relevant joint probability densities. These lead in turn to the derivation of all ∑ relationships valid for all the space groups.

A 249-Year Record of Floods at Appleby in Westmorland, UK

An analysis of nearly 250 years of flood records on the river Eden at Appleby-in-Westmorland has enabled a flood frequency relationship to be established. The most severe floods were in the late 18th and early 19th century. With such a long history of flooding, some remedial measures would have been expected but the local people have, to some extent, adapted to the flood hazard by means of temporary and permanent flood proofing methods such as a cemented board across a doorway and removable flood boards. These measures were overwhelmed during the 2015 flood, as were the flood gates installed by the Environment Agency in 1998. A higher level of protection from floods at Appleby is called for.