Extreme Value Distribution Model Research Articles

A P–S–N curve fitting method based on mixed Weibull distribution and expectation-maximization algorithm

In practical engineering, there are many factors affecting the fatigue life of actual components, and a single Weibull distribution is insufficient to accurately describe the impact of various factors on fatigue life. In order to solve the above problems, 316L stainless steel is taken as the experimental object to study the effects of phase difference and stress levels on fatigue life based on the mixed Weibull distribution model. Firstly, the mixed Weibull distribution model is converted into the mixed extreme value distribution model, and used Euler's constant to calculate relevant parameters of extreme value distribution and Expectation-Maximization (EM) algorithm to determine the probability density function of the mixed Weibull distribution. Secondly, the probability density function is integrated to obtain the distribution function and the fatigue life under different failure probabilities is calculated. Finally, the influence of non-proportional additional reinforcement and stress amplitude on fatigue life is studied by taking them as hidden variables of mixed Weibull distribution, which is used to obtain P-S-N curves for various failure probabilities. Through the proposed method, the influence of different factors on fatigue life can be considered from the perspective of statistics, and the accuracy of fatigue life prediction can be promoted.

Wave impact pressure and pressure impulse on a square column with an overhanging deck in regular waves

As the main component of semi-submersible platforms, the deck-column structure is inevitably subjected to severe wave impacts in extreme ocean environments. The wave impact pressure and its time integral, impact pressure impulse, play an important role in the structural design, especially for the analysis of dynamic response. To investigate the characteristics of impact pressure and pressure impulse, wave impact tests on a square column with overhanging deck were carried out under a series of regular waves. Wavelet denoising technique and empirical mode decomposition (EMD) method were employed to remove the noise interference and the dynamic amplification effect from raw data. Considering the stochastic feature, statistical analysis of pressure impulse was performed based on generalized extreme value (GEV) and two-parameter Weibull distribution models. The results show the strong variability of the wave pressure impulse and the necessity of statistical analysis even in regular waves. The peak impact pressure is more sensitive to the variation of initial air gap and column incline angle than the pressure impulse. The probability distribution of extreme pressure impulse agrees well with the GEV distribution and is mainly distinguished by the shape parameter. Furthermore, the probability distribution of extreme pressure impulse is significantly affected by the initial air gap, and the effect is also related to wave parameters. The present research reveals the probability distribution of wave pressure impulse in regular waves and lays a foundation for the statistical analysis of pressure impulse in irregular waves.

Modeling of Extreme Temperature Using min-Generalized Extreme Value Distribution

Extreme value theory (EVT) is one of major importance in many fields of applications where extreme values may appear and have detrimental effects and finally Generalized Extreme Value (GEV) distribution model is found as the best fitted distribution model. Extreme minimum temperature using 40 years of data is studied. Minimum of four different time periods (monthly, quarterly, half yearly and yearly) are fitted to the minimum Generalized Extreme Value (MGEV) distribution. The first objective of this study is to describe and model the behaviour of extreme minimum temperature in Sebha by using the MGEV distribution. The second object, we determine the effect of using different size blocks, and illustrate the best four different time (Monthly, Quarterly, Half yearly and yearly) selection periods that are suitable for modelling with the MGEV distribution. The method of probability-weighted moments (PWM) has been used to estimate the unknown parameters; and its corresponding Deviance Test (DT) approach to test the goodness of fit. The results show that minimum Weibull distribution as special case of MGEV distribution is the most an appropriate choice of all selection periods (quarterly half yearly and yearly) are significant except only monthly of all three periods are significant to be fitted by minimum Frechet model. We will use the R programming with packages of fExtreme, evir and ismev to calculate, parameter estimation, testing and diagnostic plots.

Wave contributions to sea levels along the coast of northern South China Sea over 2002–2022

To better understand the wave contribution to coastal sea level variation in the northern South China Sea (SCS), the total sea level time series, which is estimated as the sum of waves, tides, atmospheric surges and altimetric sea levels, over the period of 2002–2022 are used in this study. It is found that tides and waves are two dominate contributors to coastal sea level changes at seasonal (45.7 % and 40.8 %) and interannual (58.6 % and 28.4 %) time scales. The sea level trend is dominated by the altimetric sea levels, but waves can also influence the trends in the Taiwan Strait and Beibu Gulf. The amount of sea level rise that doubles the frequency of the former 50-year return level is analyzed by using the Generalized Extreme Value Distribution (GEVD) model. The results show that the amount of sea level rise is closely related to the amplitude and variance of extreme sea levels. Because waves can significantly increase probability of occurrence of exceedingly large extreme sea levels, the amount of sea level rise (∼1 m) that doubles the coastal flooding frequency is much greater than that (∼10 cm) without the wave contribution. This result demonstrates the important role of waves in changing the coastal flooding frequency.

Quantifying the influence of corrosion defects on the failure prediction of natural gas pipelines using generalized extreme value distribution (GEVD) model and Copula function with a case study

Quantifying the influence of corrosion defects on the failure prediction of natural gas pipelines using generalized extreme value distribution (GEVD) model and Copula function with a case study

Statistical analysis of wind load probabilistic models considering wind direction and calculation of reference wind pressure values in Liaoning Province, China

Wind pressure serves as the fundamental base for architectural design, particularly the reference wind pressure value, which affects the reliability and economy of high-rise, towering, and large-span structures. To facilitate the calculation of reference wind pressure values for design reference periods, load codes from various countries offer probabilistic distribution models for wind speed or reference wind pressure. However, the application of a uniform load probabilistic distribution model for calculating the reference wind pressure for the reference period often results in overestimation or underestimation of the reference wind pressure. To this end, this study collected annual maximum wind speed data from 34 meteorological stations in Liaoning Province, a region in Northeast China, and established extreme value type I, extreme value type III, lognormal, and generalized extreme value distribution models for the annual maximum wind speeds using the maximum likelihood method and method of moment, respectively. The goodness-of-fit test was conducted utilizing the Kolmogorov–Smirnov method. The results showed that the extreme value type III model and the method of moment achieved the best goodness-of-fit for the probabilistic distribution of annual maximum wind speeds. Based on the measured wind direction data corresponding to the annual maximum wind speed, joint probability density functions and cumulative probability density functions of wind speed and wind direction were established. Finally, the influence of different load statistical periods on the reference wind pressure was analyzed.

Comparative study on characteristics of typhoon gusts in the coastal and offshore areas of the South China Sea

Typhoon gusts are hazardous to buildings and structures in both coastal and offshore areas, but the gust characteristics in the two areas could be quite different. In this study, the observational data from two meteorological stations, one at Shenzhen (coastal) and the other in the offshore area of the South China Sea are used to analyze the typhoon gust-related variables and to find the theoretical distribution model that best describes them. The results show that in both coastal and offshore areas, the probability density distributions of all gust-related variables are non-Gaussian. When fitting the curve of the statistical data, the Gengamma model performs the best, followed by the Lognormal model, and the generalized extreme value (GEV) distribution model. Specifically, the gust factor and turbulence intensity are generally Gengamma- and GEV- distributed, respectively. The distributions exhibit certain differences in different gust variables in coastal and offshore areas. The theoretical probabilistic models perform better in the offshore area than in the coastal area. The gust factor increases linearly with the turbulence intensity, while previous empirical models tend to overestimate it. The gust factor and turbulence intensity are significantly higher in the offshore area than in the coastal area. Slower turbulent dissipation is found in the offshore area during typhoon process. A strong positive correlation is shown between the gust amplitude and the turbulent flux. In both coastal and offshore areas, the larger the gust amplitude is, the more the turbulent flux is transmitted.

Analysis of snow load probabilistic models and calculation of reference snow pressure using maximum likelihood method for multiple cities in Liaoning Province, China

The accurate determination of snow loads is crucial for structural design, and determining the reference snow pressure is particularly important for structures vulnerable to snow. The Load Code for the Design of Building Structures (GB50009–2012) provides a standard probabilistic model and fitting method to facilitate the calculation of reference snow pressure during the design reference period. However, using a unified load probabilistic distribution model across different provinces in China may result in overestimation or underestimation of reference snow pressure due to variations in geographic locations. Therefore, this study takes Liaoning Province, including all its cities as an example, which is the only province in northeast China that is both coastal and inland. Measured data from the Global Land Data Assimilation System (GLDAS) were used to establish the extreme value type I distribution, extreme value type III distribution, lognormal distribution, and generalized extreme value distribution models for snow depth using maximum likelihood and moment methods. The Kolmogorov–Smirnov test was used to evaluate the goodness-of-fit of the established models, and the maximum likelihood method was compared with the fitting method (moment method) recommended by the Load Code for the Design of Building Structures. The results showed that the lognormal distribution model and the maximum likelihood method achieved the best goodness-of-fit for the probabilistic distribution of snow depth. Additionally, the influence of snow density uncertainty on reference snow pressure was analyzed using measured data for snow pressure and snow depth.

Dynamic reliability analysis of structures under nonstationary stochastic excitations using tail-modified extreme value distribution

In practical engineering, it is usually necessary to compute the small first-passage probability of dynamic systems exposed to nonstationary stochastic excitations. However, it is still a challenging problem to efficiently estimate the super-small failure probability using an approximate extreme value distribution (EVD) based on a small number of simulated samples. In this study, a novel EVD model is proposed to describe the probability distribution of the structural extreme response induced by nonstationary stochastic excitations. This EVD model consists of two parts: the main body is modeled by a truncated-shifted generalized lognormal distribution, and a monotonic exponential model is proposed to fit the tail region. Besides that, a criterion for determining the breakpoint between the main body and tail region is proposed, which ensures the non-negativity and normativity of the proposed EVD model and allows the EVD to be reconstructed accurately and efficiently, particularly in its tail region. In this regard, the corresponding first passage probabilities under different thresholds can be straightly evaluated. The precision and completeness of the proposed EVD model are investigated using two numerical examples that consider linear and nonlinear frame structures subjected to nonstationary ground motion accelerations. The results show that the proposed model is in excellent agreement with the results of Monte Carlo simulation, even when the failure probability is very small.

Assessing the crash risk of mixed traffic on multilane rural highways using a proactive safety approach

The crash risk assessment of mixed traffic has been understudied due to a lack of pertinent data. In recent years, proactive methods have gained significant attention in transportation safety analysis because of their numerous advantages. In this study, we model and evaluate the effect of speed difference on the sideswipe crash risk of mixed traffic using a novel proactive safety indicator called Anticipated Collision Time (ACT). For analysis, detailed trajectory data were collected using an unmanned aerial vehicle from four-lane and six-lane rural highways. The crash risk was derived from the observed conflict risk and then used to assess the highway system's safety performance under study. Using the Extreme Value Theory (EVT), the conflict risk was mapped to the crash risk. The extreme events were identified using the Block Maxima (BM) approach. Later, the Generalized Extreme Value Distribution (GEV) models were developed for each location by extracting the sideswipe conflicts from the vehicle trajectories. The findings suggest that sideswipe conflicts are more of a safety concern than rear-end conflicts due to the frequent nature of lane changes or passing operations. Also, significant speed difference exists among different vehicle modes present in mixed traffic, and the sideswipe crash risk increases with the increase in the maximum speed difference. The analyses of speed differences also indicate that compared to the four-lane highway, the available safety margin is limited on a six-lane highway due to the higher maximum speed difference. Hence, any driver error may lead to sideswipe crashes. In light of the findings of this study, we strongly suggest the need to provide speed control strategies and restrict the frequent risky lane-changing or passing operations that mainly give rise to sideswipe conflicts on a six-lane highway. Further, this study found that the sideswipe crash risk decreases with the increase in vehicle size on both four-lane and six-lane highways. Hence, we suggest developing separate crash risk models for different vehicle modes in mixed traffic on multilane rural highways. Otherwise, the crash risk mitigation strategies may not be appropriate for mixed traffic conditions.

The Generalised Extreme Value Distribution Approach to Comparing the Riskiness of BitCoin/US Dollar and South African Rand/US Dollar Returns

In this paper, the generalised extreme value distribution (GEVD) model is employed to estimate financial risk in the form of return levels and the value at risk (VaR) for the two exchange rates, BitCoin/US dollar (BTC/USD) and the South African rand/US dollar (ZAR/USD). The Basel Committee on Banking Supervision (BCBS) responsible for developing supervisory guidelines for banks and financial trading desks recommended that VaR be computed and reported. The maximum likelihood estimation (MLE) method is used to estimate the parameters of the GEVD. The estimated risk values are used to compare the riskiness of the two exchange rates and help both traders and investors to define their position in forex trading. This is to helping understanding the risk they are taking when they convert their savings/investments to BitCoin instead of the South African currency, the rand. The high extreme value index associated with the BTC/USD compared to the ZAR/USD implies that BitCoin is riskier than the rand. The BTC/USD has higher values of expected extreme/tail losses of 13.44%, 18.02%, and 23.41% at short (6 months), medium (12 months), and long (24 months) terms, compared to the ZAR/USD expected extreme/tail losses of 2.40%, 2.84%, and 3.28%, respectively. The computed VaR estimates for losses of USD 0.17, USD 0.22, and USD 0.38 per dollar invested in BTC/USD at 90%, 95%, and 99%, compared to ZAR/USD’s USD 0.03, USD 0.03, and USD 0.04 at the respective confidence levels, confirm the high risk associated with BitCoin. The conclusion drawn from this study is that BTC/USD is riskier than ZAR/USD, despite the rand being a developing country’s currency, hence perceived as being risky. The perception is that the rand is riskier than BitCoin and perceptions do influence exchange rates. Kupiec’s backtest results confirmed the model’s adequacy. These findings are helpful to investors, traders, and risk managers when deciding on trading positions for the two currencies.

Statistical Modeling for Flood Frequency in Upper Chaophraya River Basin

The research deals with the probabilistic estimates of annual maximum flood peaks in the upper Chaophraya basin (Thailand) used the extreme value theory, the Block Maxima. The Generalized Extreme Value (GEV) distribution model, the Frèchet distribution (EV2), the extension of the Frèchet distribution such as the Kumaraswamy Frèchet distribution and the new distribution as called the Exponentiated Kumaraswamy Frèchet distribution satisfied the Goodness of fit test (Kolmokorov-smirnov test). The return levels are estimated for 3, 5, 10, 30, 50, 100, 500 and 1000 years which are consistently increasing for designs of flood protection in future. The return period of flood for each stations are estimated.
 The investigation of the new distribution and appropriated estimation technique for the flood frequency in upper Chaophraya river basin as we called the Exponentiated Kumaraswamy Frèchet distribution and the differential evolution maximum likelihood estimation were done. We derived the properties of the Frèchet family; such as the Frèchet distribution (EV2), the Kumaraswamy Frèchet distribution (KF) and the Exponentiated Kumaraswamy Frèchet distribution (EKF). We also compared Bias, Variance, Mean Square Error and Mean Absolute Percentage Error for all parameters in each distribution by generating the Frèchet family random number. For the effectiveness of analytical solutions of the parameters we provided the numerical solutions (differential evolution method) to obtain estimates for all parameters by using Scilab program.
 Accuracy of flood assessment of extreme event is of fundamental importance for many safety, engineering and financial application. In part of application we provided the probabilistic estimates of annual maximum flood peaks or momentary peak data in the upper Chaophraya river basin (Thailand). The Generalized Extreme Value (GEV) distribution model were used to be gain to compare with as the Frèchet distribution (EV2), the Kumaraswamy Frèchet distribution (KF) and the Exponentiated Kumaraswamy Frèchet distribution (EKF). The Goodness of fit test, the return level and return period were done. The return periods of flood were classified by hazard class using GEV found that in upper Chaophraya river basin flood occurred highly. The result from the Frèchet family also occurred highly, but the return period and return level from the Kumaraswamy Frèchet distribution (KF) quite closed to GEV more than another distribution.

Experimental Study on the Effect of Extreme Waves on a LNG Carrier

This paper presents a comprehensive experimental study on the effect of extreme waves on a LNG carrier. The LNG carrier model was equipped with a variety of sensors to measure motions, green water height on deck as well as local and global loads. Experiments in transient wave packets provided the general performance in waves in terms of response amplitude operators and were accompanied by tests in regular waves with two different wave steepness. These tests allowed detailed insights into the nonlinear behavior of the vertical wave bending moment in steep waves showing that green water on deck can contribute to a decrease of vertical wave bending moment. Afterwards, systematic model tests in irregular waves were performed to provide the basis for statistical analysis. It is shown that the generalized extreme value distribution model is suitable for the estimation of the extreme peak values of motions and loads. Finally, model tests in tailored extreme wave sequences were conducted comparing the results with the statistical analysis. For this purpose, analytical breather solutions of the nonlinear Schrödinger equation were applied to generate tailored extreme waves of certain critical wave lengths in terms of ship response. Besides these design extreme waves, the LGN carrier was also investigated in the model scale reproduction of the real-world Draupner wave. By comparing the motions, vertical wave bending moment, green water column and slamming pressures it is concluded that the breather solutions are a powerful and efficient tool for the generation of design extreme waves of certain critical wave lengths for wave/structure investigations on different subjects.

Utilizing Satellite Data to Establish Rainfall Intensity-Duration-Frequency Curves for Major Cities in Iraq

This study generates intensity-duration-frequency curves for three important cities in Iraq using Global Precipitation Measurement Integrated Multi-Satellite Retrievals for Global Precipitation Measurement (IMERG), Global Satellite Mapping of Precipitation near real-time (GSMaP NRT), and gauge corrected (GSMaP GC) satellite precipitation datasets. Many probability distribution functions were used to fit the maximum yearly rainfall data. The Sherman equation was used to create intensity-duration-frequency (IDF) curves for rainfall intensities with 2-, 5-, 10-, 25-, 50-, and 100-year return periods, with the estimated coefficients of the best-fit distribution serving as the fitting parameters. The discrepancy between the IDF curves produced from the satellites and the observed data was used to bias correct the satellite IDF curves. The Generalized Extreme Value Distribution model best describes the hourly rainfall distribution of satellite data. GSMaP GC was the best option for creating IDF curves with higher correlations with observed data at Baghdad, Basra, and Mosul. The study indicates the necessity of gauge correction of satellite rainfall data to reduce under- and over-estimating observed rainfall. GSMaP GC can reasonably estimate rainfall in a predominantly arid climate region like Iraq. The generated IDF curves may be an important step toward achieving sustainable urban stormwater management in the country.

True interval non-stationary Intensity-Duration-Frequency curves under changing climate and effect of temporal discretisation on rainfall extremes

The extreme rainfall intensity-duration-frequency (IDF) curves are used to design stormwater infrastructure in the urban areas and need to be developed keeping in view of the warming climate. The current study develops the non-stationary IDF relationships for 11 class-I urban cities of India under changing climate. The total 11,528 generalized extreme value distribution (GEV) models are developed to quantify non-stationarity in extreme rainfall by introducing a clock hour correction factor (CHCF) as a covariate. The observed hourly rainfall data of the selected cities located in five different regions of India, namely the western region (Mumbai, Ahmedabad, Jaipur), northern region (New Delhi, Dehradun), north-eastern region (Imphal), eastern region (Bhubaneswar, Kolkata), and southern region (Madurai, Chennai, Bengaluru) are collected and converted in the fixed and sliding interval annual maximum rainfall series of eight different durations. The said data set is used in the computation of CHCF, evaluation of discretisation effect on extreme rainfall events, trend analysis, development of stationary and non-stationary IDF curves. The CHCF values of seven (two) cities are above (below) 1.15 respectively; the other two cities show a value ∼ 1.15. The effect of temporal discretisation on the computation of extreme rainfall for 24-h (FW and SW) maximum rainfall depth was found to be highest in Bhubaneswar (50%) and Imphal (44%). The trend analysis revealed no statistically significant increasing (decreasing) trend in extreme rainfall for all durations for all cities under consideration except in the case of Bengaluru for 2-,3-, and 6-h durations (Chennai for a 48-h duration). The current study concluded that, under a non-stationarity climate, the shorter (1-h) and longer (24-h) duration extreme rainfall is influenced by local and global processes, respectively. Further, the short-duration extreme events are intensifying with the decrease in the return period. The 1-h duration non-stationary rainfall intensity for a 2-year return period and stationary rainfall intensity for a 5-year return period of 62.9 mm/h and 57 mm/h for Bengaluru, 77.7 mm/h and 77.2 mm/h for Mumbai, 60.8 mm/h and 60.7 mm/h for Ahmedabad, 47.8 mm/h and 49.4 mm/h for Jaipur, 59.8 mm/h and 59.3 mm/h for Madurai, 73.6 mm/h and 73 mm/h for Bhubaneswar, and 39.6 mm/h and 40.1 mm/h for Imphal, respectively. The ready-to-use IDF curves developed under stationary and non- stationary climate can be useful to design engineers in designing stormwater drainage systems in the selected class-I urban cities of India.

Regional non-stationary future extreme rainfall under changing climate over Asian Monsoon Region

An increase in the Intensity-Duration-Frequency (IDF) of rainfall extremes questions the assumption of stationarity in the design and planning of water infrastructures under changing climate. To address this, non-stationary-based approaches are widely used for assessing the extremes over time. However, the trends associated with future extreme rainfall would differ from that of the historical dataset. Therefore, the main objective of this study is to develop a non-stationary modelling approach to generate future regional IDF curves by incorporating the trend in the rainfall over Asian Monsoon Region (AMR). Daily rainfall data from (i) APHRODITE and (ii) baseline period (1951–2005) and future projections (2020−2100) simulated from 27 GCMs are used in this study. The proposed framework includes (i) selection of GCM models, (ii) Stationary (S) and Non-Stationary (NS) Generalized Extreme Value Distribution (GEVD) Models, (iii) delineation of extreme precipitation zones, (iv) performance evaluation of zone-wise models, and (v) estimation of future regional IDF curves for near-future (2020–2060), and far-future (2061–2100). Results show that the eight models and their corresponding GCM covariates cover around 90% of grids across the AMR compared to S-GEVD models among the 27 GCMs. Six extreme precipitation zones were obtained, and fitted regional models could mimic the individual station models. The change in extreme rainfall intensity for the future climate is higher for zone-1 (low extreme rainfall region), with an increase of 87–98% across different emission scenarios using the non-stationary models, whereas for zone-6 (higher extreme rainfall region) has a 60–68% increase from its stationary counterparts. For high and low emission scenarios, intensity increases up to 98% and 87% respectively for a lower return period (5-year), and 65% and 58% for a higher return period (100-year) by the end of the century.

Research on Distribution Model and Detection Spacing of Compaction Degree of Asphalt Pavement Based on the PQI Method

The pavement quality indicator (PQI) is a non-destructive piece of equipment for detecting the compaction degree of asphalt pavement, which can avoid primary damage to the pavement compared with the traditional core-drilling method. In this paper, the PQI method was applied to evaluate the compaction quality of asphalt pavement through data collection, calibration and statistical analysis, and the probability-distribution characteristics of compaction degree were also explored, by fitting the data with probability-distribution models. Furthermore, the optimal detection-spacing was determined by comparing the statistical results of compaction degree measured at different detection-spacings. Test results showed that the calibrated PQI data was close to the actual data of the core sample, and their error rate was within 1%. The compaction degree of the test road was mostly located between 92% and 99%, and the variable coefficient was entirely below 2%, demonstrating that the pavement-compaction quality was satisfactory and uniform. The normal distribution model, lognormal distribution model and extreme-value distribution model had relatively high accuracy in fitting the compaction-degree frequency data, while the sine-wave distribution model was low in fitting accuracy. By comparing the predicted value with the actual value of compaction degree, the normal distribution model was determined as the most appropriate model for describing the frequency distribution of compaction degree. In addition, the detection spacing was selected as 50 m, considering the reliability, accuracy and efficiency. The research results provide technical support for the compaction quality-control of asphalt pavement in a non-destructive, timely, accurate and multi-point manner, ultimately contributing to the excellent service performance and service life of asphalt pavement.

Analysis of Measured Temperature Field of Unpaved Steel Box Girder

This work used the measured data during the whole test period to study the law of temperature change in the steel rail beams, and the distribution characteristics of the sunshine temperature field, in straddle-type monorail tourist transportation systems, employing a field-test and a numerical simulation. The curve form of the temperature gradient was determined by a comparative analysis of the existing domestic and foreign norms. Finally, the generalized extreme value distribution model was used to predict the extreme value of the representative value of the temperature difference, and the value of the temperature base, for different return periods, and the complete temperature gradient model were determined. Results: During the whole test period, the maximum vertical positive temperature difference of the steel box girder was 15.21 °C, and the negative temperature difference was −5.07 °C. In addition, the effect of the ambient temperature, considering solar radiation, was found to be an important factor affecting the distribution of the vertical temperature difference. The analysis determined that the positive and negative temperature difference curves in the unpaved steel box girder were multi-segment polylines and linear straight lines, respectively. The extreme value predicts that the representative temperature differences between T1 and T2 of the 450 mm beam during the 50-year return period were 17.2 °C and 4.58 °C, respectively, and T1 and T2 under the 100-year return period were 17.38 °C and 4.62 °C, respectively.

Design Wave Height Parameter Estimation Model Reflecting the Influence of Typhoon Time and Space

Typhoon storm surge disasters are one of the main restrictive factors of sustainable development in coastal areas. They are one of several important tasks in disaster prevention and reduction in coastal areas and require reasonable and accurate calculations of wave height in typhoon-affected sea areas to predict and resist typhoon storm surge disasters. In this paper, the design wave height estimation method based on the stochastic process and the principle of maximum entropy are theoretically advanced, and it can provide a new idea as well as a new method for the estimation of the return level for marine environmental elements under the influence of extreme weather. The model uses a family of random variables to reflect the influence of a typhoon on wave height at different times and then displays the statistical characteristics of wave height in time and space. At the same time, under the constraints of the given observations, the maximum uncertainty of the unobtainable data is maintained. The new model covers the compound extreme value distribution model that has been widely used and overcomes the subjective interference of the artificially selected distribution function—to a certain extent. Taking the typhoon wave height data of Naozhou Observatory as an example, this paper analyzes the probability of typhoon occurrence frequency at different times and the characteristics of typhoon intensity in different time periods. We then calculate the wave height return level and compare it with traditional calculation models. The calculation results show that the new model takes into account the time factor and the interaction between adjacent time periods. Furthermore, it reduces the subjective human interference, so the calculated results of the typhoon’s influence on wave height return level are more stable and accurate.

Bayesian Updates for an Extreme Value Distribution Model of Bridge Traffic Load Effect Based on SHM Data

As the distribution function of traffic load effect on bridge structures has always been unknown or very complicated, a probability model of extreme traffic load effect during service periods has not yet been perfectly predicted by the traditional extreme value theory. Here, we focus on this problem and introduce a novel method based on the bridge structural health monitoring data. The method was based on the fact that the tails of the probability distribution governed the behavior of extreme values. The generalized Pareto distribution was applied to model the tail distribution of traffic load effect using the peak-over-threshold method, while the filtered Poisson process was used to model the traffic load effect stochastic process. The parameters of the extreme value distribution of traffic load effect during a service period could be determined by theoretical derivation if the parameters of tail distribution were estimated. Moreover, Bayes’ theorem was applied to update the distribution model to reduce the statistical uncertainty. Finally, the rationality of the proposed method was applied to analyze the monitoring data of concrete-filled steel tube arch bridge suspenders. The results proved that the approach was convenient and found that the extreme value distribution type III might be more suitable as the traffic load effect probability model.