Exceedance Probability Research Articles

Traditional seismic hazard analyses underestimate hazard levels when compared to observations from the 2023 Kahramanmaras earthquakes

A sequence of two major earthquakes, Mw7.8 Pazarcik, and Mw7.5 Elbistan, struck Southeastern Turkey in February 2023. The large magnitudes of the earthquakes and the short time between the two events raised questions about whether this sequence was an extremely rare disaster. Here, based on prior knowledge, we perform seismic hazard assessment for the region to estimate exceedance probabilities of observed magnitudes and ground motions. We discuss that many regional studies indicated the seismic gap in the area but with lower magnitude estimations. Observed ground motions generally agree with empirical models for the Pazarcik event. However, some records with high amplitudes exceed the highest observed amplitudes in an extensive database of shallow crustal earthquakes. We observe a notable trend of residuals for the Elbistan earthquake, leading to underestimation at long periods. We discuss potential advances in science for better characterization of such major earthquakes in the future.

Shaking table tests of sliding‐prone blocks subjected to unidirectional and bidirectional ground and floor motions

AbstractFreestanding museum collections with low friction coefficients and high aspect ratios may be damaged due to excessive sliding displacements during earthquakes. However, several key issues have not been adequately addressed, such as the friction and sliding behavior of museum collections under actual conditions. Unidirectional and bidirectional shaking table tests were conducted to determine the maximum sliding displacements (MSDs) of a freestanding glass block on sandpaper, which had the lowest friction coefficient among forty‐two contact interfaces in slow‐pull tests. Fourteen far‐field and fourteen near‐fault pulse‐like ground motion records were applied with peak ground accelerations (PGAs) of the major components scaled from 0.05 to 0.6 g. Shaking table tests of a full‐scale three‐story reinforced concrete frame structure containing glass blocks were carried out. Seismic fragility curves corresponding to the sliding failure of the glass block were generated based on the experimental results considering the friction coefficient uncertainty. The results show that the influence of the bidirectional interaction on the MSD is more significant for near‐fault pulse‐like ground motions than far‐field ground motions. For a specific ground motion record, the sliding displacement of the glass block may not increase with the increase of the PGA or peak floor acceleration due to the friction coefficient uncertainty, but this has a negligible influence on the fragility. A clearance around sliding‐prone museum collections with friction coefficients larger than 0.20 is recommended to ensure that the probability of exceedance is lower than 5%.

The Seismicity Rate Model for the 2022 Aotearoa New Zealand National Seismic Hazard Model

ABSTRACT A seismicity rate model (SRM) has been developed as part of the 2022 Aotearoa New Zealand National Seismic Hazard Model revision. The SRM consists of many component models, each of which falls into one of two classes: (1) inversion fault model (IFM); or (2) distributed seismicity model (DSM). Here we provide an overview of the SRM and a brief description of each of the component models. The upper plate IFM forecasts the occurrence rate for hundreds of thousands of potential ruptures derived from the New Zealand Community Fault Model version 1.0 and utilizing either geologic- or geodetic-based fault-slip rates. These ruptures are typically less than a couple of hundred kilometers long, but can exceed 1500 km and extend along most of the length of the country (albeit with very low probabilities of exceedance [PoE]). We have also applied the IFM method to the two subduction zones of New Zealand and forecast earthquake magnitudes of up to ∼Mw 9.4, again with very low PoE. The DSM combines a hybrid model developed using multiple datasets with a non-Poisson uniform rate zone model for lower seismicity regions of New Zealand. Forecasts for 100 yr are derived that account for overdispersion of the rate variability when compared with Poisson. Finally, the epistemic uncertainty has been modeled via the range of models and parameters implemented in an SRM logic tree. Results are presented, which indicate the sensitivity of hazard results to the logic tree branches and that were used to reduce the overall complexity of the logic tree.

Mean-to-median spectral acceleration ratios in Senior Seismic Hazard Analysis Committee Level 3 probabilistic seismic hazard analyses: An analysis of reported results

In many countries, seismic characterization of the site selected for a critical structure or industrial facility is required in terms of site-specific seismic ground motion hazard. For this purpose, a probabilistic seismic hazard analysis (PSHA), performed under the Senior Seismic Hazard Analysis Committee (SSHAC) protocol, is an extended practice for nuclear facilities. In the past decade, SSHAC Level 3 studies have been performed for sites in North America, Europe, Japan, Taiwan, and South Africa. When analyzing PSHA results, the mean-to-median spectral acceleration ratios given by the hazard curves can be interpreted as a measure of the degree of epistemic uncertainty associated with the results. In this article, results of 33 SSHAC Level 3 studies have been used to determine mean-to-median spectral acceleration ratios and the statistics of these ratios, as a function of spectral frequency and annual frequency of exceedance (AFE). The purpose was to develop a reference for the range of uncertainty that is typically captured in this kind of studies. It has been found that, for a given AFE, ratios corresponding to different sites are within a relatively small interval, especially for the spectral frequency band between 2.5 and 10 Hz, which is the band normally more relevant for the seismic design of nuclear installations. In this band, for 10−4 yr−1 AFE, a mean/median ratio of 1.40 would envelop practically all investigated sites.

Processes Towards Sedimentation around a Reed Island in a Shallow Lake

There are many studies on the hydromorphological impacts of emergent aquatic vegetation, but many of these focus on gravity-driven flows in riverine or tidal environments. However, an added effect of emergent vegetation in lakes is that it reduces the main external force (wind) significantly and in a spatially coherent way. We performed long Monte Carlo simulations using a 2D hydrodynamic model and a spectral wind wave model to study resuspension dynamics around a 100-m-wide reed island in southern Lake Fertő/Neusiedl. Wave-current interaction, computed in a post-processing step, was found to enhance maximum bed shear stresses only on the leeward side of the reed island, and even there to a small extent. We have found evidence that the present bed topography is close to an equilibrium where simulated combined wave-current shear stresses have a reasonably uniform exceedance probability over the critical shear stress of the bed sediment. We also found that an artificially flattened lakebed around the reed island would start evolving towards the present bed topography and grain size distribution (both of which were surveyed in the field). Despite the limitations of our modelling framework, our results illustrate the importance of how wind climate is translated to an uneven distribution of sediment entrainment around the reed island, explaining tendencies of sediment accumulation and sorting. Our results lead to a better understanding of the complicated processes involving interaction among wind, vegetation, circulation, wind waves, sediment and bathymetry.

Toward a New Flood Assessment Paradigm: From Exceedance Probabilities to the Expected Maximum Floods and Damages

AbstractTo assess flood risks, we seek to estimate the probability distribution of the worst possible single‐event over a contiguous period of N years rather than the cumulative losses expected over a planning horizon. For this we use the probability distribution FN of extreme flood events over a multi‐year period, which is different from using the conventional single‐valued exceedance probability of 1/N years. FN can be used to estimate the hazard and then proceed to the estimation of risk, which we define as the “largest expected damage” over the set period. It also allows for a more coherent determination of design values, which descend from fully acknowledging the aleatoric uncertainty of the underlying natural river flow process. The epistemic uncertainty is removed by marginalizing the aleatoric‐epistemic uncertainty joint distribution over the parameter space. The advantage of the proposed Bayesian approach, which can be summarized in 12 steps, is demonstrated for the 2021 River Ahr flood in Germany, which caused casualties and huge material damage. Adopting the multi‐year maxima extreme value distribution can potentially lead to the reclassification of vulnerability levels for flood‐prone areas and reconsideration of current policy‐making and flood risk communication.

Low-Complexity Prediction of Energy Statistic Exceedance Probability for $\eta$-$\mu$ Variates

Low-Complexity Prediction of Energy Statistic Exceedance Probability for $\eta$-$\mu$ Variates

Avaliação probabilística da carga variável de projeto para garagens brasileiras de veículos leves

Abstract Design loads for parking garages should be reviewed every few years due to changes in fleet characteristics and the impact of design loads on carbon emissions by the built environment. Specifically for Brazil, the authors are unaware of existing studies to justify the design values and corresponding exceedance probabilities stated in NBR 6120:2019 - Design Loads for Structures. In this paper, a simplified probabilistic model for live loads in parking garages is presented. A set of updated statistics characterizing the gross curb weight of the fleet in circulation was obtained based on technical specifications and sales reports between 2003 and 2022. These statistics and the probabilistic load model are employed to derive the equivalent uniform design load corresponding to a 30% probability of being exceeded in 50 years, according to the definition stated in NBR 6120:2019 and NBR 8681:2003. The results provide support for a significant reduction of the current design load for light-duty vehicle parking garages, from the current 3.0 kN/m2 to at least 2.5 kN/m2. Such a reduction has a significant impact on new building construction costs and carbon emissions and would not compromise the structural safety of parking garages built in Brazil.

Impact of Climate Change on the Number of Frost-free Winter Days in Prairies and Eastern Provinces of Canada

Highlights In northern region of Prairies and eastern provinces of Canada, the change in Frost-Free Days (FFDs) for the period of 1938–2022 is nearly negligible. In the stations located at the south of Ontario (called southern stations here), a maximum increase of 4.4 to 5.8 in FFDs per month was noted during the study period at different locations. The rates of change in FFDs per unit °C of the monthly mean of the daily minimum temperature (MMDMT) vary from a minimum of 0.001 to a maximum value of 2.92 days at the selected stations. Abstract. Although a considerable number of studies related to the impact of climate change on temperature-related variables have been conducted, studies exploring the changes in indices of daily winter temperatures, such as variation in the number of frost-free days (FFDs), for the winter season or for each month of the season are very few. The main objective of this study was to explore temporal trends in FFDs for each month of the winter season as well as examine the relationship between FFDs and the monthly mean of daily minimum temperature (MMDMT) at the selected stations in the central and eastern provinces of Canada. Daily minimum temperature data between 1938 and 2022 from 11 meteorological stations situated along a wide range of latitudes across the Prairies and eastern provinces of Canada has been analyzed. An exceedance probability model is developed to predict the FFDs for each winter month. The analysis leads to the conclusion that the number of FFDs per month exhibited an exponential relationship with the MMDMT for November, April, and the entire winter season, while the relationship for December through March followed a second-order polynomial curve. The results further highlight that the rate of change in FFDs per month varies across stations for each month. Notably, while the change is minimal for stations such as Kuujjuaq, Kuujjuarapik, and The Pas, it has notably increased by 23.1, 17.9, and 14.2 days at the Toronto, Windsor, and London stations, respectively. Additionally, it was observed that the rates of change in FFDs per unit increase in MMDMT (in °C) are consistently positive for all months and selected stations. The rate of change varies, ranging from a minimum of 0.001 at The Pas in December to a maximum value of 2.92 days at Montreal in April.Moreover, coefficient of determination (R2) values of more than 0.96 were observed for both exponential and second-order polynomial relationships in the months of November and April, as well as for the entire winter. A rising trend in MMDMT values, along with a decreasing trend in the MMDMT standard deviation values, was observed across all stations from 1938 to 2022. This trend indicates a more pronounced and predictable rise in temperature over time. Overall, the number of FFDs is increasing for all winter months, albeit with a few exceptions, at central and eastern stations in Canada. These warming trends during the winter months contribute to the expansion in the number of FFDs, which is expected to significantly impact hydrological, agricultural, and environmental processes within the study region. Keywords: Climate change, Exceedance probability model, Frost-free days, Monthly mean of daily minimum temperature.

Probabilistic seismic performance estimation through surrogate model and unbiased multi‐fidelity Monte Carlo predictor

AbstractThis study introduces an approach for probabilistic seismic performance estimation, which focuses on the probability of intensity measures exceeding a specified value based on engineering demand parameters. Conventional methods face challenges owing to the increase in computational costs associated with the uncertainties in earthquake scenarios. To address this, we use high‐fidelity (HF) and low‐fidelity (LF) model data to develop a multilevel hierarchy of surrogate models, which improves the simulation‐based probabilistic estimation. However, designing a reliable LF model and ensuring the accuracy of the surrogate model hierarchy remains challenging. Herein, we present a multi‐fidelity Monte Carlo (MFMC) predictor combined with a conventional surrogate model to improve probabilistic seismic performance estimation, thereby leveraging LF model efficiency and HF data accuracy for unbiased results. We addressed the challenge of constructing a suitable LF model by using a surrogate model trained from limited HF data. The MFMC predictor improves the accuracy of probabilistic analysis than the surrogate models trained from limited HF data. Further, the automatic relevance determination method is introduced to select the most appropriate inputs for the surrogate model. A case study featuring a special moment‐resistant frame, subject to uncertainties from both ground motion and structural properties, illustrates the efficiency of the method. A LF model is developed using the Kriging method, followed by the construction of the MFMC predictor for probabilistic analysis, thereby leveraging both limited HF and numerous LF data. Comparing the exceedance probability curves obtained from the MFMC predictor with those from direct Monte Carlo simulations and conventional Kriging showed that our proposed method offers a promising tool for probabilistic seismic performance estimation under uncertainty.

Seismic Hazard Map of ASEAN Countries towards Risk Assessment and Sustainability of Structures and Infrastructures

This study contains the most recent seismic hazard map of Southeast Asia. This area is located to the south of the Eurasian plate. The Ring of Fire that surrounds the region makes it one of the most active in terms of earthquakes and volcanoes. Malaysia, Indonesia, Thailand, Singapore, the Philippines, Myanmar, Vietnam, Laos, Cambodia, and Brunei are among the countries being studied. The goals of this project are to provide Peak Ground Acceleration (PGA) values for all regions in ASEAN countries, and then to create seismic zoning maps for these countries so that zones with non-seismic regions can be identified and zones with no special steel reinforcement-detailing requirements can be specified. The final step is to create design response spectra. Based on each nation's most recent body of literature, the PGA hazard map is created. There are two maps that need to be created, one for 10% and one for 2% probability of exceeding. The PGA contours of all the compiled maps were then reconstructed, and the baseline colours were compared to an Indonesia seismic hazard map. The maximum PGA value for Southeast Asia is as high as 0.8g at 10% and 2.0g at 2% probability of exceedance, respectively, whereas the minimum PGA value is typically equal to 0.0g at both 10% and 2% probability of exceedance. The design response spectrum distribution of the stable with moderate earthquake region from 0 to 4 s (including West Malaysia, Sabah and Sarawak of East Malaysia) and the distribution of spectra for active earthquake regions including Indonesian cities (including Acheh, Padang and Palu) are plotted. Then, the design response spectra for the selected cities in regions of moderate seismicity and active earthquakes are integrated.

Detailed seismic zoning of the East Kazakhstan region in the Republic of Kazakhstan

Kazakhstan is currently drafting new construction regulations that comply with the major provisions of the Eurocodes. Such regulations are created on the basis of seismic zoning maps of various degrees of detail, developed by our Institute of Seismology using a new methodological approach for Kazakhstan. The article is about creating the first normative map of the Detailed Seismic Zoning on a probabilistic foundation for the Republic of Kazakhstan's East Kazakhstan region. We carried out the probabilistic assessment of seismic hazard using a methodology consistent with the main provisions of Eurocode 8 and updated compared with that used in developing maps of Kazakhstan's General Seismic Zoning and seismic microzoning of Almaty. The most thorough and current data accessible for the area under consideration were combined with contemporary analytical techniques. Updates have been done to not only the databases being used but also the way seismic sources were shown, including active faults now. On a scale of 1:1000000, precise seismic zoning maps of the East Kazakhstan region were created for two probabilities of exceedance: 10 % and 2 % in 50 years in terms of peak ground accelerations and macroseismic intensities. The obtained seismic hazard distribution is generally consistent with the General Seismic Zoning of Kazakhstan's previous findings. However, because active faults were included and a thoroughly revised catalog was used, there are more pronounced zones of increased danger along the fault in the western part of the region. In the west of the territory, acceleration values also increased due to a more accurate consideration of seismotectonic conditions. Zoning maps are the basis for developing new state building regulations of the Republic of Kazakhstan.

Investigation of Ambient Seismic Noise in Different Region of Georgia

Georgia, like the whole South Caucasus, is a tectonically and structurally complex region. It is one of the active segments of the Alpine-Himalayan belt, therefore it is important to assess the seismic hazard for Georgia. At the regional scale, this assessment is evaluated by applying probabilistic seismic hazard analysis that identifies the annual probability of exceedance of various ground motion levels defined in terms of selected ground motion intensity measures, such as PGA or spectral accelerations (SA) corresponding to various return periods related to possible future earthquake scenarios for a site represented by soil classes A according to EC8, Euro-code 8-EN 1998-1 (1998). At the local scale, seismic hazard assessment is made by analyzing the geological, geomorphological, geotechnical and geophysical characteristics of the site, as it is well established that the incoming seismic motion can change in amplitude, frequency, and duration due the site-specific local characteristics. That is the subject of micro-zonation investigation. Site – specific local characteristics are presented by the following parameters: Dominant frequency, Vs,30 (average shear-wave velocity to a depth of 30 meters) and amplification factor. In this work, we presented results of geophysical survey assessing local site conditions by dominant frequency that allows identification of similar seismic response areas. For this purpose, seismic noise records have been used first time in Georgia.

Occurrence and environmental risk assessment of 4 estrogenic compounds in surface water in Belgiumin the frame of the EU Watch List.

The presence of natural estrogens estrone (E1), 17β-estradiol (E2), estriol (E3) and synthetic estrogen 17α-ethynylestradiol (EE2) in the aquatic environment has raised concerns because of their high potency as endocrine disrupting chemicals. The European Commission (EC) established a Watch List of contaminants of emerging concerns including E1, E2 and EE2. The proposed environmental quality standards (EQSs) are 3.6, 0.4, 0.035ng/L, for E1, E2, EE2, respectively. A thorough evaluation of analytical procedures developed by several studies aiming to perform sampling campaigns in different European countries highlighted that the required limits of quantification in surface water were not reached, especially for EE2 and to a lesser extent for E2. Moreover, data regarding the occurrence of these contaminants in Belgian surface water are very limited. A sampling campaign was therefore performed on a wide range of rivers in Belgium (accounting for a total of 63 samples). The detection frequencies of E1, E2, E3 and EE2 were 100, 98, 86 and 48%, respectively. E1 showed the highest mean concentration (= 4.433ng/L). In contrast, the mean concentration of EE2 was 0.042ng/L. The risk quotients (RQs) were calculated based on the respective EQS of each analyte. The frequency of exceedance of the EQS was 31.7% for E1, EE2, while it increased to 44.4% for E2. The extent of exceedance of the EQS, represented by the 95th percentile of the RQ dataset, was higher than 1 for E1, E2, EE2. The use of a confusion matrix was investigated to try to predict the risk posed by E2, EE2, based on the concentration of E1.

Probability density function modelling and credible region construction for multivariate, asymmetric, and multimodal distributions of geotechnical data

Geotechnical data are typically Multivariate, Uncertain, and Irregular (MUI), so the probability distribution of geotechnical data is Multivariate, Asymmetric, and Multimodal (MAM). Probability Density Function (PDF) modelling and Credible Region (CR) construction are two key issues for a MAM distribution. There are two fundamental difficulties in characterizing a MAM distribution. The first is on joint PDF modelling as many traditional approaches collapse for a MAM distribution. Copula theory has attracted special attention for this purpose but very few works attempted to tackle the critical problem of probabilistic prediction on target variables using available information of remaining variables based on the copula-based joint PDF. The second is on CR construction of a MAM distribution as it cannot find a unique CR of a MAM distribution given an exceedance probability only. There is still a lack of a unified approach for CR construction for a MAM distribution of geotechnical data. Aiming to resolve these two fundamental difficulties, we propose the BAyeSIan Copula-based Highest density region/contour (BASIC-H) for providing a systematic framework of PDF modelling and CR construction of a MAM distribution. This framework contains Stage-PDF and Stage-CR. Stage-PDF fuses the copula theory and Bayesian inference to develop optimal, robust, and hyper-robust predictions on the posterior distribution and posterior predictive distribution. Stage-CR adopts the constraint for the CR that the probability density of every point inside the CR is at least as large as the probability density of any point outside, which is the same as the idea of the HDR (Highest Density Region). The Monte Carlo Simulation (MCS), based on the developed optimal, robust, and hyper-robust posterior distributions and posterior predictive distributions, is performed for estimation of the probability density boundary, which is a key parameter for constructing the HDR. Examples using simulated data and Quaternary clay data are presented to illustrate the capabilities of the BASIC-H in PDF modelling and CR construction of MAM distributions of geotechnical data.

The 2021 floods in the Netherlands from a river engineering perspective

In July of 2021, large areas in the catchment of the Meuse River in Belgium, the Netherlands and Germany were affected by extreme rainfall and floods. In the Netherlands, measured peak discharges in the upstream part of the Meuse and regional tributaries were the highest ever recorded. This resulted in extreme water levels in the upstream reaches, but downstream of Roermond (about 80 km downstream of the border with Belgium) water levels were significantly lower than during previous flood events with similar discharge levels near the border with Belgium. The lower water levels resulted from the implementation of the large-scale room for the river program, in combination with very strong peak attenuation of the flood wave. Peak attenuation was especially high in the so-called Lake Meuse in the Netherlands, due to large storage areas in the floodplains. The floods in the Netherlands came in certain parts of the Meuse basin rather unexpected. The flood forecasts in the upstream part of the Meuse in the Netherlands depended heavily on rainfall forecasts and rainfall-runoff modelling and underestimated the peak water levels up to 36 hours before the flood actually peaked. Further downstream, the lead time increases and forecasts are based on discharge levels that are measured in upstream parts of the catchments. This results in more accurate estimates. The estimated probability of occurrence of the measured peak water level is around 1:100 per year for the Meuse at Borgharen (rkm 16) and decreases to 1:15 per year downstream near Gennep (rkm155). In the tributaries in Limburg the probabilities of occurrence of the measured water levels vary widely: at many locations along the rivers Geul, Geleenbeek and Roer, exceedance probabilities are estimated to be between 1:100 and 1:1000 per year. The floods have also resulted in unprecedented morphological changes. The armour layer in the riverbed of the ‘Common Meuse’, consisting of very coarse gravel, was mobilized and layers of fine sand quickly eroded. This resulted in multiple scour holes with depths of 3 to 15m. Riverbank erosion was observed and large quantities of sand were deposited on the river banks.

Interpreting Warn-on-Forecast System Guidance, Part I: Review of Probabilistic Guidance Concepts, Product Design, and Best Practices

The Warn-on-Forecast System (WoFS) is a convection-allowing ensemble prediction system designed to primarily provide guidance on thunderstorm hazards from the meso-beta to storm-scale in space and from several hours to less than one hour in time. This article describes unique aspects of WoFS guidance product design and application to short-term severe weather forecasting. General probabilistic forecasting concepts for convection allowing ensembles, including the use of neighborhood, probability of exceedance, percentile, and paintball products, are reviewed, and the design of real-time WoFS guidance products is described. Recommendations for effectively using WoFS guidance for severe weather prediction include evaluation of the quality of WoFS storm-scale analyses, interrogating multiple probabilistic guidance products to efficiently span the envelope of guidance provided by ensemble members, and application of conceptual models of convective storm dynamics and interaction with the broader mesoscale environment. Part II of this study provides specific examples where WoFS guidance can provide useful or potentially misleading guidance on convective storm likelihood and evolution.

Regional seismic risk assessment based on the Unified Scaling Law for Earthquakes: The Lake Baikal railway system

Seismic hazard assessment (SHA) and evaluation of seismic risk (SR) require an adequate understanding of the actual distribution of earthquakes over magnitude, space, and time ranges. Neo-deterministic seismic hazard assessment (NDSHA) methodologies have been developed to improve the reliability and accuracy of reproducible seismic hazard maps. In the last decade, the application of NDSHA in many regions of the world has confirmed the availability of reliable and effective input for mitigating object-oriented earthquake risks NDSHA results have passed intensive testing by historical evidence and realistic modelling of scenario earthquakes. We used two NDSHA tools – (i) Unified Scaling Law for Earthquakes (USLE) and (ii) anisotropic propagation of the seismic effect – to evaluate SR for the Lake Baikal regional railroad system represented by Open Street Map (OSM) data of tracks, bridges and tunnels on the basis of seismic hazard maps of maximum macroseismic intensity expected in 50 years with 10%, 5%, and 1% probability of exceedance. We compare the achieved USLE−based results with the SR evaluations based on the General Seismic Zonation 2016 maps at identical levels of probability of exceedance.

Fluid-structure interaction analysis of wind turbine aerodynamic loads and aeroelastic responses considering blade and tower flexibility

With the increasing size of wind turbines, the aeroelastic phenomenon plays an essential role in the safety of wind turbines. A fluid-structure interaction (FSI) analysis for wind turbine by integrating the LES turbulent model and a structural dynamic model is carried out to investigate the aerodynamic loads and aeroelastic responses considering different inflow conditions, and blade and tower flexibility. For the first time, the time series and statistical features of aerodynamic loads, the exceedance probability, the equivalent fatigue loads, and the time series and statistical features of aeroelastic responses of wind turbine are calculated by the two-way FSI model. Furthermore, effects of inflow wind conditions and the blade and tower flexibility are investigated. It is noted that the turbulent winds result in increased fluctuations of aerodynamic loads and the equivalent fatigue load. The flap-wise motions of blades are more critical to load magnitude than the edgewise motions, and the inclusion of tower motion mitigates this aerodynamic load due to the coupling effects. Finally, it is also observed that the tower motion has a noticeable impact on the flap-wise displacement at the blade tip, and the flap-wise motions of blades significantly affect the fore-aft displacement at the tower top.

Statistical Modeling and Applications of Joint Distributions for Significant Wave Height, Spectral Peak Period, and Peak Direction of Propagation: A Case Study in the Norwegian Sea

The estimation of long-term extreme response is a crucial task in the design of marine structures. The target extreme responses are typically defined by annual exceedance probabilities of 10−2 and 10−4. Various approaches can be employed for this purpose, with preference given to statistical long-term analysis, which involves aggregating the exceedance probabilities of all potential sea states contributing to the exceedance of the target extremes. A joint model encompassing important metocean parameters such as wind, waves, and current is often necessary. This study specifically focuses on waves and wave-induced responses. In characterizing short-term sea state conditions, significant wave height (Hs), spectral peak period (Tp) and peak direction of propagation (Φp) are identified as the most important sea state characteristics. The objective of this work is to present the results of the joint model for the three sea state parameters, i.e., Hs, Tp and Φp, at an offshore site in the Norwegian Sea. The conditional modeling approach is applied using long-term hindcast data, and different statistical models are discussed for fitting the marginal and conditional distributions. The fitted parameters for all directional sectors are provided, offering a comprehensive representation of the joint model for direct use in long-term response analysis. Two case studies are included to illustrate the application of the fitted joint model in long-term response analyses. The case studies identify the governing wave directions and the most important combinations of short-term sea state characteristics regarding the estimation of long-term extreme responses.