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Regional envelope curves (RECs) have been used to characterize the flooding potential of regions worldwide. However, a comprehensive assessment for Europe is still missing. In this study we use the largest European flood database to quantify the magnitude of record floods, their dependence on catchment size, and the amount of available independent information, which is needed for estimatinig the REC's exceedance probability. We propose a framework for estimating REC parameters across large areas, consisting in partitioning the domain according to the observation density and estimating the REC slope through quantile regression. The results show that the REC parameters vary substantially across Europe. The envelope unit flood associated with a catchment area of 1,000 km2 varies between 0.1 and 6 m3s−1 km−2 and is highest in Mediterranean and Alpine areas and lowest in central‐eastern Europe. The slope of the envelope varies between 0 and −1 and is larger in Southern Europe than in Northern Europe. These differences are explained by steeper landscape in mountaineous regions and localized short duration storms producing large floods in small catchments in the Mediterranean, whose intensities are larger than in other parts of Europe. Based on the framework of probabilistic envelope curves we show that, despite the uneven observation density, the obtained RECs are associated with comparable exceedance probabilities. Key Points We propose a framework to estimate regional envelope curves for large regions that is not sensitive to outliers and number of sites In Europe the envelope flood is highest in the Mediterranean and the Alps and lowest in the center‐east. The envelope slope is highest in the south Envelope curves are associated with a similar amount of independent information content and a comparable exceedance probability

The kurtosis of stress response significantly affects the fatigue failure time of structures under nonstationary excitation, making it a vital parameter for characterizing the study of fatigue damage caused by nonstationary vibrations. However, the existing methods have not yet considered the assessment of response kurtosis when the structural modal damping is low, which poses a hindrance to the advancement of vibration fatigue acceleration theories. This study focuses on analyzing the envelope characteristics of the response of linear structures under nonstationary excitation produced by the amplitude modulation method. A novel approach is proposed to assess kurtosis by leveraging the envelope curve of the nonstationary signal response. The simulation results demonstrate that the frequency resolution of signal sampling also impacts the response’s kurtosis. The proposed method offers an accurate evaluation and rapid control of response kurtosis in both numerical and experimental examples.

Devastating flood events are recurrently impacting West Africa. To mitigate flood impacts and reduce the vulnerability of populations, a better knowledge on the frequency of these events is crucial. The lack of reliable hydrometric datasets has hitherto been a major limitation in flood frequency analysis at the scale of West Africa. Utilising a recently developed African database, we perform a flood frequency analysis on the annual maximum flow (AMF) time series, covering 246 river basins in West Africa, between 1975 and 2018. Generalized extreme value (GEV) and Gumbel probability distributions were compared to fit AMF time series with the L‐moments, Maximum Likelihood (MLE) and Generalized Maximum Likelihood (GMLE) methods. Results indicated that the GEV distribution with the GMLE method provided the best results. Regional envelope curves covering the entire West African region with unprecedented data coverage have been generated for the first‐time providing insights for the estimation in flood quantiles for ungauged basins. The correlation between flood quantiles and watershed properties shows significant correlations with catchment area, groundwater storage, altitude and topographic wetness index. The findings from this study are useful for a better flood risk assessment and the design of hydraulic infrastructures in this region, and are a first step prior to the development of regional approaches to transfer the information from gauged sites to ungauged catchments.

The empirical mode decomposition (EMD) algorithm is widely used as an adaptive time-frequency analysis method to decompose nonlinear and non-stationary signals into sets of intrinsic mode functions (IMFs). In the traditional EMD, the lower and upper envelopes should interpolate the minimum and maximum points of the signal, respectively. In this paper, an improved EMD method is proposed based on the new interpolation points, which are special inflection points (SIP n) of the signal. These points are identified in the signal and its first ( n − 1) derivatives and are considered as auxiliary interpolation points in addition to the extrema. Therefore, the upper and lower envelopes should not only pass through the extrema but also these SIP n sets of points. By adding each set of SIP i (i = 1, 2, ..., n) to the interpolation points, the frequency resolution of EMD is improved to a certain extent. The effectiveness of the proposed SIP n-EMD is validated by the decomposition of synthetic and experimental bearing vibration signals.

The applications and studies of gravity anchors in the ocean are becoming more and more extensive. Most of the research, however, has been directed toward the bearing properties of sand. Relatively less attention has been paid to the bearing properties of gravity anchors in clay. Clay is widely distributed on the seabed. The research on the bearing capacity of gravity anchors in clay is of great significance for offshore oil exploitation. Therefore, the gravity anchor was investigated by conducting reduced-scale model tests, and the bearing process of gravity anchors in clay was simulated through a 3D finite element method. Model tests and numerical simulations were used to determine the capacity curve and the V-H failure envelope of gravity anchors in clay. The simulation results and the test results are in good agreement. The failure form of the gravity anchor in clay was revealed by 3D finite element analysis. The effect of cohesion, internal friction angle, and mooring point height on bearing capacity have been studied. The influence of the height of the mooring point on the V-H failure envelope curve was explored by changing the height of the mooring point. The formula of the V-H failure envelope curve suitable for different mooring point heights was obtained.

The introduction of downhole safety valve performance envelope curves can effectively prevent the failure of the downhole safety valves during field operations. The method of drawing the performance envelope curve of high-temperature and pressure downhole safety value was proposed based on the mechanical properties of the downhole safety valve. The numerical simulation method was used for the mechanical performance of the downhole safety valve, and the stress change law of the overall structure of the downhole safety valve under the ultimate load was obtained. The ultimate bearing state and the failure threshold stress value of the key components of the downhole safety valve were further determined. The performance envelope curve of the downhole safety valve was finally completed. The results of the study show that the downhole safety value envelope curve can be obtained by studying the mechanical properties of the downhole safety valve, and each section of the envelope curve corresponded to the cause of failure of the downhole safety valve, giving the theoretical calculation idea of the downhole safety valve performance envelope curve. This study provides theoretical and methodological support for the study of the performance envelope curves of the downhole safety valves, packers, and other complex working conditions of downhole tools and their application in the field.

Fly ash (FA) is composed of particles produced from power plants during coal burning. The fragmentary substitutions (20 and 30%) of cement by fly ash have been determined by consistent values of concrete compressive strength. These FA replacement percentages have been implemented on exterior beam-column joint (BCJ) segments to reveal the comparative investigations in aspects of various cyclic loading attributes to identify performance index and stable development on account of curing periods (28 and 90 days) in this research. Five different exterior BCJs have been inspected with specified replaced percentages of FA subjected to with and without a superplasticizer keeping the flexural strength ratio at 2.0 and water-binder (w/b) ratio at 0.4. All (ten) specimens are shrunk to one-third dimension for further convenient interpretation and assessment. The test method was based on quasi-static lateral cyclic approaches, where stress, strain and displacement fields are caused by load response. These experiments exhibit gradual evolvement of fractures, hysteretic responses, load envelope curves, stiffness degradations, ductility displacements and brittleness indexes from 28 to 90 days of curing. The fundamental goal of this research is to explore the seismic performance and stability of BJC in the context of maturity in the perspective of all cyclic loading features. Extensive research is executed to draw a distinction and scrutinize the outputs accompanying control specimens. In an aspect of dissipation energy, the 20FAS (20% fly ash with superplasticizer) specimen exhibits an approximately 50–60% increase and also stable and gradual variation throughout the displacements at 90 days compared to 28 days of curing. Again, 100% yield energy growth is evidently noticed only for the 20FAS specimen irrespective of curing days. Moreover, by the analytical hierarchy process (AHP) it has been found that the 30FAS specimen had highly unreliable fluctuations for ultimate loads (2.620) and displacements (2.655). Among all including control specimens, the most dependable and consistent variations (1.0925 and 1.2367) for ultimate loads and displacements are seen for the 20FAS specimens. Designers can implement this documentation to develop a viable, satisfactory and productive improvement approach for a moment-resisting frame in seismic-prone territories irrespective of eco-friendly and economical conceptualization.

Extreme flood events have detrimental effects on society, the economy and the environment. Widespread flooding across South East Queensland in 2011 and 2013 resulted in the loss of lives and significant cost to the economy. In this region, flood risk planning and the use of traditional flood frequency analysis (FFA) to estimate both the magnitude and frequency of the 1-in-100 year flood is severely limited by short gauging station records. On average, these records are 42 years in Eastern Australia and many have a poor representation of extreme flood events. The major aim of this study is to test the application of an alternative method to estimate flood frequency in the form of the Probabilistic Regional Envelope Curve (PREC) approach which integrates additional spatial information of extreme flood events. In order to better define and constrain a working definition of an extreme flood, an Australian Envelope Curve is also produced from available gauging station data. Results indicate that the PREC method shows significant changes to the larger recurrence intervals (≥100 years) in gauges with either too few, or too many, extreme flood events. A decision making process is provided to ascertain when this method is preferable for FFA.

The depth‐duration envelope curves (DDECs) are regional upper bounds on observed rainfall maxima for several durations. Recently, a probabilistic interpretation has been proposed in the literature in order to associate a recurrence interval T to the DDECs and, consequently, to retrieve point rainfall quantiles for ungauged sites. Alternatively, extreme rainfall quantiles can be retrieved from long synthetic rainfall series obtained with stochastic rainfall generators calibrated to local time series of rainfall events. While DDECs are sensitive to outliers and data errors, the stochastic rainfall generator performance is affected by the limited record lengths used for calibration. The objective of this study is to assess the reliability of the two alternative methods by verifying if they give consistent results for a wide study region in Austria. Relative to previous studies, we propose some generalizations of the DDEC procedure in order to better represent the Austrian data. The comparison of rainfall quantiles estimated with the two methods for large T shows an excellent agreement for intermediate durations (from 1 to 6 h), while the agreement worsen for very short (15 min) and long (24 h) durations. The results are scrupulously analyzed and discussed in light of the exceptionality of rainfall events that set the regional envelopes and the characteristics of the stochastic generator used. Our study points out that the combined use of these regional and local methods can be very useful for estimating reliable point rainfall quantiles associated with large T within regions where many rain gauges are available, but with limited record lengths. Key Points Estimation of point rainfall quantiles for very high recurrence intervals Combination of two independent methods to increase estimates accuracy Generalization of one of the methods relative to its original formulation

Detention devices are often used as alternative measures for stormwater control. The Envelope Curve Method is widely used in Brazil to estimate detention device volumes. This method estimates the storage volume based on inlet and outlet balance, where the inlet is obtained by the Rational Method and the outlet by orifice bottom discharge. Usually, the outlet flow is adopted as a constant and equivalent to the maximum allowed, and this procedure can cause reservoir undersizing. This paper evaluates detention control measures’ hydraulic behavior for the Envelope Curve Method and proposes the inclusion of an outflow adjustment coefficient (Cout), seeking to compensate for the adoption of constant outlet flow simplification. Values for this coefficient were estimated for several Brazilian state capitals, ranging from 0.62 up to 0.65. The undersizing hypothesis due to the adoption of constant outlet flow was confirmed, as the simulations showed the need for an increase between 8.4% to 16.8% in the device size. This undersizing may be compensated for by applying the outflow adjustment coefficient (Cout). Keywords: adjustment coefficient, detention facilities, envelope curve, hydrologic design outflow adjustment coefficient.