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In order to consider the impact of source-load uncertainty on traditional power system planning methods, a medium- and long-term optimization planning method based on source-load uncertainty modeling and time-series production simulation is proposed. First, a new energy output probability model is developed using non-parametric kernel density estimation, and the spatial correlation of the new energy output is described using pair-copula theory to model the uncertainty analysis of the new energy output. Secondly, a large number of source-load scenarios are generated using the Markov chain Monte Carlo simulation method, and the optimal selection method for discrete state numbers is provided, and then the scenario reduction is carried out using the fast forward elimination technology. Finally, the typical time-series curves of the source-load uncertainty characteristics obtained are incorporated into the optimization planning method together with various flexible resources, such as the demand-side response and energy storage, and the rationality of the planning scheme is judged and optimized based on key indicators such as the cost, wind–light abandonment rate, and loss-of-load rate. Based on the above methods, this paper offers an example of the power supply planning scheme for a certain region in the next 30 years, providing effective guidance for the development of new energy in the region. [ABSTRACT FROM AUTHOR]

Typhoons and their associated disaster chains pose serious threats to the lives and property of coastal residents, and they remain a focal point for research and response. Previous studies on typhoon disaster chains often employed high-dimensional symmetric Copula models to establish the joint distribution of multiple hazard factors, however they failed to explore the complex nonlinear and asymmetric dependencies among them. This study aimed to depict these complex relationships more comprehensively and efficiently to provide a more accurate typhoon hazard assessment. Focusing on Zhoushan, a city comprising numerous islands in Zhejiang Province that faces multiple typhoon threats, this study employed the C-Vine Copula function to model the complex dependencies among "strong wind-rainstorm-storm surge" in the typhoon disaster chain. Utilizing observational data from 1979 to 2018, this study involves three main steps: first, fitting the marginal distribution of each hazard factor and identifying the best one from Lognormal, Gamma, GEV (Generalized Extreme Value), and Burr functions based on the K-S test; second, fitting the bivariate joint distributions of wind speed-rainfall and wind speed-storm surge using Gaussian, Clayton, Gumbel, Frank, and Joe Copula functions, and determining the best fit based on the AIC (Akaike Information Criterion); and finally, estimating the trivariate joint probability distribution and corresponding return periods for wind speed-rainfall-storm surge using the C-Vine Copula function. This revealed (1) a strong correlation between wind speed and rainfall observed within regular value ranges (non-extreme conditions), were best represented by the Frank Copula, In addition, wind speed and storm surge exhibit an upper-tail dependence, best captured by the Gumbel Copula. (2) The rainfall distribution under certain wind speed conditions revealed dual peaks, whereas the storm surge distribution maintained a uniform pattern, with the best joint distribution fitting the Gumbel Copula. (3) Considering a 100-year return period for individual variables, the bivariate return periods for wind speed-rainfall and wind speed-storm surge events were significantly reduced to 29 and 30 years, respectively, while the trivariate return period for the wind speed-rainfall-storm surge combination was further reduced to 17 years. Overall, the C-Vine Copula function effectively characterizes the complex nonlinear and asymmetric dependencies among the typhoon disaster chain "strong wind-rainstorm-storm surge", reducing high-dimensional parameter estimation complexity. This method provides new insights for constructing joint probability and return period models for multiple hazard factors and offers a scientific basis for disaster risk assessment and management strategies. Therefore, this enhances the accuracy of disaster prevention and mitigation efforts. Additionally, the application of the C-Vine Copula assists to deeply understand the mechanisms and development processes of natural disasters, providing new tools for on-site emergency response and decision-making.

The urban flood management program and the scale construction of drainage facilities are closely related to the urban rainstorm intensity and the flood level of the outer river, so it is necessary to conduct an in-depth study on the joint probability distribution of rainstorm intensity and the flood level of the outer river. Taking Wuhan City as an example, the Copula function is used to establish the joint distribution of hourly-scale urban rainstorm intensity and outer-river flood level, and the performance of different Copula models is evaluated by using the Max-Likelihood estimator, the model selection criterion, the RMSE and the NSE goodness-of-fit. The Local optimization(LO)and Markov chain Monte Carlo(MCMC)methods are used to analyze the uncertainty of Copula models. The results are as follows. There is an obvious positive correlation between the heavy rainfall intensity and the flood level of the outer river, and the correlation between the 1-h maximum continuous precipitation and the maximum daily water level is the highest, and the optimal joint distribution function is the Gumbel Copula function. The uncertainty analysis of model shows that the optimal parameters of the MCMC simulation basically match with the theoretical parameter values, which is obviously superior to the local optimization algorithm. The results of the model uncertainty are consistent with that of the evaluation of the goodness-of-fit, which further verifies the validity of the parameters of the joint distribution function. Under the same frequency, the univariate values are lower than the values of heavy rainfall intensity and outer flood river level corresponding to the two-variable joint frequency, and higher than those corresponding to the two-variable co-occurring frequency. The two-variable co-occurring reproduction period is higher than that of the single-variable design reproduction period, and the joint reproduction period is lower than that of the single-variable design reproduction period. The combined risk rate of both storm intensity and flood level at the same frequency is much lower than the frequency value in the univariate case, and the risk rate of drainage above 50 a is greater than that of the design storm return period, but the maximum risk rate does not exceed the joint risk rate. [ABSTRACT FROM AUTHOR]

Baseflow is a critical hydrological variable linked to a variety of environmental factors. The construction of a dam may modify baseflow generation and adjust its environmental dependence via the regulation of discharge. However, its effects on the relationships among air temperature, water temperature, and baseflow remain unclear. Here, we use copula functions to explore the relationships among these variables in the Yangtze River and show how they have changed in response to the Three Gorges Dam (TGD). Because of the buffering effects of the baseflow, baseflow is negatively correlated to water temperature, and the relationship between baseflow and water temperature lessens as air temperature rises. Construction of the TGD attenuates the relationship between baseflow and water temperature when air temperature is low, and this attenuation is especially prominent in winter and spring. Our findings will enhance environmental protection in the Yangtze River and improve the ecological operations of the TGD. [ABSTRACT FROM AUTHOR]

In order to consider the impact of source-load uncertainty on traditional power system planning methods, a medium- and long-term optimization planning method based on source-load uncertainty modeling and time-series production simulation is proposed. First, a new energy output probability model is developed using non-parametric kernel density estimation, and the spatial correlation of the new energy output is described using pair-copula theory to model the uncertainty analysis of the new energy output. Secondly, a large number of source-load scenarios are generated using the Markov chain Monte Carlo simulation method, and the optimal selection method for discrete state numbers is provided, and then the scenario reduction is carried out using the fast forward elimination technology. Finally, the typical time-series curves of the source-load uncertainty characteristics obtained are incorporated into the optimization planning method together with various flexible resources, such as the demand-side response and energy storage, and the rationality of the planning scheme is judged and optimized based on key indicators such as the cost, wind–light abandonment rate, and loss-of-load rate. Based on the above methods, this paper offers an example of the power supply planning scheme for a certain region in the next 30 years, providing effective guidance for the development of new energy in the region.

Abstract Accurate and reliable assessment of wind energy potential has important implication to the wind energy industry. Most previous studies on wind energy assessment focused solely on wind speed, whereas the dependence of wind energy on wind direction was much less considered and documented. In this paper, a copula‐based method is proposed to better characterize the direction‐related wind energy potential at six typical sites in Hong Kong. The joint probability density function (JPDF) of wind speed and wind direction is constructed by a series of copula models. It shows that Frank copula has the best performance to fit the JPDF at hilltop and offshore sites while Gumbel copula outperforms other models at urban sites. The derived JPDFs are applied to estimate the direction‐related wind power density at the considered sites. The obtained maximum direction‐related wind energy density varies from 41.3 W/m2 at an urban site to 507.9 W/m2 at a hilltop site. These outcomes are expected to facilitate accurate micro‐site selection of wind turbines, thereby improving the economic benefits of wind farms in Hong Kong. Meanwhile, the developed copula‐based method provides useful references for further investigations regarding direction‐related wind energy assessments at various terrain regions. Notably, the proposed copula‐based method can also be applied to characterize the direction‐related wind energy potential somewhere other than Hong Kong.

This study introduces methodologies for constructing joint probability distribution functions utilizing the Copula function and neural networks, and evaluates their efficacy in marine and civil engineering projects. Through an analytical comparison of both models using a numerical example, it is revealed that the neural network model exhibits superior adaptability to large sample sizes. This adaptability is attributed to the neural network's ability to learn complex relationships within the data, which is especially beneficial when dealing with large datasets. The neural network model also demonstrates higher accuracy in constructing joint probability distribution functions compared to the Copula function model. In marine and civil engineering, the adaptability and accuracy of neural networks are of paramount importance due to the variable and complex nature of weather patterns. A practical engineering application is presented, wherein a joint probabilistic distribution neural network model of wind velocity and rain intensity is established for the Lanzhou–Xinjiang high-speed railroad in China. This model illustrates the promising application of neural networks in engineering projects where weather factors play a critical role. Subsequent to the construction of the joint probability distribution functions, a feature importance analysis is incorporated to quantify the contribution of different weather parameters such as wind velocity and rain intensity to the joint distribution function. This analysis provides an objective assessment of the relative importance of various weather factors and offers data-driven insights that are essential for engineering applications where weather conditions are a significant consideration. The study concludes by highlighting the potential benefits of neural network models in marine and civil engineering, suggesting areas for future exploration. [ABSTRACT FROM AUTHOR]

Accurate and reliable assessment of wind energy potential has important implication to the wind energy industry. Most previous studies on wind energy assessment focused solely on wind speed, whereas the dependence of wind energy on wind direction was much less considered and documented. In this paper, a copula‐based method is proposed to better characterize the direction‐related wind energy potential at six typical sites in Hong Kong. The joint probability density function (JPDF) of wind speed and wind direction is constructed by a series of copula models. It shows that Frank copula has the best performance to fit the JPDF at hilltop and offshore sites while Gumbel copula outperforms other models at urban sites. The derived JPDFs are applied to estimate the direction‐related wind power density at the considered sites. The obtained maximum direction‐related wind energy density varies from 41.3 W/m2 at an urban site to 507.9 W/m2 at a hilltop site. These outcomes are expected to facilitate accurate micro‐site selection of wind turbines, thereby improving the economic benefits of wind farms in Hong Kong. Meanwhile, the developed copula‐based method provides useful references for further investigations regarding direction‐related wind energy assessments at various terrain regions. Notably, the proposed copula‐based method can also be applied to characterize the direction‐related wind energy potential somewhere other than Hong Kong. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]

Sustainable aquaculture in nearshore waters faces challenges such as stakeholder conflicts, environmental pollution, and spatial constraints. Offshore aquaculture offers a promising solution but requires robust engineering design to withstand extreme weather conditions. This study develops the environmental conditions essential for engineering the design of a continuous mussel dropper system in New England offshore waters. A potential farm location was identified using criteria including water depth, federal boundaries, seafloor suitability, farm size, and proximity to ports, based on bathymetric and sedimentary maps. Historical data from five wave monitoring stations and two current velocity stations were analyzed to model extreme environmental conditions, as waves and currents pose primary threats. The extreme wave and current conditions are modeled using the Weibull distribution, on the annual maximum hourly significant wave height data and the largest 0.3 % of current speeds. A newly proposed method combining Spalding's wall function with a fourth-order polynomial is used to enhance the current profile analysis. Additionally, a joint probability density function was developed for wave height and current velocity at a specific depth, providing insights into wave height, period, and wavelength for various return periods such as 10, 25, 50, and 100 years. The results suggest a 10-yr wave of 8 m significant wave height and a current speed of 1.68 m/s, while a 50-yr values are 9.4 m and 1.96 m/s respectively. These findings offer critical data on extreme wave and current conditions in New England's offshore waters, providing practical guidance for the engineering design of offshore mussel farms. This research advances offshore mussel farming and benefits the development of all types of offshore aquaculture systems. [ABSTRACT FROM AUTHOR]

The southeastern coastal region of China frequently faces typhoon attacks, posing significant threats to its ever-growing infrastructure. Quantifying multiple typhoon-induced hazards in terms of wind, wave, and surge would provide valuable data to support structural design, risk assessments, and disaster mitigation. This study simulated the evolution of wave and surge driven by typhoon wind fields using the SWAN + ADCIRC coupling model, generating extreme samples of wind speed, significant wave height, and surge height. Trivariate joint probability distributions were established at six typical coastal stations (Hong Kong, Xiamen, Fuzhou, Wenzhou, Zhoushan, and Shanghai) based on optimal copula functions. Using the environmental contour and conditional return period methods, appropriate combinations of design environmental loads were analyzed for a specific return period. The results revealed two reasonable combination types for the 100-year design period. One involves the combination of the 100-year dominant variable value computed using a univariate probability distribution, with two 20-year secondary variable values calculated using the second conditional return period. The second combination selects a variable group corresponding to the maximum value of the dominant variable on the environmental surface. These methods and findings were further extended to the entire computational area to develop hazard maps covering the Southeast Sea area of China. The hazard maps show that the design values of significant wave height increase with distance from the coast. In contrast, the spatial distribution of surge presents the opposite pattern. This study provides a novel perspective on structural design values subjected to multiple disasters and offers a reference for offshore engineering construction in the sea area of southeast China. • Typhoon-induced multi-hazard maps along Southeast China are developed. • A database of typhoon-induced wind, wave and surge along Southeast China from 1987 to 2022 is developed. • Trivariate joint probability distribution of wind speed, significant wave height and surge height is analyzed. • Two combination methods of multiple environmental loads are proposed. [ABSTRACT FROM AUTHOR]

This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable's outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr's contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of "pure contextuality" from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities. [ABSTRACT FROM AUTHOR]

This study aims to investigate the change in spectral patterns of droughts in Iran based on the concepts of reliability, resilience, and vulnerability (RRV) in the context of time. To achieve this goal, RRV values were first estimated based on monthly gridded soil moisture data for a period of 64 years (1955–2018) for the framework of Iran's political borders. The pairwise comparison of the values of the three variables RRV indicates a positive relationship between reliability–resilience and a negative relationship between reliability–vulnerability and resilience–vulnerability. In order to obtain the Joint Probability Distribution between reliability–vulnerability, Drought Management Index (DMI) for all the gridded points within Iran's political borders were calculated by fitting the Gaussian copula. According to this index, drought is an unfavourable climatic phenomenon that is associated with increased Vulnerability and decreased Reliability. The temporal and spatial changes of this index indicate that DMI values are always high for the south, east and centre of Iran and low for the western and northern half. To study the change in spectral patterns of droughts in Iran, the 64‐year period studied (1955–2018) was divided into two equal periods of 32 years. Then, using spectral analysis through Fourier transform method, the first three periodicities related to each period that had the highest powers were extracted. Finally, their periodicity was compared. The results indicated that the drought periodicities in the north‐west, north‐east, west, south‐west, and south of Iran have become longer, that is, their nature has been changed from shorter periodicities to longer ones. This change of nature in their first three periodicities has been sometimes from 2–10 years to 2–15 years, from 2–10 years to 3–30 years, and from 3–8 years to 8–15 years. However, the periodicities of droughts in the eastern, south‐eastern, and central Iran has changed from longer periodicities to shorter ones. It has been changed from 3–15 years to 2–6 years, from 3–15 years to 2–3 years, and from 3–30 years to 3–15 years. [ABSTRACT FROM AUTHOR]

This article regards the dependency structure of wind power and load time series at each moment as the conditional probability of a high-dimensional discrete stochastic process. A dynamic Bayesian network (DBN) model is proposed to calculate the joint probability distribution of high-dimensional stochastic processes, which can completely describe the potential dependency structure of wind power and load at each time. The DBN model is based on a data-driven approach, using Bayesian information criteria (BICs) as the scoring function, and using a greedy search algorithm to determine the initial network and transmission network DBN structure. Maximum likelihood estimation (MLE) is used to estimate the parameters of the initial network and the transmission network. The DBN model is established from these two networks, and the joint probability distribution of the stochastic process is obtained. Sequential Monte Carlo (SMC) sampling is performed on the DBN model to generate the dependent simulation sequence of wind power and load. Using probability density, mean value, maximum output fluctuation, and autocorrelation and cross-correlation functions as evaluation indicators, the statistical characteristics of the historical sequence, simulation sequence based on the DBN model, and simulation sequence based on the hidden Markov model (HMM) are comprehensively compared and analyzed to verify the effectiveness of the DBN model. [ABSTRACT FROM AUTHOR]

The application of adaptive support vector regression (SVR) models in tunnel reliability analysis is limited. A two-stage adaptive SVR-based metamodel is proposed for tunnel reliability estimation, addressing efficiency and accuracy by ensuring the selection of samples in the most critical region. The new training samples are selected from a reduced space built from the Monte Carlo simulation (MCS) population with small limit state function values having maximum chances of misclassification. The adjacent samples are excluded based on the Euclidian distance to avoid clustering. The second step chooses the data point from the reduced space with the maximum joint probability distribution value as the training data to add to the prevailing training data. The SVR model is updated accordingly to rebuild the reduced space. The iteration is continued until the coefficient of variation of the estimated failure probability is significantly less and no data is left in the reduced space. Otherwise, the MCS population is augmented by additional samples for further iterations. The efficacy of the proposed approach is demonstrated by considering two underground tunnel reliability problems. The reliability estimates by the proposed approach with fewer training data are very close to those obtained by the direct MCS technique. [ABSTRACT FROM AUTHOR]

• Sparse PCE-based active learning algorithm for reliability analysis. • A new learning function that considers the weight of the joint PDF. • Sparse PCE coefficients are estimated using Bayesian compressive sensing. • Adds new training samples iteratively using the proposed learning function. • The approach is found to be quite efficient and accurate in estimating reliability. Sparse polynomial chaos expansion (PCE) combined with the bootstrap resampling method is a viable alternative to obtain an active learning algorithm for reliability analysis. The existing learning functions in PCE-based active learning algorithms do not consider the joint probability density function (PDF) information. The present study explores a sparse PCE-based active learning algorithm based on a newly proposed learning function that maintains a balance between the misclassification probability and the joint PDF information of sample points. In doing so, the coefficients of the sparse PCE are estimated using a Bayesian compressive sensing regressor, as it is noted to be one of the best-performing regression solvers for PCE, irrespective of sampling schemes. The proposed learning function considers the weight of the joint PDF with the local accuracy measure of bootstrap PCE (bPCE) to add new samples iteratively in the existing training set. The convergence is achieved when the ten consecutive failure estimates are within a negligible discrepancy and also checks the confidence bounds of the bPCE estimates. The effectiveness of the proposed approach is demonstrated using two structural engineering examples and one well-known analytical test function and is found to be quite efficient and accurate in estimating reliability. [ABSTRACT FROM AUTHOR]

Source separation has numerous applications, namely, biomedical signal processing, exploration seismology, speech and image enhancement, localization, etc., which includes the estimation of the mixing model. The technique of source separation aims to estimate both the original sources and the mixing model using only the observations. We have analysed the source separation problem with the assumption that sources are statistically independent. On the basis of prior statistical information of the source signals and joint probability distributions function (PDF) between the observed signals, the information of the mixing model has been extracted and examined. It has been observed that the shape of joint PDF is highly useful in characterizing the mixing coefficients. [ABSTRACT FROM AUTHOR]

River morphological processes are among the most complex and least understood phenomenon in nature. Recent research indicates that the braiding of marine waterways of the estuary zone occurs at an aspect ratio similar to the alluvial braided river. The instability of complex sporadic fluvial processes at river-sea interface is responsible for bar formation in alluvial as well as in marine waterbodies Due to the lack of knowledge of flow characteristics around bar, the flow structure around the sand bar is analyzed. The bursting events play the crucial role in understanding the fluvial characteristics in the vicinity of submerged structure. The study of bursting events around the mid-channel bar is only done by the present author. The effect of submergence ratio on the turbulence behavior in the proximity of bar is analyzed in this study. The flow turbulence generated by the mid-channel bar is also analyzed in detail. The extreme turbulent burst is segregated from low intensity turbulent events by using the hole size concept. The effect of hole size on the parameter Dominance Function is analysed which is not yet studied by any researcher for mid-channel bar. The Momentum Dominance Function (MDF) parameter increases with increase in the Hole Size. This indicates that the magnitude of upward flux increases with increase in the hole size. The effect of bar height on the turbulent burst which is not yet studied by any researchers is analyzed in the present research. The joint probability distribution of bursting events is modeled using the Gram-Charlier bivariate joint probability function. The joint probability distribution gives the details of probabilistic structure of flow in the vicinity of bar. The effect of bar is predominant only in the lower flow layer. The joint probability distribution graph becomes more eccentric toward the dominant quadrants with increase in the submergence ratio. This indicates that the probability of dominant events further increases with increase in the submergence ratio. [ABSTRACT FROM AUTHOR]

This study presents a statistical approach that allows estimating the sea wave power (Pmax) by using the joint probability distribution of the wave’s significant height (Hm) and period (T), pHm,T. Unlike other works in the literature, the goal of the present paper is not to find the best locations for wave farming or to extrapolate the data in space or time, but to achieve a more suitable design of wave electric generators in terms of a reduced delivery uncertainty. When the raw values of Hm and T are used, the estimations of Pmax end up spanning over several orders of magnitude owing to the nonlinear amplification of the fluctuations through the calculations. This typically results in large overestimations of Pmax that preclude their use for a modest design. Another associated issue is the low temporal resolution of the data available, which forbids using measurements of Hm and T in numerical simulations directly. These issues have been overcome with the proposed methodology, whose core feature consists of generating a new series of random Hm,T pairs, based on pHm,T, which allow estimating the wave power potential realistically while reducing the chances of over/underrating. In this new series, large fluctuations are suppressed, but the essential statistics of the measurements are preserved. Additionally, since the new series of Hm,T pairs is time-independent, it can be fed directly into numerical simulations. To illustrate our proposal, we used one-year long datasets of hourly measurements of Hm and T recorded at a maritime buoy, for the design and simulation of a linear electric generator with a single degree of freedom.

To accurately recognize similar objects in different domains, the key for domain adaptation is to learn new metrics so as to minimize the discrepancy of two domains. Recent works utilize joint probability domain adaptation to tackle this problem but get poor performance due to poor discriminability or transferability of data sets. The inaccurate pseudo‐labeling in the feature subspace can lead to a chain reaction of errors during iterations, and varieties of the joint probability distribution values further aggravate the miscalculation. To cope with the above problems, this paper proposes a unified framework by introducing Incremental Confidence Samples into Classification (ICSC). ICSC includes both incrementally labeling and adaptively adjusting. With the increase of confidence samples in each iteration, incrementally labeling is used to reduce error accumulations and progressively guarantee good classification performance effectively. Moreover, the tradeoff weight between within‐class and between‐ class distance is adaptively adjusted according to the importance of transferability and discriminability. Consequently, the discrepancy minimization of within‐ class and the discrepancy maximization of between‐ class are achieved. Extensive experiments on several benchmark data sets demonstrate the effectiveness of the proposed method over the state‐of‐the‐art methods. [ABSTRACT FROM AUTHOR]

This paper proposes a Bayesian network (BN) that can construct the nonlinear dependence among wind speed, solar irradiation, and load. The correlations of random variables (RVs) are analyzed using the Pearson correlation coefficient, Kendall rank correlation coefficient, and Spearman rank correlation coefficient. According to Bayesian theory, the Bayesian information criterion (BIC) and maximum likelihood estimation (MLE) methods are employed to determine the structure and parameters of a BN. Then the BN model of RVs is established. The constructed model is the joint probability distribution of RVs that can present the nonlinear dependence and marginal distribution (MD) of RVs without limitation. The testing samples of wind speed, solar irradiation, and load are generated using the autoregressive integrated moving average (ARMA) model. Then these samples are utilized to construct the probability model of a BN and C-vine copula, whose modeling accuracy and efficiency are compared, and the quality of their output synthetic samples are analyzed. In the modified IEEE 118-bus test system, two kinds of synthetic samples are used to calculate the probabilistic load flow (PLF), whose accuracy and efficiency based on the BN are tested. The validity of the BN model is verified.

Stochastic chance-constrained optimization has a wide range of real-world applications. In some real-world applications, the decision-maker has to formulate the problem as a fractional model where some or all of the coefficients are random variables with joint probability distribution. Therefore, these types of problems can deal with bi-objective problems and reflect system efficiency. In this paper, we present a novel approach to formulate and solve stochastic chance-constrained linear fractional programming models. This approach is an extension of the deterministic fractional model. The proposed approach, for solving these types of stochastic decision-making problems with the fractional objective function, is constructed using the following two-step procedure. In the first stage, we transform the stochastic linear fractional model into two stochastic linear models using the goal programming approach, where the first goal represents the numerator and the second goal represents the denominator for the stochastic fractional model. The resulting stochastic goal programming problem is formulated. The second stage implies solving stochastic goal programming problem, by replacing the stochastic parameters of the model with their expectations. The resulting deterministic goal programming problem is built and solved using Win QSB solver. Then, using the optimal value for the first and second goals, the optimal solution for the fractional model is obtained. An example is presented to illustrate our approach, where we assume the stochastic parameters have a uniform distribution. Hence, the proposed approach for solving the stochastic linear fractional model is efficient and easy to implement. The advantage of the proposed approach is the ability to use it for formulating and solving any decision making problems with the stochastic linear fractional model based on transforming the stochastic linear model to a deterministic linear model, by replacing the stochastic parameters with their corresponding expectations and transforming the deterministic linear fractional model to a deterministic linear model using the goal programming approach. [ABSTRACT FROM AUTHOR]

This is a review devoted to the complementarity–contextuality interplay with connection to the Bell inequalities. Starting the discussion with complementarity, I point to contextuality as its seed. Bohr contextuality is the dependence of an observable’s outcome on the experimental context; on the system–apparatus interaction. Probabilistically, complementarity means that the joint probability distribution (JPD) does not exist. Instead of the JPD, one has to operate with contextual probabilities. The Bell inequalities are interpreted as the statistical tests of contextuality, and hence, incompatibility. For context-dependent probabilities, these inequalities may be violated. I stress that contextuality tested by the Bell inequalities is the so-called joint measurement contextuality (JMC), the special case of Bohr’s contextuality. Then, I examine the role of signaling (marginal inconsistency). In QM, signaling can be considered as an experimental artifact. However, often, experimental data have signaling patterns. I discuss possible sources of signaling—for example, dependence of the state preparation on measurement settings. In principle, one can extract the measure of “pure contextuality” from data shadowed by signaling. This theory is known as contextuality by default (CbD). It leads to inequalities with an additional term quantifying signaling: Bell–Dzhafarov–Kujala inequalities.

The temperature-induced response of long-span steel bridges can be more significant than the structural responses associated with operational loads or structural damage. These responses depend on the spatio-temporal temperature variation in bridge members, including the effective temperature and temperature difference within members. Bridges are designed to withstand the extreme temperature variations predicted for a given site. Hence, numerous studies have employed statistical analysis techniques to provide critical information for the design and maintenance of bridges during life cycles. However, the correlation between the effective temperature and temperature difference is usually ignored, which can result in inaccurate assessment of the extreme temperatures in members. In this work, the joint probability distribution for the temperature variation in a long-span steel truss arch bridge is investigated based on field monitoring data. The extreme temperature variations are mapped on contours with relevant return periods; the results show that the probability distribution of the effective temperature can be described using the normal distribution; the weighted sum of two lognormal distributions can describe the distribution of temperature difference. Moreover, extreme values of the effective temperature and temperature difference do not occur concurrently. The effective temperature and temperature difference in the structural member directly exposed to solar radiation vary significantly, while the temperature of the shaded member can be assumed uniform, which is mainly affected by air temperature. The study leads to more accurate estimation of the temperature extremes in long-span steel truss arch bridges, which is of great importance for proper design and maintenance of bridges. [ABSTRACT FROM AUTHOR]

Blind image quality assessment (BIQA) aims to evaluate the quality of an image without pristine image objectively, which is highly desired in many perception-oriented image processing systems. Distortions degrade the visual contents and cause image quality degradation. Moreover, the visual contents of an image suffer from individual degradations by different types and different levels of distortions, which makes us difficult to analyze the quality degradation. From the perspective of information theory, there is a decrease in the amount of the visual contents when images are distorted. Therefore, in this paper, the image quality is assessed through its visual entropy degradation. Researches on the neuroscience indicate that the simple cells in the local receptive field can be characterized as being spatially localized and oriented, then the local intensity, gradient, and orientation features are extracted to represent the visual contents of an image. By deducing the joint entropy equation, the joint entropy is related to the statistical distributions. Next, in order to measure the visual entropy, the joint statistical distributions of those features are calculated. Finally, by measuring the degradations on these distributions of distorted images, a novel BIQA method is proposed. The experimental results on the databases of LIVE, CSIQ, and TID2013 show that the proposed method has superior performance than other state-of-the-art BIQA methods.

This paper concentrates on considering the down/up crossing property of weighted Markov collision processes. The joint probability generating function of down crossing and up crossing numbers of weighted Markov collision processes until its extinction are obtained by constructing and studying a related multi-dimensional Markov chain. Hence, the joint probability distribution of down crossing and up crossing numbers and the mean numbers are obtained. [ABSTRACT FROM AUTHOR]

In a multi-regional interconnected grid, the probabilistic load flow (PLF) of any region cannot be calculated individually but should consider the uncertainties introduced in other areas. Accordingly, the topologies, loads, and generations of every region are needed. Although the renewable generation data could be assumed as publicly known, some regional independent system operators (ISOs) still would not share important parameters with others. This motivates the development of a privacy-preserving distributed (PPD) PLF method. The challenge is to identify the mapping between the regional flows and uncertain power injections across regions without full information about the entire grid. The main idea of this paper is to respectively calculate the coefficient matrix and constant vector of the mapping: for the former, a PPD accelerated projection-based consensus algorithm is proposed; for the latter, a privacy-preserving accelerated average consensus algorithm is leveraged. Consequently, a PLF method is derived for each ISO to analytically obtain its regional joint PLF in a distributed way without sharing parameters — the key contribution of this paper. Experiments on the 118- and 1354-bus systems demonstrate that this method can generate the same results as the corresponding centralized method, and has satisfactory accuracy compared with frequently used PLF methods. [ABSTRACT FROM AUTHOR]

The evaluation of slope stability reliability under the condition of incomplete probability information is one of the most popular issues in geotechnical engineering. The key difficulty in the issue lies in how to effectively establish a joint probability distribution model that conforms to the distribution characteristics of shear strength parameters under the condition of incomplete probability information. In this paper, based on the incomplete probability information of the nonlinear strength parameters of rockfill, the joint distribution model of the nonlinear strength parameters will be established using the Copula function. Combined with a radial basis function network (RBFN), an intelligent response surface method for reliability analysis of rockfill dam slope stability systems will be proposed. Its feasibility and validity will be demonstrated through an example. The influences of the Copula function type and sample number on the reliability of the stability system of rockfill dam slope will be systematically studied based on the constructed intelligent response surface. The results indicate that the Copula function could reasonably describe the correlated, nonnormal distribution characteristics of the nonlinear strength parameters and effectively construct their joint distribution model. The Copula function could provide reliable, statistically significant parameter samples for reliability analysis of the stability system of rockfill dam slopes. The traditional independent normal distribution ignores the correlated, nonnormal distribution characteristics of the nonlinear strength parameters of the rockfill, which result in the smaller failure probability and overestimation on the reliability of the stability system of the dam slope. The Copula function type and the number of samples have a significant impact on the reliability of the stability system of a rockfill dam slope. Therefore, it is recommended that as much test data as possible is obtained for statistical analysis, and the optimal marginal distribution function and Copula function are selected to improve the accuracy of the failure probability analysis of the rockfill dam slope stability system, which is of great engineering significance in the safety evaluation of a dam. [ABSTRACT FROM AUTHOR]

This study develops an efficient Bayesian approach using the parametric bootstrap method for characterizing the joint probability density function (PDF) of c′ and ϕ′ based on limited site-specific test data and prior knowledge. An example using real data of c′ and ϕ′ obtained from direct shear tests on alluvial fine-grained soils at the Paglia River alluvial plain in Central Italy is presented to illustrate and demonstrate the parametric bootstrap method. A sensitivity study is performed to investigate the impact of the amount of site-specific test data and prior knowledge on the posterior statistics of c′ and ϕ′. The results indicate that the parametric bootstrap method has a good accuracy and efficiency in characterizing the joint PDF of c′ and ϕ′. By reconstructing the likelihood function and rewriting the joint PDF of c′ and ϕ′ based on a large number of parametric bootstrap samples, the parametric bootstrap method significantly improves the efficiency of the conventional Bayesian approach while retaining the same accuracy as the conventional Bayesian approach. The equivalent sample pairs of c′ and ϕ′ generated using the Markov chain Monte Carlo simulation represent the joint PDF of c′ and ϕ′ well. The amount of site-specific test data and prior knowledge have a significant impact on the posterior statistics of c′ and ϕ′. Increasing the amount of the site-specific data and informativeness of the prior knowledge can reduce the statistical uncertainty in the posterior statistics. In addition, the role of prior knowledge decreases as the amount of the site-specific data increases. [ABSTRACT FROM AUTHOR]

Our aim is to compare the fundamental notions of quantum physics - contextuality vs. incompatibility. One has to distinguish two different notions of contextuality, Bohr-contextuality and Bell-contextuality. The latter is defined operationally via violation of noncontextuality (Bell type) inequalities. This sort of contextuality will be compared with incompatibility. It is easy to show that, for quantum observables, there is no contextuality without incompatibility. The natural question arises: What is contextuality without incompatibility? (What is "dry-residue"?) Generally this is the very complex question. We concentrated on contextuality for four quantum observables. We shown that, for "natural quantum observables" , contextuality is reduced to incompatibility. But, generally contextuality without incompatibility may have some physical content. We found a mathematical constraint extracting the contextuality component from incompatibility. However, the physical meaning of this constraint is not clear. In Appendix 1, we briefly discuss another sort of contextuality based on Bohr's contextuality-incompatibility principle. Bohr-contextuality plays the crucial role in quantum foundations. Incompatibility is, in fact, a consequence of Bohr-contextuality. Finally, we remark that outside of physics, e.g., in cognitive psychology and decision making Bell-contextuality distilled of incompatibility can play the important role. [ABSTRACT FROM AUTHOR]

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The eastern coastal areas of China span multiple climatic zones, and the impacts of climate warming on their ecological environment show regional differences. In this research, the Normalized Difference Vegetation Index (NDVI) was used as the indicator to characterize the ecological environment, and selected Guangdong, Jiangsu, and Liaoning as its typical research areas. The authors selected the NDVI, average temperature, and precipitation data of the yearly growth season, respectively, from 1982 to 2016. This study adopted the copula functions model based on Markov Chain Monte Carlo to carry out the research of bivariate joint distribution so as to calculate the joint probability, the joint exceedance probability, the joint return period and the co-occurrence return period. The results showed that 1) the temperature and precipitation in the three regions were respectively related to the NDVI sequence showing the characteristic that was correlated at the upper tail and asymptotically independent at the lower tail, which demonstrated that the temperature and precipitation had little effect on NDVI when they reached their minimum values, and the temperature and precipitation had obvious effect on NDVI when they reached their maximum values. 2) The shorter the return period was, the wider the ranges of the climate factor and the NDVI were, showing that when the climate factor was constant, the probability of the NDVI having a shorter return period was higher. The greater the climate factor was, the longer the return period was, indicating that the probability of plant growth inhibition was higher when the climate factor exceeded a certain threshold. 3) The suitable temperature and precipitation for vegetation growth in the three regions gradually decreased from south to north. These results provide some theoretical guidance and scientific foundation for the protection of regional ecological environment and enhance the understanding of the impact of climate change on the ecosystem.

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. [ABSTRACT FROM AUTHOR]

Joint relaxation-diffusion measurements can provide new insight about the tissue microstructural properties. Most recent methods have focused on inverting the Laplace transform to recover the joint distribution of relaxation-diffusion. However, as is well-known, this problem is notoriously ill-posed and numerically unstable. In this work, we address this issue by directly computing the joint moments of transverse relaxation rate and diffusivity, which can be robustly estimated. To zoom into different parts of the joint distribution, we further enhance our method by applying multiplicative filters to the joint probability density function of relaxation and diffusion and compute the corresponding moments. We propose an approach to use these moments to compute several novel scalar indices to characterize specific properties of the underlying tissue microstructure. Furthermore, for the first time, we propose an algorithm to estimate diffusion signals that are independent of echo time based on the moments of the marginal probability density function of diffusion. We demonstrate its utility in extracting tissue information not contaminated with multiple intra-voxel relaxation rates. We compare the performance of four types of filters that zoom into tissue components with different relaxation and diffusion properties and demonstrate it on an in-vivo human dataset. Experimental results show that these filters are able to characterize heterogeneous tissue microstructure. Moreover, the filtered diffusion signals are also able to distinguish fiber bundles with similar orientations but different relaxation rates. The proposed method thus allows to characterize the neural microstructure information in a robust and unique manner not possible using existing techniques. [ABSTRACT FROM AUTHOR]

The aim of this study is to reveal statistical characteristics and exceedance probability of discharge under the combined effect of climate change and human activities. The study is conducted in the Xiaoqing River in Jinan, China, based on data of discharge, land-use types and precipitation from the period 1970–2016. A multivariate joint probability distribution of the data is established to test the univariable, bivariable and trivariable change points. These are then used to calculate and analyse the risk probability of discharge exceeding the specific values under different conditions of precipitation and land-use type. The results show that the change point calculated by trivariate joint distribution can reduce the disturbance of the change point obtained with the univariable or bivariable approach and reflect the changes of various factors in the hydrological processes more objectively. When the land-use type is taken into consideration, the trivariate distribution can reflect the variation of hydrological processes more reasonably. [ABSTRACT FROM AUTHOR]

A data-driven method is presented for improving sampling designs from times series (1D approach) or spatial arrays (2D approach) of digital information. We present the autocorrelated conditioned Latin Hypercube Sampling (acLHS). This method combines a conditioned Latin Hypercube (cLHS) to obtain a representative sample of the joint probability distribution function and an autocorrelation model to reproduce the spatial or temporal dependency function (i.e., temporal or spatial variability). The acLHS method was tested with two case studies using data of soil CO 2 efflux (i.e., the CO 2 flux from soils to the atmosphere known as soil respiration) that are useful for carbon cycle science. First, we used data representing a time series (1D approach), and then spatial data (2D approach) across the conterminous United States (CONUS). Results show that acLHS was more efficient than other sampling methods (i.e., fixed sampling, cLHS) as it better reproduced the joint probability distribution and the temporal or spatial variability of the variable of interest. Finally, we use a Bernstein copula-based stochastic co-simulation method (BCSCS) and demonstrated that the acLHS reduces modeling prediction errors compared with other methods. The acLHS is a flexible method that can be applied to any variable of interest as a time series (1D approach) or as a spatial format (2D approach). • A geostatistical sampling method to improve representativeness of samples. • Implementation works for time series (1D) and spatial information (2D). • The method improves accuracy and precision for prediction purposes. [ABSTRACT FROM AUTHOR]

In this study we develop an alternative way to model the ocean reflecting the chaotic nature of ocean flows and uncertainty of ocean models — instead of making use of classical deterministic or stochastic differential equations we offer a probabilistic evolutionary approach (PEA) that capitalizes on the use of probabilistic dynamics in phase space. The main feature of the data-driven version of PEA proposed in this work is that it does not require to know the physics behind the flow dynamics to model it. Within the PEA framework we develop two probabilistic evolutionary methods, which are based on probabilistic evolutionary models using quasi time-invariant structures in phase space. The methods have been tested on complete and incomplete reference data sets generated by the Lorenz 63 system and by an idealized two-layer quasi-geostrophic model. The results show that both methods reproduce large- and small-scale features of the reference flow by keeping the probabilistic dynamics within the phase space of the reference flow. The proposed approach offers appealing benefits and a great flexibility to ocean modellers working with mathematical models and measurements. The most remarkable one is that it provides an alternative to the mainstream ocean parameterizations, requires no modification of existing ocean models, and is easy to implement. Moreover, it does not depend on the nature of input data, and therefore could work with both numerically-computed flows and real measurements from different sources (drifters, weather stations, etc.). • A probabilistic evolutionary approach (PEA) to ocean modelling is proposed. • Probabilistic nudging methodology is proposed. • PEA has been tested on a quasi-geostrophic model with incomplete reference data sets. • PEA preserves nominally-resolved on the grids flows at low- and high-resolutions. • PEA works well even on relatively short reference data records. [ABSTRACT FROM AUTHOR]

Mastering the lodging risk of planting environment is of great significance to the optimal layout of maize varieties and the breeding of lodging resistant varieties. However, the existing lodging risk models are still at the stage of single or multi-factors independent analysis, and lack of assessment for different lodging types. To address this issue, based on the mechanism of different lodging types, the Archimedean copula function was used to describe the joint probability distribution of wind speed and precipitation, and the lodging risk assessment model of maize was established. By comparing the goodness of fit, when the rank correlation coefficient of these two is positive and negative, the corresponding optimal joint probability distribution functions are the Gumbel copula and Frank copula. According to the spatial distribution of lodging risk, the area from Liaodong Bay northward to Tongyu, Jilin province in the Northeast and the North China Plain has a high frequency of lodging, in which the probability of stalk lodging is two to four times that of root lodging. Finally, we discussed how to apply the lodging risk distribution results to optimize the maize variety test sites to improve the efficiency and reliability of the existing test system. The method proposed in this paper comprehensively considers the synergistic effect of multiple factors and can provide technical support for other risk assessment.