Joint Probability Research Articles

Probabilistic model for fatigue damage estimation of wind turbines with hidden markov model and neural network

The growing demand for sustainable and affordable energy sources has led to rapid development in wind energy systems. Ensuring the long-term performance and reliability of wind turbines requires accurate estimation of fatigue damage under diverse environmental conditions. By incorporating probabilistic methods, this paper presents a comprehensive framework for long-term fatigue damage evaluation for wind turbines with high accuracy and efficiency. The proposed framework adopts the multivariate kernel density estimation to construct the high-dimensional joint probability distribution of environmental variables. A hidden Markov model serves as the driver to build the connection between historical records and future events. The short-term fatigue damage is estimated by the deep neural network based on future environmental parameters. The long-term fatigue damage is then achieved by accumulating the short-term fatigue damage evaluations with sufficient event instances. To demonstrate the applicability and effectiveness of the proposed framework, a case study is conducted with a wind turbine in the North Sea region. The fatigue damage analysis results highlight the necessity of regular inspections and maintenance for wind turbines to ensure their long-term service life and optimal performance. The framework is capable of considering a wide range of environmental factors and accounting for the inherent uncertainties and stochastic nature, providing a robust and comprehensive approach for estimating fatigue damage of wind turbines as well as other structures under long-term environmental conditions.

A robust joint frequency spectrum and power allocation strategy in a coexisting radar and communication system

The resource allocation technique is of great significance in achieving frequency spectrum coexistence in Joint Radar-Communication (JRC) systems, by which the problem of radio frequency spectrum congestion can be well alleviated. A Robust Joint Frequency Spectrum and Power Allocation (RJFSPA) strategy is proposed for the Coexisting Radar and Communication (CRC) system. Specifically, we consider the uncertainty of target Radar Cross Section (RCS) and communication channel gain to formulate a bi-objective optimization model. The joint probabilities that the Cramér-Rao Lower Bound (CRLB) of each target satisfying the localization accuracy threshold and the Communication Data Ratio (CDR) of each user satisfying the communication threshold are simultaneously maximized, under the constraint of the total power budget. A Three-Stage Alternating Optimization Method (TSAOM) is proposed to obtain the Best-Known Pareto Subset (BK-PS) of this problem, where the frequency spectrum, radar power, and communicator power are allocated using the greedy search and standard convex optimization methods, respectively. Simulation results confirm the effectiveness of the proposed RJFSPA strategy, compared with the resource allocation methods in a uniform manner and that ignores the uncertainties. The efficiency of the TSAOM is also verified by the comparison with the exhaustive search-based method.

Extremely high wall pressure events in shock wave and turbulent boundary layer interactions using DNS data

This study investigates high-amplitude Extreme Wall Pressure fluctuation Events (EWPEs) in Shock wave/Turbulent Boundary Layer Interactions (STBLIs) through the conditional sampling of direct numerical simulation databases. The aim is to evaluate the effect of STBLIs and their strength on the statistical properties and associated turbulent structures of EWPEs using the conditional-averaging and clustering method. The temporal statistical results show that the occurrence probability and contribution ratio of EWPEs decrease downstream of strong STBLI, but their duration and interval time increase. Regarding two-dimensional wall pressure structures, the large population of small-scale structures becomes more elongated, but strong interactions induce a greater number of large-scale structures. The pairing of wall pressure events with a higher occurrence probability is verified by the joint probability density functions. Conditional analysis reveals that, as the interaction strength increases, the ejection motion associated with positive events occurs farther downstream and the spanwise vortex core locating above negative events is lifted up along the wall-normal direction. Moreover, analysis associates the paired wall pressure events with the sweep, ejection, and swirl motions in STBLIs, where hairpin eddies play an important role in the formation of positive–negative paired wall pressure structures.

Change in high-temperature intensity-duration-frequency under different warming scenarios over India

This study examined the hottest temperature events in each year for a period of 1 to 10 consecutive days across India under 1.5 °C, 2 °C, and 3 °C global warming levels (GWLs) and two periods (T1: 2021–2050, T2: 2071–2100) using the Coupled Model Intercomparison Phase 6 (CMIP6) framework. Bivariate copula analysis was applied to determine the joint probability distribution of the intensity and duration of high-temperature extremes across various GWLs. We also evaluated the change in return values for 10, 20, 50, and 100-year return periods over 2, 5, and 10-day durations. The intensity of the high-temperature extremes indicates a gradual rising trend across the country for durations ranging from 1 to 10 days for different GWLs. For the 2-day duration, the intensity of average temperature increases by 0.7–2.6 °C under all GWLs. The Western Himalaya region (2–4.3 °C) shows the highest increase in intensity of 2-day duration followed by the Northwest (0.93–2.51 °C) and Eastern Coastal (0.86–2.5 °C) regions under different GWLs. Whereas, the Interior Peninsula (0.56–2.15 °C) and Western coastal (0.56–1.9 °C) regions show a lower increase. Similar patterns were observed for 5- and 10-day duration. The 20-year return value of the intensity for a 2-day duration increases by 7–24% under all GWLs across India. The highest increase was observed in the Western Himalayas (23–48%) followed by the Northeast and Eastern Coastal (9–25%) regions under all GWLs. We have derived Temperature-Intensity-Duration-Frequency (TIDF) curves for eight selected urban agglomerations cities. Among them, Srinagar exhibits the highest increase in intensity (ranging from 19 to 32%) followed by Guwahati (9–16%) and Mumbai (5.5–12.8%). Whereas, Hyderabad exhibits the smallest increase in intensity (0.02%–8%). The duration of high-temperature extreme events increases for a given intensity and return period. It is also observed that for a given intensity and duration, the exceedance probability of high-temperature extremes increases under different GWLs. These insights are crucial for climate mitigation and adaptation strategies and can inform decisions by urban planners, policymakers, and communities in addressing the challenges posed by high-temperatures extreme.

Compounded wind gusts and maximum temperature via semiparametric copula in the risk assessments of power blackouts and air conditioning demands for major cities in Canada

A semiparametric copula joint framework was proposed to model wind gust speed (WGS) and maximum temperature (MT) in Canada, using Gaussian kernel density estimation (GKDE) with parametric copulas. Their joint probability estimates allow for a better understanding of the risk of power blackouts and the demand for air conditioning in the community. The bivariate framework used two extreme sample groups to define extreme pairs at different time lags, i.e., 0 to ± 3 days, annual maximum WGS (AMWGS) and corresponding MT and annual highest MT (AHMT) and corresponding WGS. A thorough model performance comparison indicated that GKDE outperformed the parametric models in defining the marginal distribution of selected univariate series. Significant positive correlations were observed among extreme pairs, except for Calgary and Halifax stations, with inconsistent correlation variations based on selected cities and lag time. Various parametric 2-D copulas were selected to model the dependence structure of bivariate pairs at different time lags for selected stations. AMWGS or AHMT events, when considered independently, would be stressful for all stations due to high estimated quantiles with low univariate RPs. The bivariate events exhibited lower AND-joint RPs with moderate to high design quantiles, indicating a higher risk of power blackouts and heightened air-conditioning demands, which varied inconsistently with time lags across the station. The bivariate AMWGS and corresponding MT events would be stressful in Regina, Quebec City, Ottawa, and Edmonton, while AHMT and corresponding WGS events in Toronto, Regina, and Montreal. Conversely, Vancouver poses a lower risk of joint action of pairs AHMT and corresponding WGS events. These hazard statistics can help in better planning for community well-being during extreme weather.

Characterizing the geometry of the Kirkwood–Dirac-positive states

The Kirkwood–Dirac (KD) quasiprobability distribution can describe any quantum state with respect to the eigenbases of two observables A and B. KD distributions behave similarly to classical joint probability distributions but can assume negative and nonreal values. In recent years, KD distributions have proven instrumental in mapping out nonclassical phenomena and quantum advantages. These quantum features have been connected to nonpositive entries of KD distributions. Consequently, it is important to understand the geometry of the KD-positive and -nonpositive states. Until now, there has been no thorough analysis of the KD positivity of mixed states. Here, we investigate the dependence of the full convex set of states with positive KD distributions on the eigenbases of A and B and on the dimension d of the Hilbert space. In particular, we identify three regimes where convex combinations of the eigenprojectors of A and B constitute the only KD-positive states: (i) any system in dimension 2; (ii) an open and dense probability one set of bases in dimension d = 3; and (iii) the discrete-Fourier-transform bases in prime dimension. Finally, we show that, if for example d = 2m, there exist, for suitable choices of A and B, mixed KD-positive states that cannot be written as convex combinations of pure KD-positive states. We further explicitly construct such states for a spin-1 system.

Formation of Superthin Galaxies in IllustrisTNG

Superthin galaxies are observed to have stellar disks with extremely small minor-to-major axis ratios. In this work, we investigate the formation of superthin galaxies in the TNG100 simulation. We trace the merger history and investigate the evolution of galaxy properties of a selected sample of superthin galaxies and a control sample of galaxies that share the same joint probability distribution in the stellar-mass and color diagram. Through making comparisons between the two galaxy samples, we find that present-day superthin galaxies had similar morphologies as the control sample counterparts at higher redshifts, but have developed extended flat “superthin” morphologies since z ∼ 1. During this latter evolution stage, superthin galaxies undergo an overwhelmingly higher frequency of prograde mergers (with orbit-spin angle θ orb ≤ 40°). Accordingly the spins of their dark matter halos have grown significantly and become noticeably higher than those of their normal disk counterparts. This further results in the buildup of their stellar disks at larger distances much beyond the regimes of normal disk galaxies. We also discuss the formation scenario of those superthin galaxies that live in larger dark matter halos as satellite galaxies therein.

Bivariate Lomax Distribution Based on Clayton Copula: Estimation and Prediction

Lomax distribution has been studied by many statisticians due to its important role in reliability modeling and lifetime testing. The bivariate Lomax distribution is an important lifetime distribution in survival analysis. In this article, a bivariate Lomax distribution is constructed based on Clayton copula. The joint probability density function and the joint cumulative distribution function are derived in closed forms. Some properties of this bivariate distribution are discussed. The maximum likelihood and Bayes estimators for the unknown parameters are derived. Also, the maximum likelihood and Bayesian two-sample prediction for the future observations are obtained. The performance of the proposed bivariate distribution is examined using a simulation study. Finally, one real data set under the proposed distribution is considered to illustrate its flexibility and applicability for real-life applications.

Drought and wetness events encounter and cascade effect in the Yangtze River and Yellow River Basin

Under the background of global change, the multivariate attributes, multi-temporal and multi-watershed regional characteristics of extreme drought and flood disasters are significant. It is very important to identify the drought and wetness encounter law and spatial cascade effect in the source region-upper-middle-lower reaches of the basin. In this paper, the Yangtze River and Yellow River basins are taken as the research objects. Based on the standardized precipitation index (SPI) characterizing meteorological drought and wetness and the standardized runoff index (SRI) characterizing hydrological drought and wetness, the evolution law of extreme drought and flood events in the source region-upper-middle-lower reaches of the two basins is analyzed. On this basis, the correlation analysis and transfer function analysis are used to explore the response relationship and lag effect between the two in different partitions. A two-dimensional joint distribution model is constructed by Copula function to quantitatively analyze the joint probability of drought and wetness encounters of 9 combined events, and to deeply analyze the impact of different drought and wetness encounter scenarios. The results show that: from 1957 to 2020, the two basins showed a trend from drought to wet. The SPI-12 in the Yellow River Basin ranged from-1.57 to 1.32, and that in the Yangtze River Basin ranged from-1.24 to 1.11. The severity of drought and wetness in the Yellow River Basin was higher than that in the Yangtze River Basin; The correlation coefficients between SPI and SRI in the source-upper-middle-lower reaches of the Yellow River (Yangtze River) were 0.78 (0.76), 0.23 (0.73), 0.44 (0.55) and 0.23 (0.63), respectively. The correlation degree of meteorological-hydrological drought and wetness in the Yangtze River Basin was significantly higher than that in the Yellow River Basin. The average probability of synchronous combination events of drought and wetness in the two basins is greater than 51.43 %. The probability of drought in the Yellow River Basin is greater than that of flood, while the Yangtze River Basin is the opposite. In the same drought and wetness scenario, an average of 54.1% of the event pairs were aggravated by disasters, and more than 52 % of the events in the wetness-drought scenario had obvious drought mitigation effects. The research results can provide important support for improving the early warning and risk management of river basin disasters.

A PINN-DeepONet framework for extracting turbulent combustion closure from multiscalar measurements

In this study, we develop a novel framework to extract turbulent combustion closure, including closure for species chemical source terms, from multiscalar and velocity measurements in turbulent flames. The technique is based on a physics-informed neural network (PINN) that combines models for velocity and scalar measurements and a deep operator network (DeepONet) to accommodate spatial measurements and experimental parameters as separate input streams. An additional key innovation is the estimate of the unconditional means of the species’ chemical source terms as additional “observations” to constrain the prediction of these rates. This estimate is based on a convolution of the means of species reaction rates conditioned on principal components of the multiscalar data and the joint probability density functions of these principal components. The PINN-DeepONet method is implemented on the so-called Sydney flames, where training is carried out on 3 flames and validated on 4 flames. The results show that, despite the limited samples of experimental parameters, including the inlet flow and the fuel jet recess length within the air flow, the PINN-DeepONet approach can construct velocity and scalar fields along with important closure terms for turbulent transport and reaction rates.

Estimation of complete mutual information exploiting nonlinear magnitude-phase dependence: Application to spatial FNC for complex-valued fMRI data

BackgroundReal-valued mutual information (MI) has been used in spatial functional network connectivity (FNC) to measure high-order and nonlinear dependence between spatial maps extracted from magnitude-only functional magnetic resonance imaging (fMRI). However, real-valued MI cannot fully capture the group differences in spatial FNC from complex-valued fMRI data with magnitude and phase dependence. MethodsWe propose a complete complex-valued MI method according to the chain rule of MI. We fully exploit the dependence among magnitudes and phases of two complex-valued signals using second and fourth-order joint entropies, and propose to use a Gaussian copula transformation with a lower bound property to avoid inaccurate estimation of joint probability density function when computing the joint entropies. ResultsThe proposed method achieves more accurate MI estimates than the two histogram-based (normal and symbolic approaches) and kernel density estimation methods for simulated signals, and enhances group differences in spatial functional network connectivity for experimental complex-valued fMRI data. Comparison with existing methodsCompared with the simplified complex-valued MI and real-valued MI, the proposed method yields higher MI estimation accuracy, leading to 17.4 % and 145.5 % wider MI ranges, and more significant connectivity differences between healthy controls and schizophrenia patients. A unique connection between executive control network (EC) and right frontal parietal areas, and three additional connections mainly related to EC are detected than the simplified complex-valued MI. ConclusionsWith capability in quantifying MI fully and accurately, the proposed complex-valued MI is promising in providing qualified FNC biomarkers for identifying mental disorders such as schizophrenia.

Updating direct methods II. Reduction of the structural complexity when triplet invariants are estimated via the Patterson map

Direct methods have practically solved the phase problem for small–medium-size molecules but have substantially failed in macromolecular crystallography. They have two main limitations: a strong dependence on structural complexity and the need to work with atomic-resolution data. Many attempts have been made to broaden their field of applicability, for example the use of some a priori information to make the estimate of the triplet invariant phases more effective. Unfortunately none of these new approaches allowed the successful application of direct methods to proteins and nucleic acids. Direct methods are still a niche tool in macromolecular crystallography. In a recent publication [Giacovazzo (2019). Acta Cryst. A75, 142–157] the method of joint probability distributions has been modified to take into account new sources of prior information, one of which is relevant to this article: the Patterson map. In practice, it has been shown that with prior knowledge of the interatomic vectors one is able to modify the classic Cochran reliability parameter for estimating the triplet invariant phases. The article was essentially theoretical in nature, and no attempt was described to test the practical usefulness of the new probabilistic formulas. This work is therefore the first application of the new method. It is shown that the use of the Patterson map as prior information substantially improves the Cochran estimate of triplet phases; the phase error distribution for the new estimates, even if it is related to macromolecular structures, becomes similar to that obtained for medium-size structures. In some ways, it is as if the use of the Patterson information reduces the structural complexity, thus allowing a more general use of direct methods in macromolecular crystallography. Atomic resolution no longer seems to be a necessary ingredient for the applicability of direct methods; tests show that the apparent reduction in structural complexity also occurs in macromolecular structures with experimental data having a resolution of 2.3 Å. A number of test structures have been used to show the potential of the new technique.

Bell inequality violation in relativity theory

A violation of Bell local realism inequalities in Clauser–Horne–Shimony–Holt form has been discovered in a relativistic Gedankenexperiment. This means that there are no definite joint probabilities and this finds a classical explanation in the structure of special relativity. The discovered nonlocality is weaker than Albert Einstein’s quantum ‘spooky action at a distance’, and its presence suggests certain parallels between special relativity and quantum mechanics.

The short-term intermittency evaluation of distributed photovoltaic power

Uncertainty of distributed photovoltaic(PV) power brings great challenges to the safe and stable operation of power system, in which the intermittency problem is more challenging than the fluctuation. This paper focuses on the intermittency problem of distributed PV power, firstly, an intermittency evaluation method based on generalized extreme value(GEV) theory is proposed to solve the problem of the lack of "small-sample big-gap" events. Secondly, focusing on high risk events such as high-frequency and warning mutation events, probabilistic evaluation indexes were established, including T-hour-period mutation intensity and T-hour-period mutation frequency. Finally, a two-dimensional joint probability distribution of intermittency elements is established, and the concepts of return period and return level are introduced into the photovoltaic field to provide data support for the configuration of energy storage capacity and duration, and to provide auxiliary decision-making for the execution time and development cycle of interactive projects. The proposed method provides a solution for intermittency evaluation in small sample status quo with strong data compatibility and engineering replicability.

Satisficing Approach to On-Demand Ride Matching

Online ride-hailing platforms have developed into an integral part of the transportation infrastructure in many countries. The primary task of a ride-hailing platform is to match trip requests to drivers in real time. Although both passengers and drivers prefer a prompt pickup to initiate the trips, it is often difficult to find a nearby driver for every passenger. If the driver is far from the pickup point, the passenger may cancel the trip while the driver is heading toward the pickup point. For the platform to be profitable, the trip cancellation rate must be maintained at a low level. We propose a computationally efficient data-driven approach to ride matching, in which a pickup time target is imposed on each trip request and an optimization problem is formulated to maximize the joint probability of all the pickup times meeting the targets. By adjusting pickup time targets individually, this approach may assign more high-value trip requests to nearby drivers, thus boosting the platform’s revenue while maintaining a low cancellation rate. In numerical experiments, the proposed approach outperforms several ride-matching policies used in practice. History: Accepted by Andrea Lodi, Area Editor for Design & Analysis of Algorithms—Discrete. Funding: This work of D. Rong and X. Sun was supported in part by the National Natural Science Foundation of China [Grant 71971165], the National Key Research and Development Program of China [Grant 2021YFB3301801], the MOE Project of Humanities and Social Science of China [Grant 19YJE630002], and the Soft Science Research Program of Shannxi [Grant 2018KRZ005]. The work of S. He was supported in part by the Singapore Ministry of Education Social Science Research Council [Grant MOE2022-SSRTG-029]. Supplemental Material: The software that supports the findings of this study is available within the paper and its Supplemental Information ( https://pubsonline.informs.org/doi/suppl/10.1287/ijoc.2021.0210 ) as well as from the IJOC GitHub software repository ( https://github.com/INFORMSJoC/2021.0210 ). The complete IJOC Software and Data Repository is available at https://informsjoc.github.io/ .

Code and Data Repository for Satisficing Approach to On-Demand Ride Matching

Online ride-hailing platforms have developed into an integral part of the transportation infrastructure in many countries. The primary task of a ride-hailing platform is to match trip requests to drivers in real time. Although both passengers and drivers prefer a prompt pickup to initiate their trips, it is often difficult to find a nearby driver for every passenger. If the driver is far from the pickup point, the passenger may cancel the trip while the driver is heading toward the pickup point. In order for the platform to be profitable, the trip cancellation rate must be maintained at a low level. We propose a data-driven, computationally efficient approach to ride matching, in which a pickup time target is imposed on each trip request and an optimization problem is formulated to maximize the joint probability of all the pickup times meeting the targets. By adjusting pickup time targets individually, this approach may assign more high-value trip requests to nearby drivers, thus boosting the platform’s revenue while maintaining a low cancellation rate. In numerical experiments, the proposed approach outperforms several ride-matching policies used in practice.

Performance-based design of environmental parameters for offshore wind turbine foundations

Taking into account the coupling effects of wind, wave, and current on offshore wind turbines (OWTs), a combined approach utilizing non-linear finite element analysis (FEA), back propagation neural network (BPNN), and probabilistic statistical methodology (PSM) is proposed for accurate environmental parameter estimation in OWT foundation design. The structural bearing performances of OWT foundations are precisely predicted through a combination of FEA and BPNN models, and then serve as constraints for probabilistic statistical analysis. Furthermore, for PSM, a robust multivariate joint probability distribution is constructed leveraging copula functions, which not only maximizes marginal information but also effectively captures the intricate dependencies among ocean environmental parameters. Subsequently, the proposed models, along with traditional univariate analysis, are utilized to estimate the return values of diverse load combinations. The results indicate that, for a given return period, the conditional probability model yields lower wave heights and current velocities compared to univariate analysis, while the joint probability model results in lower values for all ocean parameters, making both approaches more suitable for OWT foundation design. This coupled approach presents a more rational and cost-effective solution compared to univariate analysis, potentially resulting in decreased investment costs.

Parameter estimation of grouting pressure and surface subsidence on the reliability of shield tunnel excavation under incomplete probability information

Most of the results obtained from traditional tunnel reliability models are based on conclusions of deterministic parameters, and ignoring the correlation between parameters tends to generate unreliable conclusions for the analysis. This study investigated the influence of grouting pressure and surface subsidence on the reliability of shield tunnel excavation considering the dependency structures between parameters. A probabilistic analysis approach based on copula method is applied to evaluate the bivariate dependency structure. Firstly, 88 sets of measured data are selected from various tunnel projects at home and abroad, and their statistical parameters and marginal distribution functions are determined. Secondly, a bivariate joint probability distribution model of shield grouting excavation is established, and Monte Carlo Simulation is applied to explore the influence of the selection of the copula function on the failure probability of the shield grouting excavation. The results indicate that under incomplete probabilistic information, disregarding the negative correlation between the parameters will underestimate the reliability of shield grouting construction and yield an overly conservative reliability design. Subsequently, varying the magnitude of the parameter limit values to explore the effect on the failure probability will be advantageous for reliability analysis in dynamic construction. Finally, by varying the sample size of the simulation and original measured data, it is found that excessively small simulated and original sample sizes can lead to inaccurate reliability assessment.

Field theory of active chiral hard disks: a first-principles approach to steric interactions

A first-principles approach for active chiral hard disks is presented, that explicitly accounts for steric interactions on the two-body level. We derive an effective one-body equation for the joint probability distribution of positions and angles of the particles. By projecting onto the angular modes, we write a hierarchy for the lowest hydrodynamic modes, i.e. particle density, polarisation, and nematic tensor. Introducing dimensionless variables in the equations, we highlight the assumptions, which—though inherent—are often included implicit in typical closure schemes of the hierarchy. By considering different regimes of the Péclet number, the well-known models in active matter can be obtained through our consideration. Explicitly, we derive an effective diffusive description and by going to higher orders in the closure scheme, we show that this first-principles approach results in the recently introduced Active Model B +, a natural extension of the Model B for active processes. Remarkably, here we find that chirality can change the sign of the phenomenological activity parameters.

Framework for assessing the performance of overhead transmission lines under wind-temperature effects

This paper presents a framework for evaluating the wind-induced resistance of overhead transmission lines (OTLs), aiming to overcome the limitations associated with disregarding temperature effects and relying on a single metric for failure assessment. The proposed framework factors in temperature influence, carefully considers applied loads and structural characteristics, and accurately calculates failure probability based on a specific case study. Meteorological data is initially collected to create a probabilistic model of wind speed and temperature distribution, accounting for correlation. Components and systems are graded based on structural characteristics and damage modes. The neural network surrogate model is trained with finite element computations for load-structural response sample sets. The surrogate model, in conjunction with logistic regression, generates samples to determine fragility. Finally, the total structural failure probability and monthly failure likelihood are computed by integrating the joint probability model and fragility. Analyses highlight temperature's significant impact on conductor-ground line safety, validating the proposed framework's rationale.