Search Results (46)

Reliable estimation of extreme waves is essential for offshore wind turbine system design; however, site-specific conditions limit the application of one-size-fits-all statistical methods. We analyzed extreme wave conditions at potential offshore wind farm sites in South Korea using high-resolution hindcast data (1979–2022) based on the Weather Research and Forecasting (WRF) model. While previous studies have typically relied on a limited combination of distribution types and parameter estimation methods, this study systematically applied various Weibull distribution models and parameter estimation techniques to the environmental contour (EC) method. The results show that the optimal statistical approach varied by site according to the tail characteristics of the wave height distribution. The inverse second-order reliability method (I-SORM) provided the highest accuracy in regions with rapidly decaying tails, achieving root mean square error (RMSE) values of 0.21 in Shinan (using the three-parameter Weibull distribution with maximum likelihood estimation, MLE) and 0.34 in Chujado (with the method of moments, MOM). In contrast, the inverse first-order reliability method (I-FORM) yielded superior performance in areas where the tail decays more gradually, such as Yokjido (RMSE = 0.47 with MLE using the exponentiated Weibull distribution) and Ulsan (RMSE = 0.29, with MLE using the exponentiated Weibull distribution). These findings underscore the importance of selecting site-specific combinations of statistical models and estimation techniques based on wave distribution characteristics, thereby improving the accuracy and reliability of extreme design wave predictions. The proposed framework can significantly contribute to the establishment of reliable design criteria for offshore wind turbine systems by reflecting region-specific marine environmental conditions. Full article

This study evaluates six parameter estimation methods for the generalized extreme value (GEV) distribution: maximum likelihood estimation (MLE), two probability-weighted moments (PWM-UE and PWM-PP), and three robust two-stage order statistics estimators (TSOS-ME, TSOS-LMS, and TSOS-LTS). Their performance was assessed using simulation experiments under varying tail behaviors, represented by three types of GEV distributions: Weibull (short-tailed), Gumbel (light-tailed), and Fréchet (heavy-tailed) distributions, based on the mean squared error (MSE) and mean absolute percentage error (MAPE). The results showed that TSOS-LTS consistently achieved the lowest MSE and MAPE, indicating high robustness and forecasting accuracy, particularly for short-tailed distributions. Notably, PWM-PP performed well for the light-tailed distribution, providing accurate and efficient estimates in this specific setting. For heavy-tailed distributions, TSOS-LTS exhibited superior estimation accuracy, while PWM-PP showed a better predictive performance in terms of MAPE. The methods were further applied to real-world monthly maximum PM2.5 data from three air quality stations in Bangkok. TSOS-LTS again demonstrated superior performance, especially at Thon Buri station. This research highlights the importance of tailoring estimation techniques to the distribution’s tail behavior and supports the use of robust approaches for modeling environmental extremes. Full article

This research introduces and studies the performance of the $\alpha$-Fluctuating Nakagami-m model, which addresses the limitations of conventional models for wireless communications. For the assumed channel model, the research presents a complete first-order statistical description (including the probability density function (PDF), cumulative distribution function (CDF), moment generating function (MGF), and raw moments) and provides closed-form results for system performance (assessed in terms of outage probability, average bit error rate (ABER), and channel capacity). All of the expressions have the same numerical complexity as the base-line Fluctuating Nakagami-m model, and are accompanied by their high signal-to-noise ratio (SNR) asymptotics. The derived results helped to identify the amount of fading (AoF) and diversity/coding gain of the proposed channel model. In-depth analysis of the system performance was carried out for all possible fading channel parameter values. Numerical analysis of the proposed solutions demonstrated their high computational efficiency. The comparison with experimental results demonstrated that the model offers enhanced flexibility and better characterization of fading regimes. Numerical analysis and simulation results show a high degree of correspondence with the analytical work and help study the dependence of channel nonlinearity effects on overall system performance. Full article

This study investigates the computation of fractional and higher integer-order moments for a stochastic process governed by a one-dimensional, non-homogeneous linear stochastic differential equation (SDE) driven by fractional Brownian motion (fBm). Unlike conventional approaches relying on moment-generating functions or Fokker–Planck equations, which often yield intractable expressions, we derive explicit closed-form formulas for these moments. Our methodology leverages the Wick–Itô calculus (fractional Itô formula) and the properties of Hermite polynomials to express moments efficiently. Additionally, we establish a recurrence relation for moment computation and propose an alternative approach based on generalized binomial expansions. To validate our findings, Monte Carlo simulations are performed, demonstrating a high degree of accuracy between theoretical and empirical results. The proposed framework provides novel insights into stochastic processes with long-memory properties, with potential applications in statistical inference, mathematical finance, and physical modeling of anomalous diffusion. Full article

We propose a field mapping approach for the propagation of laser beams through atmospheric turbulence, leveraging a Generative Adversarial Network (GAN). The proposed GAN utilizes a U-Net architecture as its generator, with turbulence characteristic parameters introduced into the bottleneck layer of the U-Net network, enabling effective control over the generator. This design allows for the flexible simulation of Gaussian beam propagation across a range of turbulence intensities and transmission distances. A comparative analysis between the neural network predictions and numerical simulation results indicates that the neural network can achieve a field mapping speedup of four orders of magnitude while maintaining a relative error within 16% for the second-order statistical moments of the light spot. Additionally, the study investigates the effect of varying turbulence intensities on prediction accuracy. The results indicate that high-frequency speckle patterns caused by beam breakup are the primary factor limiting prediction accuracy under strong or saturated turbulence conditions. Full article

Background: This study aimed to analyze image biomarkers of the parotid glands in ultrasonography images with reduced shape effects, providing a reference for the radiomic diagnosis of parotid gland lesions. Methods: Ultrasound (US) and sialography images of the parotid glands, acquired from September 2019 to March 2024, were reviewed along with their clinical information. Parotid glands diagnosed as within the normal range were included. Overall, 91 US images depicting the largest portion of the parotid glands were selected for radiomic feature extraction. Regions of interest were drawn twice on 50 images using different shapes to assess the intraclass correlation coefficient (ICC). Feature dimensions were statistically reduced by selecting features with an ICC > 0.8 and applying four statistical algorithms. The selected features were used to distinguish age and sex using the four classification models. Classification performance was evaluated using the area under the receiver operating characteristic curve (AUC), recall, and precision. Results: The combinations of the information gain ratio algorithm or stochastic gradient descent and the naïve Bayes model showed the highest AUC for both age and sex classification (AUC = 1.000). The features contributing to these classifications included the first-order and gray-level co-occurrence matrix (high-order) features, particularly discretized intensity skewness and kurtosis, intensity skewness, and GLCM angular second moment. These features also contributed to achieving one of the highest recall (0.889) and precision (0.926) values. Conclusions: The two features were the most significant factors in discriminating radiomic variations related to age and sex in US images with reduced shape effects. These radiomic findings should be assessed when diagnosing parotid gland pathology versus normal using US images and radiomics in a heterogeneous population. Full article

This paper addresses key challenges in the static and dynamic reliability analysis of engineering structures, particularly the difficulty in accurately estimating large reliability indices and small failure probabilities. For static reliability problems, a dual power transformation is employed to transform the performance function into a form approaching a normal distribution. The high-order unscented transformation is then applied to compute the first four moments of the transformed performance function. Subsequently, the fourth-moment method is used to calculate large reliability indices, offering a novel improvement over traditional methods such as FORM and SORM. For dynamic reliability problems, the low-discrepancy sampling technique is integrated to efficiently compute structural responses under random seismic excitation, improving computational efficiency for complex dynamic systems. The Yeo–Johnson transformation is introduced to normalize the extreme values of dynamic responses, and the first four moments of the transformed extreme values are statistically evaluated. Additionally, a third-order polynomial transformation (TPT) is applied to approximate the probability density function, leading to the derivation of the probability of exceedance (POE) curve. The optimal transformation parameters for both the dual power and Yeo–Johnson transformations are determined using the Jarque–Bera (JB) test. Four numerical examples, coupled with Monte Carlo simulation, validate the proposed framework’s accuracy and efficiency, providing a robust tool for static and dynamic reliability analysis. This unified approach represents a significant advancement by integrating novel transformations and fourth-moment method, providing a powerful and efficient tool for static and dynamic reliability analysis of engineering structures. Full article

Deep learning (DL) networks are a popular choice for short-term load forecasting (STLF) in the residential sector. Hybrid DL methodologies based on convolutional neural networks (CNNs) and long short-term memory networks (LSTMs) have a higher forecasting accuracy than conventional statistical STLF techniques for different types of single-household load series. However, existing load forecasting methodologies are often inefficient when a high load demand persists for a few hours in a day. Peak load consumption is explicitly depicted as a tail in the probability distribution function (PDF) of the load series. Due to the diverse and uncertain nature of peak load demands, DL methodologies have difficulty maintaining consistent forecasting results, particularly when the PDF of the load series has a longer tail. This paper proposes a multihousehold load forecasting strategy based on the collective moment measure (CMM) (which is obtained from the PDF of the load series), data augmentation, and a CNN. Each load series was compared and ordered through CMM indexing, which helped maintain a minimum or constant shifting variance in the dataset inputted to the CNN. Data augmentation was used to enlarge the input dataset and solve the existing data requirement issues of the CNN. With the ordered load series and data augmentation strategy, the simulation results demonstrated a significant improvement in the performance of both single-household and multihousehold load forecasting. The proposed method predicts day-ahead multihousehold loads simultaneously and compares the results based on a single household. The forecasting performance of the proposed method for six different household groups with 10, 20, 30, 50, 80, and 100 household load series was evaluated and compared with those of existing methodologies. The mean absolute percentage error of the prediction results for each multihousehold load series could be improved by more than 3%. This study can help advance the application of DL methods for household load prediction under high-load-demand conditions. Full article

Uncertainties in the atmosphere and flight conditions can drastically impact the performance of an aircraft and result in certification delays. However, uncertainty propagation in high-fidelity simulations, which have become integral to the design process, can pose intractably high computational costs. This study presents a non-intrusive, parametric reduced order modeling (ROM) method to enable the prediction of uncertain fields with thousands of random variables and nonlinear features under limited sampling budgets. The methodology combines linear dimensionality reduction with sparse polynomial chaos expansions and is assessed in a variety of CFD-based test cases, including 3D supersonic flow over a passenger aircraft with uncertain flight conditions. Each problem has strong nonlinearities, such as shocks, to investigate the effectiveness of models in real-world aerodynamic simulations that may arise during conceptual or preliminary design. The performance is assessed by comparing the uncertain mean, variance, point predictions, and integrated quantities of interest obtained using the ROMs to Monte Carlo simulations. It is observed that if the flow is entirely supersonic or subsonic, then the method can predict the pressure field accurately and rapidly. Moreover, it is also seen that statistical moments can be efficiently obtained using closed-form analytical expressions and closely match Monte Carlo results. Full article

In the field of image watermarking, imperceptibility, robustness, and watermarking capacity are key indicators for evaluating the performance of watermarking techniques. However, these three factors are often mutually constrained, posing a challenge in achieving a balance among them. To address this issue, this paper presents a novel image watermark detection algorithm based on local fast and accurate polar harmonic Fourier moments (FAPHFMs) and the BKF–Rayleigh distribution model. Firstly, the original image is chunked without overlapping, the entropy value is calculated, the high-entropy chunks are selected in descending order, and the local FAPHFM magnitudes are calculated. Secondly, the watermarking signals are embedded into the robust local FAPHFM magnitudes by the multiplication function, and then MMLE based on the RSS method is utilized to estimate the statistical parameters of the BKF–Rayleigh distribution model. Finally, a blind image watermarking detector is designed using BKF–Rayleigh distribution and LO decision criteria. In addition, we derive the closed expression of the watermark detector using the BKF–Rayleigh model. The experiments proved that the algorithm in this paper outperforms the existing methods in terms of performance, maintains robustness well under a large watermarking capacity, and has excellent imperceptibility at the same time. The algorithm maintains a well-balanced relationship between robustness, imperceptibility, and watermarking capacity. Full article

In the past, numerous stratovolcanoes worldwide witnessed catastrophic flank collapses. One of the greatest risks associated with stratovolcanoes is a massive rock failure. On 18 May 1980, we witnessed a rock slope failure due to a volcano eruption, and a 2185.60 m high rock slope of Mount St. Helens was collapsed. Thus, from the serviceability perspective, this work presents an effective computational technique to perform probabilistic analyses of Mount St. Helens situated in Washington, USA. Using the first-order second-moment method, probability theory and statistics were employed to map the uncertainties in rock parameters. Initially, Scoops3D was used to perform slope stability analysis followed by probabilistic evaluation using a hybrid computational model of artificial neural network (ANN) and firefly algorithm (FF), i.e., ANN-FF. The performance of the ANN-FF model was examined and compared with that of conventional ANN and other hybrid ANNs built using seven additional meta-heuristic algorithms. In the validation stage, the proposed ANN-FF model was the best-fitted hybrid model with R² = 0.9996 and RMSE = 0.0042. Under seismic and non-seismic situations, the reliability index and the probability of failure were estimated. The suggested method allows for an effective assessment of the failure probability of Mount St. Helens under various earthquake circumstances. The developed MATLAB model is also attached as a supplementary material for future studies. Full article

In order to ensure that a perimeter security system can work effectively, a convenient and effective event detection algorithm has an important engineering significance. Given the above background, in this paper, we propose a high reliability intrusion event recognition method and vibration sensing system, based on ultra-weak fiber Bragg grating array, by using high dimensional random matrix. We obtain a high sensitivity optical interference signal by constructing a patch-matched optical interference system, then compose the demodulated interference signal into a high-dimensional random matrix. The statistical characteristics of the matrix for the Marcenko-Pastur (M-P) law and ring law are used to confirm the presence of intrusion events efficiently, which can reflect the limit spectrum distribution of the high-dimensional random matrix; meanwhile, the abnormal state quantity and moment are obtained. Further, the average spectral radius value is used to judge the fault cause. Field experimental results show that the proposed method can effectively obtain the correct monitoring data for the sensor array. By comparing the monitoring results of normal operation and crusher operation, we can detect the intrusion event in 4.5 s, and the accuracy rate can reach more than 90%, which verifies that the proposed high-dimensional random matrix analysis method can work properly, proving a practical engineering application prospect. Full article

Knowable moments, abbreviated as K-moments, are redefined as expectations of maxima or minima of a number of stochastic variables that are a sample of the variable of interest. The new definition enables applicability of the concept to any type of variable, continuous or discrete, and generalization for transformations thereof. While K-moments share some characteristics with classical and other moments, as well as with order statistics, they also have some unique features, which make them useful in relevant applications. These include the fact that they are knowable, i.e., reliably estimated from a sample for high orders. Moreover, unlike other moment types, K-moment values can be assigned values of distribution function by making optimal use of the entire dataset. In addition, K-moments offer the unique advantage of considering the estimation bias when the data are not an independent sample but a time series from a process with dependence. Both for samples and time series, the K-moment concept offers a strategy of model fitting, including its visualization, that is not shared with other methods. This enables utilization of the highest possible moment orders, which are particularly useful in modelling extremes that are closely associated with high-order moments. Full article

Tobacco consumption contributes to a substantial amount of household expenditures, which might lead to decreased spending on other essentials. This study examines household head tobacco expenditures in various inequality settings. In this study, we investigated the impact of gender, race, and educational inequality and the substitution effect of tobacco expenditure on essentials such as children’s education and household food. We looked at how much of the resources household heads spend on tobacco in different inequality settings that replace households’ essentials. The panel setting of the National Income Dynamics Study (NIDS), South Africa’s first nationally representative household panel survey, is used as a data collection source for this study. These are household surveys conducted by the Presidency’s Office of Planning, Monitoring, and Evaluation. The panel data are subject to attrition in longitudinal research. We compared the conditional expenditure shares of various types of households using econometric models such as moment quantile regression. A negative and statistically significant estimated coefficient of tobacco expenditure and the coefficient of the interacted term (inequality and tobacco expenditure) demonstrated the substitution effect. The findings reveal that low-income households whose heads smoke tobacco invest less in their children’s education, while well-educated heads of high-income households’ place as much value on their children’s education as they do on cigarette expenditure. The study also points out that the share of income spent on cigarettes by black household heads is negatively connected to their children’s education across all quantiles compared to non-blacks. We conclude that low-income households are more likely to experience the substitution impact than high-income households. This study recommends, among other things, that low-income households should prioritize needs over non-essentials in order to maximize household satisfaction, and government should implement policies that will limit tobacco consumption expenditure. Full article

This paper focuses on the non-Gaussian properties of tornado pressure loading on a Texas Tech University (TTU) building model. External pressures of the model were measured at multiple radial positions in a two-celled tornado-like vortex generated by a tornado-like vortex simulator. High-order statistical moments of pressure coefficients were studied. The spatial distributions of non-Gaussian zones were presented and compared with the figure for boundary layer wind. Four exponential models were used to fit the probability density of tornado pressures. The peak factors obtained by five methods were also investigated. Results indicate that non-Gaussian regions of a low-rise building in a tornado-like vortex significantly differ from that in boundary layer wind. The peak pressure coefficients exhibit a maximum value near the end of windward eaves when the model is located at a tornadic core radius. The probability density of tornado pressure time series cannot be fitted by a single exponential distribution. The gamma distribution and generalized extreme value (GEV) distribution can describe the probabilistic behavior of pressure coefficients at the most unfavorable load position. Compared with other methods, the skewness-dependent peak factor method exhibits the advantages of reliable results, easy calculation, and wide applicability. Full article