Search Results (14)

Rolling bearings serve as the most widely utilized general components in drive systems for rotating machinery, and they are susceptible to regular malfunctions. To address the performance degradation encountered by current convolutional neural network-based rolling-bearing-fault diagnosis methods due to significant noise interference and variable working conditions in industrial settings, we propose a rolling-bearing-fault diagnosis method based on dual multi-scale mechanism applicable to noisy-variable operating conditions. The suggested approach begins with the implementation of Variational Mode Decomposition (VMD) on the initial vibration signal. This is succeeded by a denoising process that utilizes the goodness-of-fit test based on the Anderson–Darling (AD) distance for enhanced accuracy. This approach targets the intrinsic mode functions (IMFs), which capture information across multiple scales, to obtain the most precise denoised signal possible. Subsequently, we introduce the Dynamic Weighted Multi-Scale Feature Convolutional Neural Network (DWMFCNN) model, which integrates two structures: multi-scale feature extraction and dynamic weighting of these features. Ultimately, the signal that has been denoised is utilized as input for the DWMFCNN model to recognize different kinds of rolling-bearing faults. Results from the experiments show that the suggested approach shows an improved denoising performance and a greater adaptability to changing working conditions. Full article

Thanks to the performance improvement introduced by micro sized functional fillers, application of epoxy composites for electrical insulation purposes has become popular. This paper investigates the dielectric properties of epoxy micro-composites filled with alumina (Al₂O₃). In particular, measurements of relative permittivity, dissipation factor, and electrical breakdown are performed, and a comprehensive statistical analysis on dielectric properties was conducted. AC breakdown strength (AC-BDS) was analyzed for normal distribution using four methods (Anderson–Darling, Shapiro–Wilk, Ryan–Joiner, and Kolmogorov–Smirnov). In addition, the AC-BDS was analyzed at risk probabilities of 1%, 5%, 10%, and 50% using Weibull distribution functions. Both normal and Weibull distributions were evaluated using the Anderson–Darling (A-D) statistic and p-value. Additionally, the log-normal, gamma, and exponential distributions of AC-BDS were examined by A-D goodness-of-fit test. The hypothesis test results of AC-BDS were fit by normal and Weibull distributions, and the compliance was evaluated by p-value and each method statistics. In addition, the experimental results of AC-BDS were fit by log-normal and gamma distributions, and the goodness-of-fit was evaluated by p-value and A-D testing. On the other hand, exponential distribution was not suitable for p-value and A-D testing. The results showed that the distributions of AC-BDS were the best using log-normal distribution. Meanwhile, statistical analysis results verified the apparent effect of temperature on dielectric properties using a paired t-test. The analysis results of this paper not only contribute to better characterization of epoxy/Al₂O₃ micro-composites but also introduce a comprehensive approach for performing statistical analysis for electrical insulation materials. Full article

The Jarque–Bera test is commonly used in statistics and econometrics to test the hypothesis that sample elements adhere to a normal distribution with an unknown mean and variance. This paper proposes several modifications to this test, allowing for testing hypotheses that the considered sample comes from: a normal distribution with a known mean (variance unknown); a normal distribution with a known variance (mean unknown); a normal distribution with a known mean and variance. For given significance levels, $\alpha =0.05$ and $\alpha =0.01$, we compare the power of our normality test with the most well-known and popular tests using the Monte Carlo method: Kolmogorov–Smirnov (KS), Anderson–Darling (AD), Cramér–von Mises (CVM), Lilliefors (LF), and Shapiro–Wilk (SW) tests. Under the specific distributions, 1000 datasets were generated with the sample sizes $n=25,50,75,100,150,200,250,500,$ and 1000. The simulation study showed that the suggested tests often have the best power properties. Our study also has a methodological nature, providing detailed proofs accessible to undergraduate students in statistics and probability, unlike the works of Jarque and Bera. Full article

While overdispersion is a common phenomenon in univariate count time series data, its exploration within bivariate contexts remains limited. To fill this gap, we propose a bivariate integer-valued autoregressive model. The model leverages a modified binomial thinning operator with a dispersion parameter $\rho$ and integrates random coefficients. This approach combines characteristics from both binomial and negative binomial thinning operators, thereby offering a flexible framework capable of generating counting series exhibiting equidispersion, overdispersion, or underdispersion. Notably, our model includes two distinct classes of first-order bivariate geometric integer-valued autoregressive models: one class employs binomial thinning (BVGINAR(1)), and the other adopts negative binomial thinning (BVNGINAR(1)). We establish the stationarity and ergodicity of the model and estimate its parameters using a combination of the Yule–Walker (YW) and conditional maximum likelihood (CML) methods. Furthermore, Monte Carlo simulation experiments are conducted to evaluate the finite sample performances of the proposed estimators across various parameter configurations, and the Anderson-Darling (AD) test is employed to assess the asymptotic normality of the estimators under large sample sizes. Ultimately, we highlight the practical applicability of the examined model by analyzing two real-world datasets on crime counts in New South Wales (NSW) and comparing its performance with other popular overdispersed BINAR(1) models. Full article

We present a study of the flux distribution of a sample of 15 Intermediate and Low-energy peaked blazars using XMM-Newton observations in a total of 57 epochs on short-term timescales. We characterise the X-ray variability of all of the light curves using excess fractional variability amplitude and found that only 24 light curves in 7 sources are significantly variable. In order to characterise the origin of X-ray variability in these blazars, we fit the flux distributions of all these light curves using Gaussian and lognormal distributions, as any non-Gaussian perturbation could indicate the imprints of fluctuations in the accretion disc, which could be Doppler boosted through the relativistic jets in blazars. However, intra-day variability, as seen in our observations, is difficult to reconcile using disc components as the emissions in such sources are mostly dominated by jets. We used Anderson–Darling (AD) and ${\chi }^2$ tests to fit the histograms. In 11 observations of 4 blazars, namely, ON 231, 3C 273, PKS 0235+164 and PKS 0521-365, both models equally fit the flux distributions. In the rest of the observations, we are unable to model them with any distribution. In two sources, namely, BL Lacertae and S4 0954+650, the lognormal distribution is preferred over the normal distribution, which could arise from non-Gaussian perturbations from relativistic jets or linear Gaussian perturbation in the particle time scale leading to such flux distributions. Full article

The Coherent Pixels Technique Interferometry Synthetic Aperture Radar (CPT-InSAR) method of inverting surface deformation parameters by using high-quality measuring points possesses the flaw inducing sparse measuring points in non-urban areas. In this paper, we propose the Adaptive Coherent Distributed Pixel InSAR (ACDP-InSAR) method, which is an adaptive method used to extract Distributed Scattering Pixel (DSP) based on statistically homogeneous pixel (SHP) cluster tests and improves the phase quality of DSP through phase optimization, which cooperates with Coherent Pixel (CP) for the retrieval of ground surface deformation parameters. For a region with sparse CPs, DSPs and its SHPs are detected by double-layer windows in two steps, i.e., multilook windows and spatial filtering windows, respectively. After counting the pixel number of maximum SHP cluster (MSHPC) in the multilook window based on the Anderson–Darling (AD) test and filtering out unsuitable pixels, the candidate DSPs are selected. For the filtering window, the SHPs of MSHPC’ pixels within the new window, which is different compared with multilook windows, were detected, and the SHPs of DSPs were obtained, which were used for coherent estimation. In phase-linking, the results of Eigen decomposition-based Maximum likelihood estimator of Interferometric phase (EMI) results are used as the initial values of the phase triangle algorithm (PTA) for the purpose of phase estimation (hereafter called as PTA-EMI). The DSPs and estimated phase are then combined with CPs in order to retrievesurface deformation parameters. The method was validated by two cases. The results show that the density of measuring points increased approximately 6–10 times compared with CPT-InSAR, and the quality of the interferometric phase significantly improved after phase optimization. It was demonstrated that the method is effective in increasing measuring point density and improving phase quality, which increases significantly the detectability of the low coherence region. Compared with the Distributed Scatterer InSAR (DS-InSAR) technique, ACDP-InSAR possesses faster processing speed at the cost of resolution loss, which is crucial for Earth surface movement monitoring at large spatial scales. Full article

Uncertainty and variability are inherent to pile design and consequently, there have been considerable researches in quantifying the reliability or probability of failure of structures. This paper aims at examining and comparing the applicability and adaptability of Minimax Probability Machine Regression (MPMR), Emotional Neural Network (ENN), Group Method of Data Handling (GMDH), and Adaptive Neuro-Fuzzy Inference System (ANFIS) in the reliability analysis of pile embedded in cohesionless soil and proposes an AI-based prediction method for bearing capacity of pile foundation. To ascertain the homogeneity and distribution of the datasets, Mann–Whitney U (M–W) and Anderson–Darling (AD) tests are carried out, respectively. The performance of the developed soft computing models is ascertained using various statistical parameters. A comparative study is implemented among reliability indices of the proposed models by employing First Order Second Moment Method (FOSM). The results of FOSM showed that the ANFIS approach outperformed other models for reliability analysis of bearing capacity of pile and ENN is the worst performing model. The value of R² for all the developed models is close to 1. The best RMSE value is achieved for the training phase of the ANFIS model (0 in training and 2.13 in testing) and the poorest for the ENN (2.03 in training and 31.24 in testing) model. Based on the experimental results of reliability indices, the developed ANFIS model is found to be very close to that computed from the original data. Full article

We compare the usefulness of nonparametric and parametric methods of diameter distribution modeling. The nonparametric method was represented by the new tool—kernel estimator of cumulative distribution function with bandwidths of 1 cm (KE1), 2 cm (KE2), and bandwidth obtained automatically (KEA). Johnson S_B (JSB) function was used for the parametric method. The data set consisted of 7867 measurements made at breast height in 360 sample plots established in 36 managed black alder (Alnus glutinosa (L.) Gaertn.) stands located in southeastern Poland. The model performance was assessed using leave-one-plot-out cross-validation and goodness-of-fit measures: mean error, root mean squared error, Kolmogorov–Smirnov, and Anderson–Darling statistics. The model based on KE1 revealed a good fit to diameters forming training sets. A poor fit was observed for KEA. Frequency of diameters forming test sets were properly fitted by KEA and poorly by KE1. KEA develops more general models that can be used for the approximation of independent data sets. Models based on KE1 adequately fit local irregularities in diameter frequency, which may be considered as an advantageous in some situations and as a drawback in other conditions due to the risk of model overfitting. The application of the JSB function to training sets resulted in the worst fit among the developed models. The performance of the parametric method used to test sets varied depending on the criterion used. Similar to KEA, the JSB function gives more general models that emphasize the rough shape of the approximated distribution. Site type and stand age do not affect the fit of nonparametric models. The JSB function show slightly better fit in older stands. The differences between the average values of Kolmogorov–Smirnov (KS), Anderson–Darling (AD), and root mean squared error (RMSE) statistics calculated for models developed with test sets were statistically nonsignificant, which indicates the similar usefulness of the investigated methods for modeling diameter distribution. Full article

Background and Objectives: The structural diversity of an urban forest affects ecosystem service provision, and can inform management, planning, as well as policy. Trunk diameter at breast height (DBH) is amongst the most common measures of tree structure due to its ease of measurement and strong relationships with other structural and non-structural urban forest characteristics. Materials and Methods: In this study, the DBH distributions of urban forests are summarised for 38 American cities with a combined population of over 30 million people and a range of geographic, climatic, and demographic conditions. The Anderson–Darling (AD) test was used to test the hypothesis that all DBH distributions came from a common population. Moreover, structural diversity was compared using the Shannon–Wiener index. Results: The AD test results failed to identify any statistically significant differences in DBH distributions. However, qualitatively, the DBH distributions have two primary forms, which have important functional, management, and planning implications. The vast majority of cities have an exponentially inverse-proportional distribution, such that the proportion of trees in each successively larger DBH class decreases exponentially. The Shannon–Wiener index indicates an uneven DBH distribution in the cities with an exponentially inverse-proportional diameter distribution; these cities are dominated by trees in the smallest diameter class. Potential explanations for a large proportion of trees in the smallest diameter classes include a large number of small, naturally regenerating trees; a preference for smaller trees in urban areas; or a recent increase in tree planting efforts. Conclusions: Despite no statistical differences in DBH distributions for the 38 study cities, the functional, management, and planning implications will differ considerably. Full article

In social and health sciences, many statistical procedures and estimation techniques rely on the underlying distributional assumption of normality of the data. Non-normality may lead to incorrect statistical inferences. This study evaluates the performance of selected normality tests within the stringency framework for skewed alternative space. The stringency concept allows us to rank the tests uniquely. The Bonett and Seier test (T_w) turns out to represent the best statistics for slightly skewed alternatives and the Anderson–Darling (AD); Chen–Shapiro (CS); Shapiro–Wilk (W); and Bispo, Marques, and Pestana (BCMR) statistics are the best choices for moderately skewed alternative distributions. The maximum loss of Jarque–Bera (JB) and its robust form (RJB), in terms of deviations from the power envelope, is greater than 50%, even for large sample sizes, which makes them less attractive in testing the hypothesis of normality against the moderately skewed alternatives. On balance, all selected normality tests except T_w and Daniele Coin’s COIN-test performed exceptionally well against the highly skewed alternative space. Full article

The aim of the present work was the modeling of the wastewater treatment plant operation work using Monte Carlo method and different random variables probability distributions modeling. The analysis includes the following pollutants indicators; BOD₅ (Biochemical Oxygen Demand), COD_Cr (Chemical Oxygen Demand), Total Suspended Solids (SS_t), Total Nitrogen (TN), and Total Phosphorus (TP). The Anderson–Darling (A–D) test was used for the assessment of theoretical and empirical distributions compatibility. The selection of the best-fitting statistical distributions was performed using peak-weighted root mean square (PWRMSE) parameter. Based on the performed calculations, it was stated that pollutants indicators in treated sewage were characterized by a significant variability. Obtained results indicate that the best-fitting pollutants indicators statistical distribution is Gauss Mixed Model (GMM) function. The results of the Monte Carlo simulation method confirmed that some problems related to the organic and biogenic pollutants reduction may be observed in the Wastewater Treatment Plant, in Jaworzno. Full article

The correct application of a statistical test is directly connected with information related to the distribution of data. Anderson–Darling is one alternative used to test if the distribution of experimental data follows a theoretical distribution. The conclusion of the Anderson–Darling test is usually drawn by comparing the obtained statistic with the available critical value, which did not give any weight to the same size. This study aimed to provide a formula for calculation of p-value associated with the Anderson–Darling statistic considering the size of the sample. A Monte Carlo simulation study was conducted for sample sizes starting from 2 to 61, and based on the obtained results, a formula able to give reliable probabilities associated to the Anderson–Darling statistic is reported. Full article

Floods are costly natural disasters that are projected to increase in severity and frequency into the future. Exceedances over a high threshold and analysis of their distributions, as determined through the Peak Over Threshold (POT) method and approximated by a Generalized Pareto Distribution (GPD), respectively, are widely used for flood frequency analysis. This study investigates the combined effects of threshold selection and GPD parameter estimation on the accuracy of flood quantile estimates, and develops a new, widely-applicable framework that significantly improves the accuracy of flood quantile estimations. First, the performance of several parameter estimators (i.e., Maximum Likelihood; Probability Weighted Moments; Maximum Goodness of Fit; Likelihood Moment; Modified Likelihood Moment; and Nonlinear Weighted Least Square Error) for the GPD was compared through Monte Carlo simulation. Then, a calibrated Soil and Water Assessment Tool (SWAT) model for the province of Alberta, Canada, was used to reproduce daily streamflow series for 47 watersheds distributed across the province, and the POT was applied to each. The Goodness of Fit for the resulting flood frequency models was measured by the upper tail Anderson-Darling (AD) test and the root-mean-square error (RMSE) and demonstrated improvements for more than one-third of stations by averages of 65% (AD) and 47% (RMSE), respectively. Full article

A constant false alarm rate (CFAR) target detector in non-homogenous backgrounds is proposed. Based on K-sample Anderson-Darling (AD) tests, the method re-arranges the reference cells by merging homogenous sub-blocks surrounding the cell under test (CUT) into a new reference window to estimate the background statistics. Double partition test, clutter edge refinement and outlier elimination are used as an anti-clutter processor in the proposed Modified AD (MAD) detector. Simulation results show that the proposed MAD test based detector outperforms cell-averaging (CA) CFAR, greatest of (GO) CFAR, smallest of (SO) CFAR, order-statistic (OS) CFAR, variability index (VI) CFAR, and CUT inclusive (CI) CFAR in most non-homogenous situations. Full article