First-order Moment Research Articles

Gearbox Fault Diagnosis Based on Adaptive Variational Mode Decomposition–Stationary Wavelet Transform and Ensemble Refined Composite Multiscale Fluctuation Dispersion Entropy

Existing gearbox fault diagnosis methods are prone to noise interference and cannot extract comprehensive fault signals, leading to misdiagnosis or missed diagnosis. This paper proposes a method for gearbox fault diagnosis based on adaptive variational mode decomposition–stationary wavelet transform (AVMD-SWT) and ensemble refined composite multiscale fluctuation dispersion entropy (ERCMFDE). Initially, the kurtosis coefficient and autocorrelation coefficient are presented, and the Intrinsic Mode Functions are denoised through the application of AVMD-SWT. Secondly, the coarse-grained processing method of composite multiscale fluctuation dispersion entropy is extended to encompass three additional approaches: first-order central moment, second-order central moment, and third-order central moment. This enables the comprehensive extraction of feature information from the time series, thereby facilitating the formation of an initial hybrid feature set. Subsequently, recursive feature elimination (RFE) is employed for feature selection. Ultimately, the outcomes of the faults diagnoses are derived through the utilization of a Support Vector Machine with a Sparrow Search Algorithm (SSA-SVM), with the actual faults data collection and analysis conducted on an experimental platform for gearbox fault diagnosis. The experiments demonstrate that the method can accurately identify gearbox faults and achieve a high diagnostic accuracy of 98.78%.

A Morley Type Triangular Finite Element with High Convergence for the Biharmonic Problem

In this work, we construct a theoretical framework to develop non C0 Morley type nonconforming high-convergence elements for biharmonic problems. For each element domain, P3 should be included in the space of shape functions. Besides the degrees of freedom of Morley elements, we add the integrals and first-order moments of the normal derivatives on edges. The choice of degrees of freedom and shape function space guarantees the possibility of improving the convergence order. As an application, we specifically construct a Morley type element on triangular meshes. Lastly, numerical experiments are carried out to verify the feasibility of the element.

Wind Power Curve Model Combining Smoothed Spline with First-Order Moments and Density-Adjusted Wind Speed Strategy

Given the variety of potential application scenarios, it is crucial to develop wind power curves that are more accurate, smoother, efficient, and applicable across a wider range of contexts. To this end, a wind power curve model combining smoothed spline with first-order moments (FOM) and density-adjusted wind speed (DAWS) strategy is proposed in this paper. First, the DAWS strategy is employed to consider the influence of meteorological factors on the wind power curve by adjusting wind speed. This strategy reduces the root mean square error (RMSE) by 5.81%-6.17% and the mean absolute error (MAE) by 5.84%-6.44% without adding complexity to the model. Secondly, FOM is proposed as a substitute for the original data during the modeling process. This approach reduces the number of operations on the similar data, resulting in a reduction of modeling time by 48.11%-99.89%. Furthermore, the impact on model accuracy is minimal. Finally, a the wind power curve model based on smooth spline is constructed, which exhibits superior smoothness, a broader range of generalizability, enhanced model accuracy, and reductions in RMSE by 5.67%-23.87% and MAE by 4.79%-22.35% in comparison to the control method.

Comprehensive analysis of soil electrical conductivity: an experimental and machine learning approach

Experimental test is conducted to find a relation between soil electrical conductivity with some soil properties. Five input parameters namely water content (w), dry density of soil (γd), degree of saturation (Sr), porosity (η) and voltage (V) are considered to compute electrical conductivity of soil (SEC). The effect of w, γd, Sr and η on SEC are analyzed. These datasets are used in soft computing technique to predict SEC. Five hybrid models namely ANN-GA, ANN-PSO, ANN-FA, ANN-GWO and ANN-MFO are used to predict SEC. To check the performance of these hybrid model, numerous statistical performance parameters (R2, a-10 index, VAF, LMI, RMSE, MAE, MAD and U95) are used. On the basis of these performance parameters, ANN-GA performs better (Due to higher value of R2, VAF, a-10 index and LMI and lower value of RMSE, MAE, MAD and U95) as compare to the other proposed model. The model's performance is also examined using rank analysis, regression curve, Williams plot, error matrix, objective function (OBJ) criterion, and Akaike information criterion (AIC). By applying all the above criteria, it has been observed that ANN-GA model outperforms than the other model to predict SEC. This was recognized to its maximum R2 = 0.9998 and the lowest RMSE = 0.0041 during the training phase, as well as R2 = 0.9975 and RMSE = 0.0112 during the testing phase. The model's reliability index (β) is calculated using the first-order second moment (FOSM) approach, and the result is compared to its actual condition. Additionally, a sensitivity analysis is carried out to ascertain the impact of each input parameter on the output (SEC).Based on the results, the hybrid model of ANN i.e., ANN-GA is potential to assist engineers to predict SEC in the design phase of high voltage buried power cables, ground modification techniques or in the field of agriculture.

Mean Absolute Deviation (About Mean) Metric for Kurtosis

In this paper, we introduce a MAD (about mean) alternative metric to classical kurtosis. Using the formula for mean absolute deviation, we identify two special points and construct the corresponding distributions with these reference points as their means. The proposed alternative is computed from mean absolute deviations for these distributions. These measures are bounded, require only the existence of first-order moments, and are easy to interpret. We illustrate the computation of these measures for several well-known distributions.

High-order oscillation-eliminating Hermite WENO method for hyperbolic conservation laws

This paper proposes high-order accurate, oscillation-eliminating, Hermite weighted essentially non-oscillatory (OE-HWENO) finite volume schemes for hyperbolic conservation laws, motivated by the oscillation-eliminating (OE) discontinuous Galerkin schemes recently proposed in [M. Peng, Z. Sun, and K. Wu, 2024 [30]]. The OE-HWENO schemes incorporate an OE procedure after each Runge–Kutta stage, by dampening the first-order moments of the HWENO solution to suppress spurious oscillations without any problem-dependent parameter. The OE procedure acts as a moment filter and is derived from the solution operator of a novel damping equation, which is exactly solved without any discretization. Thanks to this distinctive feature, the OE-HWENO method remains stable with a normal CFL number, even for strong shocks resulting in highly stiff damping terms. To ensure the essentially non-oscillatory property of the OE-HWENO method across problems with varying scales and wave speeds, we design a scale-invariant and evolution-invariant damping equation and propose a generic dimensionless transformation for HWENO reconstruction. The OE-HWENO method offers several notable advantages over existing HWENO methods. First, the OE procedure is highly efficient and straightforward to implement, requiring only simple multiplication of first-order moments by a damping factor. Furthermore, we rigorously prove that the OE procedure maintains the high-order accuracy and local compactness of the original HWENO schemes and demonstrate that it does not compromise the spectral properties via the approximate dispersion relation for smooth solutions. Notably, the proposed OE procedure is non-intrusive, enabling seamless integration as an independent module into existing HWENO codes. Finally, we rigorously analyze the bound-preserving (BP) property of the OE-HWENO method using the optimal cell average decomposition approach [S. Cui, S. Ding, and K. Wu, 2024 [8]], which relaxes the theoretical BP constraint for time step-size and reduces the number of decomposition points, thereby further enhancing efficiency. Extensive benchmarks validate the accuracy, efficiency, high resolution, and robustness of the OE-HWENO method.

2D and 3D numerical modelling for preliminary assessment of long-term deterioration in Irish glacial till geotechnical slopes

ABSTRACT Long-term geotechnical slope deterioration, influenced by weathering and meteorological factors, presents stability challenges to infrastructure. Wetting and drying cycles lead to pore water pressure variations, causing deformations and slope failure. Studies on glacial tills which investigate deterioration in geotechnical slopes focus on variables like pore water pressure, soil water retention, compaction, freeze–thaw cycles and cracking. This research conducts a preliminary assessment of an Irish glacial till-cut slope, establishing a data-driven foundation for long-term slope behaviour studies. Data analysis, geospatial modelling and numerical simulations were performed on a cut slope in Castleblayney (Ireland), considering short-term/undrained and long-term/drained conditions. FLAC/Slope and Scoops3D were used for 2D and 3D slope stability analyses, applying the First-Order Second Moment (FOSM) probabilistic approach to assess how minor soil property changes affect slope stability, including long-term deterioration scenarios. The study underscores the importance of precise instrument placement within Irish glacial till geotechnical cut slopes, particularly at the uppermost part where shallow and deep failures coincide under long-term and short-term scenarios. This informs strategic instrument positioning for accurate slope deterioration investigations. This research lays the groundwork for understanding mechanisms driving geotechnical slope deterioration and provides insights for future studies on geotechnical asset deterioration models in Irish glacial tills.

Hyperspectral Image Denoising Based on Deep and Total Variation Priors

To address the problems of noise interference and image blurring in hyperspectral imaging (HSI), this paper proposes a denoising method for HSI based on deep learning and a total variation (TV) prior. The method minimizes the first-order moment distance between the deep prior of a Fast and Flexible Denoising Convolutional Neural Network (FFDNet) and the Enhanced 3D TV (E3DTV) prior, obtaining dual priors that complement and reinforce each other’s advantages. Specifically, the original HSI is initially processed with a random binary sparse observation matrix to achieve a sparse representation. Subsequently, the plug-and-play (PnP) algorithm is employed within the framework of generalized alternating projection (GAP) to denoise the sparsely represented HSI. Experimental results demonstrate that, compared to existing methods, this method shows significant advantages in both quantitative and qualitative assessments, effectively enhancing the quality of HSIs.

Universally Robust Quantum Control.

We study the robustness of the evolution of a quantum system against small uncontrolled variations in parameters in the Hamiltonian. We show that the fidelity susceptibility, which quantifies the perturbative error to leading order, can be expressed in superoperator form and use this to derive control pulses that are robust to any class of systematic unknown errors. The proposed optimal control protocol is equivalent to searching for a sequence of unitaries that mimics the first-order moments of the Haar distribution, i.e., it constitutes a 1-design. We highlight the power of our results for error-resistant single- and two-qubit gates.

Infall Motions in the Hot Core Associated with the Hypercompact H ii Region G345.0061+01.794 B

We report high angular resolution observations, made with the Atacama Large Millimeter Array in band 6, of high excitation molecular lines of CH3CN and SO2 and of the H29α radio recombination line toward the G345.0061+01.794 B HC H ii region in order to investigate the physical and kinematical characteristics of its surroundings. Emission was detected in all observed components of the J = 14 →13 rotational ladder of CH3CN and in the 304,26–303,27, and 324,28–323,29 lines of SO2. The peak of the velocity-integrated molecular emission is located ∼0.″4 northwest of the peak of the continuum emission. The first-order moment images and channel maps show a velocity gradient of 1.1 km s−1 arcsec−1 across the source and a distinctive spot of blueshifted emission toward the peak of the zero-order moment. The rotational temperature is found to decrease from 252±24 K at the peak position to 166±16 K at its edge, indicating that our molecular observations are probing a hot molecular core that is internally excited. The emission in the H29α line arises from a region of 0.″65 in size, where its peak coincides with that of the dust continuum. We model the kinematical characteristics of the “central blue spot” feature as due to infalling motions, suggesting a central mass of 172.8±8.8 M ⊙. Our observations indicate that this HC H ii region is surrounded by a compact structure of hot molecular gas, which is rotating and infalling toward a central mass, that is most likely confining the ionized region. The observed scenario is reminiscent of a “butterfly pattern” with an approximately edge-on torus and ionized gas roughly parallel to its rotation axis.

Evaluating seawater intrusion forecast uncertainty under climate change in the Pajaro Valley, California

Climate change and climate variability impacts such as rising sea levels have the potential to exacerbate seawater intrusion and the strain on coastal freshwater resources in already stressed groundwater basins such as those in the Pajaro Valley groundwater basin, California. Regional hydrologic models are often coupled with climate projections to forecast future hydrologic conditions and inform adaptive resources management strategies. However, there is high uncertainty in the future projections of water resources due to uncertainties from downscaling global general circulation models (GCMs) to local scale climate change projections, future land use changes, and the inherent uncertainty of developed hydrologic models. Future climate projections and the magnitude of their influence on modeled hydrologic drivers are highly variable. Therefore, to develop a forecast model, an ensemble of different projections can be used to capture a wider range of basin responses and the associated uncertainties in the modeled forecasts. Understanding the reliability and uncertainty of forecasts is important for developing climate adaptation strategies such as developing protective thresholds, particularly at the basin scale where the impacts are felt, and adaptation is implemented. To demonstrate this, an uncertainty analysis of groundwater level and seawater intrusion forecasts for the Pajaro Valley groundwater basin was performed using an ensemble of three future climate projections with the Pajaro Valley Integrated Hydrologic Model (PVIHM) and the first-order second moment (FOSM) method. FOSM uncertainty analysis of hydrologic forecasts across a multi-GCM climate ensemble provides an upper and lower bound of potential impacts of climate change on sustainability targets related to mitigating seawater intrusion. The groundwater level forecasts’ narrow range of variability can help policymakers in adaptation planning by constraining possible outcomes to a focused range for risk-management decisions. However, less than one-third of groundwater level forecasts met the current protection thresholds to prevent chronic lowering of groundwater. Therefore, sustainability targets may need to be reassessed. Relative to groundwater level changes, the seawater intrusion forecasts had larger uncertainty due to the GCM climate projections and the simulated hydrologic response that were compounded by the propagation of scaling and bias from the GCMs and model simplifications in simulating the coastal boundary.

Investigation and assessment of production- and dissipation-limited DDES methods for rocket combustion chamber simulations

This paper compares two different delayed detached-eddy simulation (DDES) techniques, namely iDDES and l2-ω-DDES. Their performance is investigated with and without combustion. While iDDES limits the dissipation term of the turbulent kinetic energy equation, l2-ω-DDES confines its production term. In this way, both models achieve that resolved turbulence is enhanced in regions of separated flow. On the other hand, the models show significant differences. In a first step this is investigated using three non-reactive test cases. While here the first-order moments are in a fairly good agreement, the second-order moments exhibit slight differences. Despite the similarities in first- and second-order moments, the instantaneous flow fields differ considerably with the iDDES displaying finer vortex structures. This is caused by different levels of eddy viscosity. These disparities are even more pronounced in case of a laboratory-scale rocket combustion chamber, where strong differences in quantities as the wall heat flux are observed. This clearly demonstrates an impact on the combustion process.

Why Does Cross-Sectional Analyst Coverage Incorporate Market-Wide Information?

This paper shows that the empirical distribution of cross-sectional analyst coverage in China's stock markets follows an exponential law in a given month from 2011 to 2020. The findings hold in both the emerging (Shanghai) and the developed market (Hong Kong). Moreover, the unique distribution parameter (i.e., mean) is directly related to the amount of market-wide information. Average analyst coverage exhibits a significant negative predictive power for stock-market uncertainty, highlighting the role of security analysts in diminishing the total uncertainty. The exponential law can be derived from the maximum entropy principle (MEP). When analysts, who are constrained by average ability in generating information (i.e., the first-order moment), strive to maximize the amount of market-wide information, this objective yields the exponential distribution. Contrary to the conventional wisdom that security analysts specialize in the generation of firm-specific information, empirical findings suggest that analysts primarily produce market-wide information for 25 countries. Nevertheless, it remains unclear why cross-sectional analyst coverage reflects market-wide information, this paper provides an entropy-based explanation.

Theory of the Second Order for Braced and Bracing Columns

When analyzing slender columns, the second-generation Eurocode FprEN [2] recommends the calculation of the bending moment envelope, which consists of both first-order and second-order moments. This paper presents the aforementioned calculation method for both braced and bracing columns, utilizing a comprehensive “general” nonlinear approach.

Robust network of globally coupled heterogeneous limit cycle oscillators due to inertia

We investigate the phase transition from macroscopic oscillatory state to stable homogeneous steady state in a heterogeneous network of globally coupled Stuart–Landau limit cycle oscillators in the presence of the inertial effect. The phase transition, known as aging transition, onsets above a critical fraction of inactive constituents in the mixed population of active and inactive units. We show that even a feeble increase in the inertial strength increases the critical fraction of inactive units significantly for the onset of the phase transition to the macroscopic steady state thereby resulting in a more robust network, in general. In contrast, a large coupling strength, in the case of a homogeneous network, facilitates the manifestation of the phase transition even for a small fraction of inactive oscillators leading to a more fragile network. Nevertheless, a large coupling strength, in the case of a heterogeneous network, increases the resilience of the network by facilitating the phase transition at a large fraction of inactive oscillators. Furthermore, a larger standard deviation of the natural frequencies always leads to a more fragile network. We derive the macroscopic evolution equations for the order parameters and the stability curve using the first-order moment expansion around the mean-field. In addition, we also deduce the critical fraction of inactive units and the critical inertial strength analytically that matches with the simulation results. Interestingly, we find that the critical inertial strength is reciprocally related to the square of the mean frequency of the network.

Barrier Lyapunov function–based command-filtered adaptive fuzzy control of random quadrotor systems

This paper is devoted to adaptive trajectory tracking of quadrotor systems with full-state constraints and random disturbances. The command-filtering technology combined with error compensation mechanisms is proposed to deal with the “explosion of complexity” problem in traditional backstepping design and reduction of the filtering errors. The Barrier Lyapunov functions (BLFs) are constructed to ensure that all system states do not violate the boundary of its constraints. The command-filtered adaptive fuzzy controller is designed such that the state constraints are not breached almost surely, all signals in the closed-loop system are bounded almost surely, and the first-order moment of the tracking error converges to an arbitrarily small neighborhood of zero by parameters tuning. Finally, the effectiveness of the proposed control method is illustrated by simulation results.

Evolutionary analysis of rainstorm momentum and non-stationary variating patterns in response to climatic changes across diverse terrains

This study aims to analyze time-series measurements encompassing rainstorm events with over a century of datasets to identify rainstorm evolution and dimensional transitions in non-stationarity. Rainstorm events are identified using partial duration series (PDS) to extract changes in rainstorm characteristics, namely maximum intensity (MAXI), duration (D), total rainfall (TR), and average rainfall intensity (ARI), in response to climate change. Ensemble empirical mode decomposition is used for trend filtering and non-stationary identification to explore spatiotemporal insight patterns. Trend models for the first–second-order moments of rainstorm characteristics are used to formulate the identified mean–variance trends using combined multi-dimensional linear-parabolic regression. Best-fitting combinations of various distributions (probability density functions) and trend models for multiple characteristic series are identified based on the Akaike information criterion. We analyze the dimensional transition in rainfall non-stationarity based on sensitivity analysis using PDS to determine its natural geophysical causes. The integrated methodology was applied to the data retrieved from nine weather stations in Taiwan. Our findings reveal rainstorm characteristics of “short D but high rainfall intensity” or “lower MAXI but high TR” across multiple stations. The parabolic trend of the first-order moment (i.e., mean) of ARI, D, and TR appears at the endpoint of the mountain ranges. Areas receiving monsoons and those on the windward plain show a rising parabolic trend in the first- and second-order moments (i.e., mean–variance) characterizing MAXI, implying that the occurrence frequency and magnitude of extreme MAXI increases. Non-stationary transitions in MAXI appear for mountain ranges exposed to the monsoon co-movement effect on both windward and leeward sides. Stations in the plains and rift valleys show upgraded and downgraded transitions in the non-stationary dimensions for D, respectively.

Remote State Estimation With Posterior-Based Stochastic Event-Triggered Schedule

This paper aims to study the state estimation problem under the stochastic event-triggered (SET) schedule. A posterior-based SET mechanism is proposed, which determines whether to transmit data by the effect of the measurement on the posterior estimate. Since this SET mechanism considers the whole posterior probability density function, it has better information screening capability and utilization than the existing SET mechanisms that only consider the first-order moment information of measurement and prior estimate. Then, based on the proposed SET mechanism, the corresponding exact minimum mean square error estimator is derived by Bayes rule. Moreover, the prediction error covariance of the estimator is proved to be bounded under moderate conditions. Meanwhile, the upper and lower bounds on the average communication rate are also analyzed. Finally, two different systems are employed to show the effectiveness and advantages of the proposed methods.

Variational calculus in hybrid turbulence transport models with passive scalar

Non-zonal methods of hybrid Reynolds Averaged Navier–Stokes (RANS) equations-Large Eddy Simulation (LES) with subfilter transport equations enable to simulate turbulent flows out of spectral equilibrium on relatively coarse grid resolution. They can operate from RANS to LES depending on a control parameter linked to the grid step size. Variational analysis gives a useful framework to specify the functional dependence of this parameter to the grid size. This is the case for the partially integrated transport modelling method originally established in spectral space for homogeneous turbulence. The partitioning control function then monitors the ratio of the subfilter part to the total turbulent energy and the same process is developed in the present work for the thermal or transported scalar variance as well. So, we demonstrate here that this control function mechanism can be derived by variational calculus from a mathematical physics formalism developed both for first-order and second-order moment closures. We show that the result is entirely consistent with the spectral model derivation made in previous papers and that this approach can be transposed to almost any subfilter transport model developed in hybrid RANS-LES methodology in full generality. As a result, it will be evidenced also that resolved turbulent diffusion terms play a significant role in the acting mechanisms of turbulence and cannot be therefore neglected, even if these terms do not explicitly appear in LES subfilter closure because they are computed by the simulation itself and not modelled by the subfilter model. In addition, numerical simulations have been performed for illustrating the theoretical results of the variational analysis.

A mathematica code for evaluating lateral-torsional buckling of tapered cantilevers

Lateral-torsional buckling (LTB) is the primary failure mode where slender cantilevers experience nonuniform twisting and buckling about their weak axes. The studies focused on the elastic LTB load of cantilevers are limited, most of which are numerical since the LTB failure mode of cantilevers is much more complicated than those of simply supported beams. Furthermore, there are only a few studies of the LTB of tapered I-section cantilevers, which are aesthetic and structurally efficient. Structural designers tend to evaluate the LTB of tapered cantilevers using finite element simulations, but it requires specific experience and computational effort. The present study intends to close the gap in the literature related to tapered cantilevers, establish an analytical procedure providing rapid treatment, and develop a code for the solution. The analytical model considers first-order moment gradient through the cantilever, load position along the cross-section, mono-symmetry property of I-section, tapering of web, flange, or simultaneously web and flange to assess LTB of tapered cantilevers. The developed Mathematica code based on the analytical model has been verified with 3D finite element analysis, and it is demonstrated that the proposed code can be safely used to assess the LTB of tapered cantilevers.