Legendre Orthogonal Polynomials Research Articles

On the resonance frequency of the irregular shaped visco-acoustic Helmholtz cavity problem

In this paper we develop a closed-form mathematical solution for the resonance frequency of the axisymmetric irregular shaped visco-acoustic Helmholtz cavity problem. The solution is based on a conformal mapping that transforms the governing visco-acoustic equations of motion for the irregular cavity geometry into a new domain described by a set of orthogonal curvilinear coordinates. These orthogonal curvilinear coordinates have an important characteristic relative to the transformation of the physical boundary: the mapped domain is constructed such that the locus of all points for the length-wise profile of the physical boundary coincides with a constant value for a (quasi radial) coordinate in the new mapped domain. In these orthogonal curvilinear coordinates we obtain an analytical solution for the visco-acoustic equations of motion and exactly satisfy the no-slip fluid boundary conditions over the irregular shaped cavity walls by matching the coefficients of an orthogonal Legendre polynomial series representation for the non-uniform velocity on the cavity walls. The mathematical solution is an approximation to the extent that the scale factors chosen for the mapping consist of strictly the mutual-coupling terms of the true scale factors. Thus we analyze some results to understand the correlation of the analytical solution frequency response spectra with numerical finite element analyses of the idealized boundary conditions with various irregular shaped cavity geometries. The results for fundamental resonance frequency were found to exhibit good correlation with the results of finite element analyses over a significant range of fluid properties with different irregular cavity geometries. As the primary motivation for the derivation stems from the lack of a rapid yet accurate alternative to computationally intensive MultiPhysics FEA in the formulation of acoustic trendlines for sensor development, the solution’s acoustic impedance was applied as dispersive loading in a simple lumped parameter model of a fluid identification sensor for comparison. The resulting acoustic trendlines of the reduced (5 DOF) model were found to exhibit good correlation with the results of the MultiPhysics FEA (>105 DOF). Thus the solution was found to enable a closed-form analytical method for rapid construction of parametric studies in the practical design of fluid analysis sensors based on complex resonant cavity geometries.

Prolonged lymphopenia and prognoses among inpatients with different respiratory virus infections: A retrospective cohort study

BackgroundLymphopenia is common in respiratory viral infection. However, no studies elucidated the impact of prolonged lymphopenia on worse outcome in the way of quantitative risk. MethodsAdult patients with laboratory-confirmed respiratory virus infection (influenza, SARS-CoV-2, and other viruses) between January 1st, 2016, and February 1st, 2023 were enrolled in this retrospective cohort study. Serial data of laboratory examination during hospitalization were acquired. The primary outcome was in-hospital all-cause death, and all information was obtained from the electronic medical records system. Legendre orthogonal polynomials (LOP), restricted cubic splines, and multivariable logistic regression were performed. ResultsFinally, 2388 inpatients were involved in this study, including 436 patients with influenza, 1397 with SARS-CoV-2, and 319 with other respiratory virus infections. After being adjusted for age, corticosteroids, chronic kidney disease, chronic respiratory disease, cardiovascular disease, lymphopenia on admission and length of hospital stay, prolonged lymphopenia was significantly associated with death in influenza (OR 7.20, 95 % CI 2.27–22.77, p = 0. 0008 for lasting for 3–7 days; OR 17.80, 95 % CI 5.21–60.82, p < 0.0001 for lasting for more than 7 days) and SARS-CoV-2 (OR 3.07, 95 % CI 1.89–5.01, p < 0.0001 for lasting for 3–7 days; OR 6.28, 95 % CI 3.53–11.18, p < 0.0001 for lasting for more than 7 days), compared with a transient lymphopenia of 1–2 days, while no significant association was found in other respiratory viruses. Prolonged lymphopenia was also associated with multi-organ damage in influenza and SARS-CoV-2 infections. ConclusionsProlonged lymphopenia was significantly associated with worse clinical prognoses in influenza and SARS-CoV-2 infections, but not in other respiratory virus infections.

Approximation of the Profile of Gas Turbine Engine Blades

Introduction. Increasing the durability of gas turbine engine (GTE) blades is achieved through the use of special protective coatings on their surface. For the development of such coatings, the basic source information is the geometric profile of the blade section. To transfer a given blade cross-section profile to the appropriate CAD/CAM system or engineering analysis package, parametric modeling methods are used to automate this operation. However, the known approaches to creating a parametric model of a blade profile are not without a number of disadvantages, and a generally accepted method for creating it does not currently exist. The research was aimed at creating a technique for approximating the profile of gas turbine engine blades, convenient for use in the subsequent analysis of the operating conditions of special coatings on the surface of the blades.Materials and Methods. When constructing parametric models of the profile of gas turbine engine blades, a method based on the orthogonal Legendre polynomials was used. This made it possible to provide high accuracy of approximation and construction of a continuous mapping for the parameters of the blade profile approximation. A Python application was created for automated processing of source profiles. It provided the calculation of the coefficients of approximating polynomials for the contour lines of the blade, visualization of the calculation results, and creation of a dxf file based on the points of approximating functions to transfer it to the CAD system. Next, geometric models of blades were used to solve the problem of a stationary aerodynamic flow around a blade. The results of solving this problem were used to study the effect of the blade profile on its cooling in an aerodynamic flow.Results. As an example, three options of blade profiles belonging to different types of GTE were considered. It was shown that for all three studied profiles, the proposed technique provided obtaining parametric models that maintained high accuracy in constructing approximating lines, which was confirmed by the values of the determination coefficients close to unity. To illustrate the possibility of using the obtained models, examples of solving the gas dynamic problem with a potential flow around a blade in a stationary aerodynamic flow were given. The distributions of pressure and temperature on the surface of the blade were calculated using the finite element method.Discussion and Conclusion. The calculation results show that the proposed technique of approximating the profile of the GTE blade, based on the use of orthogonal polynomials, is a convenient tool to automate the creation of a geometric model of the blade and compare different types and profiles of blades, solving the corresponding gas dynamic problems. At the same time, for a given blade profile and GTE operating conditions, it is possible to obtain the distribution of temperatures and forces acting on the surface of the blade, which is required for predicting the durability of special coatings.

Modelling the lactation curve in Alpine × Beetal crossbred dairy goats using random regression models fitted with Legendre polynomial and B-spline functions.

The current study sought to genetically assess the lactation curve of Alpine × Beetal crossbred goats through the application of random regression models (RRM). The objective was to estimate genetic parameters of the first lactation test-day milk yield (TDMY) for devising a practical breeding strategy within the nucleus breeding programme. In order to model variations in lactation curves, 25,998 TDMY records were used in this study. For the purpose of estimating genetic parameters, orthogonal Legendre polynomials (LEG) and B-splines (BS) were examined in order to generate suitable and parsimonious models. A single-trait RRM technique was used for the analysis. The average first lactation TDMY was 1.22 ± 0.03 kg and peak yield (1.35 ± 0.02 kg) was achieved around the 7th test day (TD). The present investigation has demonstrated the superiority of the B-spline model for the genetic evaluation of Alpine × Beetal dairy goats. The optimal random regression model was identified as a quadratic B-spline function, characterized by six knots to represent the central trend. This model effectively captured the patterns of additive genetic influences, animal-specific permanent environmental effects (c2 ) and 22 distinct classes of (heterogeneous) residual variance. Additive variances and heritability (h2 ) estimates were lower in the early lactation, however, moderate across most parts of the lactation studied, ranging from 0.09 ± 0.04 to 0.33 ± 0.06. The moderate heritability estimates indicate the potential for selection using favourable combinations of test days throughout the lactation period. It was also observed that a high proportion of total variance was attributed to the animal's permanent environment. Positive genetic correlations were observed for adjacent TDMY values, while the correlations became less pronounced for more distant TDMY values. Considering better fitting of the lactation curve, the use of B-spline functions for genetic evaluation of Alpine × Beetal goats using RRM is recommended.

Спектральные методы полиномиальной интерполяции и аппроксимации

Classical problem of interpolation and approximation of functions with polynomials is considered here as a special case of spectral representation of functions. We developed this approach earlier for Legendre and Chebyshev orthogonal polynomials. Here we use Newton's fundamental polynomials as basis functions. We demonstrate that the spectral approach has computational advantages over the divided differences method. In a number of problems, Newton and Hermite interpolations are indistinguishable in our approach and computed by the same formulas. Also, computational algorithms that we constructed earlier with the use of orthogonal polynomials are adapted without modifications for use of Newton and Hermite polynomials.

PES and transport properties of the He⋯HBr complex from kinetic theory and molecular dynamics simulations.

The ab initio intermolecular potential of the He⋯HBr van der Waals (vdW) complex was calculated at the CCSD(T)/a5zBF level of theory and expanded in terms of the orthogonal Legendre polynomials. The PES then was implemented to calculate the interaction viscosity (η12) and diffusion (D12) coefficients through classical Mason-Monchick approximation (MMA), quantum mechanical close-coupling (CC), and molecular dynamics (MD) simulations. Energy-dependent Senftleben-Beenakker (SB) cross-sections were calculated using rotationally averaged cross-sections, and Boltzmann averaging was used to reveal the temperature dependence of the SB cross-sections over the temperature range of T = 50-1000 K. The calculated transport properties from MMA are in close agreement with the CC results, especially for temperatures lower than T = 900 K. The ab initio potential data then were used to derive LJ (12,6) and Vashishta MD force fields, and the equilibrium MD simulation methods were implemented to extract η12 and D12 coefficients using Einstein formulas. It was found that the Vashishta 3-body interaction potential model shows better accuracy than the LJ (12,6) model in MD simulations of D12. For η12, however, both MD potential models are successful, and an average absolute deviation of lower than 1% was obtained when compared to the quantum mechanical CC method.

FREE VIBRATION MODELING IN A FUNCTIONALLY GRADED HOLLOW CYLINDER USING THE LEGENDRE POLYNOMIAL APPROACH

Introduction: The building industry is under increasing pressure to maximize performance while reducing the costs and the environmental impact. To solve this problem, a new type of materials, i.e., functionally graded materials (FGMs), are proposed. These materials have the advantage of being able to withstand harsh environments without losing their properties. Purpose of the study: The paper aims to further extend the understanding of the propagation modes and characteristics of guided waves in FGM cylinders with infinite lengths. In the course of the study, we analyzed a cylindrical shell composed of three annular layers, each separated by a gradient layer across the wall thickness. A modeling tool based on the Legendre orthogonal polynomial method is proposed in the paper. Methods: The method applied results in an eigenvalue/eigenvector problem. The boundary conditions are integrated into the constitutive equations of guided wave propagation. The phase velocity and normalized frequency dispersion curves are calculated. Besides, the displacement distributions and stress field profiles for a functionally graded cylinder with various graded indices in both modes (axisymmetric and symmetric) are calculated and discussed. The results show a constant fluctuation of effective FGM material. Results: It was found that the phase velocity curves of the same mode decrease as the exponents of the power law increase. In addition, the boundary conditions have a greater impact on the normal stresses. The accuracy and effectiveness of the improved orthogonal polynomial method are demonstrated through a comparison of the exact solution obtained by an analytical-numerical method and our numerical results.

Genomic analysis of feed efficiency traits in beef cattle using random regression models.

Feed efficiency plays a major role in the overall profitability and sustainability of the beef cattle industry, as it is directly related to the reduction of the animal demand for input and methane emissions. Traditionally, the average daily feed intake and weight gain are used to calculate feed efficiency traits. However, feed efficiency traits can be analysed longitudinally using random regression models (RRMs), which allow fitting random genetic and environmental effects over time by considering the covariance pattern between the daily records. Therefore, the objectives of this study were to: (1) propose genomic evaluations for dry matter intake (DMI), body weight gain (BWG), residual feed intake (RFI) and residual weight gain (RWG) data collected during an 84-day feedlot test period via RRMs; (2) compare the goodness-of-fit of RRM using Legendre polynomials (LP) and B-spline functions; (3) evaluate the genetic parameters behaviour for feed efficiency traits and their implication for new selection strategies. The datasets were provided by the EMBRAPA-GENEPLUS beef cattle breeding program and included 2920 records for DMI, 2696 records for BWG and 4675 genotyped animals. Genetic parameters and genomic breeding values (GEBVs) were estimated by RRMs under ssGBLUP for Nellore cattle using orthogonal LPs and B-spline. Models were compared based on the deviance information criterion (DIC). The ranking of the average GEBV of each test week and the overall GEBV average were compared by the percentage of individuals in common and the Spearman correlation coefficient (top 1%, 5%, 10% and 100%). The highest goodness-of-fit was obtained with linear B-Spline function considering heterogeneous residual variance. The heritability estimates across the test period for DMI, BWG, RFI and RWG ranged from 0.06 to 0.21, 0.11 to 0.30, 0.03 to 0.26 and 0.07 to 0.27, respectively. DMI and RFI presented within-trait genetic correlations ranging from low to high magnitude across different performance test-day. In contrast, BWG and RWG presented negative genetic correlations between the first 3 weeks and the other days of performance tests. DMI and RFI presented a high-ranking similarity between the GEBV average of week eight and the overall GEBV average, with Spearman correlations and percentages of individuals selected in common ranging from 0.95 to 1.00 and 93 to 100, respectively. Week 11 presented the highest Spearman correlations (ranging from 0.94 to 0.98) and percentages of individuals selected in common (ranging from 85 to 94) of BWG and RWG with the average GEBV of the entire period of the test. In conclusion, the RRM using linear B-splines is a feasible alternative for the genomic evaluation of feed efficiency. Heritability estimates of DMI, RFI, BWG and RWG indicate enough additive genetic variance to achieve a moderate response to selection. A new selection strategy can be adopted by reducing the performance test to 56 days for DMI and RFI selection and 77 days for BWG and RWG selection.

Traveling Wave Characteristics of a Rotating Functionally Graded Laminated Cylindrical Shell with General Boundary Conditions

The traveling wave modes of rotating functionally graded laminated cylindrical shells with general boundary conditions are studied by using different admissible displacement functions. Firstly, the effective temperature-dependent material properties of the functionally graded materials (FGMs) are described by the Voigt model and the Sigmoid-type volume fraction. Subsequently, considering Love’s thin shell theory, the motion equations of the FGMs shell subjected to the Coriolis force, the centrifugal inertial force, the hoop initial tension and the internal thermal force are derived. Thereafter, the displacement functions are expanded by six different sets of admissible displacement functions. The Rayleigh–Ritz method is utilized to derive the eigenvalue equations of the rotating FGMs laminated shells. In the end, the convergence rate and computational efficiency of the six polynomial functions are compared and parameter study is carried out. Results indicate that the Legendre orthogonal polynomials (LOP) are the best ones in terms of convergence rate and computational efficiency for predicting the traveling wave modes. The patterns of [Formula: see text] expressed by Sigmoid law are more sensitive to the modal frequency of the shell than the ceramic volume fraction exponents. The stiffness of the axial springs plays a more significant role in the traveling wave modes than the stiffness of other springs.

A New Approach to the Evaluation of the Lightning Horizontal Electric Field Over a Lossy Ground Based on the Time-Domain Cooray–Rubinstein Formula Fitted by Orthogonal Polynomials

The calculation of lightning return stroke electromagnetic field is the basis for evaluating transmission line lightning-induced voltages. The Cooray–Rubinstein formula in the time domain is widely used to evaluate the horizontal electric field of lightning return stroke on a lossy ground, but the evaluation of the formula requires high computation cost. Therefore, this study presents a new approach to evaluate the Cooray–Rubinstein formula based on orthogonal polynomial fitting. This method converts the complex convolution in the Cooray–Rubinstein formula into the sum of multiple simple convolutions by using an effective truncation scheme of Legendre orthogonal polynomial and the second Chebyshev orthogonal polynomial. The objective is to realize an efficient evaluation method to the horizontal electric field of the lightning return stroke. On the premise of ensuring the calculation accuracy, the effectiveness and correctness of the proposed method are verified through numerical experiments. Moreover, the application of the time-domain Cooray–Rubinstein formula based on two orthogonal polynomial fitting methods is discussed. Compared with the existing numerical methods for solving the Cooray–Rubinstein formula, the proposed method is easy to implement and efficient, which provides a new idea for evaluating the horizontal electric field of lightning return stroke above the lossy ground in the time domain.

A semi-analytical method for vibro-acoustic characteristics of orthogonal stiffened laminated cylindrical shells

This paper presents a semi-analytical model for vibro-acoustic characteristics of submerged orthogonal stiffened laminated cylindrical shells strengthened with orthogonal stiffeners. The first-order shear deformation theory (FSDT) combined with the Lekhnitsky smeared stiffener technique is adopted to describe the displacement field, and the spectral boundary element method is utilized to model the sound field. For modeling of a complex stiffened shell, the shell is divided into several main structures with the additional stiffness and mass of the smeared stiffeners. Then, the main structure is separated into sub-segments that match the boundary elements to ensure high accuracy of acoustic calculations. The continuous boundary conditions between sub-segments are simulated by using the artificial spring technique. The Fourier series and Legendre orthogonal polynomials are selected as admissible functions to describe the displacement field and the sound field. The vibration governing equations and Helmholtz integral equation are coupled with each other and solved simultaneously. High accuracy is demonstrated by comparing the results of the developed model with the literature. In numerical investigations, the influences of different external fluids, layup schemes, quantities and shapes of stiffeners (width and height) on vibro-acoustic characteristics of orthogonal stiffened laminated cylindrical shells (OSLCS) are investigated.

Dynamic Performance of Hygrothermal Mechanically Preloaded Variable-Stiffness Composite Fairing Structures

Since the introduction of variable-stiffness composites, the design philosophy for high-performance lightweight composite structures has broadened greatly. Indeed, variable-stiffness composites have been shown to increase buckling performance and dynamic stability, as well as to modify the dynamic response by tailoring stiffness distributions. Thus, efficient linear analysis tools play a significant role in the early design of variable-stiffness structures, allowing designers to identify many viable solutions when considering preloaded dynamically excited aerospace components. To address this need, a Ritz-based method for eigenfrequency and dynamic instability analysis of hygrothermal and mechanically prestressed variable-stiffness laminated doubly curved payload fairing structures is presented. Flexibility in modeling and design is achieved using Sanders–Koiter-based shell kinematics that allow general orthogonal surfaces to be modeled without further assumptions on the shallowness or on the thinness of the structure. The efficiency of the proposed Ritz method is enabled by using Legendre orthogonal polynomials as displacement trial functions. By comparing the present approach with finite element solutions for variable-curvature, variable-angle tow fairing shell geometries, excellent accuracy is shown, accompanied by an order-of-magnitude reduction in variables by the present method. Original solutions are presented comparing the dynamic behavior of prestressed constant and variable-stiffness composite shell structures, showcasing the viability of the variable-stiffness concept to significantly increase the structural performance of critical doubly curved variable-curvature components such as launch vehicle payload fairings.

Method of Particular Solutions for Second-Order Differential Equation with Variable Coefficients via Orthogonal Polynomials

In this paper, with classic Legendre polynomials, a method of particular solutions (MPS, for short) is proposed to solve a kind of second-order differential equations with a variable coefficient on a unit interval. The particular solutions, satisfying the natural Dirichlet boundary conditions, are constructed with orthogonal Legendre polynomials for the variable coefficient case. Meanwhile, we investigate the a-priori error estimates of the MPS approximations. Two a-priori error estimations in H 1 - and L ∞ -norms are shown to depict the convergence order of numerical approximations, respectively. Some numerical examples and convergence rates are provided to validate the merits of our proposed meshless method.

Inverse of initial stress in carbon fiber reinforced polymer laminates using lamb waves and deep neural network

The prediction of the initial stress in composites is essential for the non-destructive testing (NDT) and structural health monitoring (SHM) of carbon fibre reinforced polymer (CFRP). This paper examines the potential of Lamb waves in the inverse of initial stress by calculating the influence of initial stress on the dispersion characteristics of Lamb waves propagating in multilayered CFRP laminates. By introducing the mechanics of incremental deformation into the linear three-dimensional elasticity theory, the Legendre orthogonal polynomial expansion (LOPE) method is used to mathematically model the Lamb wave propagating in multilayered CFRP laminates subjected to horizontal and vertical homogeneous initial stresses. Then, a three-hidden-layers Feed Forward Deep Neural Network (DNN) with Back Propagation (BP) algorithm is constructed to invert the magnitude and direction of the initial stresses. The input features are the phase velocities of fundamental Lamb wave A0 mode at five different frequencies. Both training and testing samples are obtained by LOPE forward calculation. An ablation experiment is presented to compare the two different activation functions. Finally, the accuracy of the inverse is verified by comparing with the available outcomes of LOPE forward calculation.

Nonparametric estimation of copulas and copula densities by orthogonal projections

A nonparametric copula density estimator based on Legendre orthogonal polynomials is proposed. A nonparametric copula estimator is then deduced by integration. Their asymptotic properties are reviewed. Both estimators are based on a sequence of moments that characterize the copulas and that we shall call the copula coefficients. A data-driven method is proposed to select the number of copula coefficients to use. An intensive simulation study shows the good performance of both copulas and copula densities estimators compared to a large panel of competitors. Two real datasets illustrate this approach.

Discrete Event-Triggered Fault-Tolerant Control of Underwater Vehicles Based on Takagi–Sugeno Fuzzy Model

This article investigates the fault estimation and fault-tolerant control problem for underwater vehicles with the Takagi–Sugeno (T–S) fuzzy model. In order to deal with the disturbance of complex ocean environment, a stable fuzzy controller for underwater vehicle is proposed to realize efficient operation, which is on the basis of T–S fuzzy model with pitch angle membership function. Meanwhile, to reduce the waste of communication resources, a novel discrete event-triggered control scheme is proposed to use multiple historical sampled data to determine the next release instant. The discrete event-triggered fault-tolerant controller compensates for the influence of system faults by using state estimators and fault estimators. It is noted that the canonical Bessel–Legendre inequality and delay-dependent canonical orthogonal Legendre polynomials play an important role in dealing with the asymptotical stability of the T–S fuzzy delayed model with an <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$H_{\infty }$ </tex-math></inline-formula> performance. Finally, a simulation example is carried out to show the validity of the presented theorem.

Genomic-based genetic parameters for milkability traits derived from automatic milking systems in North American Holstein cattle

The number of dairy farms adopting automatic milking systems (AMS) has considerably increased around the world aiming to reduce labor costs, improve cow welfare, increase overall performance, and generate a large amount of daily data, including production, behavior, health, and milk quality records. In this context, this study aimed to (1) estimate genomic-based variance components for milkability traits derived from AMS in North American Holstein cattle based on random regression models; and (2) derive and estimate genetic parameters for novel behavioral indicators based on AMS-derived data. A total of 1,752,713 daily records collected using 36 milking robot stations and 70,958 test-day records from 4,118 genotyped Holstein cows were used in this study. A total of 57,600 SNP remained after quality control. The daily-measured traits evaluated were milk yield (MY, kg), somatic cell score (SCS, score unit), milk electrical conductivity (EC, mS), milking efficiency (ME, kg/min), average milk flow rate (FR, kg/min), maximum milk flow rate (FRM, kg/min), milking time (MT, min), milking failures (MFAIL), and milking refusals (MREF). Variance components and genetic parameters for MY, SCS, ME, FR, FRM, MT, and EC were estimated using the AIREMLF90 software under a random regression model fitting a third-order Legendre orthogonal polynomial. A threshold Bayesian model using the THRGIBBS1F90 software was used for genetically evaluating MFAIL and MREF. The daily heritability estimates across days in milk (DIM) ranged from 0.07 to 0.28 for MY, 0.02 to 0.08 for SCS, 0.38 to 0.49 for EC, 0.45 to 0.56 for ME, 0.43 to 0.52 for FR, 0.47 to 0.58 for FRM, and 0.22 to 0.28 for MT. The estimates of heritability (± SD) for MFAIL and MREF were 0.02 ± 0.01 and 0.09 ± 0.01, respectively. Slight differences in the genetic correlations were observed across DIM for each trait. Strong and positive genetic correlations were observed among ME, FR, and FRM, with estimates ranging from 0.94 to 0.99. Also, moderate to high and negative genetic correlations (ranging from -0.48 to -0.86) were observed between MT and other traits such as SCS, ME, FR, and FRM. The genetic correlation (± SD) between MFAIL and MREF was 0.25 ± 0.02, indicating that both traits are influenced by different sets of genes. High and negative genetic correlations were observed between MFAIL and FR (-0.58 ± 0.02) and MFAIL and FRM (-0.56 ± 0.02), indicating that cows with more MFAIL are those with lower FR. The use of random regression models is a useful alternative for genetically evaluating AMS-derived traits measured throughout the lactation. All the milkability traits evaluated in this study are heritable and have demonstrated selective potential, suggesting that their use in dairy cattle breeding programs can improve dairy production efficiency in AMS.

Data-Driven Intelligent Recognition of Flatness Control Efficiency for Cold Rolling Mills

In the production process of strip tandem cold rolling mills, the flatness control system is important for improving the flatness quality. The control efficiency of actuators is a pivotal factor affecting the flatness control accuracy. At present, the data-driven methods to intelligently identify the flatness control efficiency have become a research hotspot. In this paper, a wavelet transform longitudinal denoising method, combined with a genetic algorithm (GA-WT), is proposed to handle the big noise of the measured data from each signal channel of the flatness meter, and Legendre orthogonal polynomial fitting is employed to extract the effective flatness features. Based on the preprocessed actual production data, the adaptive moment estimation (Adam) optimization algorithm is applied, to intelligently identify the flatness control efficiency. This paper takes the actual production data of a 1420 mm tandem cold mill as an example, to verify the performance of the new method. Compared with the control efficiency determined by the empirical method, the flatness residual MSE 0.035 is 5.4% lower. The test results indicate that the GA-WT-Legendre-Adam method can effectively reduce the noise, extract the flatness features, and achieve the intelligent determination of the flatness control efficiency.

Study of fractional-order reaction-advection-diffusion equation using neural network method

In the present article the spatio-temporal fractional-order nonlinear reaction-advection-diffusion equation is solved using the neural network method (NNM). Shifted Legendre orthogonal polynomials with variable coefficients are used in the network’s construction. The characteristics of a fractional-order derivative are used to determine the loss function of a neural network. The permissible learning rate range is discussed in detail, assuming that the Lipschitz hypothesis is accurate for the nonlinearity in reaction term. We have demonstrated the application of the NNM on two numerical examples by utilizing the neural networks which had been repeatedly trained on the training set. In other words, we have validated the effectiveness of the method for such problems. The effects of reaction term and also the degree of nonlinearity in reaction and advection terms on the solution profile are visualized through graphical presentations for specific test cases.

Unraveling the phenotypic and genomic background of behavioral plasticity and temperament in North American Angus cattle

BackgroundLongitudinal records of temperament can be used for assessing behavioral plasticity, such as aptness to learn, memorize, or change behavioral responses based on affective state. In this study, we evaluated the phenotypic and genomic background of North American Angus cow temperament measured throughout their lifetime around the weaning season, including the development of a new indicator trait termed docility-based learning and behavioral plasticity. The analyses included 273,695 and 153,898 records for yearling (YT) and cow at weaning (CT) temperament, respectively, 723,248 animals in the pedigree, and 8784 genotyped animals. Both YT and CT were measured when the animal was loading into/exiting the chute. Moreover, CT was measured around the time in which the cow was separated from her calf. A random regression model fitting a first-order Legendre orthogonal polynomial was used to model the covariance structure of temperament and to assess the learning and behavioral plasticity (i.e., slope of the regression) of individual cows. This study provides, for the first time, a longitudinal perspective of the genetic and genomic mechanisms underlying temperament, learning, and behavioral plasticity in beef cattle.ResultsCT measured across years is heritable (0.38–0.53). Positive and strong genetic correlations (0.91–1.00) were observed among all CT age-group pairs and between CT and YT (0.84). Over 90% of the candidate genes identified overlapped among CT age-groups and the estimated effect of genomic markers located within important candidate genes changed over time. A small but significant genetic component was observed for learning and behavioral plasticity (heritability = 0.02 ± 0.002). Various candidate genes were identified, revealing the polygenic nature of the traits evaluated. The pathways and candidate genes identified are associated with steroid and glucocorticoid hormones, development delay, cognitive development, and behavioral changes in cattle and other species.ConclusionsCow temperament is highly heritable and repeatable. The changes in temperament can be genetically improved by selecting animals with favorable learning and behavioral plasticity (i.e., habituation). Furthermore, the environment explains a large part of the variation in learning and behavioral plasticity, leading to opportunities to also improve the overall temperament by refining management practices. Moreover, behavioral plasticity offers opportunities to improve the long-term animal and handler welfare through habituation.