Weight Distribution Function Research Articles

Enhanced probabilistic damage localization for composite plate based on joint recurrence plots

Localizing damage is a key aspect of monitoring composite laminate structural health. To address the problem of generating the damage index (DI) of composite laminates using Lamb waves, a reconstruction approach for probabilistic damage inspection (RAPID) based on joint recurrence plots (JRP) was proposed. First, the dynamics of the Lamb wave signals are analyzed using phase space reconstruction. Second, the damage information in each sensing path is represented using JRP, and the DI based on the JRP is built with variational auto-encoder (VAE). Finally, the relative magnitude of the DI was employed to modify RAPID’s weight distribution function, allowing for composite plate damage localization detection. The findings of finite element modeling and experiment data reveal that the approach can achieve accurate localization imaging of the composite plate’s interior damage while also properly identifying the damage under 20 dB and 10 dB noise interference. The approach does not require an understanding of Lamb wave dispersion characteristics and involve the extraction of complicated wave packet signals, making it promising for structural health monitoring based on damage index.

Strength of minority ties: the role of homophily and group composition in a weighted social network

Homophily describes a fundamental tie-formation mechanism in social networks in which connections between similar nodes occur at a higher rate than among dissimilar ones. In this article, we present an extension of the weighted social network (WSN) model that, under an explicit homophily principle, quantifies the emergence of attribute-dependent properties of a social system. To test our model, we make use of empirical association data of a group of free-ranging spider monkeys in Yucatan, Mexico. Our homophilic WSN model reproduces many of the properties of the empirical association network with statistical significance, specifically, the average weight of sex-dependent interactions (female-female, female-male, male-male), the weight distribution function, as well as many weighted macro properties (node strength, weighted clustering, and weighted number of modules), even for different age group combinations (adults, subadults, and juveniles). Furthermore, by performing simulations with fitted parameters, we show that one of the main features of a spider monkey social system, namely, stronger male-male interactions over female-female or female-male ones, can be accounted for by an asymmetry in the node-type composition of a bipartisan network, independently of group size. The reinforcement of connections among members of minority groups could be a general structuring mechanism in homophilic social networks.

The Effect of Therapeutic Exercise on Body Weight Distribution, Balance, and Stifle Function in Dogs following Stifle Injury.

Stifle injury is common in the companion dog population, affecting weight bearing, neuromuscular control, and balance. Therapeutic exercises after stifle injury seem to be effective, but high-quality research evaluating the effects is lacking. This randomized controlled trial evaluated the effects of a 12-week progressive therapeutic home exercise protocol on three-legged standing, targeting balance and postural- and neuromuscular control and disability in dogs with stifle injury. Thirty-three dogs with stifle injury were randomly allocated to intervention (n = 18) and control groups (n = 15), both receiving a standard rehabilitation protocol. Additionally, the intervention group received a progressive therapeutic exercise protocol. The outcome measures were static body weight distribution between hindlimbs, balance control, the canine brief pain inventory, and the Finnish canine stifle index. Both groups improved after the intervention period, but the group using the progressive therapeutic exercise protocol improved to a greater extent regarding static body weight distribution between the hindlimbs (I: median = 2.5%, IQR = 1.0-4.5; C: median = 5.5%, IQR = 3.0-8.8), pain-related functional disability (I: median = 0.0, IQR = 0.0-0.2; C: median = 0.9, IQR = 0.1-1.8), and stifle function (I: median = 25.0, IQR = 9.4-40.6; C: median = 75.0, IQR = 31.3-87.5), with intermediate to strong effects. These clinically relevant results indicate that this home exercise program can improve hindlimb function and restore neuromuscular control.

Review of Play and Preisach Models for Hysteresis in Magnetic Materials

This paper studies the properties of the Preisach model and the play model, and compare their similarities. Both are history-dependent hysteresis models that are used to model magnetic hysteresis. They are described as discrete sums of simple hysteresis operators but can easily be reformulated as integral equations of continuous distribution functions using either a Preisach weight distribution function or a play distribution function. The models are mostly seen as phenomenological or mathematical tools but can also be related to friction-like pinning of domain-wall motions, where Rayleigh's law of magnetic hysteresis can be seen as the simplest case on either the play model or the Preisach model. They are poor at modeling other domain behavior, such as nucleation-driven hysteresis. Yet another hysteresis model is the stop model, which can be seen as the inverted version of the play model. This type of model has advantages for expressions linked to energy and can be related to Steinmetz equation of hysteresis losses. The models share several mathematical properties, such as the congruency property and wiping-out property, and both models have a history of dependence that can be described by the series of past reversal points. More generally, it is shown that the many models can be expressed as Preisach models, showing that they can be treated as subcategories of the Preisach type models. These include the play model, the stop model and also the alternative KP-hysteron model.

Improving Probability-Based Diagnostic Imaging Algorithm by Modeling Weight Distribution Coefficient for Instantaneous Baseline Damage Identification

This study used a combination of the instantaneous baseline method and a probability-based diagnostic imaging (PDI) algorithm for damage identification in a stiffener-reinforced aluminium plate. Selecting an appropriate weight distribution function plays a significant role in the PDI algorithm by expressing the probability of damage existence around a sensing path. Weight distribution functions are highly dependent on the weight distribution coefficient (β). This parameter (β) normally is estimated by trial and error, which is incorrect. In addition, determining this parameter is quite costly and time-demanding. To address these issues thoroughly, a new approach is proposed for modelling the weight distribution coefficient based on the physics of wave propagation and the actuator–sensor distance. An appropriate value for β is estimated for each sensing path between actuators and sensors in a specific structure based on the proposed model, making the results more accurate and reasonable. The proposed model was validated by identifying damages at three different locations of a structure for five scenarios (three single-damage and two multiple-damage scenarios). Moreover, the results obtained from proposed model using linear and Gaussian weight distributions were compared with the results extracted from an existing approach. The acceptable localization results clearly indicate the effectiveness of proposed approach.

Performance improvement for additive light field displays with weighted simultaneous algebra reconstruction technique and tracked views

AbstractAdditive light field displays are transparent autostereoscopic three‐dimensional displays without backlights, thus suitable for augmented reality applications. However, when the parallax between viewpoint images becomes large with the increase of viewing angle, the optimization algorithm is hard to handle too many dissimilarities evenly on all viewpoints, resulting in poor reconstructed quality. This paper presents an additive light field display using the weighted simultaneous algebraic reconstruction technique with viewing angle‐dependent weight distribution functions. We constrain the optimization to deliver a reconstructed light field of high image quality for viewpoints of large weight. When the proposed method is applied, with a wide dynamic viewing angle of 57° × 43°, the tracked views' peak signal‐to‐noise ratio exceeds 30 dB with only two additive display layers.

Random Branching and Cross‐linking of Polymer Chains, Analytical Functions for the Bivariate Molecular Weight Distributions

AbstractCross‐linking and branching of primary polymer molecules are investigated using the Galton–Watson (GW) process. Starting with the probability generating function (pgf) of the primary molecular weight distribution (MWD), analytical expressions are derived for the bivariate pgfs g(nbr, s) of branched polymers which depend also on the number of branch points nbr. The bivariate MWDs n(nbr, i) (i: number of molecular units) are then derived as Taylor expansions in s. All three cases of random branching: X‐shaped (cross‐linking), T‐shaped (only one end takes part in the branching process), and H‐shaped (both ends can take part in the branching process) are treated. An extension of the formalism does not require the construction of the pgf and allows the direct use of the MWD of the primary chains. However, using pgfs allows to go past the gel point and to determine the MWD and content of the sol. Explicit expressions are given for special distributions: the mono modal, the most probable, the Schulz‐Zimm, the Poisson, and the Catalan distribution for the cases of X‐shaped and T‐shaped branching.

An efficient online outlier recognition method of dam monitoring data based on improved M-robust regression

Common anomaly recognition methods are easy to misjudge and miss outliers for the online monitoring data. This is a bottleneck problem that needs to be overcome in dam safety management moving toward informatization. Based on the data of nine hydropower stations along Dadu River Basin, this paper analyzed existing problems of the common anomaly identification method and an algorithm was proposed based on improved M-robust regression recognition. In this algorithm, the AR factor was introduced to avoid the defect that the traditional model cannot simulate random variables. The extreme value method and robust estimation were utilized to avoid the leverage effect. The model collapse caused by maximum measured value was avoided through improving the residual calculation model of M-robust and optimizing the weight distribution function. The maximum of the three values, residual quartile difference, discrete quartile difference, and measurement accuracy, was used as an anomaly recognition criterion to improve the evaluation criteria. The algorithm compiled was used in the Dadu River Company since 2017. The statistics showed that for the 150,000 measured values per day, the evaluation time could be within 15 min, the missed judgment rate was 0%, and the misjudgment rate was less than 2%. The proposed algorithm achieved a great improvement and can meet the needs of online outlier recognition in dam safety management.

Modeling the spatial characteristics of extrusion flow instabilities for styrene-butadiene rubbers: Investigating the influence of molecular weight distribution, molecular architecture, and temperature

The extrusion flow instabilities of three commercial styrene-butadiene rubbers (SBR) are investigated as a function of molecular weight distribution (MWD); molecular architecture (linear, branched); and temperature. The samples have multimodal MWD, with the main component being SBR and a low amount, less than 10 wt. %, of low-molecular weight hydrocarbons. Deviation from the Cox–Merz rule at high angular frequencies/shear rates becomes intense as the amount of medium-molecular weight component increases. Optical analysis is used to identify and quantify spatial surface distortions, specifically wavelength (λ) and height (h), of the different types of extrusion flow instabilities. Qualitative constitutive models are reviewed and used to fit the experimental data for the spatial characteristics of extrusion flow instability. The fitting parameters as obtained by the models are correlated with molecular properties of the materials. It is found that the characteristic spatial wavelength (λ) increases as the extrusion temperature decreases. Hence, the influence of temperature on the spatial characteristic wavelength is investigated and an Arrhenius behavior is observed.

Probability-based diagnostic imaging with corrected weight distribution for damage detection of stiffened composite panel

Due to no requirement for direct interpretation of the guided wave signal, probability-based diagnostic imaging (PDI) algorithm is especially suitable for damage identification of complex composite structures. However, the weight distribution function of PDI algorithm is relatively inaccurate. It can reduce the damage localization accuracy. In order to improve the damage localization accuracy, an improved PDI algorithm is proposed. In the proposed algorithm, the weight distribution function is corrected by the acquired relative distances from defects to all actuator–sensor pairs and the reduction of the weight distribution areas. The validity of the proposed algorithm is assessed by identifying damages at different locations on a stiffened composite panel. The results show that the proposed algorithm can identify damage of a stiffened composite panel accurately.

Influence of overloaded vehicles on pavement life based on WIM data

In this paper, the weight distribution characteristics of overloaded vehicles and the influence of overloaded vehicles on pavement service life are studied based on WIM data. Based on the vehicle weight data collected from weight in motion station, the vehicle weight distribution function of different axle type trucks and the weight overload ratio distribution function of different axle types are obtained by fitting. Equivalent single axle loads of the pavement under different weight limits are calculated based on the vehicle weight distribution function, and finally the pavement life growth factors under different weight limits are determined. The calculation results show that: the maximum overload ratio of two-axle vehicle can reach 340%; the number of six-axle overloaded vehicle accounts for more than 50% of the total number of overloaded vehicles, which is the largest proportion. Pavement life can be improved effectively by limiting load, and the road life growth factor shows a quadratic parabolic trend to increase with the decrease of load limit value. For two axle trucks with serious overload, the pavement life can be increased by more than 15 times with a strict load limit value.

Minimising induced drag with weight distribution, lift distribution, wingspan, and wing-structure weight

ABSTRACTBecause the wing-structure weight required to support the critical wing section bending moments is a function of wingspan, net weight, weight distribution, and lift distribution, there exists an optimum wingspan and wing-structure weight for any fixed net weight, weight distribution, and lift distribution, which minimises the induced drag in steady level flight. Analytic solutions for the optimum wingspan and wing-structure weight are presented for rectangular wings with four different sets of design constraints. These design constraints are fixed lift distribution and net weight combined with 1) fixed maximum stress and wing loading, 2) fixed maximum deflection and wing loading, 3) fixed maximum stress and stall speed, and 4) fixed maximum deflection and stall speed. For each of these analytic solutions, the optimum wing-structure weight is found to depend only on the net weight, independent of the arbitrary fixed lift distribution. Analytic solutions for optimum weight and lift distributions are also presented for the same four sets of design constraints. Depending on the design constraints, the optimum lift distribution can differ significantly from the elliptic lift distribution. Solutions for two example wing designs are presented, which demonstrate how the induced drag varies with lift distribution, wingspan, and wing-structure weight in the design space near the optimum solution. Although the analytic solutions presented here are restricted to rectangular wings, these solutions provide excellent test cases for verifying numerical algorithms used for more general multidisciplinary analysis and optimisation.

Role of the Product λ′(0)ρ′(1) in Determining LDPC Code Performance

The objective of this work is to analyze the importance of the product λ ′ ( 0 ) ρ ′ ( 1 ) in determining low density parity check (LDPC) code performance, as far as its influence on the weight distribution function and on the decoding thresholds. This analysis is based on the 2006 paper by Di et al., as far as the weight distribution function is concerned, and on the 2018 paper by Vatta et al., regarding the LDPC decoding thresholds. In particular, the first paper Di et al. analyzed the relation between the above mentioned product and the minimum weight of an ensemble of random LDPC codewords, whereas in the second some analytical upper bounds to the LDPC decoding thresholds were determined. In the present work, besides analyzing the performance of an ensemble of LDPC codes through the outcomes of Di et al.’s 2006 paper, we give the relation between one of the upper bounds found in Vatta et al.’s 2018 paper and the above mentioned product λ ′ ( 0 ) ρ ′ ( 1 ) , thus showing its role in also determining an upper bound to LDPC decoding thresholds.

Multi-sensor network for industrial metal plate structure monitoring via time reversal ultrasonic guided wave

Active ultrasonic guided wave is considered to be the most effective and important on-line damage monitoring method for industrial steel plates structure health monitoring. Aiming at the problem of poor practicability of extracting damage scattering signal from baseline signal, a baseline-free time reversal probabilistic imaging algorithm (BFTRPI algorithm) is proposed in this paper based on ultrasound guided waves time reversal theory and probability statistics principle. Firstly, the time reversal of signal and the adaptive focusing mechanism of wave source are used to eliminate the dispersion effect of Lamb wave by the multi-sensor network. Secondly, the energy characteristic difference coefficient between the reconstructed Lamb wave signal and the original excitation signal, is taken as the damage factor. Finally, the relative distance between the damage and the direct path of the sensor-actuator channel is used to adjust the weight distribution function. The weighted probabilistic values of each sensor path in the sensor network are mapped to the discrete coordinates in the detection area, and the probabilistic imaging of the damage appearing on these discrete coordinates is constructed for multiple damages imaging and location. Experiments on aluminium sheets show that the method can clearly separate the damage scattering signals without baseline signals, achieve the focus of the original excitation signal, and obtain the damage probability images of structure. Compared to traditional probability distribution function method, it has better imaging accuracy and imaging quality. The positioning accuracy of the BFTRPI algorithm is obviously higher than that of traditional algorithm. The estimated position by BFTRPI algorithm is more close to the actual damage position. The location area of damage and artifact for traditional algorithm are both higher than that of BFTRPI algorithm. This method can accurately identify and locate multiple damages in aluminium sheet, which verifies the validity of this method and has certain engineering application value.

Using structural intensity approach to characterize vibro-acoustic behavior of the cylindrical shell structure

In this paper, the vibro-acoustic behaviors of vibrational cylindrical shells are investigated by using structural intensity approach. The reducing interior noise method for vibrating cylindrical shells is proposed by altering and redistributing the structural intensity through changing the damping property of the structure. The concept of proposed novel method is based on the properties of structural intensity distribution on cylindrical shells under different load and damping conditions, which can reflects power flow in the structures. In the study, the modal formulas of structural intensity are developed for the steady state vibration of cylindrical shell structures. The detailed formulas of structural intensity are derived by substituting modal quantities, in which the effect of main parameters such as weight coefficients and distribution functions on structure intensity are analyzed and discussed. Numerical simulations are first carried out based on the structural intensity analytical solutions of modal formulas. Through simulating the coupling vibration and acoustical radiation problems of cylindrical shell, the relationship between vibro-acoustic and structural intensity distribution is derived. We find that for cylindrical shell, by properly arranging damping conditions, the structural intensity can be efficiently changed and further the noise property can be improved. The proposed methodology has important implications and potential applications in the vibration and noise control of fuselage structure.

A Calculation Scheme for Assessing Storage Moduli and Losses as a Function of Polymer Chemical Structure and Blend Composition

A calculation scheme is proposed for assessing and predicting storage and loss moduli. The examination is based on atomic constants, which take into account the contribution of each atom and polar group and the van der Waals volume and shear modulus at high frequencies. The obtained relationship makes it possible to calculate the shear modulus and storage and loss moduli as a function of frequency, temperature, and molecular weight distribution.

Effects of Changing Body Weight Distribution on Mediolateral Stability Control during Gait Initiation.

During gait initiation, anticipatory postural adjustments (APA) precede the execution of the first step. It is generally acknowledged that these APA contribute to forward progression but also serve to stabilize the whole body in the mediolateral direction during step execution. Although previous studies have shown that changes in the distribution of body weight between both legs influence motor performance during gait initiation, it is not known whether and how such changes affect a person’s postural stability during this task. The aim of this study was to investigate the effects of changing initial body weight distribution between legs on mediolateral postural stability during gait initiation. Changes in body weight distribution were induced under experimental conditions by modifying the frontal plane distribution of an external load located at the participants’ waists. Fifteen healthy adults performed a gait initiation series at a similar speed under three conditions: with the overload evenly distributed over both legs; with the overload strictly distributed over the swing-limb side; and with the overload strictly distributed over the stance-leg side. Our results showed that the mediolateral location of center-of-mass (CoM) during the initial upright posture differed between the experimental conditions, indicating modifications in the initial distribution of body weight between the legs according to the load distribution. While the parameters related to the forward progression remained unchanged, the alterations in body weight distribution elicited adaptive changes in the amplitude of APA in the mediolateral direction (i.e., maximal mediolateral shift of the center of pressure (CoP)), without variation in their duration. Specifically, it was observed that the amplitude of APA was modulated in such a way that mediolateral dynamic stability at swing foot-contact, quantified by the margin of stability (i.e., the distance between the base of support boundary and the extrapolated CoM position), did not vary between the conditions. These findings suggest that APA seem to be scaled as a function of the initial body weight distribution between both legs so as to maintain optimal conditions of stability during gait initiation.

Features of the molecular–topological structure of γ-irradiated powdered tetrafluoroethylene–perfluoro(propyl vinyl ether) copolymer

With the use of thermomechanical spectrometry in two modes, coaxial, when the load application vector is coplanar with the compacting pressure vector (semicrystalline copolymer) during the measurement of the deformation of a copolymer of tetrafluoroethylene with perfluoro(propyl vinyl ether), and mutually perpendicular (completely amorphous copolymer), it has been established that the axial compression of the copolymer brought its topological structure to an absolutely anisotropic state. After γ-irradiation, the semicrystalline structure of the copolymer was retained regardless of the radiation dose. The minimum values of the glass transition temperature of the amorphous block and the degree of crystallinity were observed in the copolymer irradiated to a dose of 150 kGy. The molecular weight distribution functions of interjunction chains in the networks of the amorphous blocks of the initial copolymer and its γ-irradiated analogs are bimodal.

Estimating the molecular weight distribution of a polymer using acoustic relaxation spectra

An approach to estimating the molecular weight distribution function of a polymer in a solution using acoustic spectroscopy data is presented. The estimation function is based on the relationship between relaxation spectra and the molecular weight distribution function, along with the relationship between the relaxation spectra and the frequency distribution of a polymer’s loss modulus.

Supercritical Fluid Chromatography with Evaporative Light Scattering Detection (SFC-ELSD) for Determination of Oligomer Molecular Weight Distributions

Ultraviolet curable polyureas and polyurethanes enjoy a wide range of applications in the coatings industry. They demand less energy for curing compared to thermal processes that offer relatively low viscosities before photocuring, and provide mechanical property improvements due to hydrogen bonding physical crosslinks. Mechanical properties of the coatings are dependent on a variety of factors, including chemical composition, molecular weight, and molecular weight distribution. Formulations are designed for a wide variety of end use applications, ranging from soft, elastomeric coatings to harder, nonflexible sealants. This report demonstrates that the thermomechanical behavior of photocured coatings is a function of molecular weight distribution. Step-growth polymerization and endcapping afforded a variety of acrylate-terminated, urea-/urethane-containing photocurable oligomers from amine-terminated poly(propylene glycol), dicyclohexylmethane-4,4′-diisocyanate (HMDI), and 2-hydroxyethyl acrylate (HEA) at various stoichiometric ratios. The state-of-the-art supercritical fluid chromatography coupled with evaporative light-scattering detection (SFC-ELSD) enabled the elucidation of oligomeric molecular weight distributions as a function of reaction stoichiometry. SFC-ELSD demonstrated the efficient separation of oligomeric species with single repeat unit resolution (i.e., n = 2 vs. n = 3). Dynamic mechanical analysis probed thermomechanical response of photocured films as a function of molecular weight distribution and demonstrated that the presence of a hydrogen-bonding, small molecule photoactive reaction byproduct, i.e., HEA doubly-endcapped HMDI, had a much more profound effect on thermomechanical response as compared to changes in oligomer molecular weight in the molecular weight range investigated. This combination of chromatographic technique and thermomechanical analysis afforded an in-depth investigation of the structure–property relationships of urea-/urethane-containing photocurable oligomers.