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14 pages, 3425 KiB  
Article
Prediction of Wind Turbine Blade Stiffness Degradation Based on Improved Neural Basis Expansion Analysis
by Shuai Yang, Jianxiong Gao, Yiping Yuan, Jianxing Zhou and Lingchao Meng
Appl. Sci. 2025, 15(4), 1884; https://doi.org/10.3390/app15041884 - 12 Feb 2025
Viewed by 723
Abstract
To reduce the significant time and cost associated with wind turbine blade fatigue testing, the applicability of the deep learning model Neural Basis Expansion Analysis (N-BEATS) for modeling the stiffness degradation of wind turbine blades was investigated. First, on the basis of a [...] Read more.
To reduce the significant time and cost associated with wind turbine blade fatigue testing, the applicability of the deep learning model Neural Basis Expansion Analysis (N-BEATS) for modeling the stiffness degradation of wind turbine blades was investigated. First, on the basis of a traditional blade stiffness degradation model, the stiffness data were expanded to meet the data volume requirements of N-BEATS. Second, the basic block structure of N-BEATS was improved (by treating the sequence-to-sequence prediction problem as a nonlinear multivariate regression problem) to meet the specific prediction requirements of this task, and the Pinball Mean Absolute Percentage Error (Pinball-MAPE) loss function was adopted to further reduce bias during the prediction process. Additionally, two data augmentation methods—time series combination and random noise injection—were applied to mitigate the risk of model overfitting and improve prediction accuracy. Experimental results demonstrated that the model can effectively learn underlying patterns in the stiffness data and successfully predict the remaining stiffness. Full article
(This article belongs to the Special Issue Uncertainty and Reliability Analysis for Engineering Systems)
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18 pages, 12798 KiB  
Article
Experimental Study on the Properties of Basalt Fiber–Cement-Stabilized Expansive Soil
by Junhua Chen, Jiejie Mu, Aijun Chen, Yao Long, Yanjiang Zhang and Jinfeng Zou
Sustainability 2024, 16(17), 7579; https://doi.org/10.3390/su16177579 - 1 Sep 2024
Cited by 4 | Viewed by 2232
Abstract
Expansive soil is prone to rapid strength degradation caused by repeated volume swelling and shrinkage under alternating dry–wet conditions. Basalt fiber (BF) and cement are utilized to stabilize expansive soil, aiming to curb its swelling and shrinkage, enhance its strength, and ensure its [...] Read more.
Expansive soil is prone to rapid strength degradation caused by repeated volume swelling and shrinkage under alternating dry–wet conditions. Basalt fiber (BF) and cement are utilized to stabilize expansive soil, aiming to curb its swelling and shrinkage, enhance its strength, and ensure its durability in dry–wet cycles. This study examines the impact of varying content (0–1%) of BF on the physical and mechanical characteristics of expansive soil stabilized with a 6% cement content. We investigated these effects through a series of experiments including compaction, swelling and shrinkage, unconfined compressive strength (UCS), undrained and consolidation shear, dry–wet cycles, and scanning electron microscope (SEM) analyses. The experiments yielded the following conclusions: Combining cement and BF to stabilize expansive soil leverages cement’s chemical curing ability and BF’s reinforcing effect. Incorporating 0.4% BFs significantly improves the swelling and shrinkage characteristics of cement-stabilized expansive soils, reducing expansion by 36.17% and contraction by 28.4%. Furthermore, it enhances both the initial strength and durability of these soils under dry–wet cycles. Without dry–wet cycles, the addition of 0.4% BFs increased UCS by 24.8% and shear strength by 24.6% to 40%. After 16 dry–wet cycles, the UCS improved by 38.87% compared to cement-stabilized expansive soil alone. Both the content of BF and the number of dry–wet cycles significantly influenced the UCS of cement-stabilized expansive soils. Multivariate nonlinear equations were used to model the UCS, offering a predictive framework for assessing the strength of these soils under varying BF contents and dry–wet cycles. The cement hydrate adheres to the fiber surface, increasing adhesion and friction between the fibers and soil particles. Additionally, the fibers form a network structure within the soil. These factors collectively enhance the strength, deformation resistance, and durability of cement-stabilized expansive soils. These findings offer valuable insights into combining traditional cementitious materials with basalt fiber to manage expansive soil hazards, reduce resource consumption, and mitigate environmental impacts, thereby contributing to sustainable development. Full article
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17 pages, 354 KiB  
Article
On Voigt-Type Functions Extended by Neumann Function in Kernels and Their Bounding Inequalities
by Rakesh K. Parmar, Tibor K. Pogány and Uthara Sabu
Axioms 2024, 13(8), 534; https://doi.org/10.3390/axioms13080534 - 7 Aug 2024
Viewed by 944
Abstract
The principal aim of this paper is to introduce the extended Voigt-type function Vμ,ν(x,y) and its counterpart extension Wμ,ν(x,y), involving the Neumann function Yν in [...] Read more.
The principal aim of this paper is to introduce the extended Voigt-type function Vμ,ν(x,y) and its counterpart extension Wμ,ν(x,y), involving the Neumann function Yν in the kernel of the representing integral. The newly defined integral reduces to the classical Voigt functions K(x,y) and L(x,y), and to their generalizations by Srivastava and Miller, by the unification of Klusch. Following an approach by Srivastava and Pogány, we also present the multiparameter and multivariable versions Vμ,ν(r)(x,y),Wμ,ν(r)(x,y) and the r positive integer of the initial extensions Vμ,ν(x,y),Wμ,ν(x,y). Several computable series expansions are obtained for the discussed Voigt-type functions in terms of Humbert confluent hypergeometric functions Ψ2(r). Furthermore, by transforming the input extended Voigt-type functions by the Grünwald–Letnikov fractional derivative, we establish representation formulae in terms of the associated Legendre functions of the second kind Qην in the two-parameter and two-variable cases. Finally, functional bounding inequalities are given for Vμ,ν(x,y) and Wμ,ν(x,y). Particularly interesting results are presented for the Neumann function Yν and for the Struve Hν function in the form of several functional bounds. The article ends with a thorough discussion and closing remarks. Full article
21 pages, 11480 KiB  
Article
Spatiotemporal Land Use/Land Cover Changes and Impact on Urban Thermal Environments: Analyzing Cool Island Intensity Variations
by Haiqiang Liu, Zhiheng Zhou, Qiang Wen, Jinyuan Chen and Shoichi Kojima
Sustainability 2024, 16(8), 3205; https://doi.org/10.3390/su16083205 - 11 Apr 2024
Cited by 3 | Viewed by 2304
Abstract
This study pioneers the comprehensive evaluation of the spatiotemporal evolution of land use/land cover (LULC) in Hangzhou city, introducing the novel water body shape index (WBSI) to analyze its seasonal impacts on the urban thermal environment and urban cool island (UCI) effects, uncovering [...] Read more.
This study pioneers the comprehensive evaluation of the spatiotemporal evolution of land use/land cover (LULC) in Hangzhou city, introducing the novel water body shape index (WBSI) to analyze its seasonal impacts on the urban thermal environment and urban cool island (UCI) effects, uncovering distinct patterns of thermal regulation. It particularly investigates how distance gradients and the water body shape index (WBSI) influence land surface temperature (LST) in the urban core. The region’s climate, featuring hot summers and cold winters, highlights significant seasonal LST variations. Addressing a gap in existing UCI research, the analysis extends beyond the typical large-scale planning focus to include small-scale, high-resolution aspects. Employing remote sensing and geographic information system (GIS) analysis techniques, this study analyzes the seasonal dynamics in Hangzhou’s central urban area. High-resolution LST data, obtained through single-channel inversion and resolution enhancement algorithms, are crucial to this analysis. This study employs the maximum likelihood classification method to analyze land use and land cover changes from 1990 to 2020. This analysis reveals potential drivers of urban thermal environment changes, such as the expansion of residential and commercial areas and the reduction in green spaces. Different regions in LST data are delineated to assess the cool island effect, and the complexity of water body boundaries is quantified using the water body shape index. Spatial and temporal patterns of LST changes are investigated using multivariate regression and time-series analysis models. We identified significant changes in LULC over the past 30 years in Hangzhou, closely correlating with a continuous rise in LST. This observation underscores a clear finding: the strategic importance of blue–green infrastructure in mitigating urban heat, a novel insight that extends the current understanding of urban thermal dynamics. A clear and novel finding of this study is that the intensity of the cool island effect from large water bodies not only diminishes with distance but is intricately influenced by the complexity of their shapes, as quantified by the WBSI, whereas the complexity of their boundaries enhances this effect. Additionally, the regulatory role of the cool island effect is observed to vary seasonally, being most pronounced in summer and less so in autumn and winter, thereby demonstrating a positive impact. In conclusion, our findings innovatively highlight how the specific shapes of water bodies, quantified through the water body shape index (WBSI), emerge as critical, yet previously underappreciated, drivers in modulating the urban thermal environment. This underscores a new avenue for urban planning, advocating for the strategic design of water bodies within urban landscapes. It also finds that spatial factors and seasonal variations significantly affect the intensity of the cool island effect. These findings offer valuable evidence for urban planning and climate change adaptation, emphasizing balancing natural elements with the built environment in urban design. Full article
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44 pages, 534 KiB  
Article
Plea for Diagonals and Telescopers of Rational Functions
by Saoud Hassani, Jean-Marie Maillard and Nadjah Zenine
Universe 2024, 10(2), 71; https://doi.org/10.3390/universe10020071 - 2 Feb 2024
Cited by 1 | Viewed by 1678
Abstract
This paper is a plea for diagonals and telescopers of rational or algebraic functions using creative telescoping, using a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is also the case with diagonals of algebraic functions) [...] Read more.
This paper is a plea for diagonals and telescopers of rational or algebraic functions using creative telescoping, using a computer algebra experimental mathematics learn-by-examples approach. We show that diagonals of rational functions (and this is also the case with diagonals of algebraic functions) are left-invariant when one performs an infinite set of birational transformations on the rational functions. These invariance results generalize to telescopers. We cast light on the almost systematic property of homomorphism to their adjoint of the telescopers of rational or algebraic functions. We shed some light on the reason why the telescopers, annihilating the diagonals of rational functions of the form P/Qk and 1/Q, are homomorphic. For telescopers with solutions (periods) corresponding to integration over non-vanishing cycles, we have a slight generalization of this result. We introduce some challenging examples of the generalization of diagonals of rational functions, like diagonals of transcendental functions, yielding simple F12 hypergeometric functions associated with elliptic curves, or the (differentially algebraic) lambda-extension of correlation of the Ising model. Full article
14 pages, 4690 KiB  
Article
Time-Series Characterization of Grassland Biomass Intensity to Examine Management Change at Two Sites in Germany Using 25 Years of Remote Sensing Imagery
by Christopher M. Holmes, Joshua Pritsolas, Randall Pearson, Carolyn Butts-Wilmsmeyer and Thorsten Schad
Appl. Sci. 2023, 13(22), 12467; https://doi.org/10.3390/app132212467 - 17 Nov 2023
Cited by 1 | Viewed by 1596
Abstract
In cultivated landscapes, grasslands are an important land use type for insect life. Grassland management practices can have a significant impact on insect ecology. For example, intense fertilization and frequent cutting can reduce the diversity and abundance of insects by destroying their habitat [...] Read more.
In cultivated landscapes, grasslands are an important land use type for insect life. Grassland management practices can have a significant impact on insect ecology. For example, intense fertilization and frequent cutting can reduce the diversity and abundance of insects by destroying their habitat and food sources. Thus, the quality of grassland habitat for insect development depends on its management intensity. The intensification of grassland production is discussed as one factor contributing to the decline in insect biomass over recent decades. Characterizing grassland changes over time provides one piece to the larger puzzle of insect decline. We analyzed landscape-level trends in grassland biomass near Orbroich and Wahnbachtal in North Rhine-Westphalia, Germany, over a 25-year period. In both areas, pronounced insect biomass decline had been observed. More than 430 Landsat images were used. An image normalization process was developed and employed to ensure that observed changes over time were attributed to grassland changes and not systemic changes inherent within image time series. Distinct clusters of grassland parcels were identified based on intensity and temporal changes in biomass using Normalized Difference Vegetation Index (NDVI) as an indicator. Cluster separability was confirmed using the Transform Divergence method. The results showed clusters having periods of distinct trends in vegetation biomass, indicating changes in grassland agronomic and/or management practices over time (e.g., fertilization, increased silage production). Changes in management practices coincided with regional trends in cultivation as documented by official statistics. We demonstrated the feasibility of using 100+ images over multiple decades to perform a long-term remote sensing analysis examining grassland change. These temporally expansive and spatially detailed trends of grassland change can be included as factors in the multi-variate analysis of insect decline. The methodology can be applied to other geographic areas. Such improved insights can support informed landscape design and cultivation patterns in relation to insect ecology and the broader context of biodiversity enhancement. Full article
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27 pages, 514 KiB  
Review
A Systematic Review of INGARCH Models for Integer-Valued Time Series
by Mengya Liu, Fukang Zhu, Jianfeng Li and Chuning Sun
Entropy 2023, 25(6), 922; https://doi.org/10.3390/e25060922 - 11 Jun 2023
Cited by 17 | Viewed by 4722
Abstract
Count time series are widely available in fields such as epidemiology, finance, meteorology, and sports, and thus there is a growing demand for both methodological and application-oriented research on such data. This paper reviews recent developments in integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) [...] Read more.
Count time series are widely available in fields such as epidemiology, finance, meteorology, and sports, and thus there is a growing demand for both methodological and application-oriented research on such data. This paper reviews recent developments in integer-valued generalized autoregressive conditional heteroscedasticity (INGARCH) models over the past five years, focusing on data types including unbounded non-negative counts, bounded non-negative counts, Z-valued time series and multivariate counts. For each type of data, our review follows the three main lines of model innovation, methodological development, and expansion of application areas. We attempt to summarize the recent methodological developments of INGARCH models for each data type for the integration of the whole INGARCH modeling field and suggest some potential research topics. Full article
(This article belongs to the Special Issue Discrete-Valued Time Series)
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18 pages, 350 KiB  
Review
Multiple Derivative Inversions and Lagrange-Good Expansion Formulae
by Wenchang Chu
Mathematics 2022, 10(22), 4234; https://doi.org/10.3390/math10224234 - 12 Nov 2022
Viewed by 1468
Abstract
By establishing new multiple inverse series relations (with their connection coefficients being given by higher derivatives of fixed multivariate analytic functions), we illustrate a general framework to provide new proofs for MacMahon’s master theorem and the multivariate expansion formula due to Good (1960). [...] Read more.
By establishing new multiple inverse series relations (with their connection coefficients being given by higher derivatives of fixed multivariate analytic functions), we illustrate a general framework to provide new proofs for MacMahon’s master theorem and the multivariate expansion formula due to Good (1960). Further multivariate extensions of the derivative identities due to Pfaff (1795) and Cauchy (1826) will be derived and the generalized multifold convolution identities due to Carlitz (1977) will be reviewed. Full article
(This article belongs to the Special Issue Advances in Mathematical Analysis with Applications)
45 pages, 493 KiB  
Article
Fourth-Order Comprehensive Adjoint Sensitivity Analysis (4th-CASAM) of Response-Coupled Linear Forward/Adjoint Systems: I. Theoretical Framework
by Dan Gabriel Cacuci
Energies 2021, 14(11), 3335; https://doi.org/10.3390/en14113335 - 6 Jun 2021
Cited by 12 | Viewed by 2228
Abstract
The most general quantities of interest (called “responses”) produced by the computational model of a linear physical system can depend on both the forward and adjoint state functions that describe the respective system. This work presents the Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology [...] Read more.
The most general quantities of interest (called “responses”) produced by the computational model of a linear physical system can depend on both the forward and adjoint state functions that describe the respective system. This work presents the Fourth-Order Comprehensive Adjoint Sensitivity Analysis Methodology (4th-CASAM) for linear systems, which enables the efficient computation of the exact expressions of the 1st-, 2nd-, 3rd- and 4th-order sensitivities of a generic system response, which can depend on both the forward and adjoint state functions, with respect to all of the parameters underlying the respective forward/adjoint systems. Among the best known such system responses are various Lagrangians, including the Schwinger and Roussopoulos functionals, for analyzing ratios of reaction rates, the Rayleigh quotient for analyzing eigenvalues and/or separation constants, etc., which require the simultaneous consideration of both the forward and adjoint systems when computing them and/or their sensitivities (i.e., functional derivatives) with respect to the model parameters. Evidently, such responses encompass, as particular cases, responses that may depend just on the forward or just on the adjoint state functions pertaining to the linear system under consideration. This work also compares the CPU-times needed by the 4th-CASAM versus other deterministic methods (e.g., finite-difference schemes) for computing response sensitivities These comparisons underscore the fact that the 4th-CASAM is the only practically implementable methodology for obtaining and subsequently computing the exact expressions (i.e., free of methodologically-introduced approximations) of the 1st-, 2nd, 3rd- and 4th-order sensitivities (i.e., functional derivatives) of responses to system parameters, for coupled forward/adjoint linear systems. By enabling the practical computation of any and all of the 1st-, 2nd, 3rd- and 4th-order response sensitivities to model parameters, the 4th-CASAM makes it possible to compare the relative values of the sensitivities of various order, in order to assess which sensitivities are important and which may actually be neglected, thus enabling future investigations of the convergence of the (multivariate) Taylor series expansion of the response in terms of parameter variations, as well as investigating the range of validity of other important quantities (e.g., response variances/covariance, skewness, kurtosis, etc.) that are derived from Taylor-expansion of the response as a function of the model’s parameters. The 4th-CASAM presented in this work provides the basis for significant future advances towards overcoming the “curse of dimensionality” in sensitivity analysis, uncertainty quantification and predictive modeling. Full article
16 pages, 1371 KiB  
Article
Evolution of Surgical Treatment of Colorectal Liver Metastases in the Real World: Single Center Experience in 1212 Cases
by Francesca Ratti, Federica Cipriani, Guido Fiorentini, Valentina Burgio, Monica Ronzoni, Angelo Della Corte, Stefano Cascinu, Francesco De Cobelli and Luca Aldrighetti
Cancers 2021, 13(5), 1178; https://doi.org/10.3390/cancers13051178 - 9 Mar 2021
Cited by 8 | Viewed by 3698
Abstract
Background: In recent years, the treatment of colorectal liver metastases (CRLM) has undergone significant evolution thanks to technical improvements as well as oncological advances, which have been the subject of targeted studies aimed at understanding the details of this heterogeneous disease. The purpose [...] Read more.
Background: In recent years, the treatment of colorectal liver metastases (CRLM) has undergone significant evolution thanks to technical improvements as well as oncological advances, which have been the subject of targeted studies aimed at understanding the details of this heterogeneous disease. The purpose of this study is to put together pieces of this complex scenario by providing an overview of the evolution that has occurred in the context of a single center within a multidisciplinary management approach. Methods: Between 2005 and 2020, 1212 resections for CRLM were performed at the Hepatobiliary Surgery Division of San Raffaele Hospital, Milan. The series was divided into three historical periods, which were compared in terms of disease characteristics and short- and long-term outcomes: Period 1, 2005–2009 (293 cases); Period 2, 2010–2014 (353 cases); Period 3, 2015–2020 (566 cases). The trends for surgical technical complexity, oncological burden of the disease, use of the laparoscopic approach and use of techniques for hepatic hypertrophy were analyzed year by year. Uni- and multivariate analyses were performed to identify factors associated with inclusion to a laparoscopic approach and with long-term prognosis. Results: The number of resections performed over the years progressively increased, with an increase in the number of cases with a high Clinical Risk Score and a high profile of technical complexity. The proportion of cases performed laparoscopically increased, but less rapidly compared to other malignant tumors. The risk of postoperative morbidity and mortality was similar in the three analyzed periods. Long-term survival, stratified by Clinical Risk Score, improved in Period 3, while overall survival remained unchanged. Conclusion: The cultural background, the maturation of technical expertise and the consolidation of the multidisciplinary team have resulted in safe expansion of the possibility to offer a curative opportunity to patients, while continuously implementing into clinical practice evidence provided by the literature. Full article
(This article belongs to the Special Issue Theranostic Advances in Hepatobiliary Tumors)
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21 pages, 466 KiB  
Article
Modeling Multivariate Financial Series and Computing Risk Measures via Gram–Charlier-Like Expansions
by Maria Grazia Zoia, Gianmarco Vacca and Laura Barbieri
Risks 2020, 8(4), 123; https://doi.org/10.3390/risks8040123 - 16 Nov 2020
Cited by 1 | Viewed by 2433
Abstract
This paper develops an approach based on Gram–Charlier-like expansions for modeling financial series to take in due account features such as leptokurtosis. A Gram–Charlier-like expansion adjusts the moments of interest of a given distribution via its own orthogonal polynomials. This approach, formerly adopted [...] Read more.
This paper develops an approach based on Gram–Charlier-like expansions for modeling financial series to take in due account features such as leptokurtosis. A Gram–Charlier-like expansion adjusts the moments of interest of a given distribution via its own orthogonal polynomials. This approach, formerly adopted for univariate series, is here extended to a multivariate context by means of spherical densities. Previous works proposed the Gram–Charlier of the multivariate Gaussian, obtained by using Hermite polynomials. This work shows how polynomial expansions of an entire class of spherical laws can be worked out with the aim of obtaining a wide set of leptokurtic multivariate distributions. A Gram–Charlier-like expansion is a distribution characterized by an additional parameter with respect to the parent spherical law. This parameter, which measures the increase in kurtosis due to the polynomial expansion, can be estimated so as to make the resulting distribution capable of describing the empirical kurtosis found in the data. An application of the Gram–Charlier-like expansions to a set of financial assets proves their effectiveness in modeling multivariate financial series and assessing risk measures, such as the value at risk and the expected shortfall. Full article
(This article belongs to the Special Issue Computational Methods in Quantitative Risk Management)
23 pages, 4397 KiB  
Article
CART-RF Classification with Multifilter for Monitoring Land Use Changes Based on MODIS Time-Series Data: A Case Study from Jiangsu Province, China
by Le’an Qu, Zhenjie Chen and Manchun Li
Sustainability 2019, 11(20), 5657; https://doi.org/10.3390/su11205657 - 14 Oct 2019
Cited by 5 | Viewed by 3359
Abstract
The periodic determination of land use changes over large areas is crucial for improving our understanding of land system dynamics. Jiangsu lies at the center of China’s Yangtze Delta and has one of the fastest-developing economies in China. However, it is also a [...] Read more.
The periodic determination of land use changes over large areas is crucial for improving our understanding of land system dynamics. Jiangsu lies at the center of China’s Yangtze Delta and has one of the fastest-developing economies in China. However, it is also a region where serious conflicts exist between the available land resources and the human demand for land. To address these conflicts, it is important to analyze the patterns of land use change in Jiangsu, as they can serve as a useful reference for other rapidly urbanizing regions in China as well as other developing countries. In this study, we propose a method of classification and regression tree-random forest (CART-RF) classification with a multifilter based on time-series Moderate Resolution Imaging Spectroradiometer (MODIS) imaging data. The proposed method integrates the CART decision tree and the random forest algorithms (CART-RF) to obtain accurate yearly land use data for large areas from multivariate time-series remote sensing data and employs a spatial-temporal-logical filter to exclude any abnormal changes in the multivariate time-series pixel data. The obtained results indicated that (1) the CART-RF classifier is effective for land use classification based on the multivariate time-series MODIS data, with the overall classification accuracy being greater than 90%; (2) the use of the proposed combinatorial spatial-temporal-logical filtering method effectively eliminates most anomalous changes and minimizes the effects of “salt-and-pepper” noise; and (3) from 2000 to 2015, land use in Jiangsu province underwent significant and spatiotemporally heterogeneous changes on a province-wide scale, owing to various factors, such as those related to the economy, location, and government policies. These changes were manifested as continuous expansions in the built-up land at the expense of farmland. While this expansion of built-up land has been very rapid in southern Jiangsu, especially in the region close to Yangtze River Delta, it has been relatively slower in northern Jiangsu. Full article
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12 pages, 1980 KiB  
Article
A Statistical Model Updating Method of Beam Structures with Random Parameters under Static Load
by Zhifeng Wu, Bin Huang, Yejun Li and Wuchuan Pu
Appl. Sci. 2017, 7(6), 601; https://doi.org/10.3390/app7060601 - 9 Jun 2017
Cited by 6 | Viewed by 4180
Abstract
This paper presents a new statistical model updating method of beam structures with random parameters under static load. The new updating method considers structural parameters and measurement errors to be random. To reduce the unmeasured degrees of freedom in the finite element model, [...] Read more.
This paper presents a new statistical model updating method of beam structures with random parameters under static load. The new updating method considers structural parameters and measurement errors to be random. To reduce the unmeasured degrees of freedom in the finite element model, a static condensation technique is used in this method. A statistical model updating equation with respect to element updated factors is established afterwards. The element updated factors are expanded as random multivariate power series. Using a high-order perturbation technique, the statistical model updating equation can be solved to obtain the coefficients of the power series expansions of the element updated factors. The results of two numerical examples show that for the solution of the statistical model updating equation, the accuracy of the proposed method agrees with that of the Monte Carlo simulation method very well. The static responses obtained by the updated finite element model coincide with the measured results very well. Finally, a series of static load tests of the concrete beam are conducted to testify the effectiveness of the proposed method. Full article
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14 pages, 628 KiB  
Article
Expansion of the Kullback-Leibler Divergence, and a New Class of Information Metrics
by David J. Galas, Gregory Dewey, James Kunert-Graf and Nikita A. Sakhanenko
Axioms 2017, 6(2), 8; https://doi.org/10.3390/axioms6020008 - 1 Apr 2017
Cited by 21 | Viewed by 7092
Abstract
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces of this class of problem. This study takes an approach that simplifies many [...] Read more.
Inferring and comparing complex, multivariable probability density functions is fundamental to problems in several fields, including probabilistic learning, network theory, and data analysis. Classification and prediction are the two faces of this class of problem. This study takes an approach that simplifies many aspects of these problems by presenting a structured, series expansion of the Kullback-Leibler divergence—a function central to information theory—and devise a distance metric based on this divergence. Using the Möbius inversion duality between multivariable entropies and multivariable interaction information, we express the divergence as an additive series in the number of interacting variables, which provides a restricted and simplified set of distributions to use as approximation and with which to model data. Truncations of this series yield approximations based on the number of interacting variables. The first few terms of the expansion-truncation are illustrated and shown to lead naturally to familiar approximations, including the well-known Kirkwood superposition approximation. Truncation can also induce a simple relation between the multi-information and the interaction information. A measure of distance between distributions, based on Kullback-Leibler divergence, is then described and shown to be a true metric if properly restricted. The expansion is shown to generate a hierarchy of metrics and connects this work to information geometry formalisms. An example of the application of these metrics to a graph comparison problem is given that shows that the formalism can be applied to a wide range of network problems and provides a general approach for systematic approximations in numbers of interactions or connections, as well as a related quantitative metric. Full article
(This article belongs to the Special Issue Entropy and Information Theory)
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22 pages, 659 KiB  
Article
Multivariate Analysis of Rangeland Vegetation and Soil Organic Carbon Describes Degradation, Informs Restoration and Conservation
by Devan Allen McGranahan, David M. Engle, Samuel D. Fuhlendorf, James R. Miller and Diane M. Debinski
Land 2013, 2(3), 328-350; https://doi.org/10.3390/land2030328 - 16 Jul 2013
Cited by 19 | Viewed by 9679
Abstract
Agricultural expansion has eliminated a high proportion of native land cover and severely degraded remaining native vegetation. Managers must determine where degradation is severe enough to merit restoration action, and what action, if any, is necessary. We report on grassland degraded by multiple [...] Read more.
Agricultural expansion has eliminated a high proportion of native land cover and severely degraded remaining native vegetation. Managers must determine where degradation is severe enough to merit restoration action, and what action, if any, is necessary. We report on grassland degraded by multiple factors, including grazing, soil disturbance, and exotic plant species introduced in response to agriculture management. We use a multivariate method to categorize plant communities by degradation state based on floristic and biophysical degradation associated with historical land use. The variables we associate with degradation include abundance of the invasive cool-season grass, tall fescue (Schedonorus phoenix (Scop.) Holub); soil organic carbon (SOC); and heavy livestock grazing. Using a series of multivariate analyses (ordination, hierarchical clustering, and multiple regression), we identify patterns in plant community composition and describe floristic degradation states. We found vegetation states to be described largely by vegetation composition associated primarily with tall fescue and secondarily by severe grazing, but not soil organic carbon. Categorizing grasslands by vegetation states helps managers efficiently apply restoration inputs that optimize ecosystem response, so we discuss potential restoration pathways in a state-and-transition model. Reducing stocking rate on grassland where grazing is actively practiced is an important first step that might be sufficient for restoring grassland with high native species richness and minimal degradation from invasive plants. More severe degradation likely requires multiple approaches to reverse degradation. Of these, we recommend restoration of ecological processes and disturbance regimes such as fire and grazing. We suggest old-field grasslands in North America, which are similar to European semi-natural grassland in composition and function, deserve more attention by conservation biologists. Full article
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