General Nonlinear Relationship Research Articles

Exploring Public Space Satisfaction in Old Residential Areas Based on Impact-Asymmetry Analysis

The renovation of public space environments in old residential areas has become the focal point in Chinese urban renewal and promotion of urban sustainable development; thus, an urgent need for research expansion is attached to identifying the environmental factors of public space and their impacts from the perspective of residents’ needs and satisfaction. Taking Hefei, China, as an example, and based on a satisfaction survey of the public space environment in old residential areas, this study discerned critical factors affecting public space satisfaction through gradient-boosting decision trees and impact-asymmetry analysis methods, after which the asymmetric relationship between public space environment factors and resident satisfaction was tested and the priority and goal of public space environment renovation were obtained. The results indicate that the following: (1) Compared with physical environment factors, current social environment factors, including uncivilized behavior, space occupation, and hygiene and cleanliness, exert a greater impact on the overall satisfaction. (2) The hypothesis that there exists a general nonlinear relationship between environmental factors and satisfaction is verified, with all social environment factors proving to be nonlinear and physical environment factors being highly related to social environment creation, such as nursing space for the old and young, reading and learning space, and display and communication space. (3) A priority hierarchy for the improvement of environmental factors should be established, which basically conforms to Maslow’s hierarchy of needs theory. The role of social environment renovation should be highlighted, along with the necessity to bolster community governance and public space management. At the level of the physical environment, more space should be available for the activities of residents, display and communication, and reading and learning. This study can provide a corresponding theoretical basis and planning inspiration for meeting the multiple needs of residents for public space, improving life happiness, and promoting the sustainable development of cities in the renovation of public space environments in old residential areas.

A deep transfer learning framework for mapping high spatiotemporal resolution LAI

Leaf area index (LAI) is an important variable for characterizing vegetation structure. Contemporary satellite-based LAI products with moderate spatial resolution, such as those derived from the MODIS observations, offer unique opportunities for large-scale monitoring but are insufficient for resolving heterogeneous landscapes. Although high-resolution satellite observations can derive detailed LAI maps, the low revisit frequency and the presence of cloud cover disrupt the temporal continuity of these high-resolution data, thereby leading to the fact that most current LAI inversion models for high spatial resolution data are based on single pixel and date without fully utilizing temporal information. Moreover, LAI estimation models trained solely using satellite products or simulations are also impeded by the inconsistencies between field and satellite LAI exist owing to local atmospheric, soil, and canopy conditions, while in-situ LAI measurements are sparse and insufficient for large-scale missions. To address these challenges, this study proposed a new framework based on deep transfer learning, which includes three key features that contribute to its high performance. Firstly, a Bi-directional Long Short-Term Memory (Bi-LSTM) model is pre-trained using MODIS reflectance and MODIS LAI products to capture the general non-linear relationship between reflectance and LAI and incorporate temporal dependencies as prior information to reduce uncertainties associated with ill-posed inversion problems and noises. Secondly, this pre-trained Bi-LSTM is transferred from satellite to field by fine-tuning with sparse in-situ LAI measurements to overcome issues arising from local inconsistencies. Thirdly, reconstructed Landsat time-series images via fusing MODIS and Landsat reflectance images are used as inputs of the Bi-LSTM to generate high-quality Landsat LAI products at both high spatial and temporal resolutions. To validate the proposed approach, field LAI measurements were collected at nine locations across the contiguous U.S. from 2000 to 2018, including three land cover types: croplands, grasslands, and forest. Quantitative assessments demonstrate that the Bi-LSTM outperforms three benchmarks, including a PROSAIL-based Look-Up Table (LUT) method, a random forest-based LAI retrieval and MODIS LAI (MCD15A3H), exhibiting lower RMSE and higher R2 in most cases. Additionally, the Bi-LSTM predictions yield lower random fluctuations than estimations from the LUT·, random forest and MODIS LAI, indicating the higher robustness of the proposed framework. The findings of this study highlight the value of transfer learning in estimation of vegetation biophysical parameters, which involves pre-training using sufficient existing satellite products to produce a generalized model and transferring knowledge from in-situ measurements to bridge gaps between satellite and field. By leveraging advanced transfer learning techniques and multi-source and multi-scale data, the proposed framework enables the production of long-term LAI maps at fine resolutions, facilitating downstream applications in regions characterized by high spatial heterogeneity.

Estimating safety performance functions for two-lane rural roads using an alternative functional form for traffic volume

Statistical models of expected crash frequency are referred to as Safety Performance Functions (SPFs) in the first edition of the American Association of State Highway and Transportation Officials’ Highway Safety Manual (HSM). The SPFs in the HSM specify expected annual crash frequencies as a function of various roadway and roadside features, with the most important predictor variable being traffic volume, which serves as a measure of vehicle exposure to crashes. Traffic volumes are typically measured using the average annual daily traffic and are incorporated into the SPFs using a natural logarithm transformation. This specification suggests that the relationship between expected crash frequency and traffic volume increases non-linearly with a constant elasticity over the range of observed values. While researchers concur that the relationship between expected crash frequencies and traffic volume is non-linear, further exploration of the functional form of this relationship may offer additional insights concerning the association between safety performance and vehicle exposure. This paper proposes an alternative functional form for the traffic volume variable in SPFs that allows for different elasticities between traffic volume and expected crash frequency within different traffic volume ranges, while preserving the same general non-linear relationship in existing HSM SPFs. Although other forms—like the Hoerl function—have been proposed in the literature, the proposed model allows for natural breakpoints in the traffic volume for which roadway or geometric features might have varying effects on low- or high-volume roads. The proposed functional form was applied to SPFs developed for two-lane rural roadways in Pennsylvania. Comparisons with SPFs developed using the traditional and Hoerl functional forms suggest that this proposed functional form offers an improved fit and predictive performance, and thus might be considered for the development of future SPFs.

Medium amplitude parallel superposition (MAPS) rheology. Part 1: Mathematical framework and theoretical examples

A new mathematical representation for nonlinear viscoelasticity is presented based on the application of the Volterra series expansion to the general nonlinear relationship between shear stress and shear strain history. This theoretical and experimental framework, which we call medium amplitude parallel superposition (MAPS) rheology, reveals a new material property, the third-order complex modulus, which describes completely the weakly nonlinear response of a viscoelastic material in an arbitrary simple shear flow. In this first part, we discuss several theoretical aspects of this mathematical formulation and new material property. For example, we show how MAPS measurements can be performed in strain- or stress-controlled contexts and provide relationships between the weakly nonlinear response functions measured in each case. We show that the MAPS response function is a superset of the response functions that have been previously reported in medium amplitude oscillatory shear and parallel superposition rheology experiments. We also show how to exploit inherent symmetries of the MAPS response function to reduce it to a minimal domain for straightforward measurement and visualization. We compute this material property for a few constitutive models to illustrate the potential richness of the datasets generated by MAPS experiments. Finally, we discuss the MAPS framework in the context of some other nonlinear, time-dependent rheological probes and explain how the MAPS methodology has a distinct advantage over these others because it generates data embedded in a very high-dimensional space without driving fluid mechanical instabilities, and is agnostic to the flow protocol.

KerNL: Kernel-Based Nonlinear Approach to Parallel MRI Reconstruction.

The conventional calibration-based parallel imaging method assumes a linear relationship between the acquired multi-channel k-space data and the unacquired missing data, where the linear coefficients are estimated using some auto-calibration data. In this paper, we first analyze the model errors in the conventional calibration-based methods and demonstrate the nonlinear relationship. Then, a much more general nonlinear framework is proposed for auto-calibrated parallel imaging. In this framework, kernel tricks are employed to represent the general nonlinear relationship between acquired and unacquired k-space data without increasing the computational complexity. Identification of the nonlinear relationship is still performed by solving linear equations. Experimental results demonstrate that the proposed method can achieve reconstruction quality superior to GRAPPA and NL-GRAPPA at high net reduction factors.

A visco-hyperelastic constitutive model and its application in bovine tongue tissue

Material properties of the human tongue tissue have a significant role in understanding its function in speech, respiration, suckling, and swallowing. Tongue as a combination of various muscles is surrounded by the mucous membrane and is a complicated architecture to study. As a first step before the quantitative mechanical characterization of human tongue tissues, the passive biomechanical properties in the superior longitudinal muscle (SLM) and the mucous tissues of a bovine tongue have been measured. Since the rate of loading has a sizeable contribution to the resultant stress of soft tissues, the rate dependent behavior of tongue tissues has been investigated via uniaxial tension tests (UTTs). A method to determine the mechanical properties of transversely isotropic tissues using UTTs and inverse finite element (FE) method has been proposed.Assuming the strain energy as a general nonlinear relationship with respect to the stretch and the rate of stretch, two visco-hyperelastic constitutive laws (CLs) have been proposed for isotropic and transversely isotropic soft tissues to model their stress-stretch behavior. Both of them have been implemented in ABAQUS explicit through coding a user-defined material subroutine called VUMAT and the experimental stress-stretch points have been well tracked by the results of FE analyses. It has been demonstrated that the proposed laws make a good description of the viscous nature of tongue tissues. Reliability of the proposed models has been compared with similar nonlinear visco-hyperelastic CLs.

Effect Analysis Using Nonlinear Structural Equation Mixture Modeling

In this article, we present an approach for comprehensive analysis of the effectiveness of interventions based on nonlinear structural equation mixture models (NSEMM). We provide definitions of average and conditional effects and show how they can be computed. We extend the traditional moderated regression approach to include latent continous and discrete (mixture) variables as well as their higher order interactions, quadratic or more general nonlinear relationships. This new approach can be considered a combination of the recently proposed EffectLiteR approach and the NSEMM approach. A key advantage of this synthesis is that it gives applied researchers the opportunity to gain greater insight into the effectiveness of the intervention. For example, it makes it possible to consider structural equation models for situations where the treatment is noneffective for extreme values of a latent covariate but is effective for medium values, as we illustrate using an example from the educational sciences.

Improvement in HSPF's Low-Flow Predictions by Implementation of a Power Law Groundwater Storage-Discharge Relationship

We have enhanced the ability of a widely used watershed model, Hydrologic Simulation Program — FORTRAN (HSPF), to predict low flows by reconfiguring the algorithm that simulates groundwater discharge. During dry weather periods, flow in most streams consists primarily of base flow, that is, groundwater discharged from underlying aquifers. In this study, HSPF's groundwater storage-discharge relationship is changed from a linear to a more general nonlinear relationship which takes the form of a power law. The nonlinear algorithm is capable of simulating streamflow recession curves that have been found in some studies to better match observed dry weather hydrographs. The altered version of HSPF is implemented in the Chesapeake Bay Program's Phase 5 Model, an HSPF-based model that simulates nutrient and sediment loads to the Chesapeake Bay, and is tested in the upper Potomac River basin, a 29,950 km2 drainage area that is part of the Bay watershed. The nonlinear relationship improved median Nash-Sutcliffe efficiencies for log daily flows at the model's 45 calibration points. Mean absolute percent error on low-flow days dropped in five major Potomac River tributaries by up to 12 percentage points, and in the Potomac River itself by four percentage points, where low-flow days were defined as days when observed flows were in the lowest 5th percentile range. Percent bias on low-flow days improved by eight percentage points in the Potomac River, from −11 to −3%.

Improved estimation of mineral and fluid volumetric concentrations from well logs in thinly bedded and invaded formations

Calculation of mineral and fluid volumetric concentrations from well logs is one of the most important outcomes of formation evaluation. Conventional estimation methods assume linear or quasi-linear relationships between volumetric concentrations of solid/fluid constituents and well logs. Experience shows, however, that the relationship between neutron porosity logs and mineral concentrations is generally nonlinear. More importantly, linear estimation methods do not explicitly account for shoulder-bed and/or invasion effects on well logs, nor do they account for differences in the volume of investigation of the measurements involved in the estimation. The latter deficiencies of linear estimation methods can cause appreciable errors in the calculation of porosity and hydrocarbon pore volume. We investigated three nonlinear inversion methods for assessment of volumetric concentrations of mineral and fluid constituents of rocks from multiple well logs. All three of these methods accounted for the general nonlinear relationship between well logs, mineral concentrations, and fluid saturations. The first method accounted for the combined effects of invasion and shoulder beds on well logs. The second method also accounted for shoulder-bed effects but was intended for cases where mud-filtrate invasion is negligible or radially deep. Finally, the third method was designed specifically for analysis of thick beds where mud-filtrate invasion is either negligible or radially deep. Numerical synthetic examples of application indicated that nonlinear inversion of multiple well logs is a reliable method to quantify complex mineral and fluid compositions in the presence of thin beds and invasion. Comparison of results against those obtained with conventional multimineral estimation methods confirmed the advantage of nonlinear inversion of multiple well logs in quantifying thinly bedded invaded formations with variable and complex lithology, such as those often encountered in carbonate formations.

Decomposing the Composition Effect

This paper proposes a decomposition of the composition effect, i.e. the part of the observed between-group difference in the distribution of some economic outcome that can be explained by differences in the distribution of covariates. Our decomposition contains three types of components: (i) the direct contributions of each covariate due to between-group differences in the respective marginal distributions, (ii) several “two way” and higher order interaction effects due to the interplay between two or more covariates' marginal distributions, and (iii) a effect accounting for between-group differences in dependence patterns among the covariates. Our methods can be used to decompose differences in arbitrary distributional features, like quantiles or inequality measures, and allows for general nonlinear relationships between the outcome and the covariates. It can easily be implemented in practice using standard econometric techniques. An application to wage data from the US illustrates the empirical relevance of the decomposition’s components.

A general boundary condition for liquid flow at solid surfaces

Modelling fluid flows past a surface is a general problem in science and engineering, and requires some assumption about the nature of the fluid motion (the boundary condition) at the solid interface. One of the simplest boundary conditions is the no-slip condition1,2, which dictates that a liquid element adjacent to the surface assumes the velocity of the surface. Although this condition has been remarkably successful in reproducing the characteristics of many types of flow, there exist situations in which it leads to singular or unrealistic behaviour—for example, the spreading of a liquid on a solid substrate3,4,5,6,7,8, corner flow9,10 and the extrusion of polymer melts from a capillary tube11,12,13. Numerous boundary conditions that allow for finite slip at the solid interface have been used to rectify these difficulties4,5,11,13,14. But these phenomenological models fail to provide a universal picture of the momentum transport that occurs at liquid/solid interfaces. Here we present results from molecular dynamics simulations of newtonian liquids under shear which indicate that there exists a general nonlinear relationship between the amount of slip and the local shear rate at a solid surface. The boundary condition is controlled by the extent to which the liquid ‘feels’ corrugations in the surface energy of the solid (owing in the present case to the atomic close-packing). Our generalized boundary condition allows us to relate the degree of slip to the underlying static properties and dynamic interactions of the walls and the fluid.

Application of Neural Networks for Sensor Validation and Plant Monitoring

Sensor and process monitoring in power plants requires the estimation of one or more process variables. Neural network paradigms are suitable for establishing general nonlinear relationships among ...

Estimation of Subgrade Resilient Modulus from Standard Tests

Mechanistic pavement design procedures based on elastic layer theory require the specification of elastic moduli for each material in the pavement section. Repeated load tests yielding a resilient modulus are frequently used to characterize the soil subgrade. Due to difficulties associated with cyclic testing, approximate methods are often used for design estimates of resilient modulus. These approximations are often based only on shear strength measures and do not account for the dependence on the magnitude of cyclic deviator stress. A procedure is described to relate the soil‐index properties and the moduli obtained from uncon‐fined compression tests, to resilient modulus. Two statistical models are described and demonstrated for 11 soils from throughout the state of Tennessee. One model provides an estimation of the breakpoint resilient modulus, or the modulus at a deviator stress of 6 psi (41 kPa). The second model provides a general nonlinear relationship for the modulus of fine‐grained soils as a function of deviator stress. Both models are demonstrated for a range of soils and are shown to provide a good characterization of the response for the soils investigated. Similar relationships can be developed for other subgrade soils, and may prove useful to agencies that use deterministic pavement design procedures, but lack the capability for high‐production repeated‐load testing.

Adsorption of gases on 4A synthetic zeolite

Equilibrium data are presented for the adsorption of permanent gases and C1 and C2 hydrocarbons on Linde 4A synthetic zeolite from 50 °C down to the boiling point of the adsorbate or to a temperature at which the rate was very slow. The Freundlich equation often fits isotherms accurately; however, these linear logarithmic plots seem to be only portions of a more general non-linear relationship. Generalized Polanyi plots did not yield a unique characteristic curve for individual adsorbates at different temperatures nor for groups of adsorbates; nevertheless, these plots are useful in estimating the relative strength of adsorption of gases. Ar, O2, CH4, and C2H6 were the least strongly adsorbed, followed in order of increasing strength by N2, CO, CO2, and C2H2. Ethylene was strongly but anomalously adsorbed. For the gases studied, the quadrupole moment seems to be the principal factor determining strong adsorption.