Field-based calibration and operation of low-cost sensors for particulate matter by linear and nonlinear methods

The added utility of nonlinear methods compared to linear methods in rescaling soil moisture products

Estimating errors in the determination of activation energy by nonlinear methods applied for thermoanalytical measurements performed under constant heating rates

Estimation of unknown parameters in exponential models by linear and nonlinear fitting methods is discussed. Based on the extreme value theorem and Taylor series expansion, it is proved theoretically that the parameters estimated by the linear fitting method alone cannot minimize the sum of the squared residual errors in the measurement data when measurement noise is involved in the data. Numerical simulation is performed to compare the performance of the linear and nonlinear fitting methods. Simulation results show that the linear method can obtain only a suboptimal estimate of the unknown parameters and that the nonlinear method gives more accurate results. Application of the fitting methods is demonstrated where the water spectral attenuation coefficient is estimated from underwater images and imaging distances, which supports the improvement in the accuracy of parameter estimation by the nonlinear fitting method.

Purpose Social Life Cycle Assessment (S-LCA) is a tool used to evaluate the social sustainability of products and systems. The performance reference scale is the commonly used S-LCA approach for agricultural systems but has limitations including reliance on social performance assessments, lack of sector-specific value-added activity variables, and dependence on linear reference scoring. These limitations can lead to inaccurate assessments of social issues. We aimed to develop a methodology for the pork value chain and agricultural systems to overcome these shortcomings. Methods Performance reference points were sourced from national and regional pig industry benchmarks, while generic data was used for inventory indicators. Social performance was expressed using ordinal scores which were converted to cardinal scores based on expert judgments. Social performance was converted to social risks using reversed min–max normalization. The “people” activity variable was enhanced by incorporating population and pig densities with pig per capita used to distinguish the local community from society. Social risks were aggregated with social issue weights and activity variables to calculate social risk time, which culminated in the estimation of social hotspot indices. These enhancements were compared using linear and nonlinear scoring methods. Results and discussion Average social risks were highest for pigs (0.57 vs. 0.64) and lowest for society (0.47 vs. 0.44) for linear and nonlinear methods, respectively. The distribution and ranking of social risk time for social issues varied between the scoring methods across all stakeholder groups. Both linear and nonlinear methods identified pig farm as a social risk hotspot (0.57 vs. 0.65) and the consumption value chain stage as a social opportunity hotspot (0.39 vs. 0.31). The linear scoring method showed a lack of granularity and systematic bias in estimating the social risks, while the nonlinear method was more nuanced due to incorporating contextualization into the reference scores. Conclusion The proposed methodology highlighted the importance of including social risks and hotspots, alongside social performance, for an agricultural system S-LCA. It demonstrated the advantages of nonlinear scoring over the linear method, overcoming limitations like lack of granularity and systemic bias in the assessment of social issues. However, a limitation of the nonlinear method lies in potential bias when selecting experts for social issue contextualization. This can be mitigated by carefully selecting stakeholder representatives and conducting a sensitivity analysis.

In this study, the sorption of methylene blue, a basic dye, onto tamarind fruit shell was studied by performing batch kinetic sorption experiments. The equilibrium kinetic data were analyzed using the pseudo-second-order kinetic model. A comparison between linear least squares method and nonlinear regression method of estimating the kinetic parameters was examined. Four pseudo-second-order kinetic linear equations were discussed. The coefficient of determination (r 2), and the chi-square (χ2) test were employed as error analysis methods to determine the best-fitting equation. Kinetic parameters obtained from four kinetic linear equations using the linear method differed but they were the same when nonlinear method was used. Present investigation showed that by linear method a Type 1 expression very well represent the kinetic uptake of methylene blue onto tamarind fruit shell. Linear method was found to check only the hypothesis instead of verifying the kinetic model. Nonlinear regression method was found to be the more appropriate method to determine the rate kinetic parameters.

COMPARISON OF EQUIVALENT LINEAR AND NON LINEAR METHODS ON GROUND RESPONSE ANALYSIS: CASE STUDY AT WEST BANGKA SITE. Within the framework of identifying NPP sites, site surveys are performed in West Bangka (WB), Bangka-Belitung Island Province. Ground response analysis of a potential site has been carried out using peak strain profiles and peak ground acceleration. The objective of this research is to compare Equivalent Linear (EQL) and Non Linear (NL) methods of ground response analysis on the selected NPP site (West Bangka) using DeepSoil software. Equivalent linear method is widely used because requires soil data in simple way and short time of computational process. On the other hand, non linear method is capable of representing the actual soil behaviour by considering non linear soil parameter. The results showed that EQL method has similar trends to NL method. At surface layer, the acceleration values for EQL and NL methods are resulted as 0.425g and 0.375g respectively. NL method is more reliable in capturing higher frequencies of spectral acceleration compared to EQL method.

Authors propose three-dimensional linear and simplified nonlinear soil response methods based on an input seismic wave field. An input wave field is employed to treat seismic surface waves excited by a deep structure in a shallow soil model. First, the linear method is applied to a hard- and a soft-soil site located in Mexico City, and soil responses excited by S-, surface-, and whole-wave fields reproduce the input waves fields well. Then, the linear method is applied to estimate soil responses for three large earthquakes at two soft-soil sites located in the reclaimed zone of Tokyo Bay, and again it works well. Finally, authors attempt to perform nonlinear and liquefaction soil response analyses in the reclaimed zone, on the basis of an input wave field modified according to varied soil properties. The nonlinear method seems to provide reasonable nonlinear and liquefaction soil responses.

Large survey databases for aging-related analysis are often examined to discover key factors that affect a dependent variable of interest. Typically, this analysis is performed with methods assuming linear dependencies between variables. Such assumptions however do not hold in many cases, wherein data are linked by way of non-linear dependencies. This in turn requires applications of analytic methods, which are more accurate in identifying potentially non-linear dependencies. Here, we objectively compared the feature selection performance of several frequently-used linear selection methods and three non-linear selection methods in the context of large survey data. These methods were assessed using both synthetic and real-world datasets, wherein relationships between the features and dependent variables were known in advance. In contrast to linear methods, we found that the non-linear methods offered better overall feature selection performance than linear methods in all usage conditions. Moreover, the performance of the non-linear methods was more stable, being unaffected by the inclusion or exclusion of variables from the datasets. These properties make non-linear feature selection methods a potentially preferable tool for both hypothesis-driven and exploratory analyses for aging-related datasets.

A comparison was made of the linear least-squares method and a nonlinear least-square method of the Langmuir isotherm and pseudo second order kinetic model for the biosorption of methylene blue onto rice husk. The parameters obtained from the linear method and the nonlinear method were different. The error analysis was performed. Results showed that both linear and nonlinear method can be used to fit the experimental data. The nonlinear method may be a better way to obtain the desired parameters.

Large conduit arteries are not purely elastic, but viscoelastic, which affects not only the mechanical behavior but also the ventricular afterload. Different hysteresis loops such as pressure-diameter, pressure-luminal cross-sectional area (LCSA), and stress-strain have been used to estimate damping capacity, which is associated with the ratio of the dissipated energy to the stored energy. Typically, linearized methods are used to calculate the damping capacity of arteries despite the fact that arteries are nonlinearly viscoelastic. The differences in the calculated damping capacity between these hysteresis loops and the most common linear and correct nonlinear methods have not been fully examined. The purpose of this study was thus to examine these differences and to determine a preferred approach for arterial damping capacity estimation. Pressurization tests were performed on mouse extralobar pulmonary and carotid arteries in their physiological pressure ranges with pressure (P) and outer diameter (OD) measured. The P-inner diameter (ID), P-stretch, P-Almansi strain, P-Green strain, P-LCSA, and stress-strain loops (including the Cauchy and Piola-Kirchhoff stresses and Almansi and Green strains) were calculated using the P-OD data and arterial geometry. Then, the damping capacity was calculated from these loops with both linear and nonlinear methods. Our results demonstrate that the linear approach provides a reasonable approximation of damping capacity for all of the loops except the Cauchy stress-Almansi strain, for which the estimate of damping capacity was significantly smaller (22 ± 8% with the nonlinear method and 31 ± 10% with the linear method). Between healthy and diseased extralobar pulmonary arteries, both methods detected significant differences. However, the estimate of damping capacity provided by the linear method was significantly smaller (27 ± 11%) than that of the nonlinear method. We conclude that all loops except the Cauchy stress-Almansi strain loop can be used to estimate artery wall damping capacity in the physiological pressure range and the nonlinear method is recommended over the linear method.

The use of QT-prolongation as a biomarker for arrhythmia risk requires that researchers correct the QT-interval (QT) to control for the influence of heart rate (HR). QT correction methods can vary but most used are the universal correction methods, such as Bazett's or Van de Water's, which use a single correction formula to correct QT-intervals in all the subjects of a study. Such methods fail to account for differences in the QT/HR relationship between subjects or over time, instead relying on the assumption that this relationship is consistent. To address these changes in rate relationships, we test the effectiveness of linear and non-linear individual correction methods. We hypothesize that individual correction methods that account for additional influences on the rate relationship will result in more effective and consistent correction. To increase the scope of this study we use bootstrap sampling on ECG recordings from non-human primates and beagle canines dosed with vehicle control. We then compare linear and non-linear individual correction methods through their ability to reduce HR correlation and standard deviation of corrected QT values. From these results, we conclude that individual correction methods based on post-treatment data are most effective with the linear methods being the best option for most cases in both primates and canines. We also conclude that the non-linear methods are more effective in canines than primates and that accounting for light status can improve correction while examining the data from the light periods separately. Individual correction requires careful consideration of inter-subject and intra-subject variabilities.

Pseudo second order kinetics and pseudo isotherms for malachite green onto activated carbon: Comparison of linear and non-linear regression methods

This study establishes a series of tests to examine the relative utility of nonlinear time series analysis for oceanic data. The performance of linear autoregressive models and nonlinear delay coordinate embedding methods are compared for three numerical and two observational data sets. The two observational data sets are (1) an hourly near‐bottom pressure time series from the South Atlantic Bight and (2) an hourly current‐meter time series from the Middle Atlantic Bight (MAB). The nonlinear methods give significantly better predictions than the linear methods when the underlying dynamics have low dimensionality. When the dimensionality is high, the utility of nonlinear methods is limited by the length and quality of the time series. On the application side we mainly focus on the MAB data set. We find that the slope velocities are much less predictable than shelf velocities. Predictability on the slope after several hours is no better than the statistical mean. On the other hand, significant predictability of shelf velocities can be obtained for up to at least 12 hours.

Residual stress has significant impacts on the performance of the mechanical components, especially on its strength, fatigue life, corrosion resistance, and dimensional stability. In this chapter, based on acoustoelasticity theory, the ultrasonic linear detection method of residual stress and the nonlinear detection method are analyzed in theory. In the study of ultrasonic linear detection method, the time of longitudinal wave propagation along the stress direction and shear wave with a propagation direction perpendicular to the stress direction and a polarization direction parallel to the stress direction are used to characterize the stress value. In the study of ultrasonic nonlinear detection method, ultrasonic nonlinear coefficient of second order and third order is used to characterize the stress. To build experimental systems to contrast the detection results of linear method and nonlinear method, it shows that the two methods have good agreement. At last, the linear and nonlinear method are applied to field detection of residual stress, and achieved good results.

A digital elevation model (DEM), which is used to represent a terrain surface, is normally constructed by applying an interpolation method on given sample elevation points. Interpolation methods can be classified into two classes: linear methods, which have a low time cost and are suitable for terrains where there is little change in elevation, and nonlinear methods, which normally consume comparatively more time and are more suitable for terrains where there are frequent changes in elevation. A hybrid interpolation method, which involves both a linear method and a nonlinear method of interpolation, is proposed in this paper. The proposed method aims to integrate the advantages of both linear and nonlinear interpolation methods for the refinement of regular grid DEM. Here, the bilinear is identified as the linear method, and the bi‐cubic is taken to be the nonlinear interpolation method. The hybrid method is an integration of a linear model and nonlinear interpolation model with a parameter that defines the weights for each of the models. The parameter is dependent on the complexity of the terrain, for which a DEM is to be interpolated. The experimental results in this study demonstrate that the hybrid method is effective for interpolating DEMs for various types of terrain.