Common Linear Model Research Articles

Improving extrapolation capabilities of a data-driven prediction model for control of an air separation unit

In model predictive control, fully data-driven prediction models can be used besides common (non-)linear prediction models based on first-principles. Although no process knowledge is required while relying only on sufficient data, they suffer in their extrapolation capability which is shown in the present work for the control of an air separation unit. In order to compensate for the deficits in the extrapolation behavior, a further data source, here a digital twin, is deployed for additional data generation. The plant data set is augmented with the artificially generated data giving rise to a hybrid model in terms of data generation. It is shown that this model can significantly improve the prediction quality in former extrapolation areas of the plant data set. Even conclusions about the uncertainty behavior of the prediction model can be found.

Efficient trust region filter modeling strategies for computationally expensive black-box optimization

The study and application of contemporary optimization techniques considerably enhance the efficiency of chemical research and manufacturing. With the dynamic progression of modern manufacturing technologies, the emergence of numerous black-box models characterized by inaccessible mathematical formulations and high evaluation costs poses new challenges to traditional optimization methods, leading to difficulty in programming and solving. Hence, based on the trust region filter (TRF) method, we define a new framework to elevate optimization efficiency in this study for chemical systems involving computationally expensive black-box functions. Sampling size per iteration is reduced, and sampling efficiency is improved by incorporating the known data beyond the trust region to assist in constructing reduced models, which is achieved by the application of the Gaussian process. Through comparison and validation of benchmark tests and case studies, this approach demonstrates that using the Gaussian process as the reduced model can lower the number of calls to black-box functions by more than half compared to common linear and quadratic models, and convergence to first-order critical points can still be guaranteed.

Optimal biochar selection for cadmium pollution remediation in Chinese agricultural soils via optimized machine learning

Biochar is effective in mitigating heavy metal pollution, and cadmium (Cd) is the primary pollutant in agricultural fields. However, traditional trial-and-error methods for determining the optimal biochar remediation efficiency are time-consuming and inefficient because of the varied soil, biochar, and Cd pollution conditions. This study employed the machine learning method to predict the Cd immobilization efficiency of biochar in soil. The predictive accuracy of the random forest (RF) model was superior to that of the other common linear and nonlinear models. Furthermore, to improve the reliability and accuracy of the RF model, it was optimized by employing a root-mean-squared-error-based trial-and-error approach. With the aid of the optimized model, the empirical categories for soil Cd immobilization efficiency were biochar properties (60.96 %) > experimental conditions (19.6 %) ≈ soil properties (19.44 %). Finally, this study identified the optimal biochar properties for enhancing agricultural soil Cd remediation in different regions of China, which was beneficial for decision-making regarding nationwide agricultural soil remediation using biochar. The immobilization effect of alkaline biochar was pronounced in acidic soils with relatively high organic matter. This study provides insights into the immobilization mechanism and an approach for biochar selection for Cd immobilization in agricultural soil.

Magnetic alginate supported potassium manganese ferrocyanide for the recovery of uranium from acidic wastewater

Abstract With the rapid development of the atomic energy industry, the demand for nuclear fuel has risen, while the limited resources of uranium mines make it difficult to meet the needs of the future development of nuclear energy. Expanding sources of uranium acquisition is necessary, and the enrichment and recovery of precious uranium from uranium-containing wastewater is invaluable. By synthesizing alginate supported potassium manganese ferrocyanide nanocomposites with magnetic response (KMnFC/MA/Fe3O4), the high efficiency adsorption and separation of uranium in acidic uranium-containing wastewater can be realized conveniently and quickly. The magnetic composite was characterized by a variety of technical means, and the adsorption behavior of the magnetic material on uranium was studied by static adsorption experiments under different environmental conditions. The adsorption kinetics and isotherm of uranium by KMnFC/MA/Fe3O4 were studied by using some common linear adsorption models. The results show that the adsorption rate of KMnFC/MA/Fe3O4 on uranium is fast, and the adsorption equilibrium can be reached within 90 min. The adsorption process conforms to a pseudo-secondary kinetic model and is dominated by chemisorption. The adsorption of uranium by KMnFC/MA/Fe3O4 magnetic material is single molecular layer adsorption, and the maximum adsorption capacity is 425.5 mg g−1 at 35 °C. KMnFC/MA/Fe3O4 is a promising adsorbent in the field of acidic low-concentration uranium wastewater treatment because of its good effect on the treatment of low concentration uranium wastewater, the concentration of uranium in the wastewater reaches the emission standard after treatment and it is easy to be separated magnetically after adsorption.

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.

Modeling Thermal Developmental Trajectories and Thermal Requirements of the Ladybird Stethorus gilvifrons.

The development rate of the predatory ladybird, Stethorus gilvifrons (Mulsant), fed on Tetranychus urticae Koch, was determined at 15, 20, 25, 27, 30, 34, and 38 °C. The total development time from egg to adult emergence for females was estimated to be 61.4, 31.6, 14.4, 13.3, 12.5, and 11.7 days, respectively. The development time decreased with increasing temperature from 15 to 34 °C, but all eggs failed to hatch at 38 °C. The lower temperature threshold (T0) for the entire development period and the thermal constant (K) for female S. gilvifrons were estimated to be 11.64 °C and 194.50 degree-days (DD) using the common linear model, and 11.96 °C and 187.87 DD using the Ikemoto and Takai model, respectively. Data were fitted to 20 non-linear development rate models and the thermal thresholds (Tmin and Tmax) and optimal temperature (Topt) were estimated. Among non-linear models, the Briere-2 and Ikemoto and Takai linear model provided adequate descriptions of the temperature-dependent development of S. gilvifrons. The upper-temperature threshold was estimated to be about 44 °C using the Logan-10 non-linear model. The estimated thermal development characteristics can be used to predict the occurrence and the population dynamics, as well as to improve the mass rearing and release, of S. gilvifrons for the biological control of T. urticae.

Application of elastic net in quantitative analysis of major elements using Martian laser-induced breakdown spectroscopy datasets

Multiple sets of laser-induced breakdown spectroscopy (LIBS) instruments, including ChemCam (Curiosity), SuperCam (Perseverance), and the Mars Surface Composition Detector (MarSCoDe, Zhurong), are working currently on the surface of Mars, a booming scene of LIBS technology application to planetary exploration. One of the primary challenges faced by those LIBS instruments is accurate and quantitative chemical composition determination of unexplored geological targets. Elastic net is a linear regression model that combines ridge regression and lasso model, which inherits the sparseness of lasso and the stability of ridge. In this work, we investigated the spectral features selected by elastic net model, the model performance and application to over 23,000 LIBS points. Selected features exhibit significant emission lines that are attributed to a certain single element and a few lines attributed to other related elements. These features enhance the interpretability of the model and weaken the matrix effect in LIBS quantitative analysis. In comparison, the results of elastic net are comparable and may be slightly better in some cases than other common linear regression models. For igneous calibration targets (norite, picrite, and shergottite), the predictions of elastic net are closer to the values measured in Earth laboratory than the final multivariate oxide composition values predicted by ChemCam team. Finally, we predicted the oxide abundances of 8 major elements from Mars LIBS spectra of over 23,000 points using elastic net. The predicted values of the elastic net models are highly correlated with those from the ChemCam team model. These results indicate that elastic net is viable for quantitative analysis Mars LIBS spectra. We propose that elastic net is an important candidate model for the quantitative analysis of the Zhurong MarSCoDe LIBS spectra.

Machine Learning Framework for Intelligent Detection of Wastewater Pollution by IoT-Based Spectral Technology

Industrial wastewater contains excessive micro insoluble solids (MIS) that probably cause environmental pollutions. Near-infrared (NIR) spectroscopy is an advanced technology for rapid detection of the complex targets in wastewater. An Internet of Things (IoT) platform would support intelligent application of the NIR technologies. The studies of intelligent chemometric methods mainly contribute to improve the NIR calibration model based on the IoT platform. With the development of artificial intelligence, the backward interval and synergy interval techniques were proposed in combination use with the least square support vector machine (LSSVM) method, for adaptive selection of the informative spectral wavelength variables. The radial basis function (RBF) kernel is applied for nonlinear mapping. The regulation parameter and the kernel width are fused together for smart optimization. In the design for waveband autofittings, the total of digital wavelengths in the full scanning range was split into 43 equivalent subintervals, and then, the back interval LSSVM (biLSSVM) and the synergy interval LSSVM (siLSSVM) models were both established for the improvement of prediction results based on the adaptive selection of quasidiscrete variable combination. In comparison with some common linear and nonlinear models, the best training model was acquired with the siLSSVM method while the best testing model was obtained with biLSSVM. The intelligent optimization of model parameters indicated that the proposed biLSSVM and siLSSVM deep learning methodologies are feasible to improve the model prediction results in rapid determination of the wastewater MIS content by the IoT-based NIR technology. The machine learning framework is prospectively applied to the fast assessment of the environmental risk of industrial pollutions and water safety.

Fast nonlinear Froude\u2013Krylov force calculation for prismatic floating platforms: a wave energy conversion application case

Computationally fast and accurate mathematical models are essential for effective design, optimization, and control of wave energy converters. However, the energy-maximising control strategy, essential for reaching economic viability, inevitably leads to the violation of linearising assumptions, so the common linear models become unreliable and potentially unrealistic. Partially nonlinear models based on the computation of Froude–Krylov forces with respect to the instantaneous wetted surface are promising and popular alternatives, but they are still too slow when floaters of arbitrary complexity are considered; in fact, mesh-based spatial discretisation, required by such geometries, becomes the computational bottle-neck, leading to simulations 2 orders of magnitude slower than real-time, unaffordable for extensive iterative optimizations. This paper proposes an alternative analytical approach for the subset of prismatic floating platforms, common in the wave energy field, ensuring computations 2 orders of magnitude faster than real-time, hence 4 orders of magnitude faster than state-of-the-art mesh-based approaches. The nonlinear Froude–Krylov model is used to investigate the nonlinear hydrodynamics of the floater of a pitching wave energy converter, extracting energy either from pitch or from an inertially coupled internal degree of freedom, especially highlighting the impact of state constraints, controlled/uncontrolled conditions, and impact on control parameters’ optimization, sensitivity and effectiveness.

Time-space characteristics of viscoelastic post-seismic deformations corresponding to different rheology models

On a long time (> 1 a) scale, the viscoelastic properties of mantle media significantly affect post-seismic deformation. The stress field disturbance in viscoelastic medium caused by fault slip gradually relax, and the relaxation process and its temporal-spatial characteristics are determined by the viscoelastic model. In this paper, we assume that the mantle media are types of common linear rheological models, i.e., the Burgers body, the standard linear solid, and the Maxell body, and we calculate the dislocation Love number and Green function for a spherically symmetric, non-rotating, viscoelastic, and isotropic (SNRVEI) Earth model. The characteristics of the post-seismic relaxation deformations corresponding to the different models are compared. Our results show that for a short time period, the Burgers body and standard linear solid are similar; while for the long time period, the Burgers body and Maxwell body are similar. This suggests that the observations of post-seismic deformation on the surface have a great potential for the inversion of underground viscoelastic structures. However, the potential of using surface displacement to distinguish different rheological models is limited when the observation period is not long enough.

Notes on self-confidence in opinion dynamics

In some research involving opinion formation, there are some details that have not been studied deeply, just as the role of a person’s self-confidence in opinion dynamics. This small but important detail needs to be cleared up. Hence, in this paper, we want to discuss the self-confidence in opinion dynamics with regard to some common linear and nonlinear models: DeGroot, Friedkin–Johnsen, Deffuant–Weisbuch and Hegselmann–Krause (HK) model. We unfold that (1) A person’s self-confidence assumption has an important impact on the consensus condition in DeGroot model; (2) The relationship between the self-confidence on the initial opinion and the current opinion follows a Kuznets curve in Friedkin–Johnsen model; (3) A person’s self-confidence has a close relationship with the convergence parameter in Deffuant–Weisbuch model, which has little impact on the number of opinion clusters at the stable stage; and (4) A person’s self-confidence varies with time at first and then stays at a certain level finally in the HK model, while the person’s self-confidence does not change with time in above three models.

Spatiotemporal variations of total suspended matter in complex archipelagic regions using a sigmoid model and Landsat-8 imagery

Total suspended matter (TSM) is an important parameter of ocean water quality and for aquatic environmental assessment. The Zhoushan Islands are near the estuarine and coastal regions of the Yangtze River and Qiantang River and TSM occurs at very high concentrations and in long-term suspended states. The distribution and variation of TSM in the Zhoushan Islands has great impacts on its coastal water quality and activities such as ferry services, fisheries, and tourism. Based on Landsat-8’s blue and near-infrared bands, this study developed a sigmoid TSM inversion model that was more accurate and robust than the other common linear and exponential models. We also checked three types of atmospheric correction models, FLAASH, 6S, and ACOLITE and determined that ACOLITE is better than the other two methods when using Landsat-8 in ocean color in estuarine and coastal regions. The sigmoid model was then applied to a series of Landsat-8 images covering the Zhoushan Islands from 2013 to 2018, and the image-derived results show that TSM absorption coefficients in the Zhoushan Islands are extremely high and range from 0.26 to 444.29 m−1 with a mean of 113.14 m−1. Furthermore, they have a clear downward gradient from the Hangzhou Bay to the open sea. In addition, the TSM concentrations in winter are usually much higher than those in summer. Our results indicate that TSM spatiotemporal variations in the Zhoushan Islands are not only controlled by many natural environmental factors, such as riverine discharge, but are also significantly influenced by many human activities such as transportation, tourism, and fisheries.

Robust Estimation for Partial Functional Linear Regression Model Based on Modal Regression

This paper presents a robust estimation procedure by using modal regression for the partial functional linear regression, which combines the common linear model with the functional linear regression model. The outstanding merit of the new method is that it is robust against outliers or heavy-tail error distributions while performs no worse than the least-square-based estimation method for normal error cases. The slope function is fitted by B-spline. Under suitable conditions, the authors obtain the convergence rates and asymptotic normality of the estimators. Finally, simulation studies and a real data example are conducted to examine the finite sample performance of the proposed method. Both the simulation results and the real data analysis confirm that the newly proposed method works very well.

Simple Nonlinear Models for Glucose-Insulin Dynamics: Application to Intraperitoneal Insulin Infusion

The design of a model-based control method for an Artificial Pancreas requires a relatively simple and identifiable mathematical model to control glucose levels through hormone delivery. In this work we introduce new, simple nonlinear models to simulate data from experiments where insulin boluses are administrated in the peritoneal cavity. The models account for the delay between insulin administration and its nonlinear transport to other compartments. They were calibrated using experimental data from pigs. The results show that the suggested models are able to describe the data well, with average BIC value of 145. Moreover, the new models were compared with a common linear model which was not able to describe the data well, with BIC value of 920. They were also compared with a common nonlinear model which failed to represent insulin increases in the data and had BIC value of 637. Finally, profile likelihoods were applied for assessing the identifiability of one of the new models.

Estimating development and temperature thresholds of Ephestia kuehniella: toward improving a mass production system.

The development of the Mediterranean flour moth, Ephestia kuehniella (Zeller), was evaluated at 10, 15, 17.5, 20, 22.5, 25, 27.5, 30 and 32.5°C with no lighting. None successfully completed development at 10 and 32.5°C. The total development time from egg to adult emergence was 164, 140, 98, 76, 61, 62 and 50 days, respectively, at the remaining temperatures. The developmental rate of E. kuehniella was described by the common linear model and six non-linear models. The lower temperature threshold for the immature stages and the thermal constant for E. kuehniella were 9°C and 1111 degree-days (DD) to complete development from egg to newly emerged adult. Non-linear models estimated the lower and upper thermal thresholds (Tmin and Tmax) and optimal temperature (Topt). The values of Tmax calculated by three nonlinear models ranged from 34°C to 46°C; Topt for each stage of development varied from 24 and 31°C, consistent with the temperature (30°C) at which the most rapid development occurred. Information on the threshold temperatures for development and thermal requirements can be utilized to predict E. kuehniella population dynamics and phenology and to evaluate optimal temperature conditions for mass rearing in stored products.

On the calculation of daytime CO2 fluxes measured by automated closed transparent chambers

Automated transparent chambers have gained increasing popularity in recent years to continuously measure net CO2 fluxes between low-statured canopies and the atmosphere. In this study, we carried out four field campaigns with chamber measurements in a variety of mountainous grasslands. A mathematic stationary point (or critical point, a point at which the derivative of a function is zero) in the CO2 mixing ratio time series was found in a substantial fraction of the measurements at all the sites, which had a significant influence on the performances of the regression algorithms. The stationary point was probably due to condensed water on the inner wall of the chamber dome, which reduced the solar radiation and resulted in a reversal of the CO2 mixing ratio time series in the chamber (so called Clouded-Glass Effect or CGE in this study). This effect may be the cause of the observed underestimation of daytime CO2 fluxes when using common linear and exponential regression models on continuous automated chamber observations. In order to avoid biased flux estimation of daytime CO2 fluxes, we introduced a linearly increasing term to the exponential function so as to compensate for the influence of the CGE, which gives acceptable model errors and improves the CO2 flux estimation by 5% for temperate mountainous grasslands. We conclude that exponential regression models should be favoured over linear models and recommend to account for the effects of CGE by either excluding ambiguous observations from the flux computations where stationary points can be identified in the CO2 mixing ratio time series, or by adding a linearly increasing term to the exponential regression model.

Comparison of Linear and Nonlinear Behavior of Track Elements in Contact-Impact Models

Existence of short wave length irregularities and discontinuities in the rail, such as corrugation, isolated rail joints, crossings and rail breakage, result in impact forces and an increase in wheel-rail contact force. Extreme forces in such could result in non-linear behavior of ballast and pads, and as a result, employing common linear models mihgt over/under estimate contact forces. A 3D model of wheel and rail is developed in this paper, and by considering rail breakage, validity of linear models and considering non-linear behavior of materials are studied. Wheel-rail interactions are studied for two common pads with high stiffness (HDPE) and low stiffness (Studded) for speeds of 20 to 160 km/h. Three behavioral patterns are considered for the developed 3D model: linear pad and ballast (LP-LB), nonlinear pad and linear ballast (NLP, LB), and nonlinear pad and ballast (NLP, NLB), and results are compared. According to the results, for HDPE pads and impact forces of up to 30 tons, linear model for material could estimate acceptable results. Yet for studded pads, linear model estimates forces that are comparably less than those estimated by non-linear model. Moreover employing NLP-LB model overestimates pad and wheel-rail contact forces by a rather small margin, compared to those estimated by NLP-NLB model, and hence, could be a suitable replacement for it. It is also observed that in order to have a reliable estimate of ballast forces, using non-linear ballast models are mandatory, and neither LP-LB nor NLP-LB could be acceptable replacements.

From Social to Individuals: A Parsimonious Path of Multi-Level Models for Crowdsourced Preference Aggregation.

In crowdsourced preference aggregation, it is often assumed that all the annotators are subject to a common preference or social utility function which generates their comparison behaviors in experiments. However, in reality, annotators are subject to variations due to multi-criteria, abnormal, or a mixture of such behaviors. In this paper, we propose a parsimonious mixed-effects model, which takes into account both the fixed effect that the majority of annotators follows a common linear utility model, and the random effect that some annotators might deviate from the common significantly and exhibit strongly personalized preferences. The key algorithm in this paper establishes a dynamic path from the social utility to individual variations, with different levels of sparsity on personalization. The algorithm is based on the Linearized Bregman Iterations, which leads to easy parallel implementations to meet the need of large-scale data analysis. In this unified framework, three kinds of random utility models are presented, including the basic linear model with L2 loss, Bradley-Terry model, and Thurstone-Mosteller model. The validity of these multi-level models are supported by experiments with both simulated and real-world datasets, which shows that the parsimonious multi-level models exhibit improvements in both interpretability and predictive precision compared with traditional HodgeRank.

Investigating the relationship between physical characteristics of watersheds and nonlinearity of daily streamflow processes

Using time series models is one of the practical methods for simulation and prediction of hydrological data. But often, without examining linear or nonlinear system, common linear time-series models are used. And it is expected that streamflow nonlinearity is heavily influenced by physiographic characteristics of the watershed. In this study, using BDS test, nonlinearity of daily streamflow was examined, then its relationship with the watershed slope and area of hydrometric stations was examined. ADF test was used to test stationarity of data time series. The results of ADF test revealed that with the elimination of non-stationarity factors, streams' flow series become stationary. Also, BDS test results showed that flow was nonlinear. In examining the relationship between streamflow nonlinearity and watershed area, the results revealed that despite R2 = 0.91, nonlinearity of flow was in the significant relationship with the third power area. Regarding the relationship between streamflow nonlinearity and watershed slope, no significant relationship was found. It should be noted that the relationship between these two parameters and the intensity of nonlinearity is the novelty of this article.

Investigating the relationship between physical characteristics of watersheds and nonlinearity of daily streamflow processes

Using time series models is one of the practical methods for simulation and prediction of hydrological data. But often, without examining linear or nonlinear system, common linear time-series models are used. And it is expected that streamflow nonlinearity is heavily influenced by physiographic characteristics of the watershed. In this study, using BDS test, nonlinearity of daily streamflow was examined, then its relationship with the watershed slope and area of hydrometric stations was examined. ADF test was used to test stationarity of data time series. The results of ADF test revealed that with the elimination of non-stationarity factors, streams' flow series become stationary. Also, BDS test results showed that flow was nonlinear. In examining the relationship between streamflow nonlinearity and watershed area, the results revealed that despite R2 = 0.91, nonlinearity of flow was in the significant relationship with the third power area. Regarding the relationship between streamflow nonlinearity and watershed slope, no significant relationship was found. It should be noted that the relationship between these two parameters and the intensity of nonlinearity is the novelty of this article.