Verhulst Model Research Articles

Evolution of aging depth gradient distribution in SBS-modified bitumen during the aging of field

This study investigated the distribution of aging depth gradients in styrene-butadiene-styrene modified bitumen (SBSMB) during natural aging. SBSMB was sourced from bitumen recycling tests and was stratified into upper, middle, and lower layers according to depth. To examine the effects of various aging depths, SBSMB samples from different depths were prepared for subsequent bitumen recycling tests. Then, studying the rheological performance of the SBSMB involved conducting multiple stress creep recovery tests. Subsequently, investigating the bee structure and nanoscale indicators of SBSMB at various aging depths involved utilizing atomic force microscopy testing. Finally, the Verhulst model was applied to assess the aging of SBSMB at different depths. The results have shown that natural aging has gradually diffused from the surface to the interior of the bitumen. An increase in aging time leads to a more pronounced aging effect at the upper levels and an accelerated the downward diffusion rate. This ultimately results in a gradient behavior of the rheological properties of SBSMB at different depths. The quantity of bee structures and the distribution density of bee structures in SBSMB both progressively decrease with increased aging depth. As aging time increases, the aging properties of SBSMB exhibit significant gradient behavior at different depths. Simultaneously, the Verhulst model accurately explain the aging trend of bitumen at different nanoscale depths.

Settlement Forecast of Marine Soft Soil Ground Improved with Prefabricated Vertical Drain-Assisted Staged Riprap Filling

By comparing different settlement forecast methods, eight methods were selected considering the creep of marine soft soils in this case study, including the Hyperbolic Method (HM), Exponential Curve Method (ECM), Pearl Growth Curve Modeling (PGCM), Gompertz Growth Curve Modeling (GGCM), Grey (1, 1) Model (GM), Grey Verhulst Model (GVM), Back Propagation of Artificial Neural Network (BPANN) with Levenberg–Marquardt Algorithm (BPLM), and BPANN with Gradient Descent of Momentum and Adaptive Learning Rate (BPGD). Taking Lingni Seawall soil ground improved with prefabricated vertical drain-assisted staged riprap filling as an example, forecasts of the short-term, medium-term, long-term, and final settlements at different locations of the soft ground were performed with the eight selected methods. The forecasting values were compared with each other and with the monitored data. When relative errors were between 0 and −1%, both the forecasting accuracy and engineering safety were appropriate and reliable. It was concluded that the appropriate forecast methods were different not only due to the time periods during the settlement process, but also the locations of soft ground. Among these methods, only BPGD was appropriate for all the time periods and locations, such as at the edge of the berm, and at the center of the berm and embankment.

Application of Grey Prediction Models for Efficient Traffic Flow Prediction

Traffic flow prediction is crucial in transportation management and optimizing control strategies and infrastructure planning. However, traditional prediction methods often need help handling traffic data's inherent uncertainty and complexity. This paper explores the application of Grey prediction models as a promising approach for efficient traffic flow prediction. Grey prediction models, rooted in Grey systems theory, offer a robust framework for modelling systems with incomplete and uncertain information. The paper provides a comprehensive overview of Grey prediction models, including the Grey Verhulst, Grey-Markov, and Grey differential equation models. It discusses the process of data collection, pre-processing, and model application in traffic flow prediction. Case studies and experimental results demonstrate the effectiveness of Grey prediction models in accurately forecasting traffic flow patterns. Despite challenges such as data sparsity and model complexity, Grey prediction models offer significant advantages over traditional methods, including improved prediction accuracy and adaptability to dynamic traffic conditions. The paper concludes with recommendations for practitioners and researchers interested in leveraging Grey prediction models for efficient traffic management.

Coordinated development of island ecotourism: A comprehensive evaluation of Amami-Oshima Island

Island tourism has garnered growing attention especially with the rapid expansion of ecotourism in island destinations. While past research has explored the integrated development of island tourism, environment, and economy, there exists a demand for a more comprehensive exploration that incorporates social aspects. This study aimed to establish a comprehensive evaluation index system for island ecotourism using Amami-Oshima Island as an example. It uses four tourism subtypes, including environment, economic, social, and other-sector tourism, within the framework for island ecotourism. We employed a Coupling Coordination Degree Model and a Grey Verhulst model, utilizing data from Amami-Oshima Island from 2010 to 2021 as a basis for quantitative analysis of the current status of island ecotourism coupling coordination development and for making predictions. The research outcomes reveal the following: (1) Between 2010 and 2021, Amami-Oshima Island exhibited an overall upward trajectory in the comprehensive development of ecotourism. The environment-tourism subsystem demonstrated robust performance, the social-tourism subsystem displayed fluctuating growth, and the economic and the other-sector tourism dimensions generally progressed in tandem. (2) The coupling degree and coordination level of Amami-Oshima Island ecotourism showed an overall upward trend, with coordination evolving from a state of minimal coordination to an intermediate level. However, opportunities remain to enhance high-quality coordination through mutual influences and interdependencies. (3) Predictions indicate a slight increase in ecotourism coupling coordination on Amami-Oshima Island over the next nine years (2022–2030). Based on these findings, this paper presents several policy recommendations, serving as a guideline for ecotourism development on Amami-Oshima Island. The research results carry significant implications for understanding the present status and future trends of ecotourism on Amami-Oshima Island and offer valuable policy suggestions for the development of ecotourism on other islands.

Study on the Gender Change of the Lamprey in Ecosystem Based on Verhulst and Logistic Models

This paper focuses on the environmental impacts of changes in the sex ratio of the lampreys, the assessment of the strengths and weaknesses of lamprey’s adaptations, and their effects on ecosystem stability. In this paper, we first considered Verhulst and Logistic models of ecosystem-sex-ratio interactions, and predicted and analyzed the potential cascading effects of changes in lampreys sex ratio on larger ecosystems under different scenarios. Then, by integrating the Logistic model, we simulated the development and change of the ecosystem under various conditions, identified assessment metrics, and evaluated the relative strengths and weaknesses of the lampreys. The research in this paper provides important evidence for a deeper understanding of the role of the lampreys in ecosystems and the effects of changes in their sex ratio.

An Analysis of Some Models of Prey-predator Interaction

Biological models of basic prey-predator interaction have been studied. This consisted, at first, in analyzing the basic models of population dynamics such as the Malthus model, the Verhulst model, the Gompertz model and the model with Allee effect ; then, in a second step, to analyze the Lotka-Volterra model and its models improved by taking into account certain important hypotheses such as competition and/or cooperation between species, existence of refuge for prey and migration of species. For each population evolution model presented, a numerical illustration was made for its verification.

IS THE EMPLOYMENT SITUATION IN INDONESIA FAVORABLE? IMPLEMENTATION OF VERHULST MODEL DIFFERENTIAL EQUATION

This research aims to calculate the limit number of workers and unemployment in each province of Indonesia which is estimated to use Carrying Capacity and calculate the employment growth rate of each province in Indonesia. This calculation will help to identify provinces in Indonesia where the growth rate of the working population is negative, the unemployment rate is positive. All of these calculations use the Verhulst Model Differential Equation. The data used in this research is secondary data obtained from the internet from the official website of the BPS-Statistics Indonesia regarding the Labor Force Situation in Indonesia from 2020-2023. The provinces with a lower working population growth rate, especially have negative value demands particular focus on labor absorption that are West Papua, Central Sulawesi that have high level warning status as well as Maluku and Bali that have medium level warning status. Besides the province with a greater unemployment population growth rate, especially has positive value demands particular focus on labor absorption that is Central Java that have medium level warning status

Dynamic prediction of landslide life expectancy using ensemble system incorporating classical prediction models and machine learning

With the development of landslide monitoring system, many attempts have been made to predict landslide failure-time utilizing monitoring data of displacements. Classical models (e.g., Verhulst, GM (1,1), and Saito models) that consider the characteristics of landslide displacement to determine the failure-time have been investigated extensively. In practice, monitoring is continuously implemented with monitoring data-set updated, meaning that the predicted landslide life expectancy (i.e., the lag between the predicted failure-time and time node at each instant of conducting the prediction) should be re-evaluated with time. This manner is termed “dynamic prediction”. However, the performances of the classical models have not been discussed in the context of the dynamic prediction yet. In this study, such performances are investigated firstly, and disadvantages of the classical models are then reported, incorporating the monitoring data from four real landslides. Subsequently, a more qualified ensemble model is proposed, where the individual classical models are integrated by machine learning (ML)-based meta-model. To evaluate the quality of the models under the dynamic prediction, a novel indicator termed “discredit index (β)” is proposed, and a higher value of β indicates lower prediction quality. It is found that Verhulst and Saito models would produce predicted results with significantly higher β, while GM (1,1) model would indicate results with the highest mean absolute error. Meanwhile, the ensemble models are found to be more accurate and qualified than the classical models. Here, the performance of decision tree regression-based ensemble model is the best among the various ML-based ensemble models.

Comparison of Ten Different Mathematical Models Used in In-Vitro Gas Production Technique

In this study, the usability of models commonly used in in vitro gas production techniques in different feed sources was comparatively investigated. For this purpose, Richard, Logistic, Orskov, Verhulst, Janoschek, Weibull, Bridges, Mitscherling, Monomolecular and Von Bertalanffy models, which are widely used in the literature, were used. In comparing these models, criteria such as mean square error (MSE), coefficient of determination(𝑅2), corrected coefficient of determination (R ̅^2), accuracy factor (AF), bias factor (BF), Akaike information criterion (AIC) and Bayesian information criterion (BIC) were used. As a result of the research, according to these criteria, the best model in Arbutus andrachne plant was determined as Richard, and the worst model was determined as Janoscheck and Weibull model. For Arbutus unedo, Ceratonia siliqua and Laurus nobilis L. plants, the best models were determined as Orskov, Mitscherling, Monomolecular and Von Bertalanffy models, and the worst models were Logistic and Verhulst models.

Value Assessment of Online Educational Resources in the Context of Blended Learning

In the context of promoting informatization education and reforming blended learning, how to accurately assess the value of online educational resources has become an important research topic. However, most existing assessment methods rely on direct data statistics and experience-based judgment, lacking scientific prediction models and comprehensive consideration of learning cycles. To solve this problem, this study constructed a hit prediction model of online educational resources based on the fusion of extreme learning machine and grey Verhulst model, and a hit-based value assessment model of the resources considering the learning cycles of students. The research results showed that the proposed model not only predicted and assessed the value of online educational resources more accurately, but also provided theoretical support and decision-making reference for the implementation of blended learning reform, thereby promoting the effective utilization of online educational resources.

Settlement trend of embankment–bridge transition section reinforced with thermosyphons in permafrost regions

Differential settlement of embankment–bridge transition section (EBTS) is easy to occur in permafrost regions, so it is necessary to carry out a long-term dynamic investigation, maintenance, and reinforcement on EBTS. In this study, settlement characteristics of two EBTSs reinforced by thermosyphons along the Qinghai–Tibet Railway (QTR) in 2010 were analyzed. In addition, the Pettitt test method was used to analyze the time when the thermosyphons showed a significant cooling effect after reinforcement, and the Verhulst model and exponential curve method were used to analyze the long-term settlement trend of an EBTS in the next 10 years. The results indicate that the accumulated settlements and settlement rates of monitoring EBTSs after reinforcement were obviously lower than the requirements of the design code for railway embankments in China. The fifth year after the completion of thermosyphon is the abrupt change point of the settlement data. The maximum difference between the change rate of the settlement rate before and after the abrupt change point is 78.5%. Thermosyphon will make the EBTSs close to the deformation stability after reinforcement for 10 years. Finally, according to the settlement evolution results, the accumulated settlements of the abutment of monitoring sites will be less than 50 mm in the 10 years after 2020. In general, thermosyphon, as a reinforcement measure, can significantly and rapidly slow down the settlement trend of the EBTSs and maintain its long-term stability. This study aims to deepen the understanding of the effect of EBTS reinforcement measures and provide a scientific basis for EBTS reinforcement in permafrost regions.

Short‐term estimations of PM10 concentration in the Middle Black Sea region based on grey prediction models

AbstractThe Middle Black Sea region has experienced severe air pollution, with a significant increase in particulate matter (PM) concentration due to a growth in population, financial activity, and an expansion of transportation in recent years. Therefore, the prediction of PM concentration has become a topic of great significance to reduce air pollution and assess the effects on public health. In this study, the grey prediction model (GM (1,1)), the discrete grey model (DGM (1,1)), and the grey Verhulst model (GVM (1,1)) were used to estimate the PM10 concentration of the cities Amasya, Çorum, Ordu, and Samsun in the Middle Black Sea region, for the period from 2022 to 2026. The accuracy of the GM (1,1), DGM (1,1), and GVM (1,1) models in fitting data was calculated using the mean absolute percentage error (MAPE) value. Since three types of prediction models of MAPEs were less than 20%, they were considered a good value for prediction performance. Furthermore, the results showed that the PM10 concentrations of Amasya, Çorum, and Ordu showed a downward trend over the next 5 years. However, the GVM (1,1) model showed an upward trend in the yearly average PM10 concentration in Samsun. In conclusion, these models could be considered a reliable approach in early warning systems for emissions reduction and as a long‐term policy for managing air quality in the Middle Black Sea region.

Prediction of urban residential electricity security based on Verhulst grey model

Abstract This paper firstly analyzes the urban residential electricity load characteristics and extracts residential electricity load data through a non-intrusive electricity load monitoring framework with electricity load characteristics. Secondly, the gray Verhulst model is improved by using function transformation and residual correction to further improve its prediction accuracy. Finally, a prediction example analysis is carried out for the electric load under urban residential electricity security. The results show that the maximum prediction error of the improved gray Verhulst model is 2.28%, which is 1.34 percentage points lower than the 3.62% of the genetic algorithm GM(1,1) model. This indicates that the prediction of urban residential electricity security can be achieved using the improved gray Verhulst model.

Predicting of elderly population structure and density by a novel grey fractional-order model with theta residual optimization: a case study of Shanghai City, China

Background Accurately predicting the future development trend of population aging is conducive to accelerating the development of the elderly care industry. This study constructed a combined optimization grey prediction model to predict the structure and density of elderly population.MethodsIn this paper, a GT-FGM model is proposed, which combines Theta residual optimization with fractional-order accumulation operator. Fractional-order accumulation can effectively weaken the randomness of the original data sequence. Meanwhile, Theta residual optimization can adjust parameter by minimizing the mean absolute error. And the population statistics of Shanghai city from 2006 to 2020 were selected for prediction analysis. By comparing with the other traditional grey prediction methods, three representative error indexes (MAE, MAPE, RMSE) were conducting for error analysis.ResultsCompared with the FGM model, GM (1,1) model, Verhulst model, Logistic model, SES and other classical prediction methods, the GT-FGM model shows significant forecasting advantages, and its multi-step rolling prediction accuracy is superior to other prediction methods. The results show that the elderly population density in nine districts in Shanghai will exceed 0.5 by 2030, among which Huangpu District has the highest elderly population density, reaching 0.6825. There has been a steady increase in the elderly population over the age of 60.ConclusionsThe GT-FGM model can improve the prediction accuracy effectively. The elderly population in Shanghai shows a steady growth trend on the whole, and the differences between districts are obvious. The government should build a modern pension industry system according to the aging degree of the population in each region, and promote the balanced development of each region.

Prediction of energy-related carbon emission intensity in China, America, India, Russia, and Japan using a novel self-adaptive grey generalized Verhulst model

Excessive energy-related carbon emission intensity will lead to deterioration of environmental quality and hinder green economic growth. This paper proposes a novel self-adaptive fractional order grey generalized Verhulst model (SAFGGVM) to predict energy-related carbon emission intensity in China, America, India, Russia, and Japan with nonlinear and complex characteristics effectively. Firstly, self-adaptive fractional order and dynamic background value coefficient are introduced to capture the nonlinear evolutionary trends. Subsequently, the optimal nonlinear parameters are determined using Grey Wolf Optimization algorithm through comprehensive comparison. Furthermore, the flexibility of SAFGGVM is verified by presenting its relevance to existing models. Finally, the validity, applicability, and robustness of SAFGGVM are confirmed by comparing with two machine learning models and four grey prediction models. The empirical results exhibit that the overall precision of SAFGGVM model significantly prevails over the others in five cases, with MAPE values less than 6% in both the simulation and prediction intervals. The out-of-sample forecast results indicate that the energy-related carbon emission intensity of five countries will fall into 5.7024, 1.6030, 7.3668, 8.1633, 2.0399 tons/10,000 USD by 2025, and the decreasing rate of developing countries tends to catch up with, or even exceed, developed countries. Projection results can serve as a reference point for countries to achieve green and sustainable development.

A novel grey Verhulst model with four parameters and its application to forecast the carbon dioxide emissions in China

In the context of dual carbon targets, a reliable prediction of China's carbon dioxide emissions is of great significance to the design and formulation of emission reduction policies by Chinese government. To this end, a novel grey Verhulst model with four parameters is proposed in this paper according to the evolution law and the data characteristics of China's carbon dioxide emissions. The new model solves the defect of poor structural adaptability of the traditional grey Verhulst model by introducing a nonlinear correction term. Besides, the range of values for the order of the grey generation operator of the new model is expanded from a positive real number to any real number (r ∈ R+ → r ∈ R) by expanding the value range of the Gamma function. The new model is used to simulate China's carbon dioxide emissions, and its comprehensive mean relative percentage error is only 0.65 %, which is better than that of the other three grey models (2.39 %, 2.34 %, 2.35 % respectively). It shows that the proposed new model has better modeling ability. Finally, the new model is applied to predict China's carbon dioxide emissions, and the results show that it will still increase year by year, reaching 13,687 million tons by 2028 (only 11,420 million tons in 2021). Therefore, some countermeasures and suggestions are proposed to control China's carbon dioxide emissions in this paper.

Predicting the occurrence of natural and technological disasters in Greece through Verhulst, multinomial and exponential models

A rising number and variety of hazards has threatened local communities, possibly leading to disasters that are cause of important (human and economic) losses across regions and countries. As a consequence, both preparedness and management of hazard risk emerged as relevant issues in advanced economies. The present study proposes an original framework to estimate the number of future disasters in Greece using the Emergency Database (EM-DAT) as primary data. This information is vital to adopt precaution measures and design official plans for the protection of resident population. For this purpose, a logistic model based on Verhulst equations was tested here – using multinomial and exponential models as computational alternatives – on a complete database considering disasters occurred in Greece between 1904 and 2020. The outcomes of all models have documented the increasing frequency of all kinds of disasters over time. Predictions covering a time horizon that includes the 2020 s estimated the occurrence of 1 to 9 disasters per year as a whole (1 to 6 events per year for natural disasters and 1 to 3 events per year for technological disasters). These findings justify the urgent need of effective policies improving preparedness of local communities.

Growth modeling approach with the Verhulst coexistence dynamic properties for regulation purposes

For this research, the properties of the logistic growth model for independent and coexisting species were used to set definitions for the possible regulation of one or two growth variables through their coupling parameters. The present analysis is done for the single-species Verhulst model without coupling, the single-species Verhulst model coupled with an exogenous signal, and the two-species Verhulst coexistence growth model which represents six different ecological regimes of interaction. The models’ parameters, such as the intrinsic growth rate and the coupling, are defined. Finally, the control results are expressed as lemmas for regulation, and they are shown using a simulation example of a fish population growing independent of human interaction (no harvesting, no fishing) and the simulation of the regulation of said population when the coupling of fish and humans is involved (harvesting, fishing).

Estimation of global waste smartphones and embedded critical raw materials: An industry life cycle perspective

Considering the quarterly fluctuation characteristics of global smartphone shipment, a novel and improved Verhulst model was proposed for forecasting smartphone shipments under different industry life cycle scenarios. The number of waste smartphones between 2007 and 2039 was estimated via using the lifespan distribution of electronics. The weight of the disposals was then converted by using product data collected from 2766 sampled smartphone devices. It was found that under the scenario of maturity, approximately 126,000 tons critical raw materials (CRMs) were expected to be recovered by 2039. According to the CRMs lists published by China and the European Union, the recoverable amount compared to about 62,000 tons and 64,000 tons, respectively. Enhancing the recycling of waste smartphones worldwide, will provide a new option to ensure an important part of the stability of the CRMs supply chains.

Nanoscale study on adhesion performance and aging degree prediction of warm mix asphalt under UV aging condition

Compared with hot mix asphalt, warm mix asphalt ( WMA) has inferior adhesion performance, and ultraviolet (UV) aging will further weaken the adhesion performance of WMA. There are, however, few investigations on the aging mechanism under conditions of single UV radiation, and the majority of current research on UV aging is conducted under the combined action of UV radiation and oxygen. In this paper, an indoor accelerated experimental equipment for UV aging was developed, and two experimental schemes of oxygen isolation condition and light-oxygen coupling condition were designed. The developed UV aging tests were carried out on WMA this for 0–50–100–150 and 200 h. The nano adhesion properties were studied by atomic force microscopy ( AFM) and gel permeation chromatography ( GPC) experiments. The characterization method of WMA nano adhesion performance was proposed using correlation analysis. In addition, the nonlinear differential equations between nano-indexes and aging time were established by the Verhulst model. The results showed that the generation of microcracks and the increase of large molecular weight during UV aging will decrease WMA adhesion performance, and the degradation is more significant under the light-oxygen coupling conditions. Moreover, the correlation coefficients between large molecular weight and nano-adhesion under two UV aging conditions were higher than 0.90, showing that large molecular weight could characterize the degradation of nano-adhesion of WMA after UV aging. The saturation characteristics of the honeycomb structure area ratio were prominent, and the coefficient of determination of the nonlinear equations were higher than 0.93 for both two UV aging conditions. The aging model can be used to accurately characterize and predict the WMA UV aging state through the variation of honeycomb structure area ratio.