Asphalt Concrete Modulus Research Articles

Cost-Effective Approaches Based on Machine Learning to Predict Dynamic Modulus of Warm Mix Asphalt with High Reclaimed Asphalt Pavement.

Warm mix asphalt (WMA) technology, taking advantage of reclaimed asphalt pavements, has gained increasing attention from the scientific community. The determination of technical specifications of such a type of asphalt concrete is crucial for pavement design, in which the asphalt concrete dynamic modulus (E*) of elasticity is amongst the most critical parameters. However, the latter could only be determined by complicated, costly, and time-consuming experiments. This paper presents an alternative cost-effective approach to determine the dynamic elastic modulus (E*) of WMA based on various machine learning-based algorithms, namely the artificial neural network (ANN), support vector machine (SVM), Gaussian process regression (GPR), and ensemble boosted trees (Boosted). For this, a total of 300 samples were fabricated by warm mix asphalt technology. The mixtures were prepared with 0%, 20%, 30%, 40%, and 50% content of reclaimed asphalt pavement (RAP) and modified bitumen binder using Sasobit and Zycotherm additives. The dynamic elastic modulus tests were conducted by varying the temperature from 10 °C to 50 °C at different frequencies from 0.1 Hz to 25 Hz. Various common quantitative indications, such as root mean square error (RMSE), mean absolute error (MAE), and correlation coefficient (R) were used to validate and compare the prediction capability of different models. The results showed that machine learning models could accurately predict the dynamic elastic modulus of WMA using up to 50% RAP and fabricated by warm mix asphalt technology. Out of these models, the Boosted algorithm (R = 0.9956) was found as the best predictor compared with those obtained by ANN-LMN (R = 0.9954), SVM (R = 0.9654), and GPR (R= 0.9865). Thus, it could be concluded that Boosted is a promising cost-effective tool for the prediction of the dynamic elastic modulus (E*) of WMA. This study might help in reducing the cost of laboratory experiments for the determination of the dynamic modulus (E*).

Integrated finite element and artificial neural network methods for constructing asphalt concrete dynamic modulus master curve using deflection time-history data

Dynamic modulus |E*| is one of the essential material properties input in the American Association of State Highway and Transportation Officials (AASHTO) Mechanistic-Empirical Pavement Design Guide (MEPDG). Asphalt concrete (AC) dynamic modulus master curve is used to determine the modulus of asphalt concrete over a wide range of temperature and frequency. However, the standard laboratory test procedures for establishing asphalt concrete |E*| and plotting the AC |E*| master curve are time consuming and require considerable resources. Therefore, this study aims to predict AC |E*| master curve by using data from a falling weight deflectometer (FWD) deflection time-history. Prior to developing the model, a simple performance testing (SPT) dynamic modulus test was conducted in the laboratory on five core specimens to obtain the dynamic modulus data at several test temperatures and load frequencies. Results of SPT dynamic modulus show that the |E*| of all specimens is influenced by both loading rate and test temperature. The specimens are stiffer at low temperature and high frequency, and the |E*| values are the lowest at the highest temperature and lowest frequency. Artificial neural network (ANN) models are designed using the FWD deflection-time history data obtained by the finite element method (FEM) to predict the AC |E*| master curve. This study uses two types of ANN models, namely multilayer feed-forward neural network (MLFN) and radial basis function network (RBFN). ANN results show that both MLFN and RBFN models have a promising potential in the construction of AC |E*| master curve. A comparison of the two types of ANNs revealed that RBFN has a lower percentage of error, and is therefore more accurate than MLFN.

Mechanistic-Based Approach to Utilize Traffic Speed Deflectometer Measurements in Backcalculation Analysis

Backcalculation analysis of pavement layer moduli is typically conducted based on falling weight deflectometer (FWD) deflection measurements; however, the stationary nature of the FWD requires lane closure and traffic control. In recent years, traffic speed deflection devices such as the traffic speed deflectometer (TSD), which can continuously measure pavement surface deflections at traffic speed, have been introduced. In this study, a mechanistic-based approach was developed to convert TSD deflection measurements into the equivalent FWD deflections. The proposed approach uses 3D-Move software to calculate the theoretical deflection bowls corresponding to FWD and TSD loading configurations. Since 3D-Move requires the definition of the constitutive behaviors of the pavement layers, cores were extracted from 13 sections in Louisiana and were tested in the laboratory to estimate the dynamic complex modulus of asphalt concrete. The 3D-Move generated deflection bowls were validated with field TSD and FWD data with acceptable accuracy. A parametric study was then conducted using the validated 3D-Move model; the parametric study consisted of simulating pavement designs with varying thicknesses and material properties and their corresponding FWD and TSD surface deflections were calculated. The results obtained from the parametric study were then incorporated into a Windows-based software application, which uses artificial neural network as the regression algorithm to convert TSD deflections to their corresponding FWD deflections. This conversion would allow backcalculation of layer moduli using TSD-measured deflections, as equivalent FWD deflections can be used with readily available tools to backcalculate the layer moduli.

Asphalt concrete master curve using dynamic backcalculation

ABSTRACT The dynamic backcalculation of pavement layer properties, and more specifically the ability to determine the asphalt concrete master curve, using Falling Weight Deflectometer (FWD) data has caught the attention of many researchers for years. The damaged or aged master curve of existing pavement structures allows the accurate prediction of the pavement structural capacity and remaining life – a goal that cannot be achieved through laboratory testing. To address this need, the authors developed a dynamic backcalculation application that employs the ABAQUS software for forward calculation using implicit dynamic analyses, and the Newton-Raphson’s root-solving algorithm for optimisation. The capabilities of the application were demonstrated for three simulated flexible pavement structures and two asphalt concrete mixes using 40 combinations. The asphalt concrete moduli at the FWD most dominant frequencies around 17 Hz, and the variables of unbound layers converged to the exact values in few iterations for all combinations. The master curves, and mainly the maximum moduli, were reliably determined to less than 1% and 4% error for about 60% and 85% of the combinations, respectively. The potential for determining the master curve and maximum modulus was shown to be dependent on the asphalt concrete mix, asphalt concrete temperature and pavement structure.

A Comparative Study on Dynamic Modulus of Asphalt Concrete with Different Loading Mode

Abstract Loading mode is an important but under-estimated factor for the dynamic modulus test of asphalt concrete. This article presents a comparative laboratory study of using uniaxial-compression, two-point bending and three-point bending to test dynamic modulus of 12.5 mm asphalt concrete (AC) with two asphalt materials. Dynamic moduli |E*| and phase angle φ between different tests were compared and analyzed in multiple ways. Results show that good correlations exist between |E*| and φ of different loading modes, but the values of |E*| and φ, as well as their temperature sensitivities are different. When subjected to bending, AC demonstrates a smaller |E*|, a larger φ, and is more thermal sensitive. The Black Space diagram also shows that the linear viscoelastic property and the pure elastic modulus of AC under different loading modes are different. It is indicated from master curve analysis that the loading mode has a significant influence on |E*| and φ, and the main reason is that the stress state varies with the loading mode. The influence of the loading mode becomes more significant as the temperature increases. The small size specimen of three-point bending brings in larger variation, and the inferior aggregate structure causes a smaller |E*|. However, with at least four replicates, the small size specimen in this study can still represent the overall characteristics of material. Statistical analysis shows that dynamic modulus from the three loading modes are significantly different, indicating that when choosing a test method for the dynamic modulus test, the influence of the loading mode should be taken into consideration.

Dynamic Inversion Analysis of Structural Layer Modulus of Semirigid Base Pavement considering the Influence of Temperature and Humidity

This paper is aimed to solve the overlearning problem of the neural network algorithm used to calculate the asphalt concrete pavement structural modulus in reverse. The firefly algorithm was adapted to optimize the selection of support vector machine (SVM) parameters. Based on the optimized SVM model, a new method for dynamic inversion of the semirigid base asphalt concrete pavement structural layer modulus was presented. The results show that the absolute value of relative error of each layer modulus is not more than 3.73% by using the proposed method. Then, the influences of temperature and humidity on the inversion modulus of semirigid base asphalt concrete pavement in the seasonal frozen area were analyzed, and the correction formula of the inversion modulus was established. The paper is of practical significance for improving the safety performance of semirigid base pavement in the seasonal frozen area in China.

Numerical Simulation of Construction Process of Large Building Project Based on Discrete Element Method

Assembling integrated concrete cutting construction technology is a kind of construction engineering means commonly used in large stadiums at present. The advantage of this method lies in that it is connected by reinforcing bars, connecting pieces or applying prestress and pouring concrete members on site, which significantly enhances the mechanical resistance of construction engineering. And milling and planing machine as a large stadium assembly integrated concrete cutting construction indispensable important engineering machinery, its demand continues to grow, domestic independent research and development of high-performance milling and planing machine is urgent. Based on three-dimensional discrete element method model conforms to the macroscopic mechanical properties of the road, establish milling planer operation simulation model of quantitative stadium assembled monolithic concrete construction process of milling planer cutting resistance, using uniaxial compression and splitting tensile test to determine the compressive modulus of asphalt concrete pavement and tensile modulus, obtain the macro level check micro contact connection parameters. Discrete element specimens with coarse aggregate of irregular shape are generated by using the algorithm of 3d discrete element software PFC3D. Through the establishment of kinematics model, the critical condition expression of vibration planer is deduced, and the improvement of the working process force by adding different vibration modes is studied, so as to calculate the optimal combination value of vibration planer amplitude and vibration frequency, and obtain the better vibration mode of milling planer.

Backcalculated Modulus of Asphalt Concrete

Asphalt Concrete (AC) is considered a spatially homogeneous material when analyzing and designing asphalt pavement. However, the modulus of AC along the wheel path and the middle of the wheel path may not be the same considering the continuous compaction by wheel loading. This study conducted monthly Falling Weight Deflectometer (FWD) tests to determine the AC modulus of a pavement section on Interstate 40 (I-40) in the state of New Mexico, USA from 2013 to 2015. The AC moduli on the wheel path, on the middle of the wheel path, on the shoulder with friction course, and on the shoulder without friction course are determined. It is mentionable that the driving lane and the shoulder have the same geometry, materials, and compaction effort. Results show that the modulus along the wheel path is almost the same as that of along the middle of the wheel path. The shoulder without friction course has a modulus greater than that of the lane AC modulus and the shoulder with the friction course. In addition, FWD backcalculated moduli at different temperatures are compared with the dynamic modulus values of the AC layer. It is found that the dynamic modulus at a loading frequency of 5 Hz is 1.7 to 1.9 times the backcalculated AC modulus.

Shear behavior of hydraulic asphalt concrete at different temperatures and strain rates

Asphalt concrete is a viscoelastoplastic material and its behavior depends on temperature and time. Asphalt concrete used as impervious core in embankment dams is subjected to different loading conditions at different temperatures. A shear apparatus is described and used to investigate the stress-strain-strength behavior of asphalt concrete by carrying out shear tests at different temperatures and shear strain rates. The domains of shear modulus and shear strength values of asphalt concrete are established by applying the time-temperature superposition principle. Shear modulus and shear strength values of asphalt concrete for different loading conditions are compared. The documented behavior can be used in the design of the asphalt core in embankment dams.

Prediction of Longitudinal Cracking of Asphalt Pavements

Longitudinal cracking is one of the major structural distresses of asphalt pavement. These cracks appear on the pavement along the direction of moving traffic. This study makes an attempt to predict the extent of longitudinal cracking based on three parameters which are: asphalt binder content, traffic load repetitions and asphalt stiffness modulus. For the study, the data has been used from Long Term Pavement Performance (LTPP) database. Linear Least Square (LLS) regression method is employed to model the observed trends between the longitudinal cracking and the three parameters. The results of the analyses has shown that longitudinal cracking vary linearly with respect to each parameter. It is observed that (i) longitudinal cracking decreases linearly with increase in percentage asphalt binder content in asphalt concrete (ii) longitudinal cracking increases linearly with increasing traffic load repetitions and (iii) longitudinal cracking decreases linearly with increase in stiffness modulus of asphalt concrete.

Structural assessment of asphalt pavement condition using backcalculated modulus and field data

Abstract This study aims to assess asphalt pavement condition in terms of backcalculated moduli of asphalt concrete (AC) and unbound material layers. An integrated Artificial Neural Network – Genetic Algorithm (ANN-GA) program was developed to backcalculate layer moduli using pavement surface deflection measured under falling weight deflectometer (FWD) test. Three pavement sections with FWD testing conducted at different time periods were used in the analysis. As damage developed in AC layer over years, the master curve of AC dynamic moduli showed the similar sigmoidal shapes but the modulus decreases as compared to the undamaged AC. The relatively greater variation of modulus degradation was observed for dynamic modulus in the high frequency range. On the other hand, the nonlinearity parameters obtained from backcalculation can be used to characterize modulus distribution at different depths in granular base layer and subgrade. The slight modulus degradation was observed in granular base layer and subgrade. The deterioration trend of AC modulus was found consistent with fatigue cracking measured at pavement surface based on field distress survey results. The study results indicate that FWD testing with advanced analysis can be successfully used to evaluate in situ pavement condition from structural point of view.

Automated Non-contact Resonance Excitation Method to Assess Low Temperature Dynamic Modulus of Asphalt Concrete

This paper studies the applicability of an automated non-destructive testing method to monitor the stiffness of asphalt concrete at low temperatures. A loudspeaker is used as a source of non-contact excitation of the axially symmetric fundamental resonant frequencies of a disc-shaped asphalt concrete specimen positioned inside an environmental chamber. Measured resonant frequencies are used to calculate the dynamic moduli of the specimen at different temperatures. The repeatability of the method as well as the effect of loudspeaker height above the sample are studied. Results show that the main advantage of the non-contact excitation method, compared to manually applied impact hammer excitation, is that repeatable automated measurements can be performed while the specimen is placed inside an environmental temperature chamber. This methodology enables to study the effect of only low temperature conditioning on the dynamic modulus of asphalt concrete without interference from mechanical loading.

Precision of modal analysis to characterise the complex modulus of asphalt concrete

Modal analysis is an economic and efficient test method to characterise the complex modulus of asphalt concrete. In this paper, the precision of modal analysis was evaluated by performing testing at several laboratories on two cylindrical asphalt concrete specimens. In addition, the complex moduli characterised by modal analysis were compared to cyclic tension-compression testing. The results showed that the coefficient of variation was less than 3% at loading frequencies above 10 Hz for the complex modulus determined through modal analysis. The comparison of the complex modulus determined from modal analysis and tension-compression testing resulted in a coefficient of variation values not more than 9% for loading frequencies ranging from 0.1 to 109 Hz.

The Influence of Hydrated Lime on IT-CY Stiffness Modulus of Foam-Based Asphalt Concrete Compacted at 95 °C

For a number of years worldwide, the road construction industry has been seeking new technologies for producing energy-saving asphalt mixtures in order to meet new environmental requirements and laws. Some of these techniques include new classes of mixtures characterized by reduced processing temperatures compared to the conventional Hot Mix Asphalt (HMA) production temperature of 165 °C and paving temperature of approximately 145 °C. These techniques include Half Warm Mix Asphalt (HWMA) mineral mixtures produced with the use of foamed bitumen as a binder at temperatures of about 100 °C and paved at 95 °C. Although generally HWMA mixes are comparable to HMA, depending on the mix, they may suffer from decreased mechanical parameters resulting in a reduced service life of the asphalt pavement. The implemented research program investigated asphalt concrete (AC 8) with foamed bitumen (HWMA) compacted at 95 °C and the control HMA sample produced and compacted at a regular temperature. A typical 50/70 road paving bitumen modified with 0.6% surface active agent SAA (fatty acid amide) was used as the foamed binder, dosed at 5.6% and 6.2% by weight to the mixture. Mineral filler replacement with hydrated lime at 15% and 30% by weight was evaluated. The content of voids in the asphalt mixture was examined. The indirect tensile stiffness modulus (IT-CY) characterizing the durability of the mixture was measured at -10 °C, 0 °C, 10 °C, 20 °C and 25 °C. The results of statistical analysis showed significant correlations between the mix production technology used and the content of foamed bitumen and hydrated lime in terms of the temperature of stiffness modulus testing. As confirmed by the stiffness modulus values, the application of hydrated lime provided the half-warm mix asphalt concrete AC8 produced with foamed bitumen with mechanical properties comparable to those of the HMA mix.

Analiza trwałości zmęczeniowej betonów asfaltowych z uwzględnieniem typu mieszanki i rodzaju lepiszcza

Przedmiotem prac badawczych przedstawionych w artykule jest trwałość zmęczeniowa mieszanek mineralno-asfaltowych do warstwy podbudowy. W badaniach uwzględniono dwa rodzaje mieszanek mineralno-asfaltowych: beton asfaltowy i beton asfaltowy o wysokim module sztywności. W ramach każdej z mieszanek przygotowano warianty z różnymi asfaltami, tj. drogowymi, modyfikowanymi polimerem i tzw. wysokomodyfikowanymi. Przeprowadzono badania trwałości zmęczeniowej, na podstawie których opracowano charakterystyki zmęczeniowe mieszanek. Wykonano analizę trwałości zmęczeniowej mieszanek oraz typowych konstrukcji nawierzchni podatnych. Dokonano oszacowania tzw. współczynnika przesunięcia, który umożliwia wykorzystanie laboratoryjnych charakterystyk zmęczeniowych w projektowaniu nawierzchni. Zaproponowano definicję dwóch parametrów zmęczeniowych: odkształcenia krytycznego i wskaźnika trwałości zmęczeniowej. Pozwalają one bardziej racjonalnie porównać wyniki trwałości zmęczeniowej mieszanek mineralno-asfaltowych z uwzględnieniem trwałości konstrukcji nawierzchni. Przeprowadzone analizy pozwoliły na ocenę odporności na zmęczenie mieszanek mineralno-asfaltowych z uwzględnieniem typu mieszanki i rodzaju asfaltu.

Optimum parafibre length according to mechanical properties in hot mix asphalt

Fibre is additive to hot mix asphalt that can improve fatigue life, rutting resistance, durability of asphalt concrete mixtures, creep compliance, tensile strength, dynamic modulus, elasticity, viscoelasticity, and reflective cracking. The fibres can be useful in controlling the cracks. Previous studies on various fibres have mostly focused on changing and optimising fibre percentage. No study has been conducted on appropriate fibre length in the mixture. Therefore, the effect of various fibre lengths on mixture properties needs to be clearly determined. The aim of this study was to evaluate the effect of various parafibre lengths on mechanical properties of hot mix asphalt through Marshall strength, indirect tensile strength, and resilient modulus tests. To achieve this, we added 0.5% fibre by weight of the asphalt mixture with lengths of 3, 6, 9, 12, 15, and 18 mm to hot mix asphalt samples and performed the above tests on the samples. The results showed that fibre improves hot mix asphalt mechanical properties; however, fibre percentage needs to be increased as the length increases, so that there are sufficient fibres present in the mixture to act against cracks. Accordingly, in all three tests, 12 mm fibres at 1% fibre content created the highest values. Therefore, the optimal fibre length was 12 mm, and for this length the most affected properties were resilient modulus, indirect tensile strength, and Marshall strength, respectively.

Numerical study on the effect of phase change materials on heat transfer in asphalt concrete

This work aims at exploring the impacts of phase change materials (PCMs) in asphalt pavement, particularly regarding their potential of minimizing high temperatures, responsible of the rutting failure in asphalt concrete pavement. For this purpose, we developed and validated a numerical model for the prediction of temperatures in asphalt pavement under real weather conditions, and accounting also for the presence of PCM in asphalt concrete pavement. The effects of PCM volume fraction in asphalt concrete were investigated by numerically simulating the thermal behavior of conventional asphalt concrete pavements with and without PCM components under real weather conditions. Parametric studies were additionally conducted to tailor the thermal behavior of asphalt concrete pavement (e.g. reducing surface temperature). Then, the effects of each thermal behavior modification on the mechanical properties of the asphalt concrete pavement were quantified, considering the complex modulus of bitumen and asphalt concrete. The developed numerical tool will help in future designs and optimizations of the thermal behavior of asphalt concrete with phase change materials with regards to real weather conditions.

Resilient Behavior of Modified Asphalt Concrete Mixture

Asphalt concrete pavement is designed to exhibit elastic behavior under loading at cold weather condition and a combination of elastic, plastic and viscous behavior at hot weather condition. Distress of the pavement usually starts with initiation of micro cracking due to load repetition, while such cracks can heal by themselves in slow process under repeated loading, external or internal heating, and provision of rest period at ambient temperature. The aim of this work was to assess the resilient behavior of modified asphalt concrete using three types of polymer additives such as starien- butadien- stairen (SBS), low density poluetheline (LDPE), and scrap tire rubber. Beam specimens of 381.0 mm length, 76.2 mm width, and 76.2mm thickness have been prepared with optimum asphalt content requirement and with extra 0.5% asphalt above and below the optimum. Beam specimens were tested under repeated flexure stress. The applied stress level was 138 kPa at 25°C. The loading cycle consist of 0.1 second loading application followed by 0.9 seconds of rest period. The test was conducted for 660 load repetitions using the Pneumatic repeated load system (RPLS) to allow for the initiation of micro cracks. After the specified loading cycles, the test was stopped and the Specimens have been withdrawn from the testing chamber of PRLS and stored in the oven for two hours at 60°C environment to allow for possible micro crack healing. The specimens were then subjected to another loading cycle. Permanent, total and resilient deformations were captured through LVDT. The resilient modulus was calculated and compared among various conditions. Test results showed that the implemented polymer additives and the process of micro crack healing have positive influence on resilient modulus and deformation variables of asphalt concrete.

Evaluation of interface bonding conditions based on non-destructing testing deflection measurements

Interface bonding conditions between pavement layers have a major impact on pavement performance. The objective of this study was to assess interface bonding conditions between pavement layers using falling weight deflectometer deflection measurements. In addition, the effect of interface bonding conditions on the backcalculated layer moduli was investigated. To achieve these objectives, a new methodology was developed based on FWD measurements collected in 46 sections in Louisiana. These measurements were used to backcalculate the layer moduli using MODULUS 6.0 software. BISAR 3.0 software was then used in conjunction with MODULUS 6.0 to backcalculate the asphalt concrete (AC)/base bonding condition and to correct the backcalculated base layer moduli. The results of the proposed methodology were verified through evaluation of extracted cores. Based on the results of this analysis, it was found that the interface bonding conditions significantly influenced the accuracy of the backcalculation analysis. The impact of interface bonding conditions was more significant on the base moduli than on the AC moduli. A bonding index, which is a function of the interface bonding condition, was introduced to describe the quality of bonding between the AC and base layers. Results showed that the bonding index varied with the characteristics of the base layer. Non-stabilised base layers experienced relatively weak interface bonding at the AC/base interface. Cement-stabilised granular bases mostly experienced weak to moderate interface bonding. On the other hand, stabilised base layers treated with reclaimed asphalt pavement exhibited superior interface bonding. A simple artificial neural network model was developed to allow pavement engineers to correct the backcalculated base layer moduli based on interface bonding conditions. The developed model showed an acceptable overall prediction accuracy of 95.1%.

Modelling of Asphalt Concrete Stiffness in the Linear Viscoelastic Region

Stiffness modulus is a fundamental parameter used in the modelling of the viscoelastic behaviour of bituminous mixtures. On the basis of the master curve in the linear viscoelasticity range, the mechanical properties of asphalt concrete at different loading times and temperatures can be predicted. This paper discusses the construction of master curves under rheological mathematical models i.e. the sigmoidal function model (MEPDG), the fractional model, and Bahia and co-workers’ model in comparison to the results from mechanistic rheological models i.e. the generalized Huet-Sayegh model, the generalized Maxwell model and the Burgers model. For the purposes of this analysis, the reference asphalt concrete mix (denoted as AC16W) intended for the binder coarse layer and for traffic category KR3 (5×105 <ESAL100kN <2.5×106) was prepared. Measurement of the stiffness modulus of asphalt concrete under steady-state strain was performed using the simple axial compression-tensile test under controlled strain mode. The fixed strain level was set at 25με to guarantee that the stiffness modulus of the asphalt concrete would be tested in a linear viscoelasticity range. The master curve was formed using the time-temperature superposition principle (TTSP). The stiffness modulus of asphalt concrete was determined at temperatures 10°C, 20°C and 40°C and at loading times (frequency) of 0.1, 0.3, 1, 3, 10, 20 Hz. The model parameters were fitted to the rheological models using the original programs based on the nonlinear least squares sum method. All the rheological models under analysis were found to be capable of predicting changes in the stiffness modulus of the reference asphalt concrete to satisfactory accuracy. In the cases of the fractional model and the generalized Maxwell model, their accuracy depends on a number of elements in series. The best fit was registered for Bahia and co-workers model, generalized Maxwell model and fractional model. As for predicting the phase angle parameter, the largest discrepancies between experimental and modelled results were obtained using the fractional model. Except the Burgers model, the model matching quality was more than 0.985 (determination coefficient) at the root mean squared error of less than 10%. From the point of view of their practical application, it is best to apply the generalized Huet-Sayegh model and the sigmoidal model.