ANN based simulation and experimental verification of analytical four- and five-parameters models of PV modules

In this article, artificial neural network (ANN) is adopted to predict photovoltaic (PV) panel behaviors under realistic weather conditions. ANN results are compared with analytical four and five parameter models of PV module. The inputs of the models are the daily total irradiation, air temperature and module voltage, while the outputs are the current and power generated by the panel. Analytical models of PV modules, based on the manufacturer datasheet values, are simulated through Matlab/Simulink environment. Multilayer perceptron is used to predict the operating current and power of the PV module. The best network configuration to predict panel current had a 3–7–4–1 topology. So, this two hidden layer topology was selected as the best model for predicting panel current with similar conditions. Results obtained from the PV module simulation and the optimal ANN model has been validated experimentally. Results showed that ANN model provide a better prediction of the current and power of the PV module than the analytical models. The coefficient of determination (R²), mean square error (MSE) and the mean absolute percentage error (MAPE) values for the optimal ANN model were 0.971, 0.002 and 0.107, respectively. A comparative study among ANN and analytical models was also carried out. Among the analytical models, the five-parameter model, with MAPE = 0.112, MSE = 0.0026 and R² = 0.919, gave better prediction than the four-parameter model (with MAPE = 0.152, MSE = 0.0052 and R² = 0.905). Overall, the 3–7–4–1 ANN model outperformed four-parameter model, and was marginally better than the five-parameter model.     

Artificial neural networks for rapid WWTP performance evaluation: Methodology and case study

Reliable performance evaluation of wastewater treatment plants (WWTPs) can be done by simulating the plant behavior over a wide range of influent disturbances, including series of rain events with different intensity and duration, seasonal temperature variations, holiday effects, etc. Such simulation-based WWTP performance evaluations are in practice limited by the long simulation time of the mechanistic WWTP models. By moderate simplification (avoiding big losses in prediction accuracy) of the mechanistic WWTP model only a limited reduction of the simulation time can be achieved. The approach proposed in this paper combines an influent disturbance generator with a mechanistic WWTP model for generating a limited sequence of training data (4 months of dynamic data). An artificial neural network (ANN) is then trained on the available WWTP input-output data, and is subsequently used to simulate the remainder of the influent time series (20 years of dynamic data) generated with the influent disturbance generator. It is demonstrated that the ANN reduces simulation time by a factor of 36, even when including the time needed for the generation of training data and for ANN training. For repeated integrated urban wastewater system simulations that do not require repeated training of the ANN, the ANN reduces simulation time by a factor of 1300 compared to the mechanistic model. ANN prediction of effluent ammonium, BOD₅ and total suspended solids was good when compared to mechanistic WWTP model predictions, whereas prediction of effluent COD and total nitrogen concentrations was a bit less satisfactory. With correlation coefficients R² > 0.95 and prediction errors lower than 10%, the accuracy of the ANN is sufficient for applications in simulation-based WWTP design and simulation of integrated urban wastewater systems, especially when taking into account the uncertainties related to mechanistic WWTP modeling.     

Comparison of individual and combined ANN models for prediction of air and dew point temperature

Predicted air and dew point temperatures can be valuable in decision making in many areas including protecting crops from damage, avoiding heat stress on animals and humans, and in planning related to energy management. Current web-based artificial neural network (ANN) models on the Automated Environment Monitoring Network (AEMN) in Georgia predict hourly air and dew point temperature for twelve prediction horizons, using 24 models. The observed air temperature may approach the observed dew point temperature, but never goes below it. Current web based ANN models have prediction errors which, when the air and dew point temperatures are close, may cause air temperature to be predicted below the dew point temperature. Herein this error is referred to as a prediction anomaly. The goal of this research was to improve the prediction accuracy of existing air and dew point temperature ANN models by combining the two weather variables into a single ANN model for each prediction horizon. The objectives of this study were to reduce the mean absolute error (MAE) of prediction and to reduce the number of prediction anomalies. The combined models produced a reduction in the air temperature MAE for ten of twelve prediction horizons with an average reduction in MAE of 1.93 %. The combined models produced a reduction in the dew point temperature MAE for only six of twelve prediction horizons with essentially no average decrease in MAE. However, the combined models showed a marked reduction in prediction anomalies for all twelve prediction horizons with an average reduction of 34.1 %. The reduction in prediction anomalies ranged from 4.6 % at the one-hour horizon to 60.5 % at the eleven-hour horizon.     

A distributed optical fiber sensor for temperature detection in power cables

The power transfer capacity of an underground power cable is limited by high-temperature regions that occur along the cable. It is very difficult to determine and control these ‘hot spots’. Optimum use and temperature profile control of power cables before and during load transmission can be achieved with real-time processing of temperature data. There are various methods developed for this purpose such as conventional point temperature measurement method, where a large number of sensors and connectors are required, and methods based on mathematical models which can only approach real values by approximation.In this study, temperature detection in an XLPE insulated 154 kV power cable is performed using a distributed sensing method where the optical fiber itself behaves as a sensor. Therefore, there is no need for the devices of conventional method. Moreover, contrary to methods based on mathematical models, where it is difficult to predict environmental variations, this method considers the variations with a temperature resolution of ±1 °C. Distributed temperature sensing (DTS) method, detection system configuration and required system parameters are explained in the paper. Experimental results obtained for 126 and 412 m cables show a temperature resolution of ±1 °C and a spatial resolution of 1.22 m. Simulations for a 10 km cable are also given. Results show that DTS is a reliable method for both short and long range cable systems.     

Performance of radial basis and LM-feed forward artificial neural networks for predicting daily watershed runoff

This study investigated the effects of upstream stations’ flow records on the performance of artificial neural network (ANN) models for predicting daily watershed runoff. As a comparison, a multiple linear regression (MLR) analysis was also examined using various statistical indices. Five streamflow measuring stations on the Cahaba River, Alabama, were selected as case studies. Two different ANN models, multi layer feed forward neural network using Levenberg–Marquardt learning algorithm (LMFF) and radial basis function (RBF), were introduced in this paper. These models were then used to forecast one day ahead streamflows. The correlation analysis was applied for determining the architecture of each ANN model in terms of input variables. Several statistical criteria (RMSE, MAE and coefficient of correlation) were used to check the model accuracy in comparison with the observed data by means of K-fold cross validation method. Additionally, residual analysis was applied for the model results. The comparison results revealed that using upstream records could significantly increase the accuracy of ANN and MLR models in predicting daily stream flows (by around 30%). The comparison of the prediction accuracy of both ANN models (LMFF and RBF) and linear regression method indicated that the ANN approaches were more accurate than the MLR in predicting streamflow dynamics. The LMFF model was able to improve the average of root mean square error (RMSE_ave) and average of mean absolute percentage error (MAPE_ave) values of the multiple linear regression forecasts by about 18% and 21%, respectively. In spite of the fact that the RBF model acted better for predicting the highest range of flow rate (flood events, RMSE_ave/RBF = 26.8 m³/s vs. RMSE_ave/LMFF = 40.2 m³/s), in general, the results suggested that the LMFF method was somehow superior to the RBF method in predicting watershed runoff (RMSE/LMFF = 18.8 m³/s vs. RMSE/RBF = 19.2 m³/s). Eventually, statistical differences between measured and predicted medians were evaluated using Mann-Whitney test, and differences in variances were evaluated using the Levene's test.     

Constructing a novel mortality prediction model with Bayes theorem and genetic algorithm

Intensive care is one of the most important components of the modern medical system. Healthcare professionals need to utilize intensive care resources effectively. Mortality prediction models help physicians decide which patients require intensive care the most and which do not. The Simplified Acute Physiology System 2nd version (SAPS II) is one of the most popular mortality scoring systems currently available. This study retrospectively collected data on 496 patients admitted to intensive care units from year 2000 to 2001. The average patient age was 59.96 ± 1.83 years old and 23.8% of patients died before discharge. We used these data as training data and constructed an exponential Bayesian mortality prediction model by combining BSM (Bayesian statistical model) and GA (genetic algorithm). The optimal weights and the parameters were determined with GA. Furthermore, we prospectively collected data on 142 patients for testing the new model. The average patient age for this group was 57.80 ± 3.33 years old and 21.8% patients died before discharge. The mortality prediction power of the new model was better than SAPS II (p < 0.001). The new model combining BSM and GA can manage both binary data and continuous data. The mortality rate is predicted to be high if the patient’s Glasgow coma score is less than 5.     

ENSEMBLE ARTIFICIAL NEURAL NETWORKS FOR PREDICTION OF DEW POINT TEMPERATURE

Dew point temperature is needed as an input to calculate various meteorological variables. In general, it contributes to human and animal comfort levels. The goal of this study was to develop artificial neural network (ANN) models for dew point temperature prediction to improve upon previous research. These improvements included optimizing the stopping criteria, comparing seasonal models to year-round models, and developing ensemble ANNs to blend the output of seasonal models. For an ANN trained with 100,000 patterns per epoch, the error was reduced using a 2000-pattern stopping dataset at an interval of 20 learning events to decide when to stop training. Seasonal ANN models were blended in an ensemble ANN with the weight of the member networks determined using a fuzzy membership-type function based on the day of year. These ensemble models were shown to produce lower errors than year-round, nonensemble models. The mean absolute errors (MAEs) of the final models evaluated with an independent evaluation dataset included 0.795°C for a 2-hour prediction, 1.485°C for a 6-hour prediction, and 2.146°C for a 12-hour prediction. The final model MAEs, when compared to the previous research, were reduced by 0.008°C, 0.081°C, and 0.135°C, respectively. It can be concluded that the methods used in this research were effective in more accurately predicting year-round dew point temperature. The ANN models for different prediction periods were sequenced to provide a 12-hour dew point temperature prediction system for implementation on the Georgia Automated Environmental Monitoring Network website (www.georgiaweather.net).     

Support vector regression with reduced training sets for air temperature prediction: a comparison with artificial neural networks

Sudden changes in weather, in particular extreme temperatures, can result in increased energy expenditures, depleted agricultural resources, and even loss of life. However, these ill effects can be reduced with accurate air temperature predictions that provide adequate advance warning. Support vector regression (SVR) was applied to meteorological data collected across the state of Georgia in order to produce short-term air temperature predictions. A method was proposed for reducing the number of training patterns of massively large data sets that does not require lengthy pre-processing of the data. This method was demonstrated on two large data sets: one containing 300,000 cold-weather training patterns collected during the winter months and one containing 1.25 million training patterns collected throughout the year. These patterns were used to produce predictions from 1 to 12 h ahead. The mean absolute error (MAE) for the evaluation set of winter-only patterns ranged from 0.514°C for the 1-h prediction horizon to 2.303°C for the 12-h prediction horizon. For the evaluation set of year-round patterns, the MAE ranged from 0.513°C for the 1-h prediction horizon to 1.922°C for the 12-h prediction horizon. These results were competitive with previously developed artificial neural network (ANN) models that were trained on the full data sets. For the winter-only evaluation data, the SVR models were slightly more accurate than the ANN models for all twelve of the prediction horizons. For the year-round evaluation data, the SVR models were slightly more accurate than the ANN models for three of the twelve prediction horizons.     

Prediction of flow pattern of gas–liquid flow through circular microchannel using probabilistic neural network

The present study attempts to develop a flow pattern indicator for gas–liquid flow in microchannel with the help of artificial neural network (ANN). Out of many neural networks present in literature, probabilistic neural network (PNN) has been chosen for the present study due to its speed in operation and accuracy in pattern recognition. The inbuilt code in MATLAB R2008a has been used to develop the PNN. During training, superficial velocity of gas and liquid phase, channel diameter, angle of inclination and fluid properties such as density, viscosity and surface tension have been considered as the governing parameters of the flow pattern. Data has been collected from the literature for air–water and nitrogen–water flow through different circular microchannel diameters (0.53, 0.25, 0.100 and 0.050 mm for nitrogen–water and 0.53, 0.22 mm for air–water). For the convenience of the study, the flow patterns available in literature have been classified into six categories namely; bubbly, slug, annular, churn, liquid ring and liquid lump flow. Single PNN model is unable to predict the flow pattern for the whole range (0.53 mm–0.050 mm) of microchannel diameter. That is why two separate PNN models has been developed to predict the flow patterns of gas–liquid flow through different channel diameter, one for diameter ranging from 0.53 mm to 0.22 mm and another for 0.100 mm–0.05 mm. The predicted map and their transition boundaries have been compared with the corresponding experimental data and have been found to be in good agreement. Whereas accuracy in prediction of transition boundary obtained from available analytical models used for conventional channel is less for all diameter of channel as compared to the present work. The percentage accuracy of PNN (～94% for 0.53 mm ID and ～73% for 0.100 mm ID channel) has also been found to be higher than the model based on Weber number (～86% for 0.53 mm ID and ～36% for 0.05 mm ID channel).     

An adaptive network-based fuzzy inference system (ANFIS) for the forecasting: The case of close price indices

The close price prediction model of the Zagreb Stock Exchange Crobex® index is presented in this paper. For the input/output data plan modeling the Crobex® index close price historical data are retrieved from the Zagreb Stock Exchange official internet pages. The prediction model is created in the way that for each of 5 days in advance it predicts the Crobex® close price. The prediction model is generated based on the input/output data plan by means of the adaptive neuro-fuzzy inference system method, representing the fuzzy inference system. It is of the essence to point out that for each day a separate fuzzy inference system is created by means of the adaptive neuro-fuzzy inference system method based on the same set of input/output data, the only difference being that for every separate fuzzy inference system different subsets for training and checking are used so that input variables are differently created. The input/output data set represents the historical data of the Crobex® index close price from 4 November 2010 to 24 January 2012 and the Crobex® index close price is predicted for the subsequent 5 days, the first day of prediction being 25 January 2012. After that the above mentioned input/output data set is shifted 5 days in advance and the Crobex® index close price is predicted in advance for the next 5 days starting with the last day of the input/output data set. In that way the Crobex® index close prices are predicted until 19 October 2012 based on the Crobex® index close price historical data. At the end of the paper qualitative and quantitative estimates are presented for the given approach of predicting the Crobex® index close price showing that the approach is useful for predicting within its limits.     

Runtime data center temperature prediction using Grammatical Evolution techniques

Data Centers are huge power consumers, both because of the energy required for computation and the cooling needed to keep servers below thermal redlining. The most common technique to minimize cooling costs is increasing data room temperature. However, to avoid reliability issues, and to enhance energy efficiency, there is a need to predict the temperature attained by servers under variable cooling setups. Due to the complex thermal dynamics of data rooms, accurate runtime data center temperature prediction has remained as an important challenge. By using Grammatical Evolution techniques, this paper presents a methodology for the generation of temperature models for data centers and the runtime prediction of CPU and inlet temperature under variable cooling setups. As opposed to time costly Computational Fluid Dynamics techniques, our models do not need specific knowledge about the problem, can be used in arbitrary data centers, re-trained if conditions change and have negligible overhead during runtime prediction. Our models have been trained and tested by using traces from real Data Center scenarios. Our results show how we can fully predict the temperature of the servers in a data rooms, with prediction errors below 2 °C and 0.5 °C in CPU and server inlet temperature respectively.     

Guided local search as a network planning algorithm that incorporates uncertain traffic demands

A search based heuristic for the optimisation of communication networks where traffic forecasts are uncertain and the problem is NP-complete is presented. While algorithms such as genetic algorithms (GA) and simulated annealing (SA) are often used for this class of problem, this work applies a combination of newer optimisation techniques specifically: fast local search (FLS) as an improved hill climbing method and guided local search (GLS) to allow escape from local minima. The GLS + FLS combination is compared with an optimised GA and SA approaches. It is found that in terms of implementation, the parameterisation of the GLS + FLS technique is significantly simpler than that for a GA and SA. Also, the self-regularisation feature of the GLS + FLS approach provides a distinctive advantage over the other techniques which require manual parameterisation. To compare numerical performance, the three techniques were tested over a number of network sets varying in size, number of switch circuit demands (network bandwidth demands) and levels of uncertainties on the switch circuit demands. The results show that the GLS + FLS outperforms the GA and SA techniques in terms of both solution quality and optimisation speed but even more importantly GLS + FLS has significantly reduced parameterisation time.     

Hexagon-based all-quadrilateral mesh generation with guaranteed angle bounds

In this paper, we present a novel hexagon-based mesh generation method which creates all-quadrilateral (all-quad) meshes with guaranteed angle bounds and feature preservation for arbitrary planar domains. Given any planar curves, an adaptive hexagon-tree structure is constructed by using the curvature of the boundaries and narrow regions. Then a buffer zone and a hexagonal core mesh are created by removing elements outside or around the boundary. To guarantee the mesh quality, boundary edges of the core mesh are adjusted to improve their formed angles facing the boundary, and two layers of quad elements are inserted in the buffer zone. For any curve with sharp features, a corresponding smooth curve is firstly constructed and meshed, and then another layer of elements is inserted to match the smooth curve with the original one. It is proved that for any planar smooth curve all the element angles are within [60° ? ε, 120° + ε] (ε ? 5°). We also prove that the scaled Jacobians defined by two edge vectors are in the range of [sin (60° ? ε),  sin 90°], or [0.82, 1.0]. The same angle range can be guaranteed for curves with sharp features, with the exception of small angles in the input curve. Furthermore, an approach is introduced to match the generated interior and exterior meshes with a relaxed angle range, [30°, 150°]. We have applied our algorithm to a set of complicated geometries, including the China map, the Lake Superior map, and a three-component air foil with sharp features. In addition, all the elements in the final mesh are grouped into five types, and most elements only need a few flops to construct the stiffness matrix for finite element analysis. This will significantly reduce the computational time and the required memory during the stiffness matrix construction.     

Prediction of California bearing ratio (CBR) of fine grained soils by AI methods

Advances in field of artificial intelligence (AI) offers opportunities of utilizing new algorithms and models that enable researchers to solve the most complex systems. As in other engineering fields, AI methods have widely been used in geotechnical engineering. Unlikely, there seems quite insufficient number of research related to the use of AI methods for the estimation of California bearing ratio (CBR). There were actually some attempts to develop prediction models for CBR, but most of these models were essentially statistical correlations. Nevertheless, many of these statistical correlation equations generally produce unsatisfactory CBR values. However, this paper is likely one of the very first research which aims to investigate the applicability of AI methods for prediction of CBR. In this context, artificial neural network (ANN) and gene expression programming (GEP) were applied for the prediction of CBR of fine grained soils from Southeast Anatolia Region/Turkey. Using CBR test data of fine grained soils, some proper models are successfully developed. The results have shown that the both ANN and GEP are found to be able to learn the relation between CBR and basic soil properties. Additionally, sensitivity analysis is performed and it is found that maximum dry unit weight (γ_d) is the most effective parameter on CBR among the others such as plasticity index (PI), optimum moisture content (w_opt), sand content (S), clay + silt content (C + S), liquid limit (LL) and gravel content (G) respectively.     

Prediction of cutting temperature in orthogonal machining of AISI 316L using artificial neural network

In this study, an approach based on artificial neural network (ANN) was proposed to predict the experimental cutting temperatures generated in orthogonal turning of AISI 316L stainless steel. Experimental and numerical analyses of the cutting forces were carried out to numerically obtain the cutting temperature. For this purpose, cutting tests were conducted using coated (TiCN + Al₂O₃ + TiN and Al₂O₃) and uncoated cemented carbide inserts. The Deform-2D programme was used for numerical modelling and the Johnson–Cook (J–C) material model was used. The numerical cutting forces for the coated and uncoated tools were compared with the experimental results. On the other hand, the cutting temperature value for each cutting tool was numerically obtained. The artificial neural network model was used to predict numerical cutting temperatures by means of the numerical cutting forces. The best results in predicting the cutting temperature were obtained using the network architecture with a hidden layer which has seven neurons and LM learning algorithm. Finally, the experimental cutting temperatures were predicted by entering the experimental cutting forces into a formula obtained from the artificial neural networks. Statistical results (R², RMSE, MEP) were quite satisfactory. This demonstrates that the established ANN model is a powerful one for predicting the experimental cutting temperatures.     

Application of artificial neural network (ANN)–self-organizing map (SOM) for the categorization of water,soil and sediment quality in petrochemical regions

The utilization of mathematical and computational tools for pollutant assessment frameworks has become increasingly valuable due to the capability to interpret integrated variable measurements. Artificial neural networks (ANNs) are considered as dependable and inexpensive techniques for data interpretation and prediction. The self-organizing map (SOM) is an unsupervised ANN used for data training to classify and effectively recognize patterns embedded in the input data space. Application of SOM–ANN is useful for recognizing spatial patterns in contaminated zones by integrating chemical, physical, ecotoxicological and toxicokinetic variables in the identification of pollution sources and similarities in the quality of the samples. Water (n = 11), soil (n = 38) and sediment (n = 54) samples from four areas in the Niger Delta (Nigeria) were classified based on their chemical, toxicological and physical variables applying the SOM. The results obtained in this study provided valuable assessment using the SOM visualization capabilities and highlighted zones of priority that might require additional investigations and also provide productive pathway for effective decision making and remedial actions.     

Artificial neural network-based model for predicting VO2max from a submaximal exercise test

The goal of this study is to develop an accurate artificial neural network (ANN)-based model to predict maximal oxygen uptake (VO₂max) of fit adults from a single stage submaximal treadmill jogging test. Participants (81 males and 45 females), aged from 17 to 40 years, successfully completed a maximal graded exercise test (GXT) to determine VO₂max. The variables; gender, age, body mass, steady-state heart rate and jogging speed are used to build the ANN prediction model. Using 10-fold cross validation on the dataset, the average values of standard error of estimate (SEE), Pearson’s correlation coefficient (r) and multiple correlation coefficient (R) of the model are calculated as 1.80 ml kg^?1 min^?1, 0.95 and 0.93, respectively. Compared with the results of the other prediction models in literature that were developed using Multiple Linear Regression Analysis, the reported values of SEE, r and R in this study are considerably more accurate.     

Inter-relationship between preparation methods,nickel loading,characteristics and performance in the reforming of crude ethanol over Ni/Al2O3 catalysts: A neural network approach

Artificial neural network (ANN) approach was used to design an optimum Ni/Al₂O₃ catalyst for the production of hydrogen by the catalytic reforming of crude ethanol based on determining the inter-relationships between catalyst-preparation methods, nickel loading, catalyst characteristics and catalyst performance. ANN could predict hydrogen production performance of various Ni/Al₂O₃ catalysts of various elemental compositions and methods of preparation in the production of hydrogen by the catalytic reforming of crude ethanol in terms of crude-ethanol conversion, hydrogen selectivity and hydrogen yield. Specifically on catalyst design, ANN was used to determine the optimum catalyst conditions for obtaining maximum hydrogen production performance of a Ni/Al₂O₃ catalyst for the production of hydrogen by the catalytic reforming of crude ethanol. The optimal hydrogen yield was 4.4 mol %, and the associated crude-ethanol conversion and H₂ selectivity for the optimal hydrogen yield were 79.6 and 91.4 mol%, respectively. The optimal catalyst was the one prepared by the coprecipitation method with the optimal nickel loading of 12.4 wt% and an optimal aluminum composition of 42.5 wt%.     

Investigation on thermal performance calculation of two type solar air collectors using artificial neural network

In this study, two types of solar air collectors are constructed and examined experimentally. The types are called as zigzagged absorber surface type and flat absorber surface type called Model I and Model II respectively. Experiments are carried out between 10.00 and 17.00 h in August and September under the prevailing weather conditions of Karabuk (city of the Turkey) for 5 days. Then, thermal performances belongs to experimental systems are calculated by using data obtained from experiments. To estimate thermal performances of solar air collectors an artificial neural network (ANN) model is designed. The measured data and calculated performance values are used at the design of Levenberg–Marquardt (LM) based multi-layer perceptron (MLP) in Matlab nftool module. Calculated values of thermal performances are compared to predicted values. Statistical error analysis is used to evaluate results. Comparing and statistical results demonstrate effectiveness of the proposed ANN. Also reliability of ANN and meaningfulness of input variables are tested via applying stepwise regression method to the data used in designing ANN.     

Modeling of steady state hot flow behavior of API-X70 microalloyed steel using genetic algorithm and design of experiments

API-X70 microalloyed steel is one of the most conventional materials that has been used to produce the pipelines used in oil and gas industry. This steel is produced by thermo mechanical processing (TMP). Prediction of steady state hot flow behavior of metals during TMP, for design of its forming process is of great importance. In this research, flow curves of API-X70 were obtained using hot torsion test at temperature range of 950–1150 °C and strain rates of 0.001–3 s⁻¹. Genetic algorithm (GA) was used to find parameters of steady state stress semi-empirical model in the way that minimizing the difference between experimental data and model output. The optimal combination of GA parameters were chosen by Taguchi design of experiments(DOE) method in order to increase efficiency of GA. Accuracy of developed model to predict flow stress in steady state region was evaluated through statistical methods. Results showed a good agreement between developed model and experimental data with R² = 0.99 and this model can predict steady state flow stress well.