M5 Model Tree Research Articles

Daily mean air temperature estimation from MODIS land surface temperature products based on M5 model tree

ABSTRACTThe use of satellite data to estimate air temperature (Ta) near the Earth's surface has become an effective way for a large area with high spatial and temporal resolution. In this study, M5 model tree was used to estimate Ta in Khuzestan province (in the southwest of Iran) using satellite remotely sensed land surface temperature (Ts) data acquired by the MODerate Resolution Imaging Spectroradiometer (MODIS)‐Terra sensor. The input variables for the M5 model tree were the daytime and nighttime MODIS Ts, extraterrestrial solar radiation and Julian day. A total of 365 images of MOD11A1 Ts product for the year 2007, covering the area of this study were collected from the Land Processes Distributed Active Archive Center (LP DAAC). The results of this study showed that mean daily Ta can be estimated with acceptable levels of the statistical indicators from MODIS data and from the two geographic parameters using the M5 model. Root mean square error and R2 for the comparison between observed and estimated Ta for the tested data are 2.3 and 0.96 °C, respectively.

M5 model trees and neural network based modelling of ET$_{{0}}$ in Ankara, Turkey

This paper investigates the potential of back propagation neural network and M5 model tree based regression approaches to model monthly reference evapotranspiration using climatic data of an area around Ankara, Turkey. Input parameters include monthly total sunshine hours, air temperature, relative humidity, wind speed, rainfall, and monthly time index, whereas the reference evapotranspiration calculated by FAO{56 Penman{Monteith was used as an output for both approaches. Mean square error, correlation coecient, and several other statistics were considered to compare the performance of both modeling approaches. The results suggest a better performance by the neural network approach with this dataset, but M5 model trees, being analogous to piecewise linear functions, provide a simple linear relation for prediction of evapotranspiration for the data ranges used in this study. Dierent scenario analysis with neural networks suggests that rainfall data does not have any inuence in predicting evapotranspiration.

Comparison between linear genetic programming and M5 tree models to predict flow discharge in compound channels

There are many studies on the hydraulic analysis of steady uniform flows in compound open channels. Based on these studies, various methods have been developed with different assumptions. In general, these methods either have long computations or need numerical solution of differential equations. Furthermore, their accuracy for all compound channels with different geometric and hydraulic conditions may not be guaranteed. In this paper, to overcome theses limitations, two new and efficient algorithms known as linear genetic programming (LGP) and M5 tree decision model have been used. In these algorithms, only three parameters (e.g., depth ratio, coherence, and ratio of computed total flow discharge to bankfull discharge) have been used to simplify its applications by hydraulic engineers. By compiling 394 stage-discharge data from laboratories and fields of 30 compound channels, the derived equations have been applied to estimate the flow conveyance capacity. Comparison of measured and computed flow discharges from LGP and M5 revealed that although both proposed algorithms have considerable accuracy, LGP model with R2 = 0.98 and RMSE = 0.32 has very good performance.

Estimation of Pan Coefficient using M5 Model Tree

Problem statement: Pan Evaporation has extensively been used for esti mating reference Evapotranspiration (ETo) due to its simplicity, low cost, ease of data interpretation and application and suitability for locations with limited availability of meteorological data. With this method, the pan coefficient (Kp) is a key element to be determined as well as the pan Evaporation (Ep) data. Approach: This study presents the development of new pan coe fficient (Kp) equations for Class A pan and Colorado sunken pan under green and dry fetch conditions by using M5 model tree based on soft computing technique. The Kp values were taken from FAO-24 Kp table for the development of Kp equations. Results: The results of the study indicate the usefulness a nd applicability of the M5 model tree in developing Kp equations. Those proposed equations based on the M5 model tree gave better performance in estimating Kp values than the previous Kp equations as well as the new Kp equations developed by indicator regression techniq ue. Conclusion: M5 model tree gave more accuracy in estimating Kp values. The new proposed Kp equations can be reliably used.

M5 model tree for pier scour prediction using field dataset

This paper investigates the potential of M5 model tree, a tree based regression approach to predict the local scour around bridge piers using field dataset. The dataset consisting of 232 pier scour measurements were used. Out of the total dataset, 154 measurements were used to train M5 model tree and the remaining 78 to test the trained model. Comparison of results with four predictive equations suggests an improved performance by M5 model tree in predicting the pier scour depth with dimensioned data and found it performing equally well to a back propagation neural network. A sensitivity analysis with field dataset indicates that the pier width, depth and flow velocity are important factors in predicting the scour depth with M5 model tree. Furthermore, M5 model tree based regression approach provides a linear regression function that can be used by field engineers to predict the pier scour.

Downscaling of precipitation on a lake basin: evaluation of rule and decision tree induction algorithms

We investigate the performance of existing state-of-the-art rule induction and tree algorithms, namely Single Conjunctive Rule Learner, Decision Table, M5 Model Tree, Decision Stump and REPTree. Downscaling models are developed using these algorithms to obtain projections of mean monthly precipitation to lake-basin scale in an arid region in India. The effectiveness of these algorithms is evaluated through application to downscale the predictand for the Lake Pichola region in Rajasthan state in India, which is considered to be a climatically sensitive region. The predictor variables are extracted from (1) the National Centre for Environmental Prediction (NCEP) reanalysis dataset for the period 1948–2000 and (2) the simulations from the third-generation Canadian Coupled Global Climate Model (CGCM3) for emission scenarios A1B, A2, B1 and COMMIT for the period 2001–2100. M5 Model Tree algorithm was found to yield better performance among all other learning techniques explored in the present study. The precipitation is projected to increase in future for A2 and A1B scenarios, whereas it is least for B1 and COMMIT scenarios using predictors.

Evaluation of machine learning tools as a statistical downscaling tool: temperatures projections for multi-stations for Thames River Basin, Canada

Many impact studies require climate change information at a finer resolution than that provided by global climate models (GCMs). This paper investigates the performances of existing state-of-the-art rule induction and tree algorithms, namely single conjunctive rule learner, decision table, M5 model tree, and REPTree, and explores the impact of climate change on maximum and minimum temperatures (i.e., predictands) of 14 meteorological stations in the Upper Thames River Basin, Ontario, Canada. The data used for evaluation were large-scale predictor variables, extracted from National Centers for Environmental Prediction/National Center for Atmospheric Research reanalysis dataset and the simulations from third generation Canadian coupled global climate model. Data for four grid points covering the study region were used for developing the downscaling model. M5 model tree algorithm was found to yield better performance among all other learning techniques explored in the present study. Hence, this technique was applied to project predictands generated from GCM using three scenarios (A1B, A2, and B1) for the periods (2046–2065 and 2081–2100). A simple multiplicative shift was used for correcting predictand values. The potential of the downscaling models in simulating predictands was evaluated, and downscaling results reveal that the proposed downscaling model can reproduce local daily predictands from large-scale weather variables. Trend of projected maximum and minimum temperatures was studied for historical as well as downscaled values using GCM and scenario uncertainty. There is likely an increasing trend for T max and T min for A1B, A2, and B1 scenarios while decreasing trend has been observed for B1 scenarios during 2081–2100.

Modeling of Suspended Sediment Concentration at Kasol in India Using ANN, Fuzzy Logic, and Decision Tree Algorithms

The prediction of the sediment loading generated within a watershed is an important input in the design and management of water resources projects. High variability of hydro-climatic factors with sediment generation makes the modelling of the sediment process cum- bersome and tedious. The methods for the estimation of sediment concentration based on the properties of flow and sediment have limitations attributed to the simplification of important parameters and boundary conditions. Under such circumstances, soft computing approaches have proven to be an efficient tool in modelling the sediment concentration. The focus of this paper is to present the development of models using Artificial Neural Network (ANN) with back propagation and Levenberg-Maquardt algorithms, radial basis function (RBF), Fuzzy Logic, and decision tree algorithms such as M5 and REPTree for predicting the suspended sediment concentration at Kasol, upstream of the Bhakra reservoir, located in the Sutlej basin in northern India. The input vector to the various models using different algorithms was derived con- sidering the statistical properties such as auto-correlation function, partial auto-correlation, and cross-correlation function of the time series. It was found that the M5 model performed well compared to other soft computing techniques such as ANN, fuzzy logic, radial basis function, and REPTree investigated in this study, and results of the M5 model indicate that all ranges of sediment concentration values were simulated fairly well. This study also suggests that M5 model trees, which are analogous to piecewise linear functions, have certain advantages over other soft computing techniques because they offer more insight into the generated model, are acceptable to decision makers, and always converge. Further, the M5 model tree offers explicit expressions for use by field engineers. DOI: 10.1061/(ASCE)HE.1943-5584.0000445. © 2012 American Society of Civil Engineers. CE Database subject headings: Suspended sediment; Neural networks; Fuzzy sets; Reservoirs. Author keywords: Suspended sediment concentration; Neural networks; Fuzzy Logic; M5; REPTree; Bhakra reservoir.

Estimation of Scour Downstream of a Ski-Jump Bucket Using Support Vector and M5 Model Tree

Estimation of scour downstream of a ski-jump bucket has been a topic of research among hydraulic engineers. For estimation of scour downstream of ski jump bucket, several empirical models are in use. In recent years, there has been emphasis to develop models which are capable of producing scour with high accuracy. Use of Artificial Neural Network (ANN) approach to model depth, width and length of scour hole indicates that performance of ANN models is far better than existing empirical models. At present, use of Support Vector Machines (SVMs) and M5 Pruned Model Tree are being considered in different disciplines to further improve upon the performance of ANN models as a potential alternate. With this in view, the present study deals with the development of regression models for computing various parameters of scour hole using SVMs and M5 Model Tree. A comparative evaluation of the performance of ANN versus SVMs and M5 Model Tree clearly shows that SVMs and M5 Model Tree can prove more useful than ANN models in estimation of scour downstream of a ski jump bucket. Further, M5 model tree offers explicit expressions for use by design engineers.

Predicting wave run-up on rubble-mound structures using M5 model tree

Prediction of run-up level is a key task in design of the coastal structures. For the design of the crest level of coastal structures, the wave run-up level with a 2% exceedance probability, R u2% , is most commonly used. In this study, the performance of M5 model tree for prediction of the wave run-up on rubble-mound structures was investigated. The main advantage of model trees, unlike the other soft computing tools, is their easier use and more importantly their understandable mathematical rules. Experimental data set of Van der Meer and Stam was used for developing model trees. The conventional governing parameters were selected as the input variables and the obtained results were compared with Van der Meer and Stam’s formula, recommended by the Coastal Engineering Manual (CEM, 2006). The predictive accuracy of the model tree approach was found to be superior to that of Van der Meer and Stam’s empirical formula. Furthermore, to judge the generalization capability of the model tree method, the model developed based on laboratory data set was validated with the prototype run-up measurements on the Zeebrugge breakwater, Belgium. Results show that the model tree is more accurate than empirical formulas and TS Fuzzy approach in estimating the full-scale run-up.

Effect of Pruning and Smoothing while Using M5 Model Tree Technique for Reservoir Inflow Prediction

This study reports the performance of an M5 model tree (MT) and the effects of pruning and smoothing applied to reservoir inflow prediction. The full year and seasonal monthly time step MT predictions were compared with conventional univariate autoregressive integrated moving average (stochastic) models. It was found that stochastic models could not predict the future inflows in a better way, because the observed series had not followed any particular distribution. However, it was found that the stochastic models showed better improvement using a logarithmic-transformed series, but the logarithmic-transformed MT results showed otherwise. The model validation was performed using the comparison of goodness of fit measures, standard statistics, time series, and scatter plots of predicted inflows with observed inflows. The effect of pruning each leaf in the MT model was also studied. Instead of pruning all the leaves, leading to lesser predictive accuracy, selective pruning was carried out based on the import...

Experimental investigation of the predictive capabilities of data driven modeling techniques in hydrology - Part 1: Concepts and methodology

Abstract. A comprehensive data driven modeling experiment is presented in a two-part paper. In this first part, an extensive data-driven modeling experiment is proposed. The most important concerns regarding the way data driven modeling (DDM) techniques and data were handled, compared, and evaluated, and the basis on which findings and conclusions were drawn are discussed. A concise review of key articles that presented comparisons among various DDM techniques is presented. Six DDM techniques, namely, neural networks, genetic programming, evolutionary polynomial regression, support vector machines, M5 model trees, and K-nearest neighbors are proposed and explained. Multiple linear regression and naïve models are also suggested as baseline for comparison with the various techniques. Five datasets from Canada and Europe representing evapotranspiration, upper and lower layer soil moisture content, and rainfall-runoff process are described and proposed, in the second paper, for the modeling experiment. Twelve different realizations (groups) from each dataset are created by a procedure involving random sampling. Each group contains three subsets; training, cross-validation, and testing. Each modeling technique is proposed to be applied to each of the 12 groups of each dataset. This way, both prediction accuracy and uncertainty of the modeling techniques can be evaluated. The description of the datasets, the implementation of the modeling techniques, results and analysis, and the findings of the modeling experiment are deferred to the second part of this paper.

Experimental investigation of the predictive capabilities of data driven modeling techniques in hydrology - Part 2: Application

Abstract. In this second part of the two-part paper, the data driven modeling (DDM) experiment, presented and explained in the first part, is implemented. Inputs for the five case studies (half-hourly actual evapotranspiration, daily peat soil moisture, daily till soil moisture, and two daily rainfall-runoff datasets) are identified, either based on previous studies or using the mutual information content. Twelve groups (realizations) were randomly generated from each dataset by randomly sampling without replacement from the original dataset. Neural networks (ANNs), genetic programming (GP), evolutionary polynomial regression (EPR), Support vector machines (SVM), M5 model trees (M5), K-nearest neighbors (K-nn), and multiple linear regression (MLR) techniques are implemented and applied to each of the 12 realizations of each case study. The predictive accuracy and uncertainties of the various techniques are assessed using multiple average overall error measures, scatter plots, frequency distribution of model residuals, and the deterioration rate of prediction performance during the testing phase. Gamma test is used as a guide to assist in selecting the appropriate modeling technique. Unlike two nonlinear soil moisture case studies, the results of the experiment conducted in this research study show that ANNs were a sub-optimal choice for the actual evapotranspiration and the two rainfall-runoff case studies. GP is the most successful technique due to its ability to adapt the model complexity to the modeled data. EPR performance could be close to GP with datasets that are more linear than nonlinear. SVM is sensitive to the kernel choice and if appropriately selected, the performance of SVM can improve. M5 performs very well with linear and semi linear data, which cover wide range of hydrological situations. In highly nonlinear case studies, ANNs, K-nn, and GP could be more successful than other modeling techniques. K-nn is also successful in linear situations, and it should not be ignored as a potential modeling technique for hydrological applications.

Estimation of Mean Annual Flood in Indian Catchments Using Backpropagation Neural Network and M5 Model Tree

This paper explored the potential of Backpropagation Neural Network (BNN) and M5 model tree based regression approach to estimate the mean annual flood. Data used in this study were taken from an earlier study by Swamee et al. (J Water Resour Plan Manage 121:403–407, 1995) for 93 Indian catchments spread over the entire country. The relationship proposed by Swamee et al. (J Water Resour Plan Manage 121:403–407, 1995) was compared with the predictive accuracy of a BNN and M5 model tree approach. The data were analyzed using a tenfold cross-validation. Comparison of the results showed that predictions with the backpropagation neural network fell within a scatter line of ±30% with a correlation coefficient of 0.975. Furthermore, predictions with the M5 model tree fell well within a scatter line of ±15% with a correlation coefficient as high as 0.994. The results also showed that predicted values with neural network and M5 model tree were within about 1.25 times the actual values. However, the predicted values obtained using the Swamee et al. (J Water Resour Plan Manage 121:403–407, 1995) approach fell much beyond the scatter line of ±50% and the predicted mean annual flood values were sometimes as high as eight times the actual values. The correlation coefficient with this approach was 0.897. The results from this study suggest that backpropagation neural network and M5 model tree-based modeling approaches are superior in accuracy to the model proposed by Swamee et al. (J Water Resour Plan Manage 121:403–407, 1995). This study also suggests that M5 model trees, being analogous to piecewise linear functions, have certain advantages over neural networks as they offer more insight into the generated model, are acceptable to decision makers and are very efficient in training, and always converge.

Application of model trees and other machine learning techniques for algal growth prediction in Yongdam reservoir, Republic of Korea

A promising new approach for eco-environmental modelling, such as algal growth prediction, is the data-driven modeling using machine learning techniques: an artificial neural network (ANN) being a typical method. Another method growing in popularity, based on the M5 model tree (MT) algorithm, is the use of piecewise linear regression models at the leaf nodes of the tree. M5 MTs using partial least-squares regression (PLSR) proposed in this paper were tested on a particular dataset and then compared to M5 MTs, MLF- and RBF-ANN and k nearest neighbours (kNN). With the dataset partitioned to periods of algal growth and no growth, M5 MTs using PLSR showed better results for algal growth prediction in the reservoir than using the annual dataset and other algorithms. This gives the idea that the M5-PLSR MTs, in spite of the lack of data, more effectively seeks latent vectors between the closely correlated multivariate dataset partitioned using clustering techniques. M5-PLSR MTs is a promising approach when there is a shortage of data required to build a more transparent learning process model, and a combination with clustering is recommended.

Data mining approach for supply unbalance detection in induction motor

This paper describes an approach for detection of the supply unbalance condition in induction motors by using data mining process. Simulation results have shown that a good indicator of the fault is the amplitude of the second harmonic of the supply frequency component (2 f) in the signal obtained by the differences in supply current zero crossing instants. In the study, linear regression (LR), pace regression (PR), sequential minimal optimization (SMO), M5 model tree, M5’Rules, KStar, additive regression and back propagation neural network (BPNN) models are applied within the data mining process for determining the condition of the motor supply voltage. All data mining algorithms were applied using WEKA software. The best result for the determination of the fault related dominant parameter was obtained by using the M5P algorithm model.

M5 model tree based modelling of reference evapotranspiration

AbstractThis paper investigates the potential of M5 model tree based regression approach to model daily reference evapotranspiration using climatic data of Davis station maintained by California irrigation Management Information System (CIMIS). Four inputs including solar radiation, average air temperature, average relative humidity, and average wind speed whereas reference evapotranspiration calculated using a relation provided by the CIMIS was used as output. To compare the performance of M5 model tree in predicting the reference evapotranspiration, FAO–56 Penman–Monteith equation and calibrated Hargreaves–Samani relation was used. A comparison of results suggests that M5 model tree approach works well in comparison to both FAO–56 and calibrated Hargreaves–Samani relations. To judge the generalization capability of M5 model tree approach, model created by using the Davis data set was tested with the datasets of four different sites. Results from this part of the study suggest that M5 model tree could successfully be employed in modeling the reference evapotranspiration. Further, sensitivity analysis with M5 model tree approach suggests the suitability of solar radiation, average air temperature, average relative humidity, and average wind speed as input parameters to model the reference evapotranspiration Copyright © 2009 John Wiley & Sons, Ltd.

APPLICABILITY OF ARTIFICIAL NEURAL NETWORK MODEL FOR SIMULATION OF MONTHLY RUNOFF IN COMPARISON WITH SOM OTHER TRADITIONAL MODELS

Artificial Neural Network (ANN) model along with Back Propagation Algorithm (BPA) has been applied in many fields, especially in hydrology and water resources management to simulate or forecast rainfall runoff process, discharge and water level - time series, and other hydrological variables. Several researches have recently been focusing to compare the applicability of ANN model with other theory-driven and data-driven approaches. The comparison of ANN with M5 model trees for rainfall-runoff forecasting, with ARMAX models for deriving flow series, with AR models and regression models for forecasting and estimating daily river flows have been carried out. The better results that were implemented by ANN model have been concluded. So, this research trend is continued for the comparison of ANN model with Tank, Harmonic, Thomas and Fiering models in simulation of the monthly runoffs at Dong Nai river basin, Viet Nam. The results proved ANN being the best choice among these models, if suitable and enough data sources were available.

A novel method to estimate model uncertainty using machine learning techniques

A novel method is presented for model uncertainty estimation using machine learning techniques and its application in rainfall runoff modeling. In this method, first, the probability distribution of the model error is estimated separately for different hydrological situations and second, the parameters characterizing this distribution are aggregated and used as output target values for building the training sets for the machine learning model. This latter model, being trained, encapsulates the information about the model error localized for different hydrological conditions in the past and is used to estimate the probability distribution of the model error for the new hydrological model runs. The M5 model tree is used as a machine learning model. The method is tested to estimate uncertainty of a conceptual rainfall runoff model of the Bagmati catchment in Nepal. In this paper the method is extended further to enable it to predict an approximation of the whole error distribution, and also the new results of comparing this method to other uncertainty estimation approaches are reported. It can be concluded that the method generates consistent, interpretable and improved model uncertainty estimates.

Data mining techniques for thermophysical properties of refrigerants

This study presents ten modeling techniques within data mining process for the prediction of thermophysical properties of refrigerants (R134a, R404a, R407c and R410a). These are linear regression (LR), multi layer perception (MLP), pace regression (PR), simple linear regression (SLR), sequential minimal optimization (SMO), KStar, additive regression (AR), M5 model tree, decision table (DT), M5’Rules models. Relations depending on temperature and pressure were carried out for the determination of thermophysical properties as the specific heat capacity, viscosity, heat conduction coefficient, density of the refrigerants. Obtained model results for every refrigerant were compared and the best model was investigated. Results indicate that use of derived formulations from these techniques will facilitate design and optimize of heat exchangers which is component of especially vapor compression refrigeration system.