M5 Model Tree Research Articles

Adaptive Neuro‐Fuzzy Inference System integrated with solar zenith angle for forecasting sub‐tropical Photosynthetically Active Radiation

AbstractAdvocacy for climate mitigation aims to minimize the use of fossil fuel and to support clean energy adaptation. While alternative energies (e.g., biofuels) extracted from feedstock (e.g., micro‐algae) represent a promising role, their production requires reliably modeled photosynthetically active radiation (PAR). PAR models predict energy parameters (e.g., algal carbon fixation) to aid in decision‐making at PAR sites. Here, we model very short‐term (5‐min scale), sub‐tropical region's PAR with an Adaptive Neuro‐Fuzzy Inference System model with a Centroid‐Mean (ANFIS‐CM) trained with a non‐climate input (i.e., only the solar angle, θZ). Accuracy is benchmarked against genetic programming (GP), M5Tree, Random Forest (RF), and multiple linear regression (MLR). ANFIS‐CM integrates fuzzy and neural network algorithms, whereas GP adopts an evolutionary approach, M5Tree employs binary decision, RF employs a bootstrapped ensemble, and MLR uses statistical tools to link PAR with θZ. To design the ANFIS‐CM model, 5‐min θZ (01–31 December 2012; 0500H–1900H) for sub‐tropical, Toowoomba are utilized to extract predictive features, and the testing accuracy (i.e., differences between measurements and forecasts) is evaluated with correlation (r), root‐mean‐square error (RMSE), mean absolute error (MAE), Willmott (WI), Nash–Sutcliffe (ENS), and Legates & McCabes (ELM) Index. ANFIS‐CM and GP are equivalent for 5‐min forecasts, yielding the lowest RMSE (233.45 and 233.01μ mol m−2s−1) and MAE (186.59 and 186.23 μmol m−2s−1). In contrast, MLR, M5Tree, and RF yields higher RMSE and MAE [(RMSE = 322.25 μmol m−2s−1, MAE = 275.32 μmol m−2s−1), (RMSE = 287.70 μmol m−2s−1, MAE = 234.78 μmol m−2s−1), and (RMSE = 359.91 μmol m−2s−1, MAE = 324.52 μmol m−2s−1)]. Based on normalized error, ANFIS‐CM is considerably superior (MAE = 17.18% versus 19.78%, 34.37%, 26.39%, and 30.60% for GP, MLR, M5Tree, and RF models, respectively). For hourly forecasts, ANFIS‐CM outperforms all other methods (WI = 0.964 vs. 0.942, 0.955, 0.933 & 0.893, and ELM = 0.741 versus 0.701, 0.728, 0.619 & 0.490 for GP, MLR, M5Tree, and RF, respectively). Descriptive errors support the versatile predictive skills of the ANFIS‐CM model and its role in real‐time prediction of the photosynthetic‐active energy to explore biofuel generation from micro‐algae, studying food chains, and supporting agricultural precision.

Daily pan evaporation modeling from local and cross-station data using three tree-based machine learning models

Accurate estimation of pan evaporation (Ep) is required for many applications, e.g., water resources management, irrigation system design and hydrological modeling. However, the estimation of Ep for a target station can be difficult as a result of partial or complete lack of local meteorological data under many conditions. In this study, daily Ep was estimated from local (target-station) and cross-station data in the Poyang Lake Watershed of China using four empirical models and three tree-based machine learning models, including M5 model tree (M5Tree), random forests (RFs) and gradient boosting decision tree (GBDT). Daily meteorological data during 2001–2010 from 16 weather stations were used to train the models, while the data from 2011 to 2015 were used for testing. Two cross-station applications were considered between each of the 16 stations and the other 15 stations. The results showed that the radiation-based Priestley-Taylor model (on average RMSE = 1.13 mm d−1, NSE = 0.53, R2 = 0.57, MBE = 0.21 mm d−1) gave the most accurate daily Ep estimates among the four empirical models during testing, while the mass transfer-based Trabert model (on average RMSE = 1.38 mm d−1, NSE = 0.25, R2 = 0.46, MBE = 0.65 mm d−1) performed worst. The GBDT model outperformed the RFs model, M5Tree model and the empirical models under the same input combinations in terms of prediction accuracy (on average RMSE = 0.86 mm d−1, NSE = 0.68, R2 = 0.73, MBE = 0.07 mm d−1) and model stability (average percentage increase in testing RMSE = 16.3%). The RMSE values generally increased with the increase in the distance of two cross stations. A distance of less than 100 km between two cross stations is highly recommended for cross-station applications with satisfactory prediction accuracy (median percentage increase in RMSE <5% for cross-station application #1 and <20% for application #2) in the Poyang Lake Watershed of China and maybe elsewhere with similar climates.

Evaluation of SVM, ELM and four tree-based ensemble models for predicting daily reference evapotranspiration using limited meteorological data in different climates of China

Accurate estimation of reference evapotranspiration (ET0) is of great importance for the regional water resources planning and irrigation scheduling design. The FAO-56 Penman-Monteith model is recommended as the reference model to predict ET0, but its application is commonly restricted by lack of complete meteorological data at many worldwide locations. This study evaluated the potential of machine learning models, particularly four relatively simple tree-based assemble algorithms (i.e. random forest (RF), M5 model tree (M5Tree), gradient boosting decision tree (GBDT) and extreme gradient boosting (XGBoost)), for estimating daily ET0 with limited meteorological data using a K-fold cross-validation method. For assessment of the tree-based models in terms of prediction accuracy, stability and computational costs, these models were further compared with their corresponding support vector machine (SVM) and extreme learning machine (ELM) models. Four input combinations of daily maximum and maximum temperature (Tmax and Tmin), relative humidity (Hr), wind speed (U2), global and extra-terrestrial solar radiation (Rs and Ra) with Tmax, Tmin and Ra as the base dataset were considered using meteorological data during 1961–2010 from eight representative weather stations in different climates of China. The results showed that, when lack of complete meteorological data, the machine learning models using Tmax, Tmin, Hr, U2 and Ra obtained satisfactory ET0 estimates in the temperate continental, mountain plateau and temperate monsoon zones of China (RMSE < 0.5 mm d−1). However, models with three input parameters of Tmax, Tmin and Rs were superior for daily ET0 prediction in the tropical and subtropical zones. The ELM and SVM models offered the best combination of prediction accuracy and stability. The simple tree-based XGBoost and GBDT models showed comparable accuracy and stability to the SVM and ELM models, but exhibited much less computational costs. Considering the complexity level, prediction accuracy, stability and computational costs of the studied models, the XGBoost and GBDT models have been recommended for daily ET0 estimation in different climatic zones of China and maybe elsewhere with similar climates around the world.

Modeling oblique load carrying capacity of batter pile groups using neural network, random forest regression and M5 model tree

M5 model tree, random forest regression (RF) and neural network (NN) based modelling approaches were used to predict oblique load carrying capacity of batter pile groups using 247 laboratory experiments with smooth and rough pile groups. Pile length (L), angle of oblique load (α), sand density (ρ), number of batter piles (B), and number of vertical piles (V) as input and oblique load (Q) as output was used. Results suggest improved performance by RF regression for both pile groups. M5 model tree provides simple linear relation which can be used for the prediction of oblique load for field data also. Model developed using RF regression approach with smooth pile group data was found to be in good agreement for rough piles data. NN based approach was found performing equally well with both smooth and rough piles. Sensitivity analysis using all three modelling approaches suggest angle of oblique load (α) and number of batter pile (B) affect the oblique load capacity for both smooth and rough pile groups.

Stream Flow Forecasting of Poorly Gauged Mountainous Watershed by Least Square Support Vector Machine, Fuzzy Genetic Algorithm and M5 Model Tree Using Climatic Data from Nearby Station

Forecasting stream flow is a very importance issue in water resources planning and management. The ability of three soft computing methods, least square support vector machine (LSSVM), fuzzy genetic algorithm (FGA) and M5 model tree (M5T), in forecasting daily and monthly stream flows of poorly gauged mountainous watershed using nearby hydro-meteorological data is investigated in the current study. In the first application, monthly stream flows of Hunza river are forecasted using local stream flow data of Hunza and precipitation and temperature data of nearby station. LSSVM provides slightly better forecasts than the FGA and M5T models. Stream flow and temperature inputs generally give better forecasts compared to other inputs. In the second application, daily stream flows of Hunza river are forecasted using local stream flow data of Hunza and precipitation and temperature data of nearby station. Better results are obtained from the models comprising only stream flow inputs. In general, a better accuracy is obtained from LSSVM models in relative to the FGA and M5T. The results indicate that the monthly and daily stream flows of Hunza can be accurately forecasted by using only nearby climatic data. In the third application, daily stream flows of Hunza river are forecasted using local stream flow and climatic data and the models’ accuracy is slightly increased in relative to the previous applications. LSSVM generally performs superior to the FGA and M5T in forecasting daily stream flow of Hunza river using local stream flow and climatic inputs.

The Integration of Nature-Inspired Algorithms with Least Square Support Vector Regression Models: Application to Modeling River Dissolved Oxygen Concentration

The current study investigates an improved version of Least Square Support Vector Machines integrated with a Bat Algorithm (LSSVM-BA) for modeling the dissolved oxygen (DO) concentration in rivers. The LSSVM-BA model results are compared with those obtained using M5 Tree and Multivariate Adaptive Regression Spline (MARS) models to show the efficacy of this novel integrated model. The river water quality data at three monitoring stations located in the USA are considered for the simulation of DO concentration. Eight input combinations of four water quality parameters, namely, water temperature, discharge, pH, and specific conductance, are used to simulate the DO concentration. The results revealed the superiority of the LSSVM-BA model over the M5 Tree and MARS models in the prediction of river DO. The accuracy of the LSSVM-BA model compared with those of the M5 Tree and MARS models is found to increase by 20% and 42%, respectively, in terms of the root-mean-square error. All the predictive models are found to perform best when all the four water quality variables are used as input, which indicates that it is possible to supply more information to the predictive model by way of incorporation of all the water quality variables.

Data mining based on wavelet and decision tree for rainfall-runoff simulation

Abstract This study introduced a new hybrid model (Wavelet-M5 model) which combines the wavelet transforms and M5 model tree for rainfall-runoff modeling. For this purpose, the main time series were decomposed to several sub-signals by the wavelet transform, at first. Then, the obtained sub-time series were imposed as input data to M5 model tree, and finally, the related linear regressions were presented by M5 model tree. This new technique was applied on the monthly time series of Sardrud catchment and the results were also compared with other models like WANN and sole M5 model tree. The results showed that the accuracy of the proposed model is better than the previous models and also indicated the effect of data pre-processing on the performance of M5 model tree. The determination coefficient of the training stage was 0.80 and improved 31% than the M5 model tree for Sardrud catchment which is recognized as a normal watershed with a regular four seasons' pattern.

Evaluation of mechanical properties of concretes containing coarse recycled concrete aggregates using multivariate adaptive regression splines (MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) models

This paper investigates the application of three artificial intelligence methods, including multivariate adaptive regression splines (MARS), M5 model tree (M5Tree), and least squares support vector regression (LSSVR) for the prediction of the mechanical behavior of recycled aggregate concrete (RAC). A large and reliable experimental test database containing the results of 650 compressive strength, 421 elastic modulus, 152 flexural strength, and 346 splitting tensile strength tests of RACs with no pozzolanic admixtures assembled from the published literature was used to train, test, and validate the three data-driven-based models. The results of the model assessment show that the LSSVR model provides improved accuracy over the existing models in the prediction of the compressive strength of RACs. The results also indicate that, although all three models provide higher accuracy than the existing models in the prediction of the splitting tensile strength of RACs, only the performance of the LSSVR model exceeds those of the best-performing existing models for the flexural strength of RACs. The results of this study indicate that MARS, M5Tree, and LSSVR models can provide close predictions of the mechanical properties of RACs by accurately capturing the influences of the key parameters. This points to the possibility of the application of these three models in the pre-design and modeling of structures manufactured with RACs.

Quad-PolSAR data classification using modified random forest algorithms to map halophytic plants in arid areas

In this work, fully polarized SAR (PolSAR) data are exploited to characterize halophyte plants in lakeside saline wetland environments thanks to their different scattering properties. To this aim, several polarization signatures and morphological profiles (MPs) are used as inputs to the proposed “random M5 model forest” (RM5MF) and “classification via random forest regression” (CVRFR) classifiers. The experimental results show that parameters such as pedestal height (PH), as well as 3D co-polarization and cross-polarization signature plots, are more suited than biomass index (BMI), volume scattering index (VSI), and canopy scattering index (CSI) to map halophytic plants in arid environments. When we compare the suitability of PolSAR features using RM5MF, random forest (RaF), and other five popular attribute selection approaches, all the results uniformly show that span, MPs and entropy are the most valuable features, while PH and BMI are more valuable than CSI, VSI and the radar forest degradation index (RFDI). Additionally, the diagonal elements of the coherency matrix are more valuable than are the off-diagonal elements, and double-bounce, odd-bounce and wire elements are more valuable than helix bounce and volume bounce. The study results are obtained from PolSAR L-band quad-polarimetric high-sensitivity stripmap data over two study regions by comparing RM5MF and CVRFR with more traditional algorithms (support vector machine (SVM), RaF, rotation forest (RoF), and MultiBoostAB). The RM5MF model achieves the highest accuracy value in the study regions. However, due to the binary splitting criteria in the M5 model tree, it is more computationally intensive than all the others. In contrast, the CVRFR model consumes much less time—approximately 10 times less than RM5MF, and 5 times less than RoF—but still achieves better (3%–8%) classification accuracy than SVM or RoF, and its results are comparable (less than 1% difference) to those by RaF.

Design and evaluation of SVR, MARS and M5Tree models for 1, 2 and 3-day lead time forecasting of river flow data in a semiarid mountainous catchment

Accurate and reliable river flow forecasts attained with data-intelligent models can provide significant information about future water resources management. In this study we employed a 50-model ensemble of three data-driven predictive models, namely the support vector regression (SVR), multivariate adaptive regression spline (MARS) and M5 model tree (M5Tree) to forecast river flow data in a semiarid and ecologically significant mountainous region of Pailugou catchment in northwestern China. To attain stable and accurate forecast results, 50 different models were trained by randomly sampling the entire river flow data into 80% for training and 20% for testing subsets. To attain a complete evaluation of the ensemble-model based results, the global mean of six quantitative statistical performance evaluation measures: the coefficient of correlation (R), mean absolute relative error (MAE), root mean squared error (RMSE), Nash–Sutcliffe efficiency coefficient (NS), relative RMSE, and the Willmott’s Index (WI), and Taylor diagrams, including skill scores relative to a persistence model, were selected to assess the performances of the developed predictive models. The results indicated that all of the averaged R value attained was higher than 0.900 and all of the averaged NS values were higher than 0.800, representing good performance of the SVR, MARS and M5Tree models applied in the 1-, 2- and 3-day ahead modeling horizon, and this also accorded with the deductions made through an assessment of the Willmott’s Index. However, the M5Tree model outperformed both the SVR and MARS models (with NS = 0.917 vs. 0.904 and 0.901 for 1-day, 0.893 vs. 0.854 and 0.845 for 2-day, and 0.850 vs. 0.828 and 0.810 for 3-day forecasting horizons, respectively), which was in concurrence with the high value of WI. Therefore, based on the ensemble of 50 models, the performance of the M5Tree can be considered as superior to the SVR and MARS models when applied in a problem of river flow forecasting at multiple forecast horizon. A detailed comparison of the overall performance of all three models evaluated through Taylor diagrams and boxplots indicated that the 1-day ahead forecasting results were more accurate for all of the predictive models compared to the 2- and 3-day ahead forecasting horizons. Data-intelligent models designed in this study indicate that the M5Tree method could successfully be explored for short-term river flow forecasting in semiarid mountainous regions, which may have useful implications in water resources management, ecological sustainability and assessment of river systems.

RM5Tree: Radial basis M5 model tree for accurate structural reliability analysis

The surrogate models-based prediction of performance functions is an efficient and accurate methodology in structural reliability analyses. In this paper, the M5 model tree (M5Tree) is improved based on radial basis training data set and it is named as Radial basis M5Tree (RM5Tree). To predict the performance function, the random input variables are transferred from ordinal space to radial space using several effective points for nonlinear calibrated model of RM5Tree. The input datasets are controlled using the radial dataset for high-dimensional reliability problems to reduce computational efforts to evaluate the performance function. The abilities of RM5Tree using Monte Carlo Simulation (MCS) with respect to accuracy and efficiency are investigated through five nonlinear reliability problems. The results indicate that the proposed RM5Tree performs superior manner in accuracy and efficiency compared to the M5Tree, response surface method (RSM) and first order reliability method.

Non-tuned data intelligent model for soil temperature estimation: A new approach

In knowledge-based decision-support systems, soil temperature (ST) estimation can be considered as the core modeling task used for investigating the dynamics of solar energy exchange between the land surface and the sub-surface soil layers. In addition, the impacts of meteorological processes on energy uptake into the underlying soils and the design of more resilient and sustainable agricultural systems for improved crop health and resource management. In this paper, monthly ST estimation at various soil depths (i.e., 5, 50 and 100 cm) is performed by applying data-intelligent machine learning models: extreme learning machine (ELM), artificial neural network (ANN) and M5 Model Tree (M5 Tree). The predictive models are trained using meteorological information from two stations (i.e., Mersin and Adana, Turkey). The models are constructed using monthly input variables, including air temperature (T-air), windspeed (W), relative humidity (RH), solar radiation (SR), while the objective variable is the soil temperature measurement at 5, 50 and 100 cm depths for the period 1986–2010. Multi-objective performance criteria are applied to diagnose the predictive accuracy of the data-intelligent models, entailing the correlation coefficient (R), root mean square error (RMSE), mean absolute error (MAE), Willmott's Index (WI), Nash Sutcliffe's coefficient (Nash) and the Legates & McCabe's Index (LMI). Based on the tested dataset, the ELM model is yielded the most accurate performance for Mersin station compared to the lower performance of ANN and M5 Tree models. For this case, the most accurate performance is attained for the ST estimation at a depth of 50 cm, with the highest value of R = 0.992, WI = 0.999, Nash = 0.981, LMI = 0.879 and the lowest value of the relative RMSE and MAE values (i.e., 4.7 and 4.0%, respectively), attained using T-air, W, RH and periodicity as the predictor variables. The performance results for the Adana station behave differently, where ELM is seen to exceed the ANN and M5 Tree models for ST estimation at the depths of 5 and 100 cm. On the other hand, the ANN model performs marginally better than the ELM and the M5 Tree model at a depth of 50 cm with a different set of input combinations. The assessment of the estimation skills reveals the efficacy of the ELM over the counterpart benchmark models. In accordance with the present results, it is concluded that ELM model can be applied as an ideal decision-support tool for soil temperature estimation at multiple depths, whilst ensuring that an appropriate combination of meteorological inputs is applied to yield an optimal model.

Development of an efficient surrogate model based on aquifer dimensions to prevent seawater intrusion in anisotropic coastal aquifers, case study: the Qom aquifer in Iran

Coastal aquifers are usually exposed to saltwater intrusion. Therefore, groundwater extracted from these aquifers should be regulated considering their dimensions and effective parameters. In this paper, optimum discharge from a large number of exploitation wells is evaluated according to variations of width, length, and anisotropy coefficient in the Qom aquifer near the salt lake in central Iran. First, the wells are divided into clusters to decrease the number of decision variables. Then, the location and discharge from each cluster is obtained using SEAWAT and charged system search (CSS) simulation–optimization model with the assumption of three-dimensional variable density flow. The maximum discharge considering various anisotropy rates is computed based on different values of lengths and widths of the aquifer. Finally, an M5-tree model is trained using the obtained samples to derive a linear relationship between input and output data. Based on the results, for various ranges of width and length of an aquifer with impermeable boundaries, different linear equations for optimum discharge are obtained. Also, it was found that for an aquifer with a small width, the critical discharge is a function of the length while the effect of the boundaries is negligible. Sensitivity analysis of the anisotropy coefficient reveals that with increasing the anisotropy rate, thickness and slope of the transition zone decrease and as the maximum discharge increases consequently. However, the sensitivity of the discharge to anisotropy rate is not remarkable. A comparison between the results of this study with those of the analytical method based on sharp interface assumption is carried out. For the critical condition, the best agreement between analytical equation ( $$\overline {L} =0.87\overline {W} +0.62$$ ) and proposed method ( $$\overline {L} =0.83\overline {W} - 1.41$$ ) is achieved for the anisotropic aquifer when the 50% isochlor is assumed as the measure of salt water intrusion.

Decomposition genetic programming: An extensive evaluation on rainfall prediction in the context of weather derivatives

Regression problems provide some of the most challenging research opportunities in the area of machine learning, where the predictions of some target variables are critical to a specific application. Rainfall is a prime example, as it exhibits unique characteristics of high volatility and chaotic patterns that do not exist in other time series data. Moreover, rainfall is essential for applications that surround financial securities, such as rainfall derivatives. This paper extensively evaluates a novel algorithm called Decomposition Genetic Programming (DGP), which is an algorithm that decomposes the problem of rainfall into subproblems. Decomposition allows the GP to focus on each subproblem, before combining back into the full problem. The GP does this by having a separate regression equation for each subproblem, based on the level of rainfall. As we turn our attention to subproblems, this reduces the difficulty when dealing with data sets with high volatility and extreme rainfall values, since these values can be focused on independently. We extensively evaluate our algorithm on 42 cities from Europe and the USA, and compare its performance to the current state-of-the-art (Markov chain extended with rainfall prediction), and six other popular machine learning algorithms (Genetic Programming without decomposition, Support Vector Regression, Radial Basis Neural Networks, M5 Rules, M5 Model trees, and k-Nearest Neighbours). Results show that the DGP is able to consistently and significantly outperform all other algorithms. Lastly, another contribution of this work is to discuss the effect that DGP has had on the coverage of the rainfall predictions and whether it shows robust performance across different climates.

Monthly long-term rainfall estimation in Central India using M5Tree, MARS, LSSVR, ANN and GEP models

This study investigates the performance of the M5Tree model, multivariate adaptive regression spline, least square support vector regression (LSSVR), gene expressing programming (GEP) and artificial neural networks methods in estimating monthly long-term rainfall. Data from 61 rain stations in Madhya Pradesh and Chhattisgarh states, Central India, were used in the applications. Geographical inputs and periodicity were used as inputs to the models, and the methods were compared with each other according to the determination coefficient (R2), mean absolute errors (MAE) and root-mean-square errors (RMSE). LSSVR was found to be the best model with RMSE = 13.93 mm, MAE = 9.52 mm and R2 = 0.995 while the GEP provided the worst results with RMSE = 36.74 mm, MAE = 29.89 mm and R2 = 0.955 in prediction of long-term rainfall in the test stage. The lowest RMSE (5.53 mm) and MAE (3.89 mm) were obtained for the Rajnandgaon Station, while the Raigarh Station provided the worst accuracy (RMSE = 31.8 mm and MAE = 21.56 mm) for LSSVR model.

Ensemble committee-based data intelligent approach for generating soil moisture forecasts with multivariate hydro-meteorological predictors

Soil moisture (SM) is a key component of the global energy cycle that regulates all domains of the natural environmental and the agricultural system. In this research, the challenge is to develop a low-cost data-intelligent SM forecasting model using climate dynamics (i.e., the climate indices, atmospheric and hydro-meteorological parameters) as the model inputs. A newly designed, multi-model ensemble committee machine learning approach based on the artificial neural network (ANN-CoM) is developed to forecast monthly upper layer (∼0.2 m from the surface) and the lower layer (∼0.2–1.5 m deep) SM at four agricultural sites in Australia’s Murray-Darling Basin. ANN-CoM model is validated with respect to non-tuned second-order Volterra, M5 model tree, random forest, and an extreme learning machine (ELM) models. To construct the ANN-CoM model, the input variables comprised of the hydro-meteorological data from the Australian Water Availability Project, large-scale climate indices and atmospheric parameters derived from the Interim ERA European Centre for Medium-Range Weather Forecasting ECMWF reanalysis fields leads to a total of 60 potential predictors used for SM forecasting. To reduce the model input data dimensionality for accurate forecasts, the Neighborhood Component Analysis (NCA) based feature selection algorithm for regression purposes (fsrnca) is applied to determine the relative feature weights related to the targeted variable. The optimal predictor variables are then screened with an ELM model as the fitness function of the fsrnca algorithm to identify the set of most pertinent model variables. Extensive performance evaluation using statistical score metrics with visual and diagnostic plots show that the ensemble committee based, ANN-CoM model is able to effectively capture the nonlinear dynamics involved in the modeling of monthly upper and lower layer SM levels. Therefore, the ANN-CoM multi-model ensemble-based approach can be considered to be a superior SM forecasting tool, portraying as an amicable, integrated (or ensemble) machine learning stratagem that can be explored for soil moisture modeling and applications in agriculture and other hydro-meteorological phenomena.

Two-phase particle swarm optimized-support vector regression hybrid model integrated with improved empirical mode decomposition with adaptive noise for multiple-horizon electricity demand forecasting

Real-time energy management systems that are designed to support consumer supply and demand spectrums of electrical energy continue to face challenges with respect to designing accurate and reliable real-time forecasts due to the stochasticity of model construction data and the model’s inability to disseminate both the short- and the long-term electrical energy demand (G) predictions. Using real G data from Queensland, Australia’s second largest state, and employing the support vector regression (SVR) model integrated with an improved version of empirical mode decomposition with adaptive noise (ICEEMDAN) tool, this study aims to propose a novel hybrid model: ICEEMDAN-PSO-SVR. Optimization of the model’s weights and biases was performed using the particle swarm optimization (PSO) algorithm. ICEEMDAN was applied to improve the hybrid model’s forecasting accuracy, addressing non-linear and non-stationary issues in time series inputs by decomposing statistically significant historical G data into intrinsic mode functions (IMF) and a residual component. The ICEEMDAN-PSO-SVR model was then individually constructed to forecast IMFs and the residual datasets and the final G forecasts were obtained by aggregating the IMF and residual forecasted series. The performance of the ICEEMDAN-PSO-SVR technique was compared with alternative approaches: ICEEMDAN-multivariate adaptive regression spline (MARS) and ICEEMDAN-M5 model tree, as well as traditional modelling approaches: PSO-SVR, MARS and M5 model tree algorithms. To develop the models, data were partitioned into different subsets: training (70%), validation (15%), and testing (15%), and the tuned forecasting models with near global optimum solutions were applied and evaluated at multiple horizons: short-term (i.e., weekends, working days, whole weeks, and public holidays), and long-term (monthly). Statistical metrics including the root-mean square error (RMSE), mean absolute error (MAE) and their relative to observed means (RRMSE and MAPE), Willmott’s Index (WI), the Legates and McCabe Index (ELM) and Nash–Sutcliffe coefficients (ENS), were used to assess model accuracy in the independent (testing) period. Empirical results showed that the ICEEMDAN-PSO-SVR model performed well for all forecasting horizons, outperforming the alternative comparison approaches: ICEEMDAN-MARS and ICEEMDAN-M5 model tree and the PSO-SVR, PSO-MARS and PSO-M5 model tree algorithm. Due to its high predictive utility, the two-phase ICEEMDAN-PSO-SVR hybrid model was particularly appropriate for whole week forecasts (ENS=0.95, MAPE=0.89%, RRMSE=1.22%, and ELM=0.79), and monthly forecasts (ENS=0.70, MAPE=2.18%, RRMSE=3.18%, and ELM=0.56). The excellent performance of the ICEEMDAN-PSO-SVR hybrid model indicates that the two-phase hybrid model should be explored for potential applications in real-time energy management systems.

An ensemble-ANFIS based uncertainty assessment model for forecasting multi-scalar standardized precipitation index

Forecasting drought by means of the World Meteorological Organization-approved Standardized Precipitation Index (SPI) is considered to be a fundamental task to support socio-economic initiatives and effectively mitigating the climate-risk. This study aims to develop a robust drought modelling strategy to forecast multi-scalar SPI in drought-rich regions of Pakistan where statistically significant lagged combinations of antecedent SPI are used to forecast future SPI. With ensemble-Adaptive Neuro Fuzzy Inference System (‘ensemble-ANFIS’) executed via a 10-fold cross-validation procedure, a model is constructed by randomly partitioned input-target data. Resulting in 10-member ensemble-ANFIS outputs, judged by mean square error and correlation coefficient in the training period, the optimal forecasts are attained by the averaged simulations, and the model is benchmarked with M5 Model Tree and Minimax Probability Machine Regression (MPMR). The results show the proposed ensemble-ANFIS model's preciseness was notably better (in terms of the root mean square and mean absolute error including the Willmott's, Nash-Sutcliffe and Legates McCabe's index) for the 6- and 12- month compared to the 3-month forecasts as verified by the largest error proportions that registered in smallest error band. Applying 10-member simulations, ensemble-ANFIS model was validated for its ability to forecast severity (S), duration (D) and intensity (I) of drought (including the error bound). This enabled uncertainty between multi-models to be rationalized more efficiently, leading to a reduction in forecast error caused by stochasticity in drought behaviours. Through cross-validations at diverse sites, a geographic signature in modelled uncertainties was also calculated. Considering the superiority of ensemble-ANFIS approach and its ability to generate uncertainty-based information, the study advocates the versatility of a multi-model approach for drought-risk forecasting and its prime importance for estimating drought properties over confidence intervals to generate better information for strategic decision-making.

Ensemble of M5 Model Tree Based Modelling of Sodium Adsorption Ratio

This work reports the results of four ensemble approaches with the M5 model tree as the base regression model to anticipate Sodium Adsorption Ratio (SAR). Ensemble methods that combine the output of multiple regression models have been found to be more accurate than any of the individual models making up the ensemble. In this study additive boosting, bagging, rotation forest and random subspace methods are used. The dataset, which consisted of 488 samples with nine input parameters were obtained from the Barandoozchay River in West Azerbaijan province, Iran. Three evaluation criteria: correlation coefficient, root mean square error and mean absolute error were used to judge the accuracy of different ensemble models. In addition to the use of M5 model tree to predict the SAR values, a wrapper-based variable selection approach using a M5 model tree as the learning algorithm and a genetic algorithm, was also used to select useful input variables. The encouraging performance motivates the use of this technique to predict SAR values.

Modelling daily dissolved oxygen concentration using least square support vector machine, multivariate adaptive regression splines and M5 model tree

In the present study, three types of artificial intelligence techniques, least square support vector machine (LSSVM), multivariate adaptive regression splines (MARS) and M5 model tree (M5T) are applied for modeling daily dissolved oxygen (DO) concentration using several water quality variables as inputs. The DO concentration and water quality variables data from three stations operated by the United States Geological Survey (USGS) were used for developing the three models. The water quality data selected consisted of daily measured of water temperature (TE, °C), pH (std. unit), specific conductance (SC, μS/cm) and discharge (DI cfs), are used as inputs to the LSSVM, MARS and M5T models. The three models were applied for each station separately and compared to each other. According to the results obtained, it was found that: (i) the DO concentration could be successfully estimated using the three models and (ii) the best model among all others differs from one station to another.