Quantile Regression Forest Model Research Articles

Battery state-of-health estimation incorporating model uncertainty based on Bayesian model averaging

Accurately estimating the state-of-health (SOH) of lithium-ion batteries is crucial for efficient, reliable, and safe use. However, the degradation of these batteries involves complex and intricate failure mechanisms that cannot be fully captured by a single model. To tackle this challenge, we propose an SOH estimation method based on Bayesian Model Averaging (BMA), which effectively accounts for both parameter and model uncertainties by combining estimations from different model implementations. It provides both point-value estimates and the probability distribution estimates, delivering results in a fraction of a second. Evaluated on three open-source datasets, the maximum absolute error of SOH estimation is within 0.03, and the Continuous Ranked Probability Score is within 0.015. Compared to optimal individual models, the proposed BMA method reduces the prediction error of point estimates by half to two-thirds. Additionally, the prediction error for probability estimation decreases by an order of magnitude. Moreover, the comparison studies with respect to the Gaussian Process Regression model and the Quantile Regression Forests model demonstrate the applicability and superiority of proposed method. These results highlight the potential of the BMA method to advance battery SOH estimation and facilitate reliable battery management.

Analyze QRF model for soil organic carbon map building with digital soil mapping (case study: Sumatra island and Java island)

Abstract In the current era of global warming, soil organic content is one of the most important soil properties. The goal of the entire globe is for carbon neutrality to be achieved and regularly assessed. It is hoped that a dynamic, quick and effective soil organic carbon mapping method will be able to distribute the presence of soil organic carbon to support calculations for changes in carbon stocks and carbon sequestration so that carbon neutrality can be achieved. Digital Soil Mapping (DSM) recently has become the ultimate framework for accurately representing spatial distribution based on its quantitative result and uncertainty analysis. These advantages allow DSM to be replicated uniquely in each mapped area. Digital soil mapping requires input in the form of laboratory and field observation results that are spatially modeled using machine learning techniques. Field observations and laboratory data for Sumatra and Java Island from the Indonesian Center for Agricultural Land Resources Standard Testing (1970-2022) were used in this study, and the results were modeled using Quantile Regression Forests (QRF) in the R Software. Evaluation results from this model with 5738 observation points covering a 47.3 million-hectare-sized island of Sumatra and 3398 observation points covering a 12.8 million-hectare-sized island of Java show an RMSE value of 0.78 with a coefficient of determination (R2) of 0.31 for Sumatra Island and RMSE value of 0.68 with a coefficient of determination (R2) of 0.71 for Java Island. These findings indicate that the neighborhoods for the organic carbon content on the islands of Sumatra and Java differ quite noticeably. This may be due to the relatively wide range in some soils in the Sumatra region, which are peat soils with relatively high carbon content values compared to regions in Java where mineral soils predominate. In conclusion, the evaluation results for digital mapping with the QRF model for soil organic carbon content in Indonesia referring to these 2 large islands show good results with sufficient coefficients of determination in mineral soil areas and there is a need a different modeling approach in areas where peat soil predominates.

An evaluation of variable selection methods using Southern Africa solar irradiation data

Dimensionality poses a challenge in developing quality predictive models. Often when modelling solar irradiance (SI), many covariates are considered. Training such data has several disadvantages. This study sought to identify the best variable embedded selection method for different location and time horizon combinations from Southern Africa solar irradiance data. It introduced new variable selection methods into solar irradiation studies, namely penalised quantile regression (PQR), regularised random forests (RRF), and quantile regression forest (QRF). Stability analysis, performance and accuracy metric evaluations were used to compare them with the common lasso, elastic and ridge regression methods. The QRF model performed best in all locations followed by the shrinkage methods on hourly data. However, it was found that QRF is not sensitive to associations through correlations, thereby ignoring the relevance of variables while focusing on importance. Among the shrinkage methods, the lasso performed best in only one location. On the 24-hour horizon, elastic net dominated the performances among the shrinkage methods, but QRF was best in three locations of the six considered. Results confirmed that variable selection methods performed differently on different situational data sets. Depending on the strengths of the methods, results were combined to identify the most paramount variables. Day, total rainfall, and wind direction were superfluous features in all situations. The study concluded that shrinkage methods are best in cases of extreme multicollinearity, while QRF is best on data sets with outliers or/and heavy tails.

Digital modeling of surface and subsurface soil salinity in Golestan Province, Iran

Soil salinity is a challenging issue in many arid and semiarid regions and requires suitable management strategies. In the present study, the ability of three ML algorithms (random forest (RF), quantile regression forest (QRF), and cubist (Cu)) together with a depth function were evaluated to predict and compare the spatial distribution of soil salinity, and to identify the main environmental variables that influence soil salinity spatial distribution in 105 soil profiles in 90,000 ha in Northern Iran, Golestan Province. Environmental variables to support modeling included land parameters obtained from the digital elevation model, remote sensing information retrieved from Landsat 7 ETM+ images, rainfall, and piezometric maps. The electrical conductivity was estimated (ECe – dS m−1) at five depth intervals (i.e., 0–25, 25–50, 50–75, 75–100, and 100–125 cm) by spline model in all soil profiles. The model performance was assessed using root mean squared error (RMSEcv), mean absolute error (MAEcv), and coefficient of determination (R2cv). RF, QRF, and Cu methods similarly predicted ECe at the soil surface (0 to 25 cm). At 25–50 cm depth, the QRF model (R2cv = 0.55 and RMSEcv = 12.10) outperformed the other two models. QRF produced more consistent results with the expected ECe distribution on Taylor diagrams. This result showed that QRF is a well-suited model for mapping soil salinity at different depths in the studied region. The produced maps indicated a similar trend of increasing salinity as depth increased. Additionally, results showed that rainfall, NDVI, MRVBF, and piezometer were the most important variables to predict salinity in the study area.

Quantification and mapping of the carbon sequestration potential of soils via a quantile regression forest model

Quantification and mapping of the carbon sequestration potential of soils via a quantile regression forest model

Predicting soil organic carbon with different approaches and spatial resolutions for the southern Iberian Peninsula, Spain

Quantification and monitoring of soil organic carbon (SOC) stocks across local-to-global scales are needed to assess soil resource management practices and adapt environmental policies. Multiple SOC estimates are available worldwide; however, verification and validation are required to quantify the discrepancies and provide improved estimates. Here, we evaluated four different digital soil mapping (DSM) approaches (i.e., linear models, support vector machine, random forest, and quantile regression forest) to estimate SOC concentration (SOCc) and SOC stocks (SOCs) in the Region of Murcia (11,313 km2), a complex topographic and climatic area in the southern Iberian Peninsula, at three spatial resolutions (100, 250, and 1000 m). We estimated SOC spatially using a local harmonized database of 255 soil profiles for modeling and 1100 topsoils for external validation. We found that the quantile regression forest (QRF) approach had the best data-model agreement at 100 m spatial resolution, with the highest accuracy percentage (79%), external validation (correlation coefficient of 52%), and spatial interpretability of patterns, especially for SOCc. The QRF model showed a mean SOCc of 12.18 g/kg with an overall uncertainty of 10.54 g/kg and an accuracy percentage of 79%, whereas the total SOCs was 27,572 GgC with an uncertainty of 0.016 GgC. Our results showed that using local environmental covariates and local soil information to predict SOC within this region resulted in a relative improvement in the prediction accuracy of ∼40% for SOCc and ∼ 65% for SOCs compared to the SOC products derived from national and global databases. Our results showed a large discrepancy between the national and global estimates for reporting SOC locally. Consequently, local-to-regional efforts are needed to describe SOC spatial variability better to reduce uncertainty and improve the assessment of soil resources. We provide the resulting SOC maps with associated spatial uncertainty on the public Environmental Data Initiative Repository at https://portal.edirepository.org/nis/mapbrowse?packageid=edi.1238.2.

Space-time mapping of soil organic carbon stock and its local drivers: Potential for use in carbon accounting

The measurement and tracking of changes in soil organic carbon (SOC) stocks and its underpinning drivers are important in greenhouse gas accounting and carbon trading schemes. While repeated direct measurement of a location over time is the ‘gold standard’ for SOC stock change estimation, this is currently unfeasible at scale due to sample collection and analysis costs. Here, we used a data-driven, space–time digital soil mapping modelling approach (ST-DSM) coupled with an interpretive machine learning (IML) technique to both predict and quantify the relative contributions of covariates to annual SOC stocks and their uncertainty at 0–30 cm depth and at a 90 m spatial resolution for Australia between 1990 and 2018. A quantile regression forest model was calibrated using data from a datacube comprising of SOC stock values collected over the prediction years and a suite of dynamic and static environmental covariates. The evaluation of the ST-DSM model on a test set was satisfactory. Long-term annual mean (Mg C/ha), and total (Pg C) topsoil SOC stock were 37.6 (12.3 – 101.1, 90 % PI) and 28.3 (9.25 – 83.1, 90 % PI) respectively. The mean annual rate of SOC stock change over the Australian continent was 0.11 (±0.22) Mg C/ha yr−1 and the total net change was 23.5 Tg C yr−1, indicating Australia’s soils were a net sink of SOC over the 29-year period. However, SOC stocks declined in the montane ecoregion, a great concern given its fragility and high SOC stock. The long-term mean fraction of photosynthetic vegetation was the most important individual local contributor to SOC stock prediction in many parts of Australia. The aggregated effect of covariates based on the soil forming factors indicates vegetation as the principal local driver of SOC stock across most of the Australian continent, followed by climate. The evaluation of our results against independent, temporally paired field data and estimates from a nationally accepted SOC process-based model yielded promising results. Our approach demonstrates the use of readily available and inexpensive covariates to estimate SOC stock changes, as well as the underlying drivers over a larger area but at a spatial resolution suitable for decision making. This approach presents a new monitoring and verification possibility for carbon projects and national carbon accounting especially with the growing number of existing profile observations in soil databases.

A Machine Learning Approach to Model Over-Ocean Tropical Cyclone Precipitation

Abstract Extreme rainfall found in tropical cyclones (TCs) is a risk for human life and property in many low- to midlatitude regions. Probabilistic modeling of TC rainfall in risk assessment and forecasting can be computationally expensive, and existing models are largely unable to model key rainfall asymmetries such as rainbands and extratropical transition. Here, a machine learning–based framework is developed to model overwater TC rainfall for the North Atlantic basin. First, a catalog of high-resolution TC precipitation simulations for 26 historical events is assembled for the North Atlantic basin using the Weather Research and Forecasting (WRF) Model. The simulated spatial distribution of rainfall for these historical events are then decomposed via principal component analysis (PCA), and quantile regression forest (QRF) models are trained to predict the conditional distributions of the first five principal component (PC) weights. Conditional distributions of rain-rate levels are estimated separately using historical satellite data and a QRF model. With these models, probabilistic predictions of rainfall maps can be made given a set of storm characteristics and local environmental conditions. The model is able to capture storm total rainfall compared to satellite observations with a correlation coefficient of 0.96 and r2 value of 0.93. Additionally, the model shows good accuracy in modeling hourly total rainfall compared to satellite observations. Rain-rate maps predicted by the model are also compared to historical satellite observations and to the WRF simulations during cross validation, and the spatial distribution of estimates captures rainfall variability consistent with TC rainbands, wavenumber asymmetries, and possibly extratropical transition.

Comparing quantile regression forest and mixture density long short-term memory models for probabilistic post-processing of satellite precipitation-driven streamflow simulations

Abstract. Deep learning (DL) and machine learning (ML) are widely used in hydrological modelling, which plays a critical role in improving the accuracy of hydrological predictions. However, the trade-off between model performance and computational cost has always been a challenge for hydrologists when selecting a suitable model, particularly for probabilistic post-processing with large ensemble members. This study aims to systematically compare the quantile regression forest (QRF) model and countable mixtures of asymmetric Laplacians long short-term memory (CMAL-LSTM) model as hydrological probabilistic post-processors. Specifically, we evaluate their ability in dealing with biased streamflow simulations driven by three satellite precipitation products across 522 nested sub-basins of the Yalong River basin in China. Model performance is comprehensively assessed using a series of scoring metrics from both probabilistic and deterministic perspectives. Our results show that the QRF model and the CMAL-LSTM model are comparable in terms of probabilistic prediction, and their performances are closely related to the flow accumulation area (FAA) of the sub-basin. The QRF model outperforms the CMAL-LSTM model in most sub-basins with smaller FAA, while the CMAL-LSTM model has an undebatable advantage in sub-basins with FAA larger than 60 000 km2 in the Yalong River basin. In terms of deterministic predictions, the CMAL-LSTM model is preferred, especially when the raw streamflow is poorly simulated and used as input. However, setting aside the differences in model performance, the QRF model with 100-member quantiles demonstrates a noteworthy advantage by exhibiting a 50 % reduction in computation time compared to the CMAL-LSTM model with the same ensemble members in all experiments. As a result, this study provides insights into model selection in hydrological post-processing and the trade-offs between model performance and computational efficiency. The findings highlight the importance of considering the specific application scenario, such as the catchment size and the required accuracy level, when selecting a suitable model for hydrological post-processing.

Quantifying synergistic effects of artificial and environmental variables on potato nutrient use efficiency in China

Excessive use of fertilizer has decreased nutrient use efficiency (NUE), which leads to serious resource waste and environmental pollution. Improving potato NUE is instrumental in reducing fertilizer loss and ensuring agricultural sustainable development. Currently, potato NUE exhibits great spatial variation, and the explanatory variables of potato NUE have not been comprehensively elucidated. To address these challenges, 1850 samples and 56 corresponding explanatory variables were extracted from 19 provinces in the main potato producing areas, and the NUE models were established using random forest model, in which the uncertainty was determined by quantile regression forest model. The results indicated that the partial factor productivity (PFP) and partial nutrient balance (PNB) for nitrogen (N) and phosphorus (P) in northeast China were the highest, while the PFP and PNB for potassium (K) in the northwest were the highest. South China exhibited the lowest NUE. The prediction models had good performance, with better performance of PFP models than PNB models. The models demonstrated that the relative importance of explanatory variables was agricultural management practices (AMPs) > topography > climate > soil > crop > economy. NUE model uncertainty was higher in northwest China (Shaanxi, Gansu, Ningxia) and southwest China (Hubei). In this case, model prediction might have higher performance when constructing a model with data from each region. The findings of this study could have far-reaching implications for policymakers toward understanding the spatial variation of potato NUE. More efforts should be undertaken to investigate the effects of AMPs and topography, which are beneficial for the cleaner production of potato and environmental sustainability.

Daily global solar radiation time series prediction using variational mode decomposition combined with multi-functional recurrent fuzzy neural network and quantile regression forests algorithm

Global solar radiation (GSR) prediction capability with a reliable model and high accuracy is crucial for comprehending hydrological and meteorological systems. It is vital for the production of renewable and clean energy. This research aims to evaluate the performance of combined variational mode decomposition (VMD) with a multi-functional recurrent fuzzy neural network (MFRFNN) and quantile regression forests (QRF) models for GSR prediction in daily scales. The hybrid VMD-MFRFNN and QRF models were compared with standalone MFRFNN, random forest (RF), extreme gradient boosting (XGB), and M5 tree (M5T) models across the Lund and Växjö meteorological stations in Sweden. The meteorological data from 2008 to 2017 were used to train the models, while the prediction accuracy was verified by using the data from 2018 to 2021 under five different input combinations. The various meteorological-based scenarios (including the input are air temperatures (Tmin, Tmax, T), wind speed (WS), relative humidity (RH), sunshine duration (SSH), and maximum possible sunshine duration (N)) were considered as input of predictor models. The current study resulted that the M5T model exhibited higher accuracy than RF and XGB models, while the QRF model showed equivalent performance with the M5T model at both study sites. The MFRFNN model outperformed QRF and M5T models across all input combinations at both study sites. The hybrid VMD-MFRFNN model showed the best performance when fewer input variables (Tmin, Tmax, T, WS at Lund station and Tmin, Tmax, T, WS, SSH, RH at Växjö station) were used for GSR prediction. We conclude that the MFRFNN model best predicts average daily GSR when combining all meteorological variables (Tmin, Tmax, T, WS, SSH, RH, N).

Prediction of Soil Inorganic Carbon at Multiple Depths Using Quantile Regression Forest and Digital Soil Mapping Technique in the Thar Desert Regions of India

ABSTRACT Soil inorganic carbon (SIC) is important carbon reservoirs in desert ecosystems. However, little attention was paid to estimate carbon stock in these regions. In the present study, the distribution of SIC stock was investigated using digital soil mapping in Bikaner district, Rajasthan, India. A total of 187 soil profiles were used for SIC estimation by Quantile regression forest model. Landsat data, terrain attributes and bioclimatic variables were used as environmental variables. Ten-fold cross-validation was used to evaluate model. Equal-area quadratic splines were fitted to soil profile datasets to estimate SIC at six standard soil depths (0–5, 5–15, 15–30, 30–60, 60–100 and 100–200 cm). The SIC in the study area ranged from 0.27 to 27.85 g kg−1 in 0–5 cm and 0.31 to 27.84 g kg−1 in 5–15 cm, respectively. The model could capture reasonable variability (R2 = 11–21%) while predicting SIC for different depths. The Lin’s concordance correlation coefficient values ranged from 0.20 to 0.32, indicating poor relationship between the predicted and observed values. The values of prediction interval coverage probability (PICP) recorded 86.4–91.1% for SIC at different depths. Annual precipitation and precipitation seasonality were the most important covariates in soil below the 30 cm depth. The predicted SIC stocks were 10.3 ± 0.01, 81.6 ± 0.07 and 186.7 ± 0.13 Mg ha−1 at 0–15, 0–100 and 0–200 cm, depth, respectively. The uncertainty analysis suggests that there is room to improve the current spatial predictions of SIC. It is anticipated that this digital mapping of SIC will be useful for assessment of carbon cycle in arid regions.

Interpretable Battery Cycle Life Range Prediction Using Early Cell Degradation Data

Battery cycle life prediction using early degradation data has many potential applications throughout the battery product life cycle. For that reason, various data-driven methods have been proposed for point prediction of battery cycle life with minimum knowledge of the battery degradation mechanisms. However, managing the rapidly increasing amounts of batteries at end-of-life with lower economic and technical risk requires prediction of cycle life with quantified uncertainty, which is still lacking. The interpretability (i.e., the reason for high prediction accuracy) of these advanced data-driven methods is also worthy of investigation. Here, a physics-informed Quantile Regression Forest (QRF) model, having the advantage of not assuming any specific distribution of cycle life, is introduced to make cycle life range prediction with uncertainty quantified as the width of the prediction interval, in addition to point predictions with high accuracy. The hyperparameters of the QRF model are optimized with a proposed alpha-logistic-weighted criterion so that the coverage probabilities associated with the prediction intervals are calibrated. The interpretability of the final QRF model is explored with two global model-agnostic methods, namely permutation importance and partial dependence plot.

Comparative Analysis of Battery Cycle Life Early Prediction Using Machine Learning Pipeline

Lithium-Ion battery system is one of the most critical but expensive components for both electric vehicles and stationary energy storage applications. In this regard, accurate and reliable early prediction of battery lifetime is important for optimizing life cycle management of batteries from cradle to grave. In particular, accurate aging diagnostics and prognostics is crucial for ensuring longevity, performance, safety, uptime, productivity, and profitability over a battery's lifetime. However, current state-of-art methods do not provide satisfactory prediction performance (lack of uncertainty quantification) using early degradation data. In the present work, to produce the best model for both battery cycle life point prediction and range prediction (i.e., confidence intervals or prediction intervals), a pipeline-based approach is proposed, in which a full 33-feature set is generated manually based on battery degradation knowledge, and then used to learn the best model among five machine learning (ML) models that have been reported in the battery lifetime prediction literature, and two quantile regression models for battery cycle life prediction. The calibration and sharpness property of battery cycle life range prediction is properly evaluated by their coverage probability and width respectively. The experimental results show that the gradient boosting regression tree model provides the best point prediction performance, while the quantile regression forest model provides the best range prediction performance with both full 33-feature set and the MIT 6-feature set.

Spatial prediction of soil depth using environmental covariates by quantile regression forest model.

Prediction of soil depth for larger areas provides primary information on soil depth and its spatial distribution that becomes vital for land resource management, crop, nutrient, and ecosystem modeling. The present study assessed the spatial distribution of soil depth over 160,205 km2 of Andhra Pradesh, India, using 20 covariables by quantile regression forest (QRF). An aggregate of 2854 soil datasets compiled from various physiographic units were randomly partitioned into 80:20 ratio for calibration (2283 samples) and validation (571 samples). Landsat imagery, terrain datasets (8), and bioclimatic factors (11) were utilized as covariates. The QRF model outputs signified that precipitation, multi-resolution index of valley bottom flatness (MrVBF), mean diurnal range, isothermality, and elevation were the most important variables influencing soil depth variability across the landscape. Spatial prediction of soil depth by QRF model yielded a ME of - 1.81cm, RMSE of 34cm, PICP of 90.2, and a R2 value of 42% as compared to ordinary kriging which results in a ME of - 0.14cm, a RMSE of 37cm, and a R2 value of 32%. As soil depth is spatially dynamic and has significant correlation with terrain and environmental covariates, better prediction was possible by the QRF model. However, high-density bioclimatic variables could be utilized along with high-resolution terrain variables to improve the predictive accuracy.

Spatial biases of information influence global estimates of soil respiration: How can we improve global predictions?

Soil respiration (Rs), the efflux of CO2 from soils to the atmosphere, is a major component of the terrestrial carbon cycle, but is poorly constrained from regional to global scales. The global soil respiration database (SRDB) is a compilation of in situ Rs observations from around the globe that has been consistently updated with new measurements over the past decade. It is unclear whether the addition of data to new versions has produced better-constrained global Rs estimates. We compared two versions of the SRDB (v3.0 n=5173 and v5.0 n=10,366) to determine how additional data influenced global Rs annual sum, spatial patterns and associated uncertainty (1km spatial resolution) using a machine learning approach. A quantile regression forest model parameterized using SRDBv3 yielded a global Rs sum of 88.6PgCyear-1 , and associated uncertainty of 29.9 (mean absolute error) and 57.9 (standard deviation)PgCyear-1 , whereas parameterization using SRDBv5 yielded 96.5PgCyear-1 and associated uncertainty of 30.2 (mean average error) and 73.4 (standard deviation)PgCyear-1 . Empirically estimated global heterotrophic respiration (Rh) from v3 and v5 were 49.9-50.2 (mean 50.1) and 53.3-53.5 (mean 53.4)PgCyear-1 , respectively. SRDBv5's inclusion of new data from underrepresented regions (e.g., Asia, Africa, South America) resulted in overall higher model uncertainty. The largest differences between models parameterized with different SRDVB versions were in arid/semi-arid regions. The SRDBv5 is still biased toward northern latitudes and temperate zones, so we tested an optimized global distribution of Rs measurements, which resulted in a global sum of 96.4±21.4PgCyear-1 with an overall lower model uncertainty. These results support current global estimates of Rs but highlight spatial biases that influence model parameterization and interpretation and provide insights for design of environmental networks to improve global-scale Rs estimates.

Sacral acceleration can predict whole-body kinetics and stride kinematics across running speeds.

BackgroundStress fractures are injuries caused by repetitive loading during activities such as running. The application of advanced analytical methods such as machine learning to data from multiple wearable sensors has allowed for predictions of biomechanical variables associated with running-related injuries like stress fractures. However, it is unclear if data from a single wearable sensor can accurately estimate variables that characterize external loading during running such as peak vertical ground reaction force (vGRF), vertical impulse, and ground contact time. Predicting these biomechanical variables with a single wearable sensor could allow researchers, clinicians, and coaches to longitudinally monitor biomechanical running-related injury risk factors without expensive force-measuring equipment.PurposeWe quantified the accuracy of applying quantile regression forest (QRF) and linear regression (LR) models to sacral-mounted accelerometer data to predict peak vGRF, vertical impulse, and ground contact time across a range of running speeds.MethodsThirty-seven collegiate cross country runners (24 females, 13 males) ran on a force-measuring treadmill at 3.8–5.4 m/s while wearing an accelerometer clipped posteriorly to the waistband of their running shorts. We cross-validated QRF and LR models by training them on acceleration data, running speed, step frequency, and body mass as predictor variables. Trained models were then used to predict peak vGRF, vertical impulse, and contact time. We compared predicted values to those calculated from a force-measuring treadmill on a subset of data (n = 9) withheld during model training. We quantified prediction accuracy by calculating the root mean square error (RMSE) and mean absolute percentage error (MAPE).ResultsThe QRF model predicted peak vGRF with a RMSE of 0.150 body weights (BW) and MAPE of 4.27 ± 2.85%, predicted vertical impulse with a RMSE of 0.004 BW*s and MAPE of 0.80 ± 0.91%, and predicted contact time with a RMSE of 0.011 s and MAPE of 4.68 ± 3.00%. The LR model predicted peak vGRF with a RMSE of 0.139 BW and MAPE of 4.04 ± 2.57%, predicted vertical impulse with a RMSE of 0.002 BW*s and MAPE of 0.50 ± 0.42%, and predicted contact time with a RMSE of 0.008 s and MAPE of 3.50 ± 2.27%. There were no statistically significant differences between QRF and LR model prediction MAPE for peak vGRF (p = 0.549) or vertical impulse (p = 0.073), but the LR model’s MAPE for contact time was significantly lower than the QRF model’s MAPE (p = 0.0497).ConclusionsOur findings indicate that the QRF and LR models can accurately predict peak vGRF, vertical impulse, and contact time (MAPE < 5%) from a single sacral-mounted accelerometer across a range of running speeds. These findings may be beneficial for researchers, clinicians, or coaches seeking to monitor running-related injury risk factors without force-measuring equipment.

A spatially based quantile regression forest model for mapping rural land values

Rural land valuation plays an important role in the development of land use policies for agricultural purposes. The advance of computational software and machine learning methods has enhanced mass appraisal methodologies for modeling and predicting economic values. New machine learning methods, like tree-based regression models, have been proposed as an alternative to linear regression to predict economic values from ancillary variables, since these algorithms are able to handle non-normality and non-linearity in the data. However, regression trees are commonly estimated assuming independent rather than spatially correlated data. This study aims to build a tree-based regression model that will help to tackle methodological problems related to the determination of prices of rural lands. The Quantile Regression Forest (QRF) algorithm was used to provide a regression model to predict and assess the uncertainty associated with model-derived predictions. However, the classical QRF ignores the autocorrelation underlying spatialized land values. The objective of this work was to develop, implement, and evaluate a spatial version of QRF, named sQRF, for computer-assisted mass appraisal of rural land values accounting for information from neighboring sites. We compared predictions of land values from sQRF with those obtained from spatial random forest, kriging regression, and linear regression models. sQRF performed well in predicting rural land values; indeed, it performed better than multiple linear regression. An important feature of sQRF is its ability to produce a direct uncertainty measure to assess the goodness of the predictions. Land values reflect a complex mix of agricultural returns, localization, and access to markets, which can be predicted from ancillary environmental variables. Good predictive models are essential to determine land values for multiple purposes including territorial taxation.

Modeling the monthly pan evaporation rates using artificial intelligence methods: a case study in Iraq

In arid areas, the estimation of evaporation rates plays a considerable role on both water resources management and agricultural activities. Hence, it is of utmost importance to determine the best model to predict these rates. This study investigates the applicability of using quantile regression forest in predicting the pan evaporation. The model was configured using data from three different meteorological stations located in arid to semi-arid climates in Iraq. These stations were in the cities of Baghdad, Basrah, and Mosul, which are located in the middle, south, and north of the country, respectively. The performance of quantile regression forests was compared with three kinds of artificial intelligence methods i.e. random forests, support vector machine, and artificial neural network in addition to the conventional multiple linear regression models. The maximum temperature (°C), minimum temperature (°C), relative humidity (%), and wind speed (m/sec) were used as input parameters to the predictive models. The collected data (from 1990 to 2013) was randomly partitioned into two periods; 75% for calibration and 25% for validation. The fivefold cross validation was used during the calibration stage for better model predictability. The results were evaluated using three performance criteria: determination coefficient (R2), root mean square error (RMSE), and Nash and Sutcliff coefficient efficiency (NSE). Results showed that the quantile regression forests model attained the optimum performance among the evaluated methods. The value of R2, RMSE, and NSE during validation was 0.99, 17.96 mm, and 0.99 at Baghdad; 0.98, 23.36 mm, and 0.98 at Basrah; and 0.99, 14.44 mm, and 0.99 at Mosul, respectively. Therefore, this method is the most appropriate one to use for predicting evaporation rates in arid to semi-arid climates.

Proposition of New Ensemble Data-Intelligence Models for Surface Water Quality Prediction

An accurate prediction of water quality (WQ) related parameters is considered as pivotal decisive tool in sustainable water resources management. In this study, five different ensemble machine learning (ML) models including Quantile regression forest (QRF), Random Forest (RF), radial support vector machine (SVM), Stochastic Gradient Boosting (GBM) and Gradient Boosting Machines (GBM_H2O) were developed to predict the monthly biochemical oxygen demand (BOD) values of the Euphrates River, Iraq. For this aim, monthly average data of water temperature (T), Turbidity, pH, Electrical Conductivity (EC), Alkalinity (Alk), Calcium (Ca), chemical oxygen demand (COD), Sulfate (SO <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sub> ), total dissolved solids (TDS), total suspended solids (TSS), and BOD measured for ten years period were used in this study. The performances of these standalone models were compared with integrative models developed by coupling the applied ML models with two different feature extraction algorithms i.e., Genetic Algorithm (GA) and Principal Components Analysis (PCA). The reliability of the applied models was evaluated based on the statistical performance criteria of determination coefficient (R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> ), root mean square error (RMSE), mean absolute error (MAE), Nash-Sutcliffe model efficiency coefficient (NSE), Willmott index (d), and percent bias (PBIAS). Results showed that among the developed models, QRF model attained the superior performance. The performance of the evaluated models presented in this study proved that the developed integrative PCA-QRF model presented much better performance compared with the standalone ones and with those integrated with GA. The statistical criteria of R <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> , RMSE, MAE, NSE, d, and PBIAS of PCA-QRF were 0.94, 0.12, 0.05, 0.93, 0.98, and 0.3, respectively.