Irradiance Forecasting Research Articles

Solar irradiance forecasting using a novel hybrid deep ensemble reinforcement learning algorithm

Solar irradiance forecasting is a major priority for the power transmission systems in order to generate and incorporate the performance of massive photovoltaic plants efficiently. As such, prior forecasting techniques that use classical modelling and single deep learning models that undertake feature extraction procedures manually were unable to meet the output demands in specific situations with dynamic variability. Therefore, in this study, we propose an efficient novel hybrid solar irradiance forecasting model based on three steps. In the first step, we employ a powerful variable input selection strategy named as partial mutual information (PMI) to calculate the linear and non-linear correlations of the original solar irradiance data. In the second step, unlike the traditional deep learning models designing their architectures manually, we utilize several deep long short term memory-convolutional neural network (LSTM-CNN) models optimized by a novel modified whale optimization algorithm in order to compute the forecasting results of the solar irradiance datasets. Finally, in the third step, we deploy a deep reinforcement learning strategy for selecting the best subset of the combined deep optimized LSTM-CNN models. Through analysing the forecasting results over two real-world datasets gathered from the USA solar irradiance stations, it can be inferred that our proposed algorithm outperforms other powerful benchmarked algorithms in 1-step, 2-step, 12-step, and 24-step ahead forecasting.

Short Term Solar Irradiation Forecasting using CEEMDAN Decomposition Based BiLSTM Model Optimized by Genetic Algorithm Approach

An accurate short-term solar irradiation forecasting is requiredregarding smart grid stability and to conduct bilateral contract negotiations between suppliers and customers. Traditional machine learning models are unable to acquire and to rectify nonlinear properties from solar datasets, which not only complicate model formation but also lower prediction accuracy. The present research paper develops a deep learningbased architecture with a predictive analytic technique to address these difficulties. Using a sophisticated signal decomposition technique, the original solar irradiation sequences are decomposed into multiple intrinsic mode functions to build a prospective feature set. Then, using an iteration strategy, a potential range of frequency associated to the deep learning model is generated. This method is developed utilizing a linked algorithm and a deep learning network. In comparison with conventional models, the suggested model utilizes sequences generated through preprocessing methods, significantly improving prediction accuracywhen confronted with a high resolution dataset created from a big dataset.On the other hand, the chosen dataset not only performs a massive data reduction, but also improves forecasting accuracy by up to 20.74 percent across a range of evaluation measures. The proposed model achieves lowest annual average RMSE (1.45W/m2), MAPE (2.23%) and MAE (1.34W/m2) among the other developed models for 1-hr ahead solar GHI, respectively, whereas forecast-skill obtained by the proposed model is 59% with respect to benchmark model. As a result, the proposed method might be used to predict short-term solar irradiation with greater accuracy using a solar dataset

Daily Solar Radiation Forecasting based on a Hybrid NARX-GRU Network in Dumaguete, Philippines

In recent years, solar radiation forecasting has become highly important worldwide as solar energy increases its contribution to electricity grids. However, due to the intermittent nature of solar radiation caused by meteorological parameters, forecasting errors arise, and fluctuations in the power output of photovoltaic (PV) systems become a severe issue. This paper aims to introduce a forecasting hybrid model of daily global solar radiation time series. Meteorological data and solar radiation samples from Dumaguete, Philippines, are used to assess the forecasting accuracy of the proposed nonlinear autoregressive network with exogenous inputs (NARX) – gated recurrent unit (GRU) hybrid model. Four different models were trained using the meteorological and solar radiation data, which are the Optimizable Gaussian Process Regression (GPR), Nonlinear Autoregressive Network (NAR), NARX, and the proposed Hybrid NARX-GRU Network. Results show that the hybrid NARX-GRU model has a root mean square error (RMSE) of ~0.05 and a training time of 33 seconds. The proposed hybrid model has better forecasting performance compared to the three models which obtained RMSE values of 27.741, 39.82, and 28.92, for the GPR, NAR, and NARX, respectively. The simulation results demonstrate that the NARX-GRU model significantly outperforms the regression and single models in terms of statistical metrics and training efficiency. Furthermore, this study shows that the hybridized NARX-GRU model is able to provide an effective estimation for daily global solar radiation, which is important in the operation of PV plants in the country, specifically for unit commitment purposes

A simplified seasonal forecasting strategy, applied to wind and solar power in Europe

We demonstrate levels of skill for forecasts of seasonal-mean wind speed and solar irradiance in Europe, using seasonal forecast systems available from the Copernicus Climate Change Service (C3S). While skill is patchy, there is potential for the development of climate services for the energy sector. Following previous studies, we show that, where there is skill, a simple linear regression-based method using the hindcast and forecast ensemble means provides a straightforward approach for producing calibrated probabilistic seasonal forecasts. This method extends naturally to using a larger-scale feature of the climate, such as the North Atlantic Oscillation, as the climate model predictor, and we show that this provides opportunities to improve the skill in some cases.We further demonstrate that, on seasonal-average and regional (e.g. national) average scales, wind and solar power generation are highly correlated with single climate variables (wind speed and irradiance). The detailed non-linear transformations from meteorological quantities to energy quantities, which are essential for detailed simulation of power system operations, are usually not necessary when forecasting gross wind or solar generation potential at seasonal-mean regional-mean scales.Together, our results demonstrate that where there is skill in seasonal forecasts of wind speed and irradiance, or a correlated larger-scale climate predictor, skilful forecasts of seasonal mean wind and solar power generation can be made based on the climate variable alone, without requiring complex transformations. This greatly simplifies the process of developing a useful seasonal climate service.

Hyper‐parametric improved machine learning models for solar radiation forecasting

SummarySpatiotemporal solar radiation forecasting is extremely challenging due to its dependence on metrological and environmental factors. Chaotic time‐varying and non‐linearity make the forecasting model more complex. To cater this crucial issue, the paper provides a comprehensive investigation of the deep learning framework for the prediction of the two components of solar irradiation, that is, Diffuse Horizontal Irradiance (DHI) and Direct Normal Irradiance (DNI). Through exploratory data analysis the three recent most prominent deep learning (DL) architecture have been developed and compared with the other classical machine learning (ML) models in terms of the statistical performance accuracy. In our study, DL architecture includes convolutional neural network (CNN) and recurrent neural network (RNN) whereas classical ML models include Random Forest (RF), Support Vector Regression (SVR), Multilayer Perceptron (MLP), Extreme Gradient Boosting (XGB), and K‐Nearest Neighbor (KNN). Additionally, three optimization techniques Grid Search (GS), Random Search (RS), and Bayesian Optimization (BO) have been incorporated for tuning the hyper parameters of the classical ML models to obtain the best results. Based on the rigorous comparative analysis it was found that the CNN model has outperformed all classical machine learning and DL models having lowest mean squared error and highest R‐Squared value with least computational time.

Best Combinations of Inputs for ANN-Based Solar Radiation Forecasting in Morocco

In this paper, for forecasting, with the high possible accuracy, the solar radiation intensity, an approach for identifying the optimum set of input data from large sets of input parameters is elaborated, assessed, and proposed. This approach belongs to techniques of Input Variable Selection (IVS) and was established using artificial neural networks (ANNs) as an effective means for numerically approximating the computed objective function: Monthly Average Global Solar Radiation (MAGSR). Based on the approach suggested, we could determine the best combinations of inputs that can reveal great possible correlation and approximation with the output considered parameter. Recorded data from 35 stations of different climatic zones were used for both training and testing purposes. Several new linear formulas between the MAGSR and other climatological and meteorological parameters were developed and evaluated. Based on these relationships, we can forecast other climatological and meteorological parameters like temperature, wind speed, and humidity. The statistical analysis was done, and the best performance of the proposed approach has been well checked and duly validated.

Benefits of physical and machine learning hybridization for photovoltaic power forecasting

Irradiance-to-power conversion is an essential step of state-of-the-art photovoltaic (PV) power forecasting, regardless of the source and post-processing of irradiance forecasts. The two distinct approaches for mapping the irradiance forecasts to PV power are physical and data-driven, which can also be hybridized. The contribution of this paper is twofold; first, it proposes a concept and identifies the best implementation of a hybrid physical and machine learning irradiance-to-power conversion method. Second, a head-to-head comparison of the physical, data-driven, and hybrid methods is performed for the operational day-ahead power forecasting of 14 PV plants in Hungary based on numerical weather prediction (NWP). To respect the rule of consistency but still obtain as complete picture as possible, two directives are set, namely minimizing the mean absolute error (MAE) and minimizing the root mean square error (RMSE), and separate sets of forecasts are optimized for both directives. The results reveal that for two years of training data, the hybrid method that involves the most physically-calculated predictors can reduce the MAE by 5.2% and 10.4% compared, respectively, to the optimized physical model chains and the machine learning without any physical considerations. The two most important physical modeling steps are separation and transposition modeling, and the rest of the physical PV simulation can be left to machine learning in hybrid models without a significant increase in the errors. The optimization of the physical model chains is found to be important even in the case of hybrid modeling; therefore, it should become a standard procedure in practical applications. Finally, the hybrid method is only beneficial for at least one year of training data, while in the initial period of the operation of a PV plant, it is advised to stay with optimized physical modeling. The guidelines and recommendations of this paper can help both researchers and practitioners design and optimize their power conversion model to increase the accuracy of the PV power forecasts.

Impact of the tilt angle, inverter sizing factor and row spacing on the photovoltaic power forecast accuracy

The growth of the installed photovoltaic (PV) capacity calls for accurate power forecasts, which are commonly calculated from irradiance forecasts using physical model chains. This study analyses the impact of the PV plant design parameters on the additional error of the irradiance-to-power conversion using three approaches. First, PV power curves are plotted for different design parameters to illustrate the amplification of errors and to enhance the understanding of the presented phenomena. Second, six forecast accuracy metrics are calculated as a function of the design parameters for the irradiance observation and forecast data of ten stations from five climate zones and two forecast providers. Third, the Pareto-optimal tradeoff between the annual energy production and the absolute forecast errors are obtained by the NSGA-II multi-objective optimization algorithm. The results reveal that the design parameters highly influence the PV power forecast errors, which is important to consider in all studies presenting PV power forecast verification. A tilt angle of 45° increases the error metrics up to 49% compared to a horizontal plane, and undersizing the inverters by a 1.5 sizing factor lead to an average error decrease up to 25%. Including the expected forecast errors as an objective during their design optimization process is important to maximize the net revenues of PV plants, especially if the unit imbalance costs are more than 50% of the electricity prices.

EVB-Supportive Energy Management for Residential Systems with Renewable Energy Supply

This study examines the potential role that an Electric Vehicle Battery (EVB) can play in Home Energy Management System (HEMS) based on a future development on the performance and costs of batteries. The value of EVB in an HEMS with different home connection settings and energy consumption/storage/generation capacities are investigated to advise the optimal future HEMS setups. Solar PV are considered as the residential renewal energy supply, which is the main resource of uncertainty of the system. A novel forecasting model is deployed which incorporates geographical information, solar radiation forecast and weather-related conditions into an exponential-based method to simulate day-ahead solar PV output. Optimal flows of energy and usage of storage (batteries) are then captured by a Stochastic Programming (SP) model and solved by CPLEX. Managerial insights and optimal designs of the HEMS are drawn based on the results obtained.

Correlogram, predictability error growth, and bounds of mean square error of solar irradiance forecasts

Solar forecast verification must incorporate a notion of “relativity.” Particularly for deterministic forecasts, one wishes to know the upper and lower bounds of the mean square error (MSE) for the forecasting situation of concern, such that the performance of some forecasts of interest can be quantified relative to these bounds. This work proposes a method for estimating these bounds. For the upper bound of MSE, the theory builds upon the premise that no forecast worse than that provided by the standard of reference should be used. Under some mild assumptions, the MSE of the standard of reference, which is herein defined to be the optimal convex combination of climatology and persistence, varies solely with the lag-h autocorrelation of the clear-sky index. Then, by fitting a theoretical isotropic correlogram with a nugget effect to the empirical autocorrelations, the upper bound of MSE, as a function of forecast horizon, can be derived. For the lower bound of MSE, it can be approximated by the predictability error growth, which is the difference between the controlled and perturbed forecasts from a perfect dynamical weather model. The empirical part of this work considers the irradiance forecasts from the European Centre for Medium-Range Weather Forecasts, at seven locations in United States, over a period of two years (2019–2020). Various MSEs reported in the literature are put in perspective of the estimated bounds of MSE. The proposed bounds have a profound impact on predictability quantification and skill score computation, which are essential for comparative forecast verification.

Güneş Işınım Tahmini için Farklı Güneşlenme Durumlarından Faydalanan Hibrit Bir Yöntem Tasarımı

The constant expansion of solar energy has made the accurate forecasting of radiation an important issue. An accurate prediction of solar energy production is crucial for the effective integration of photovoltaic (PV) and wind generators in smart grids. The intermittent nature of solar energy poses many challenges to renewable energy system operators in terms of operational planning and scheduling. For this reason, forecasting solar radiation by means of the hybrid methods is becoming widespread. In this paper, a hybrid method for predicting solar radiation is proposed, wherein the prediction model is determined based on the clearness index. The study used two-year solar radiation data of the province of Mardin obtained from the Turkish State Meteorological Service (TSMS). As predictors, ANN, NARX networks, and Ridge regression methods were used, and the training data were modeled with all three approaches in the first stage of the study. The clearness index was determined into three ranges; slightly cloudy, cloudy, and mostly cloudy. The training data were modeled with three methods used as estimators, and the success of each method was examined in each defined clearness index range. As a result, in the hybrid prediction algorithm, the clearness index is first estimated using artificial neural networks, and then the future solar radiation value is predicted by using the most successful model within the predicted clearness index range. Experimental results show that more successful predictions are made with the proposed hybrid method than when models are used individually.

Optimal generation scheduling and operating reserve management for PV generation using RNN-based forecasting models for stand-alone microgrids

Photovoltaic (PV) generation can drop sharply under reductions in solar irradiance due to cloud cover, resulting in adverse impacts on the performance of stand-alone microgrids. In addition, due to the stochastic nature of solar irradiance, it has remained challenging to forecast PV generation accurately. Therefore, a sufficient amount of operating reserve must be allocated for the variability and uncertainty of PV generation. However, excess operating reserve can decrease the economic efficiency of microgrids. This paper proposes an optimal generation scheduling and operating reserve management scheme for stand-alone PV-integrated microgrids, which comprises three core models. First, a two-stage recurrent neural network-based model is proposed for solar irradiance and cloud cover forecasting. Second, the operating reserve required for PV is managed more effectively based on weather conditions. Finally, an optimal generation scheduling model is applied based on the forecasting and operating reserve management models. The proposed scheme is applied to representative case studies to validate its advantages. The forecasting accuracy of the proposed model outperforms a conventional model. Under clear-sky conditions, the operating reserve for PV can be reduced down to 30% of PV output. Subsequently, the optimal operation scheduled by the proposed scheme can produce substantial savings of more than 5.5%.

One-Day-Ahead Solar Irradiation and Windspeed Forecasting with Advanced Deep Learning Techniques

In recent years, demand for electric energy has steadily increased; therefore, the integration of renewable energy sources (RES) at a large scale into power systems is a major concern. Wind and solar energy are among the most widely used alternative sources of energy. However, there is intense variability both in solar irradiation and even more in windspeed, which causes solar and wind power generation to fluctuate highly. As a result, the penetration of RES technologies into electricity networks is a difficult task. Therefore, more accurate solar irradiation and windspeed one-day-ahead forecasting is crucial for safe and reliable operation of electrical systems, the management of RES power plants, and the supply of high-quality electric power at the lowest possible cost. Clouds’ influence on solar irradiation forecasting, data categorization per month for successive years due to the similarity of patterns of solar irradiation per month during the year, and relative seasonal similarity of windspeed patterns have not been taken into consideration in previous work. In this study, three deep learning techniques, i.e., multi-head CNN, multi-channel CNN, and encoder–decoder LSTM, were adopted for medium-term windspeed and solar irradiance forecasting based on a real-time measurement dataset and were compared with two well-known conventional methods, i.e., RegARMA and NARX. Utilization of a walk-forward validation forecast strategy was combined, firstly with a recursive multistep forecast strategy and secondly with a multiple-output forecast strategy, using a specific cloud index introduced for the first time. Moreover, the similarity of patterns of solar irradiation per month during the year and the relative seasonal similarity of windspeed patterns in a timeseries measurements dataset for several successive years demonstrates that they contribute to very high one-day-ahead windspeed and solar irradiation forecasting performance.

Improvement in Solar-Radiation Forecasting Based on Evolutionary KNEA Method and Numerical Weather Prediction

Accurate forecasting of solar radiation (Rs) is significant to photovoltaic power generation and agricultural management. The National Centers for Environmental Prediction (NECP) has released its latest Global Ensemble Forecast System version 12 (GEFSv12) prediction product; however, the capability of this numerical weather product for Rs forecasting has not been evaluated. This study intends to establish a coupling algorithm based on a bat algorithm (BA) and Kernel-based nonlinear extension of Arps decline (KNEA) for post-processing 1–3 d ahead Rs forecasting based on the GEFSv12 in Xinjiang of China. The new model also compares two empirical statistical methods, which were quantile mapping (QM) and Equiratio cumulative distribution function matching (EDCDFm), and compares six machine-learning methods, e.g., long-short term memory (LSTM), support vector machine (SVM), XGBoost, KNEA, BA-SVM, BA-XGBoost. The results show that the accuracy of forecasting Rs from all of the models decreases with the extension of the forecast period. Compared with the GEFS raw Rs data over the four stations, the RMSE and MAE of QM and EDCDFm models decreased by 20% and 15%, respectively. In addition, the BA-KNEA model was superior to the GEFSv12 raw Rs data and other post-processing methods, with R2 = 0.782–0.829, RMSE = 3.240–3.685 MJ m−2 d−1, MAE = 2.465–2.799 MJ m−2 d−1, and NRMSE = 0.152–0.173.

Revealing Bias of Cloud Radiative Effect in WRF Simulation: Bias Quantification and Source Attribution

AbstractAccurate prediction of cloud radiative effect (CRE) is important to weather forecast and climate projection, and solar energy production—a major renewable energy source toward decarbonization. Here, we evaluate the capability of the Weather Research and Forecast (WRF) model to simulate solar irradiance on a short‐term timescale (days) against observations in a remote region in north China. Results illustrate that our WRF simulation systematically underestimates the CRE and three error sources are identified: (a) incorrectly predicted cloud occurrence (i.e., missed clouds and false clouds), (b) underestimated cloud condensate mass, and (c) simplified parameterization of solar irradiance extinction. The incorrect cloud occurrence is the leading bias source, because it occurred most frequently and results in a substantial magnitude of errors. The cloud occurrence bias is subject to simulations of large‐scale air ascends and planetary boundary layer turbulence. Even when cloud occurrence is correctly simulated, our WRF simulation still underestimates CRE. This is because (a) the shallow convection scheme and cloud microphysics scheme underestimate cloud condensate mass and (b) cloud water path that feeds in the radiation scheme neglects precipitating cloud condensates (i.e., raindrops and graupels). Furthermore, an evaluation of cases with small bias in cloud condensate mass and effective radius demonstrates the parameterization of solar irradiance extinction for clouds induces a mean root mean square deviation of 110 W/m2. A possible reason is the simplified calculation of cloud extinction efficiency by applying Monte Carlo integration. The gained knowledge is important for understanding CRE simulation and solar irradiance forecast.

Adaptive Neuro-Fuzzy Approach for Solar Radiation Forecasting in Cyclone Ravaged Indian Cities: A Review

The measurement of solar radiation and its forecasting at any particular location is a difficult task as it depends on various input parameters. So, intelligent modeling approaches with advanced techniques are always necessary for this challenging activity. Adaptive neuro-fuzzy inference system (ANFIS) based on modeling plays a vital role in the selection of relevant input parameters for undertaking precise solar radiation prediction. Numerous literature works focusing on ANFIS-based techniques have been reviewed during the estimation of solar energy incidents in the eastern part of India. During solar forecasting, the input parameters considered for this model are the duration of the sunshine, temperature, and humidity whereas the clearness index value has been considered as an output parameter for calculation. For designing the model, practical data sets have been prepared for some specified locations. Finally, the outcome is compared with several other techniques. During this course of analysis, several studies have been reviewed for a comprehensive literature survey work.

Multi-time-step ahead daily global solar radiation forecasting: performance evaluation of wavelet-based artificial neural network model

Multi-time-step ahead daily global solar radiation forecasting: performance evaluation of wavelet-based artificial neural network model

Hourly solar irradiation forecast using hybrid local gravitational clustering and group method of data handling methods.

The foundation for many solar energy uses as well as economic and environmental concerns is global solar irradiation information. However, due to solar irradiation and measurement variations, reliable worldwide statistics on solar irradiation are frequently impossible or challenging to acquire. In addition, more precise forecasts of solar irradiation play an increasingly important role in electric energy planning and management due to integrating photovoltaic solar systems into power networks. Hence, this paper proposes a new hybrid model for 1-h ahead solar irradiation forecasting called LGC-GMDH (local gravitational clustering-group method of data handling). The novel LGC-GMDH model is based on local clustering that adequately captures the underlying features of the solar irradiation time series. Each cluster is then forecasted using the GMDH method, which is a self-organized system capable of handling very complicated nonlinear problems. Finally, these local forecasts are reconstructed in order to obtain the global forecast. Comparative study between the proposed model and the traditional individual models such as backpropagation neural network (BP), supporting vector machines (SVM), long short-term memory (LTSM), and hybrid models such as BP-MLP, RNN-MLP, LSTM-MLP hybrid wavelet packet decomposition (WPD), convolutional neural network (CNN) with LSTM-MLP, and ANFIS clustering shows that the proposed model overcomes conventional model deficiencies and achieves more precise predicting outcome.

Prediction of daily global solar radiation and air temperature using six machine learning algorithms; a case of 27 European countries

The prediction of global solar radiation in a region is of great importance as it provides investors and politicians with more detailed knowledge about the solar resource of that region, which can be very beneficial for large-scale solar energy development. In this sense, the main objective of this study is to predict the daily global solar radiation data of 27 cities (Brussels, Paris, Lisbon, Madrid…), located in 27 countries, which have mostly different solar radiation distributions in Europe. In this research, six different machine-learning algorithms (Linear model (LM), Decision Tree (DT), Support Vector Machine (SVM), Deep Learning (DL), Random Forest (RF) and Gradient Boosted Trees (GBT)) are used. In the training of these algorithms, daily air temperature(Ta), wind speed(Va), relative humidity(RH) and solar radiation of these cities are used. The data is supplied from the Meteonorm tool and cover the last years grouped in two periods (1960–1990; 2000–2019). To decide on the success of these algorithms, four different statistical metrics (Average Relative Error (ARE), Average absolute Error (AAE), Root Mean Squared Error (RMSE), and R2 (R-Squared)) are discussed in the study. In addition, the forecasting of air temperature and global solar radiation of these cities in 2050 and 2100 were made using three of the most recent Intergovernmental Panel on Climate Change (IPCC) scenarios (RCP2.6; RCP 4.5, and RCP 8.5). The results show that ARE, R,2 and RMSE values of all algorithms are ranging from 0.114 to 6.321, from 0.382 to 0.985, from 0.145 to 2.126 MJ/m2, respectively. By analysing all the algorithms, it is noticed that the Decision tree exhibited the worst result in terms of R,2 and RMSE metrics. Among the six prediction algorithms, the DL was recognized as the only algorithm that exceeded the t-critical value (The t-critical value is the cutoff between retaining or rejecting the null hypothesis). Globally, all the six machine learning algorithms used in this research can be applied to predict the daily global solar radiation data with good accuracy. Despite this, the SVM model is the best model among all the six models used. It is followed by the DL, LM, GB, RF and DT, respectively.

Quantile mapping correction of analog ensemble forecast for solar irradiance

Probabilistic forecasts of solar irradiance are a key technology for integrating solar power into power grids. However, ensemble forecasts, the conventional probabilistic forecasting method suffers from bias inherent in numerical weather prediction. The recently proposed Analog Ensemble (AnEn) method is expected to have less bias. We therefore construct an experimental AnEn system for day-ahead solar irradiance forecasts and investigate its performance. The AnEn method finds analogs by a nearest-neighbor search, so its members can be ranked by the order found in the search. We find that the probability distribution function (PDF) for predicted irradiance deduced from members with large orders are heavily deformed from the desired PDF, namely, that of the observed solar irradiance. This induces bias in AnEn forecasts limiting their performance. The bias can be ascribed to the limited size of data available in the AnEn forecast system. In many practical cases, this limitation is unavoidable. We propose a correction scheme based on quantile mapping to deal with this situation. By enhancing forecast reliability, this scheme provides better continuous ranked probability scores compared with the basic AnEn method. However, PDF estimation in the quantile mapping process can be unstable. We therefore propose another scheme that introduces constraints to mitigate this uncertainty thereby achieving further performance gains.