Prediction Interval Coverage Probability Research Articles

Wind power interval and point prediction model using neural network based multi-objective optimization

Wind power point and interval prediction plays an important role in dispatching. However, for obtaining both point estimations and prediction intervals (PIs), the existing models like constructing the probability density function are too complicated. This paper proposes a novel multi-objective upper and lower bound and point estimation (MOULPE) model. It constructs a neural network (NN) with double outputs to directly estimate the prediction intervals (PIs) and the median of PIs is calculated as point estimation. Considering wide decision-making space, the problem formulation of MOULPE is defined as three objectives which covers both evaluation indices of PIs and point prediction. Furthermore, based on elite opposition-based learning (EOBL), this paper improves non-dominated fast sort genetic algorithm-III (INSGA-III) to search the optimal front. Two criteria called prediction interval nominal confidence (PINC) and point prediction nominal error (PPNE) are adopted to pick out the best solution. According to the general requirements in literature, four examples of real wind power data are conducted. Compared with some state-of-the-art methods, the coverage probability of PIs constructed by the proposed model not only reaches the preset PINC, but the average width is also the lowest. Similarly, the point estimation error of the proposed method is less than PPNE.

Predicting uncertainty of a chiller plant power consumption using quantile random forest: A commercial building case study

Selecting an appropriate confidence level for chillers models could lead to better prediction of the peak electricity load, to more efficiently participate in demand response programs, and to manage the operation and performance of chiller plants. Therefore, this study aims to predict the power consumption of a chiller plant in a high-rise commercial building based on Quantile Random Forest (QRF). This study proposed a simplified data-driven approach to compute the lower and upper bounds of the prediction intervals (PIs) of power consumption for a chiller plant, consisting of four chillers. An evaluation of the proposed data-driven approach using measured datasets and computed PIs metrics demonstrates that the PI coverage probability for the samples in test datasets for all chiller models with the confidence level of 80% and 90%, are above 80% and 90%, respectively. Also, the results show that by increasing the confidence level from 80% to 90%, the upper and lower bounds of the demand charge differ from the actual value by a factor of 3.3 and 1.7 times greater, respectively. This approach has implications for developing sequences of operations for chiller plants in building automation systems for evaluating past performance and for achieving future optimization of these plants.

A multi-variable hybrid system for port container throughput deterministic and uncertain forecasting

Container transport is the most environmentally friendly and sustainable way to transport bulk cargo currently. The accurate prediction of container throughput is of great significance to the operation of the port. It is directly related to the healthy development of the entire logistics system, and also serves as a reference for decision makers in the construction of port infrastructure. However, the container throughput sequence contains the influence and restriction of a variety of superimposed factors, and has the characteristics of nonlinear and non-stationary. Traditional technology cannot effectively capture the changes of external related factors. To make up for the deficiencies, a multi-variable hybrid deterministic and uncertain forecasting framework based on improved preprocessing technique and swarm intelligence optimizer is constructed. It not only considers the impact of port hinterland economic indicators, port transport system and transport capacity factors, but also calculates the upper and lower limits of container throughput under different probabilities. The results and tests show that mean absolute percentage errors obtained by the presented forecast system are 1.1551%, 2.0936% and 2.5546% respectively, and the prediction interval coverage probability values of 1 can be achieved. The hybrid system is effective, stable and has reasonable running time, which can be widely popularized. And it is conducive to the orderly operation of transportation industry and the development of container port cities.

A novel selective ensemble system for wind speed forecasting: From a new perspective of multiple predictors for subseries

Wind speed forecasting is of considerable economic and social significance; however, it remains challenging. Most state-of-the-art methods attempt to select the optimal predictor for each subseries in the framework of decomposition-ensemble forecasting; however, these do not always produce desirable forecasting results. Hence, this study innovatively proposes the idea of the validity of the forecasted subseries and considers the significance of the diversity of subseries predictors. In this context, a novel selective ensemble wind speed forecasting system is proposed from the new perspective of multiple predictors for subseries, which is advantageous owing to its data pretreatment, multiple predictors, adaptive selection, and multi-objective ensemble modules. Particularly, the data pretreatment module is designed based on successive variational mode decomposition, which can settle the limitations of the original algorithm as well as obtain desirable subseries. Meanwhile, the multiple predictors module is developed to provide a variety of predictors for each subseries by introducing the extreme learning machine series models. The adaptive selection module is designed to identify the effective subseries forecasted by multiple predictors module, whereas the multi-objective ensemble module is proposed to realize the wind speed point and interval forecasting based on a multi-objective optimization algorithm, which resolves the limitation of a single subseries predictor and further improves the power of the developed wind speed forecasting system. The interesting finding is that for the same dataset, the valid predictors of different subseries are different; furthermore, for a subseries, there may be multiple or no valid predictors. Experiments based on three datasets from the Chengde wind farm indicate that the mean absolute percentage errors of the wind speed point forecasting of the proposed system are 1.763238%, 2.169993%, and 1.578143%, respectively. For interval forecasting, when the confidence level is 90%, prediction interval coverage probability are 100.000000, 100.000000, and 99.758454, respectively. Hence, the proposed selective ensemble system can be employed as a novel solution for wind speed forecasting.

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.

Predictive uncertainty assessment in flood forecasting using quantile regression

Abstract Floods and their associated impacts are topics of concern in land development planning and management, which call for efficient flood forecasting and warning systems. The performance of flood warning systems is affected by uncertainty in water level forecasts, which is due to their inability to measure or calculate a modeled value accurately. Predictive uncertainty is an emerging type of uncertainty modeling technique that emphasizes total uncertainty quantified as a probability distribution conditioned on all available knowledge. Predictive uncertainty analysis was done using quantile regression (QR) for machine learning-based flood models – Hybrid Wavelet Artificial Neural Network model (WANN) and Hybrid Wavelet Support Vector Machine model (WSVM) for different lead times. Comparing QR models of WANN and WSVM revealed that the slope, intercept, spread of forecast, and width of confidence band of the WANN model are more for each quantile indicating more uncertainty as compared to the WSVM model. In both models, with an increase in lead time, uncertainty has shown an increasing trend as well. The performance evaluation of inference obtained from QR models was evaluated using uncertainty statistics such as prediction interval coverage probability, average relative interval length (ARIL), and mean prediction interval (MPI).

A Novel Twin Support Vector Regression Model for Wind Speed Time-Series Interval Prediction

Although the machine-learning model demonstrates high accuracy in wind speed prediction, it struggles to accurately depict the fluctuation range of the predicted values due to the inherent uncertainty in wind speed sequences. To address this limitation and enhance the reliability, we propose an effective wind speed interval prediction model that combines twin support vector regression (TSVR), variational mode decomposition (VMD), and the slime mould algorithm (SMA). In our methodology, the complex wind speed series is decomposed into multiple relatively stable subsequences using the VMD method. The principal component and residual series are then subject to interval prediction using the TSVR model, while the remaining components undergo point prediction. The SMA method is employed to search for optimal parameter combinations. The prediction interval of wind speed is obtained by aggregating the forecasting results of all TSVR models for each subseries. Our proposed model has demonstrated superior performance in various applications. It ensures that the wind speed value falls within the designated interval range while achieving the narrowest prediction interval. For instance, in the spring dataset with 1-period, we obtained a predicted interval with a prediction intervals coverage probability (PICP) value of 0.9791 and prediction interval normalized range width (PINRW) value of 0.0641. This outperforms other comparative models and significantly enhances its practical application value. After adding the residual interval prediction model, the reliability of the prediction interval is significantly improved. As a result, this study presents a novel twin support vector regression model as a valuable approach for multi-step wind speed interval prediction.

Prediction performance and reliability evaluation of three ginsenosides in Panax ginseng using hyperspectral imaging combined with a novel ensemble chemometric model

Panax ginseng C. A. Meyer (PG) is a health-promoting food, and its ginsenosides (Rb1, Rg1, Re) content, as the quality indicator, is affected by the planting modes (garden or forest ginsengs) and years. Effective prediction of this content remains to be investigated. In this study, hyperspectral (HSI) combined with ensemble model (CGRU-GPR) including the convolutional neural network (CNN), gate recurrent unit (GRU), and Gaussian process regression (GPR) realized a comprehensive evaluation of the prediction performance and predictive uncertainty. With effective wavelengths, the proposed CGRU-GPR model improved operation efficiency and obtained satisfactory prediction results with relative percent deviation (RPD) values all higher than 2.70 in three ginsenosides. Meanwhile, the interval prediction with a high prediction interval coverage probability (PICP) of 0.97 – 1.0 and a low mean width percentage (MWP) of 0.7 – 1.66 indicated a low prediction uncertainty. This study provides a rapid and reliable method for predicting ginsenosides contents in PG.

A hybrid machine learning-based multi-DEM ensemble model of river cross-section extraction: Implications on streamflow routing

Accurate representation of river channel and floodplain geometries is of prime concern for streamflow routing and flood inundation modelling under inadequate surveyed river cross-section data-condition, in many rivers across the globe. Due to global coverage and easy accessibility, the public domain medium resolution (1-arc second) DEMs such as SRTM, ASTER, and ALOS-AW3D30, with a linear vertical bias-correction approach, are widely used for hydrodynamic modelling of upland river networks. In this context, this study, for the first time, developed a hybrid machine learning-based Multi-DEM Ensemble (MDE) approach to simulate bias-corrected cross-sections using open source DEMs-extracted river cross-sections. Additionally, the hydraulic suitability of the simulated cross-sections and associated uncertainties were analysed. For this, the routing of streamflow and water level was performed using MIKE11-HD for a low-gradient flood-prone deltaic river basin of Eastern India (∼9000 km2) consisting of 19 river distributary systems. A comprehensive evaluation of the developed hybrid machine learning-based MDE models revealed an excellent performance of the Random Forest-Particle Swarm Optimisation-MDE (RF-PSO-MDE) model (NSE: 0.89–0.95; RMSE: 1.75–2.23 m) and Deep Neural Network-Particle Swarm Optimisation-MDE (DNN-PSO-MDE) model (NSE: 0.89–0.93; RMSE: 2.09–2.27 m) followed by the Support Vector Machine-Particle Swarm Optimisation-MDE (SVM-PSO-MDE) model (NSE: 0.87–0.92 and RMSE: 2.22–2.50 m). The MIKE11-HD simulations using RF-PSO-MDE and DNN-PSO-MDE model-simulated cross-sections were in close agreement with the observed streamflow and water level hydrographs, together with excellent matching of the flood peak, time to flood peak, and streamflow regimes. Predictive uncertainties analysis by the quantile regression technique confirmed an acceptable range of the Mean Prediction Interval and Percentage Interval Coverage Probability for the MIKE11-HD-RFMDE and MIKE11-HD-DNNMDE model variants including the MIKE11-HD-S model. Conclusively, the developed MDE models have potential for generating river cross-sections under sparse bathymetric conditions for the accurate simulation of streamflow and water level estimates using public domain digital elevation models.

Validation of uncertainty predictions in digital soil mapping

It is quite common in digital soil mapping (DSM) to quantify the uncertainty of issued predictions, that is to make probabilistic predictions. Yet, little attention has been paid to its validation. Probabilistic predictions are only of value for end users if they are reliable and ideally also sharp. Reliability refers to the consistency between predicted conditional probabilities and observed frequencies of independent test data. Sharpness refers to the concentration of a conditional probability distribution function, i.e. its narrowness. The prediction interval coverage probability (PICP) is currently used in DSM to validate the reliability of prediction intervals but it is ignorant of a potential one-sided bias of its boundaries. Therefore, we propose to extend the current validation procedure with metrics used in the broader probabilistic literature. These metrics not only evaluate probabilistic predictions in prediction interval format but also quantiles or full conditional probability distributions. We suggest the quantile coverage probability (QCP) and probability integral transform (PIT) histogram as alternatives to PICP and proper scoring rules for relative comparisons of competing probabilistic models. As scoring rules, we present the interval score (IS) and the continuous ranked probability score (CRPS), which can be decomposed into a reliability part (RELI). We illustrated the use of these metrics in a case study using soil pH and soil organic carbon from the LUCAS-soil database. Thereby, probabilistic predictions of five different models were compared: a reference null model (NM), quantile regression forest (QRF), quantile regression post-processing of a random forest (QRPP RF), kriging with external drift (KED) and quantile regression neural network (QRNN). For KED and QRNN, one-sided bias was found. This was not apparent from PICP but was shown by use of the PIT histogram and QCP. RELI summarized the trends found in QCP, PICP and PIT histograms to one numerical value. CRPS and IS were especially harsh to outliers and low sharpness. According to CRPS and IS, the best probabilistic predictions were obtained by QRF and QRPP RF and the worst by NM.

Spatial Prediction of Soil Particle-Size Fractions Using Digital Soil Mapping in the North Eastern Region of India

Numerous applications in agriculture, climate, ecology, hydrology, and the environment are severely constrained by the lack of detailed information on soil texture. The purpose of this study was to predict soil particle-size fractions (PSF) in the Ri-Bhoi district of Meghalaya state, India, using a random forest model (RF). For the modeling of soil particle-size fractions, we employed 95 soil profiles (456 depth-wise layers) gathered from a recent national land resource inventory as well as currently accessible environmental variables. Sand, silt, and clay content were predicted using the Random Forest model at varied depths of 0–5, 5–15, 30–60, 60–100, and 100–200 cm. Our results showed the R2 for sand was found to be 0.30 (0–5 cm), 0.28 (5–15 cm), and 0.21 (15–30 cm). For the sand, silt, and clay fractions, respectively, the concordance correlation coefficient (CCC) was found to be greater in the 0–30 cm, 0–60 cm, and 0–15 cm depths. When there is a reasonably close monitoring of the coverage probability with a confidence level along the 1:1 line, prediction interval coverage probability (PICP) gives a decent indicator of what to anticipate. The most crucial variables for the prediction of sand and silt were channel network base level (CNBL) and LS-Factor, whereas Min Temperature of Coldest Month (°C) (BIO6) was discovered for clay prediction. For all three soil texture fractions, the range between the 5% lower and 95% higher prediction bounds was large, indicating that the existing spatial predictions may be improved. The maps of soil texture were significantly more precise, and they accurately depicted the spatial variations of particle-size fractions. Additionally, there is still a need to investigate novel methodologies for extensive digital soil mapping, which will be very advantageous for many international initiatives.

Time-series generative adversarial networks for flood forecasting

Reliable flood forecasting serves as one of the fundamental tasks in flood management. However, the forecast performance of modern data-driven models depends heavily on the quantity and quality of training data. The lack of field data of flood events highly underpins the development of machine learning (ML) flood forecasting techniques. With consideration of the rareness of flood events and the high dimensionality of flood time series, two latest variants of generative adversarial networks (GANs), Time-series Generative Adversarial Network (TimeGAN) and Real-world Time Series Generative Adversarial Network (RTSGAN), were applied to generate synthetic flood timeseries. In the example analysis of the Xijiang River Basin in southern China, results show that time-series GANs can accurately and efficiently mimic the spatiotemporal correlations between flood series from multiple sites, and RTSGAN outperforms TimeGAN especially when the lengths of time series are long. Additionally, gradient boosting regression tree (GBRT), long-short term memory (LSTM) and quantile regression method integrated LSTM networks (QRLSTM) flood forecasting models were trained with real sequences and an extra amount of synthetic sequences. It shows that the expansion of training datasets in this way is promising in reducing prediction errors of classical machine learning models. In the 3-day-ahead flood forecast, the introduction of synthetic training datasets has little positive effect on both GBRT and LSTM. In 24-hour-ahead flood forecast, as the lead period increases, GBRT-RTSGAN outperforms GBRT evidenced by a 6.7% increase in Nash-Sutcliffe efficiency (NSE) metric, a 56.5% reduction in average absolute relative error (AARE) metric and a 33.1% reduction in root-mean square error (RMSE) metric. For interval forecast, the use of synthetic training datasets helps QRLSTM obtain lower prediction interval normalized averaged width (PINAW), however, at the cost of prediction interval coverage probability (PICP).

Short-Term Probabilistic Forecasting Method for Wind Speed Combining Long Short-Term Memory and Gaussian Mixture Model

Wind speed forecasting is advantageous in reducing wind-induced accidents or disasters and increasing the capture of wind power. Accordingly, this forecasting process has been a focus of research in the field of engineering. However, because wind speed is chaotic and random in nature, its forecasting inevitably includes errors. Consequently, specifying the appropriate method to obtain accurate forecasting results is difficult. The probabilistic forecasting method has considerable relevance to short-term wind speed forecasting because it provides both the predicted value and the error distribution. This study proposes a probabilistic forecasting method for short-term wind speeds based on the Gaussian mixture model and long short-term memory. The precision of the proposed method is evaluated by prediction intervals (i.e., prediction interval coverage probability, prediction interval normalized average width, and coverage width-based criterion) using 29 monitored wind speed datasets. The effects of wind speed characteristics on the forecasting precision of the proposed method were further studied. Results show that the proposed method is effective in obtaining the probability distribution of predicted wind speeds, and the forecast results are highly accurate. The forecasting precision of the proposed method is mainly influenced by the wind speed difference and standard deviation.

Probabilistic Wind Power Forecasting Using Optimized Deep Auto-Regressive Recurrent Neural Networks

Wind power forecasting is very crucial for power system planning and scheduling. Deep neural networks (DNNs) are widely used in forecasting applications due to their exceptional performance. However, the DNNs’ architectural configuration has a significant impact on their performance, and the selection of proper hyper-parameters determines the success or failure of these models. Therefore, one of the challenging issues in DNNs is how to assess their hyper-parameter values effectively. Most of the previous researches in the literature have tuned the DNNs’ hyper-parameters manually, which is a weak and time-consuming task. Using optimization/evolutionary algorithms is an effective way to obtain the optimal values of DNNs’ hyper-parameters automatically. In this article, we propose a novel evolutionary algorithm that is based on the grasshopper optimization algorithm (GOA) improved by adding two evolutionary operators, opposition-based learning and chaos theory, to the optimization process. Overall, a novel probabilistic wind power forecasting model named neural GOA deep auto-regressive (NGOA-DeepAr) is proposed based on an auto-regressive recurrent neural network in which the proposed evolutionary algorithm has optimized its hyper-parameters. The performance of the proposed NGOA-DeepAr model is tested on two different datasets: One is the publicly available GEFCom-2014 dataset and the other is the Australian Energy Market Operator dataset. The prediction interval coverage probability and pinball loss for the two datasets are <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[0.902, 0.320]$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$[0.933, 1.4885]$</tex-math></inline-formula> , respectively. According to the experimental findings, our proposed NGOA-DeepAr is much faster in learning and outperforms the benchmark DNNs and the other neuroevolutionary models.

A parallel GRU with dual-stage attention mechanism model integrating uncertainty quantification for probabilistic RUL prediction of wind turbine bearings

The accurate probabilistic prediction of remaining useful life (RUL) of bearings plays an important role in ensuring the safe operation of wind turbine maintenance decision making. However, it is still a challenge to improve prediction accuracy and quantify prediction uncertainty, leading to the inability of precision and reliable prediction results. Accordingly, this paper proposed a novel probabilistic RUL prediction method combined the parallel GRUs with dual-stage attention mechanism (PDAGRU) prediction model with the non-parametric uncertainty quantification approach to overcome the limitations. In the PDAGRU model, the dual-stage attention mechanism is developed to improve the capability of degradation information extraction. Meanwhile, the parallel structure can enhance prediction accuracy and help quantify model uncertainty. The proposed uncertainty quantification approach with less prior knowledge can provide probabilistic RUL prediction results based on the kernel density estimation (KDE) and Monte Carlo (MC) dropout. Moreover, a first prediction time (FPT) determination method based on the isotonic regression is developed to more accurately reflect the degradation trajectory of bearings’ RUL. Two cases including simulated data and real-world data are deployed to verify the effectiveness of the proposed method. Compared with other methods, the superiority of the proposed method is verified. The RUL prediction accuracy and interval coverage probability for wind turbine bearings are high to 90.4% and 99.7% respectively.

Evolutionary and ensemble machine learning predictive models for evaluation of water quality

Study regionBisham Qilla and Doyian stations, Indus River Basin of Pakistan Study focusWater pollution is an international concern that impedes human health, ecological sustainability, and agricultural output. This study focuses on the distinguishing characteristics of an evolutionary and ensemble machine learning (ML) based modeling to provide an in-depth insight of escalating water quality problems. The 360 temporal readings of electric conductivity (EC) and total dissolved solids (TDS) with several input variables are used to establish multi-expression programing (MEP) model and random forest (RF) regression model for the assessment of water quality at Indus River. New hydrological insight for the regionThe developed models were evaluated using several statistical metrics. The findings reveal that the determination coefficient (R2) in the testing phase (subject to unseen data) for the all the developed models is more than 0.95, indicating the accurateness of the developed models. Furthermore, the error measurements are much lesser with root mean square logarithmic error (RMSLE) nearly equals to zero for each developed model. The mean absolute percent error (MAPE) of MEP models and RF models falls below 10% and 5%, respectively, in all three phases (training, validation and testing). According to the sensitivity study of generated MEP models about the relevance of inputs on the predicted EC and TDS, shows that bi-carbonates and chlorine content have significant influence with a sensitiveness score more than 0.90, whereas the impact of sodium content is less pronounced. All the models (RF and MEP) have lower uncertainty based on the prediction interval coverage probability (PICP) calculated using the quartile regression (QR) approach. The PICP% of each model is greater than 85% in all three stages. Thus, the findings of the study indicate that developing intelligent models for water quality parameter is cost effective and feasible for monitoring and analyzing the Indus River water quality.

Uncertain-CAM: Uncertainty-Based Ensemble Machine Voting for Improved COVID-19 CXR Classification and Explainability.

The ongoing coronavirus disease 2019 (COVID-19) pandemic has had a significant impact on patients and healthcare systems across the world. Distinguishing non-COVID-19 patients from COVID-19 patients at the lowest possible cost and in the earliest stages of the disease is a major issue. Additionally, the implementation of explainable deep learning decisions is another issue, especially in critical fields such as medicine. The study presents a method to train deep learning models and apply an uncertainty-based ensemble voting policy to achieve 99% accuracy in classifying COVID-19 chest X-rays from normal and pneumonia-related infections. We further present a training scheme that integrates the cyclic cosine annealing approach with cross-validation and uncertainty quantification that is measured using prediction interval coverage probability (PICP) as final ensemble voting weights. We also propose the Uncertain-CAM technique, which improves deep learning explainability and provides a more reliable COVID-19 classification system. We introduce a new image processing technique to measure the explainability based on ground-truth, and we compared it with the widely adopted Grad-CAM method.

Analysis of the Relationship between Vegetation and Radar Interferometric Coherence

To effectively reduce the impact of vegetation cover on surface settlement monitoring, the relationship between normalized difference vegetation index (NDVI) and coherence coefficient was established. It provides a way to estimate coherence coefficient by NDVI. In the research, a new method is tried to make the time range coincident between NDVI results and coherence coefficient results. Using the coherence coefficient results and the NDVI results of each interference image pair in the study area, the mathematical relationship between NDVI and the coherent coefficient was established based on statistical analysis of the fitting results of the exponential model, logarithmic model, and linear model. Four indicators were selected to evaluate the fitting results, including root mean square error, determinant coefficient, prediction interval coverage probability, and prediction interval normalized average width. The fitting effect of the exponential model was better than that of the logarithmic model and linear model. The mean of error was −0.041 in study area ROI1 and −0.126 in study area ROI2.The standard deviation of error was 0.165 in study area ROI1 and 0.140 in study area ROI2. The fitting results are consistent with the coherence coefficient results. The research method used the NDVI results to estimate the InSAR coherence coefficient. This provides an easy and efficient way to indirectly evaluate the interferometric coherence and a basis in InSAR data processing. The results can provide pre-estimation of coherence information in Ningxia by optical images.

A Bayesian approach for remote sensing of chlorophyll-a and associated retrieval uncertainty in oligotrophic and mesotrophic lakes

Satellite remote sensing of chlorophyll-a concentration (chla) in oligotrophic and mesotrophic lakes faces uncertainties from sources such as atmospheric correction, complex inherent optical property compositions, and imperfect algorithmic retrieval. To improve chla estimation in oligo- and mesotrophic lakes, we developed Bayesian probabilistic neural networks (BNNs) for the Sentinel-3 Ocean and Land Cover Instrument (OLCI) and Sentinel-2 MultiSpectral Imager (MSI). The BNNs were built using an in situ dataset of oligo- and mesotrophic water bodies (1755 observations from 178 systems; median chla: 5.11 mg m−3, standard deviation: 10.76 mg m−3) and provide a per-pixel uncertainty percentage associated with retrieved chla. Shifts of oligo- and mesotrophic systems into the eutrophic regime, characterised by higher biomass levels, are widespread. To account for phytoplankton biomass fluctuation, a set of eutrophic lakes (167 observations from 31 systems) were included in this study (maximum chla 68 mg m−3). The BNNs were evaluated through five assessments including single day and time series match-ups with OLCI and MSI. OLCI BNN accuracy gains of >25% and MSI BNN accuracy gains of >15% were achieved in the assessments when compared to chla reference algorithms for oligotrophic waters (chla ≤ 8 mg m−3). In comparison to the reference algorithms, the accuracy gains of the BNNs decreased as chla and trophic levels increased. To measure the quality of the provided BNN uncertainty estimate, we calculated the prediction interval coverage probability (PICP), Sharpness and mean absolute calibration difference (MACD) metrics. The associated BNN chla uncertainty estimate included the reference in situ chla values for most observations (PICP ≥ 75%) across the different performance assessments. Further analysis showed that the BNN chla uncertainty estimate was not constantly well-calibrated across different evaluation strategies (Sharpness 1.7–6, MACD 0.04–0.25). BNN uncertainties were used to test two chla improvement strategies: 1) identifying and filtering uncertain chla estimates using scene-specific thresholds, and 2) selecting the most accurate prior atmospheric correction algorithm per individual satellite observation to retain chla with the lowest BNN uncertainty. Both strategies increased the quality of the chla result and demonstrated the significance of uncertainty estimation. This study serves as research on Bayesian machine learning for the estimation and visualisation of chla and associated retrieval uncertainty to develop harmonised products across OLCI and MSI for small and large oligo- and mesotrophic lakes.

Optimal dispatching method for integrated energy system based on robust economic model predictive control considering source–load power interval prediction

Effective source–load prediction and reasonable dispatching are crucial to realize the economic and reliable operations of integrated energy systems (IESs). They can overcome the challenges introduced by the uncertainties of new energies and various types of loads in the IES. Accordingly, a robust optimal dispatching method for the IES based on a robust economic model predictive control (REMPC) strategy considering source–load power interval prediction is proposed. First, an operation model of the IES is established, and an interval prediction model based on the bidirectional long short-term memory network optimized by beetle antenna search and bootstrap is formulated and applied to predict the photovoltaic power and the cooling, heating, and electrical loads. Then, an optimal dispatching scheme based on REMPC is devised for the IES. The source–load interval prediction results are used to improve the robustness of the REPMC and reduce the influence of source–load uncertainties on dispatching. An actual IES case is selected to conduct simulations; the results show that compared with other prediction techniques, the proposed method has higher prediction interval coverage probability and prediction interval normalized averaged width. Moreover, the operational cost of the IES is decreased by the REMPC strategy. With the devised dispatching scheme, the ability of the IES to handle the dispatching risk caused by prediction errors is enhanced. Improved dispatching robustness and operational economy are also achieved.