A stochastic sensitivity-based multi-objective optimization method for short-term wind speed interval prediction

Chen, Xuanqun; Lai, Chun Sing; Ng, Wing W. Y.; Pan, Keda; Lai, Loi Lei; Zhong, Cankun

doi:10.1007/s13042-021-01340-6

Cited by 16 publications

(9 citation statements)

References 45 publications

(66 reference statements)

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“…where TSS is the total square sum, RSS is the residual square sum, and ESS is the explained square sum. PICP represents the actual frequency that observations fall within the prediction interval and is used to evaluate the reliability of the prediction interval, which is calculated as shown in (12) [22]. The higher the PICP value, the better the prediction result and the more reliable the model.…”

Section: Data Fitting Results Evaluationmentioning

confidence: 99%

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Analysis of the Relationship between Vegetation and Radar Interferometric Coherence

Cao

Hao

et al. 2022

Sustainability

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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.

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Section: Data Fitting Results Evaluationmentioning

confidence: 99%

“…The formula for calculating the PI N AW is shown in (13). A smaller PI N AW value means a more sensitive prediction interval and more reliable model [22].…”

Section: Data Fitting Results Evaluationmentioning

confidence: 99%

Analysis of the Relationship between Vegetation and Radar Interferometric Coherence

Cao

Hao

et al. 2022

Sustainability

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“…Then, the prediction interval coverage probability (PICP) curve and the prediction intervals normalized average width (PINAW) curve are used to evaluate the effectiveness of interval prediction, [29] which are calculated as follows:…”

Section: Evaluation Criteria For Model Performancementioning

confidence: 99%

$$\text{PICP} = \frac{1}{I_{\text{test}}} \sum_{i = 1}^{I_{\text{test}}} \left{\right. \left[\right.

…”

Section: Algorithm Of Functional Relevance Vector Machinementioning

confidence: 99%

Dynamic Prediction with Statistical Uncertainty Evaluation of Phosphorus Content Based on Functional Relevance Vector Machine

Qian,

Chang,

Dong

et al. 2024

steel research int.

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In the steelmaking process, inaccurate composition of raw materials, experimental process parameter control, and other factors bring about large statistical uncertainty to the phosphorus content prediction of molten steel. Meanwhile, lots of models mainly predict the end‐point phosphorus content, but the composition change during the whole production process is still in the gray box condition, where the exact refining state is unknown. These two problems increase the difficulty in process parameter optimization and control. In order to improve the phosphorus content control in the steelmaking process, this work proposes the functional relevance vector machine (FRVM) method. This method smooths the time series of process parameters to continuous functions by functional data analysis to predict the phosphorus content change during the whole production process, and estimates the probabilistic distributions of regression weights based on the Bayesian framework to directly output the probabilistic confidence interval of the phosphorus content. The real‐world steelmaking dataset validates that the mean relative prediction error of phosphorus content by the FRVM method is less than 18.04% during the whole production process and the end‐point hit rate is 86.46% when the prediction error is within ±0.005 wt%.

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“…The performance of the interval prediction can be evaluated in terms of two aspects: the coverage probability and width. The prediction intervals coverage probability (PICP) reflects the reliability of the prediction interval [39]. If the observation value yi is within the constructed prediction interval [Li, Ui], ci = 1; otherwise, ci = 0.…”

Section: Picpmentioning

confidence: 99%

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

Feng

Yao

et al. 2023

Energies

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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.

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A stochastic sensitivity-based multi-objective optimization method for short-term wind speed interval prediction

Cited by 16 publications

References 45 publications

Analysis of the Relationship between Vegetation and Radar Interferometric Coherence

Analysis of the Relationship between Vegetation and Radar Interferometric Coherence

Dynamic Prediction with Statistical Uncertainty Evaluation of Phosphorus Content Based on Functional Relevance Vector Machine

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

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