This paper proposes a Bayesian network (BN) that can construct the nonlinear dependence among wind speed, solar irradiation, and load. The correlations of random variables (RVs) are analyzed using the Pearson correlation coefficient, Kendall rank correlation coefficient, and Spearman rank correlation coefficient. According to Bayesian theory, the Bayesian information criterion (BIC) and maximum likelihood estimation (MLE) method are employed to determine the structure and parameters of BN. Then the BN model of RVs is established. The constructed BN model is the joint probability distribution of RVs that can present the nonlinear dependence and marginal distribution (MD) of RVs without limitation. The testing samples of wind speed, solar irradiation, and load are generated using the autoregressive integrated moving average (ARMA) model. Then these samples are utilized to construct the probability model of a BN and C-vine copula. The modeling accuracy and efficiency of the probability models of BN and C-vine copula are compared, and the quality of the synthetic samples output from them are analyzed. In the modified IEEE 118-bus test system, two kinds of synthetic samples are used to calculate the probabilistic load flow (PLF), and the accuracy and efficiency of the PLF based on the BN are tested. The validity of the BN model is verified.

Airborne bathymetry LiDAR, such as Mapper5000, experienced varied water-bottom return intensities. Under the high bottom return signal condition, owing to the clear water body, high bottom reflectance, low depth, or high gain setting of the detector, the peak power of the received signal from the bottom often exceeds the linear dynamic range of the 532 nm detector assembly. The resulting signal saturation distorted the recorded bottom return waveforms and resulted in undesired depth bias exceeding 2.0 m in certain extreme cases. In this study, we developed a low-complexity peak position restoration method for this “saturation in-water range bias” correction based on an intersection point of double linear approximations of the leading and trailing edges of the saturated bottom waveform (DLI). The validation of corrected results with consistent sonar depth measurements indicated that the DLI method demonstrated considerable robustness to the effect of pulse stretching under saturation conditions and reduced the mean absolute depth bias from 1.46 m to 0.47 m. Compared with Gaussian and exponentially modified Gaussian fitting algorithms, the DLI was faster and the most effective at reducing depth bias under strong saturation conditions. The success of DLI benefited from the small width of the transmitted laser pulse and the sharp slope of the leading edge of the saturated bottom waveform. However, the interference of volume backscattering signals at shallow depths could affect the performance of DLI, which should be carefully removed.

The increasing volatility of electricity prices, driven by the growing share of renewable energy, calls for new approaches. This paper proposes a dynamic Bayesian network (DBN) method for electricity price interval forecasting. The model uses predicted values of wind power generation, total power generation, and total electricity consumption, along with historical electricity prices, as inputs. The network structure is determined using a greedy search algorithm, and the model parameters are estimated through maximum likelihood estimation (MLE). By treating the predictions of wind power, total generation, and total consumption as reasoning evidence, the method employs joint tree inference to generate discrete states and posterior probabilities for electricity prices, thereby enabling interval forecasting. The DBN-based interval predictions achieve a prediction interval coverage probability (PICP) of 95.24%, a normalized average width (PINAW) of 9.25%, and an accumulated width deviation (AWD) of 0.56%. The effectiveness of the proposed method was evaluated by comparing its predictions with actual electricity prices and with results from both particle swarm optimization-kernel extreme learning machine (PSO-KELM) and long short-term memory (LSTM)-based methods. This innovative approach not only provides prediction intervals but also associates them with corresponding probabilities, offering significant potential to enhance market participants’ decision-making and mitigate price risks.

The increasing volatility of electricity prices, driven by the growing share of renewable energy in the market, calls for a new approach to interval prediction. This paper proposes a dynamic Bayesian network (DBN) method for electricity price range forecasting. The model uses predicted values of wind power generation, total power generation, total electricity consumption, and historical electricity prices as input data. The network structure is determined using a greedy search algorithm, and the model parameters are estimated through maximum likelihood estimation (MLE).By treating the predicted values of wind power generation, total power generation, and total electricity consumption as reasoning evidence, the method employs joint tree reasoning to generate discrete values and posterior probabilities for electricity price predictions, enabling interval forecasting. The DBN-based interval prediction results achieve a forecast interval coverage probability (PICP) of 95.24%, a normalized average width of forecast interval (PINAW) of 9.25%, and a cumulative width deviation (AWD) of 0.56%.The proposed method?s effectiveness was evaluated by comparing its predictions with actual electricity prices and with results from PSO-KELM methods. This innovative approach not only provides prediction intervals for electricity prices but also associates them with corresponding probabilities, offering significant potential to enhance market participants' decision-making and mitigate price risks.