Abstract:The predictive capabilities of three nowcasting models (S-PROG, Extrapolation, and ANVIL) for extreme rainfall induced by tropical cyclones were evaluated using the 2017 Hurricane Harvey rainfall event as a case study. The results indicate that the ANVIL model shows the best performance in simulating the spatial distribution of rainfall, but systematically overestimates heavy rainfall intensity; the S-PROG model shows a lag in tracking rainfall intensity variations; and the Extrapolation model achieves the highest stability in short-term (0-2 h) nowcasting, accurately capturing the peak rainfall intensity and its temporal evolution. The fusion of high-resolution meteorological data and multi-source data can significantly enhance model performance, and the combination of radar extrapolation techniques and deep learning algorithms shows great potential.

Abstract:To reveal the influence of different physical mechanism fusion schemes on the groundwater level prediction accuracy of graph neural network (GCN), six graph convolutional network (GCN) structures with different physical mechanism fusion schemes were designed based on the daily groundwater level data from 114 monitoring stations in the Poyang Lake Basin by comprehensively considering the physical factors such as spatial correlation of groundwater levels, surface water-groundwater connectivity, and rainfall lag effect. The groundwater level prediction accuracies of the six schemes were compared. The results from the Poyang Lake Basin case validation show that the GCN demonstrated excellent overall simulation capability and accuracy when predicting the dynamic changes of groundwater levels; the R 2 of all schemes exceeds 0.9. The scheme fusing one-month-ahead rainfall and surface water-groundwater connectivity attributes achieves the highest accuracy (with an MAE of 0.060 1 m), improving the accuracy by about 6.8% compared with the single distance matrix scheme. Taking rainfall lag into account characterizes better the delayed response of groundwater levels to rainfall; moreover, the connectivity attribute matrix yields better RMSE improvements for phreatic well water-level predictions than for confined wells.

Abstract:To address the problem that traditional interpolation methods are difficult to effectively fuse rain gauge and microwave link rainfall observation data, a collaborative reconstruction framework for rainfall fields based on a stochastic hybrid Whittaker-Shannon algorithm was proposed. By constructing a synthetic rainfall reference field, the two-dimensional precipitation reconstruction performance of single-source interpolation of rain gauges and dual-source fusion of rain gauges and microwave data was systematically compared. At the same time, an image smoothing technique was used to mitigate the problems of excessive noise and lack of smoothness of the stochastic reconstruction method in rainfall field construction. The results show that the spatial reconstruction accuracy of the stochastic hybrid Whittaker-Shannon algorithm is significantly positively correlated with the rain gauge density and microwave link coverage. Moreover, as the number of possible reconstructed fields increases, the accuracy is better; however, when the number of possible reconstructed fields exceeds 20, the overestimation rate of rainfall extent increases to 80%. The 5×5 mean filter can reduce the root mean square error by 60%, which is significantly superior to the median filter and other window scale schemes. Microwave link data have complementary value in enhancing the spatial resolution (up to the 1 km scale) and dynamic representation capability of rainfall fields, providing a scalable and highly promising technical pathway for real-time data assimilation of urban hydrological models under the 5G communication context.

Abstract:To meet the needs of hydrological models for high-precision precipitation data, with the humid Tunxi Basin and the semi-humid Zijingguan Basin as the study areas, a multi-source precipitation merging algorithm based on external drift kriging was constructed to merge the measured precipitation data at stations and the IMERG satellite precipitation data, generating merged precipitation data with high precision and high spatiotemporal resolution. The WRF-Hydro hydrological model was driven by the merged precipitation data to conduct runoff simulations in the study areas, and its applicability in flood forecasting for small and medium-sized rivers was evaluated. The results show that taking the measured precipitation data at stations as the benchmark, the satellite precipitation data exhibits a serious underestimation of precipitation intensity in the Zijingguan Basin, and the evaluation indicators of the merged precipitation data are better than those of the original IMERG satellite precipitation data. Furthermore, the WRF-Hydro model driven by the merged precipitation data can better simulate the flood process than that driven by the IMERG satellite precipitation data, and the model shows stronger applicability in the humid basin than in the semi-humid basin.

Abstract:Based on the soil temperature and meteorological observation data from the Wudaogou Experimental Station in the Huaibei Plain from 2000 to 2024, the correlation function feature (CFF) method was adopted to systematically analyze the lag effects of meteorological factors, such as air temperature and air pressure, at different soil depths (10, 20, 40, 80, 160, and 320 cm). Using the lag-processed meteorological factors at each depth as inputs, the convolutional neural network (CNN), long short-term memory (LSTM), and CNN-LSTM models were driven to simulate the evolution processes of soil temperature at the six depths, and the applicability and accuracy of the three machine learning models at different depths were evaluated. The results indicate that the optimal lag time of meteorological factors increases with the increase of soil depth. The lag time of shallow soil (10-20 cm) is the shortest (0-3 d); the lag time of middle soil (40-80 cm) is 8-29 d; the lag time of deep soil (160-320 cm) extends to 44-89 d. The simulation performance of the three machine learning models exhibits clear stratified differences at different depths, with the shallow layer generally outperforming the deep layer. The CNN-LSTM model demonstrates higher accuracy and stability at all depths, and its coefficient of determination ( R 2) is generally maintained above 0.94, outperforming the single models. In the deep soil of 320 cm, the R 2 of the CNN-LSTM model is 0.941, which improves by 17% compared with the LSTM model and 45% compared with the CNN model. This reflects the advantages of coupling convolutional feature extraction with temporal memory capability.

Abstract:To address the problems of low image contrast, color distortion, and blurred details caused by turbid underwater environments, an underwater image restoration network based on multi-channel polarization and a dual-branch Transformer was proposed. A polarization feature adaptive fusion module based on the Stokes vector was used to extract the physical polarization features of water. A spatial-polarization dual-branch architecture was constructed, and a dynamic gating mechanism was utilized to adaptively fuse multi-source information, such as polarization intensity, degree of polarization, and polarization angle, with spatial features, overcoming the limitation of incomplete representation by single-modality information. An encoder-decoder structure integrating multi-scale feature interaction, channel attention, and multi-scale spatial Transformer modules was adopted for the network backbone to enhance the capabilities of degradation representation and global detail restoration. The experimental results show that this method has significant advantages in structure restoration, detail preservation, and color correction (SSIM: 0.854 0, PSNR: 32.93 dB, perceptual metric LPIPS: 0.363 3), and can significantly improve the clarity, contrast, and color fidelity of the restored images.

Abstract:To investigate the impact of cavitation on the unsteady flow and energy loss characteristics in a water-jet pump, the unsteady calculations of its internal cavitating flow field were carried out based on the unsteady Reynolds-averaged Navier-Stokes (URANS) equations, adopting the FBM-CC turbulence model and ZGB cavitation model. The unsteady flow and energy loss characteristics under typical cavitation conditions were analyzed by combining the boundary vorticity flux diagnosis and entropy generation theory. The results show: The adopted numerical simulation method has good accuracy for the calculation of cavitating flow in the water-jet pump; as the net positive suction head decreases, cavitation develops from clearance cavitation to wedge-shaped cavitation; under the deep cavitation condition (the net positive suction head is 11.32 m), cavitation covers almost the entire blade suction surface, inducing the fracture of the tip leakage vortex and the formation of cavitation-induced vortices that block the flow passage; a strong adverse pressure gradient exists at the cavitation end, and streamline distortion and flow separation appear at the tip trailing edge; in the initial stage of cavitation, the energy loss is dominated by wall friction; under the deep cavitation condition, turbulent dissipation becomes the main contributor, and the entropy generation of turbulent dissipation increases by 5% compared to the initial cavitation; at this time, the flow separation of the wake and the vortex caused by cavitation become the main sources of energy loss.

Abstract:To reveal the impacts of changes in flow and sediment on channel erosion and deposition in the lower Yellow River channel and to improve the efficiency of engineering regulation of flow and sediment for de-siltation, the formula for channel erosion and deposition in the lower reach by Chien Ning et al. was revised using flow and sediment data based on the “more incoming, more discharging” sediment transport characteristic of the Yellow River and the river sediment transport theory. Consequently, an erosion and deposition formula and a comprehensive incoming sediment coefficient with a clear physical meaning, which could more comprehensively reflect the effects of conditions such as flow and sediment volume and suspended sediment gradation, were obtained. The results show that the revised formula has a unified parameter and coefficient, and the simulated erosion and deposition intensities in both the full period and individual sub-periods have high accuracy; furthermore, it can be used to study the comprehensive flow-sediment relationship and erosion and deposition regulation mode in the lower Yellow River after reservoir sediment trapping and sediment gradation alteration; altering sediment gradation through reservoir sediment trapping and regulation can significantly affect the sediment transport capacity of the downstream channel; the optimal operation of “trapping coarse sediment and discharging fine sediment” for flood control and de-siltation reservoirs can largely reduce the deposition in the downstream channel, which is of great significance for maintaining the long-term stability of the downstream channel and ensuring the flood control capacity of the reservoirs.

Abstract:To address problems such as insufficient multi-source data integration, lacking system-level association analysis, and weak decision interpretability in current decision-making of river regulation schemes, an intelligent decision-making method for river regulation schemes via collaboration of knowledge graph and large language model was proposed. In this method, a knowledge graph for river regulation was constructed by integrating multi-source data such as river channels, sluice operating conditions, and dyke-cluster topology. A two-stage classification model was designed (Stage 1 modeled physical features and engineering ratio parameters based on random forests; Stage 2 extracted topological relationships from the knowledge graph and utilized the Node2Vec algorithm to generate 64-dimensional graph embedding features input into a logistic regression model for optimizing decision boundary). A generative evaluation engine based on DeepSeek-R1 was developed, which combined domain-knowledge-enhanced prompt learning to generate interpretable reasoning chains through multi-step reasoning for scheme feasibility assessment and improvement recommendation generation. The proposed method was validated through multi-label classification performance comparison and ablation experiments. Verification results of 228 river channels in Nansha District, Guangzhou indicate that this method can effectively alleviate the problems of insufficient multi-source data integration, missing system-level association analysis, and weak interpretability of decision-making process in traditional methods. Its F1 score (the harmonic mean of precision and recall) reaches 0.853, and the accuracy reaches 0.921, indicating that its overall performance is superior to that of the baseline models considered. Both the topological embedding and the domain-knowledge-enhanced multi-step reasoning mechanism can effectively improve method performance. The proposed method achieves the highest F1 score and the lowest Hamming loss, verifying the effectiveness of each key module.

Abstract:To address the issue of simulation bias in hydrological models caused by insufficient modeling or unmodeled behaviors under complex environmental conditions, an inflow forecasting method for hydropower stations based on machine learning and Bayesian model averaging (BMA) was proposed. Based on the Hydromad model, the inflow and residual sequences were calculated; three machine learning models, namely random forest (RF) model, XGBoost model, and support vector regression (SVR) model, were used to capture the nonlinear characteristics of the residuals. Subsequently, the multi-model prediction results were fused via BMA to achieve post-processing error correction and uncertainty assessment of the simulation errors. The case study results of Liyuan Hydropower Station on Jinsha River indicate that the proposed method can significantly improve the fitting accuracy of the Hydromad model in peak flood responses and the rising and falling water stages. After correction, indicators of inflow prediction such as NSE and KGE are significantly improved; the water volume bias is effectively controlled; the overall prediction accuracy is obviously improved. This method can provide more scientific technical support for inflow forecasting and operational decision-making of hydropower stations.

Abstract:There is high salt content in soil in the coastal tidal flat reclamation area of Jiangsu Province. In order to make rational use of rainfall and adopt underground pipe drainage facilities to improve the desalinization of soil in the tidal flat, an underground pipe drainage experiment was carried out in a typical area. By conducting tests under different underground pipe spacings, the analysis of soil’s salt content at different depths (0-80 cm) in the experimental area was carried out to study the dynamic change pattern of salinity in the soil profile. The results show that in the control area without underground pipes, the salt content of the soil at different depths shows an upward trend, while in the area with underground pipes, the salt content of the soil at different depths shows a general downward trend. Under different underground pipe spacing, the variation of the soil’s salt content at different depths is roughly the same, but the amplitude is different. A smaller underground pipe spacing indicates a more obvious soil desalinization effect; when the underground pipe spacing is the same, the soil desalinization effect will weaken as the depth of the soil layer increases.

Abstract:To reconstruct the hydrodynamics of the Shabei River Network in the Changhu water system of Jingzhou under limited water diversion, a joint gate group operation method based on gate regulation response characteristics and phased single-objective optimization was proposed. A one-dimensional hydrodynamic model was established to conduct sensitivity analysis of single-gate regulation, and key gates and their effective opening ranges were identified. Based on this, a joint gate group operation optimization model was constructed to systematically analyze and determine the optimal operation scheme. The results indicate that different gates have varying impacts on the hydrodynamics of different channels; single-gate regulation can hardly achieve coordinated improvement of hydrodynamics in both main and branch canals. Under the condition of an average daily water diversion flow of 5 m³/s, the optimal operation scheme increased the flow velocity in stagnant flow zones by over 25%, increased the average flow velocity of the river network by 14.72%-22.44%, and maintained the flow velocity above 0.1 m/s in main canals during the regulation process, effectively reconstructing the hydrodynamics of the study area and ensuring the water diversion and drainage functions of the river network.

Abstract:For the reinforcement problem of three-dimensional rock slopes under the Hoek-Brown criterion, a non-discrete multi-objective optimization design method for anti-slide piles combining mechanical analysis and the response surface method was proposed. The stability model for three-dimensional pile-reinforced slopes was established using the upper bound limit analysis method. Artificial neural networks were adopted to establish the response surface model between the safety factor and the design and strength parameters to quickly obtain a large number of safety factor samples required for reliability evaluation. Furthermore, taking the reinforcement cost and slope reliability as optimization objectives, the Pareto front was directly solved by non-discrete point selection in the continuous design variable space. The case analysis results show that, compared with the discrete design method, the non-discrete design can more comprehensively explore the feasible design domain and obtain more optimized design schemes; under the minimum cost and knee point decision strategies, the costs of the non-discrete design decrease by approximately 18% and 14%, respectively; the pile spacing, pile diameter, and pile position all exhibit significant nonlinear effects on the slope reliability index, and the reinforcement effect is optimal when the piles are placed in the upper part of the slope face.

Abstract:To investigate the crack resistance of typical asphalt mixtures under salt erosion and dynamic water conditions, direct tensile tests combined with the digital image correlation (DIC) method were conducted to examine the tensile strength evolution and principal strain field development of AH-70, SBS-modified, and rubber-modified asphalt mixtures. The results show that all the mixtures exhibited ductile failure characteristics, with cracks mostly initiating at the binder-aggregate interface and propagating along the strain concentration zones. Dynamic water cycling markedly induced interfacial stripping and moisture damage in the AH-70 asphalt mixture, whereas static saline dry-wet cycling further exacerbated pore expansion. After 20 d of dry-wet cycling in a 20% salt solution, the tensile strength and strain energy density of the AH-70 asphalt mixture decreased by 41.6% and 57.8%, respectively, and these values decreased by 56.1% and 69.4% after dynamic water cycling. In contrast, the SBS- and rubber-modified asphalt mixtures showed superior structural stability and durability. High salinity and dry-wet cycling jointly weakened the toughness of the asphalt mixtures. However, owing to its excellent viscoelasticity, rubber-modified asphalt retained a higher residual strength and energy absorption capacity, exhibiting notable advantages in crack and stripping resistance.

Abstract:To address the problems that the anti-disintegration property of surficial clayey soils is prone to deterioration under meteorological factors such as rainfall and drought, and traditional improvement materials such as cement and lime have defects such as high brittleness and irreversibility, the clayey soil in Nanjing area was taken as the research object to prepare improved soil samples with different lignin derivative contents and conduct disintegration tests. Combined with scanning electron microscopy (SEM) and energy-dispersive spectroscopy (EDS), the macroscopic and microscopic mechanisms of the anti-disintegration properties of clayey soils improved by lignin derivatives were revealed. The results show that the disintegration process of improved clayey soils is divided into three stages: initial saturation, rapid disintegration, and slow disintegration; the 1% content has the optimal effect, with the initial saturation stage extended to 9 min, the complete disintegration time doubled compared with that of untreated soil, and the average disintegration rate reduced by 20.13%; lignin derivatives form a film-like structure on particle surfaces to wrap and connect particles, reduce pore connectivity, introduce Ca2+ to enhance cementation, and inhibit water infiltration; when the lignin derivative content is too high, the films aggregate, interparticle connections weaken, and the anti-disintegration performance decreases.

Abstract:To address the problems of low computational efficiency and difficulties in multi-objective optimization during the inversion of constitutive parameters of the Duncan E-B model for gravel pile composite foundations, an intelligent inversion method integrating a radial basis function (RBF) surrogate model and a multi-objective rime (MORIME) optimization algorithm was proposed. In this method, Latin hypercube sampling was adopted to construct the parameter sample set; an RBF surrogate model was established to replace finite element computations; the MORIME optimization algorithm with a local exploitation strategy was introduced to achieve rapid inversion. A single-pile static load test at a pumped storage power station was taken as an example to verify the parameter inversion of the Duncan E-B model for the gravel pile and the surrounding soil. The results show that the inversion method has high inversion accuracy; the coefficients of determination of curves at different monitoring points obtained by substituting the optimal inverted parameters back into the finite element computations are all above 0.99; the dual-mode local exploitation strategy can significantly optimize key objectives and reduce the number of iterations for convergence. The SHAP sensitivity analysis further shows that the surrounding soil parameters K and K b have a significant influence on the pile-top displacement and the soil stress near the pile top.

Abstract:To investigate the influence of general scour on the bearing performance of the anchorage of Xiamen Liuwudian Navigation Channel Bridge, scaled model tests and finite element numerical simulations were conducted. Homogeneous quartz sand was adopted to simulate the soil surrounding the anchorage. Under working conditions with different scour depths, scaled model tests including unidirectional loading, unidirectional single-stage loading-unloading and unidirectional step-increasing cyclic loading-unloading were performed to obtain the load-displacement curves of the anchorage. The finite element modeling method was validated against the test data, and a three-dimensional numerical model of the prototype anchorage, considering actual soil stratification and replacement reinforcement, was established. The scaled model test results reveal that the ultimate bearing capacity of the anchorage decreases by approximately 14.3% with each additional scour depth of 0.33 H ( H denotes the embedded depth of the anchorage), and different loading modes exert slight effects on the ultimate bearing capacity. Numerical simulation results indicate that at the prototype site, the ultimate bearing capacity declines at a rate of about 10.3% when the scour depth increases stepwise by 0.2 H . Although slight numerical differences exist between simulation and test results, their overall variation trends are consistent. As scour intensifies, the failure mode of the anchorage gradually transitions from overturning-dominated to global sliding. Among the constitutive parameters of surrounding soil, the internal friction angle exerts the most significant influence on the ultimate bearing capacity, followed by cohesion, whereas the elastic modulus has a relatively minor effect.

Abstract:In view of the problem of the seepage behavior of fluids in low-permeability media, such as the lining and grouting zone of subsea tunnels, may deviate from Darcy seepage, the Hansbo nonlinear seepage model was employed to describe the seepage behavior within the lining and grouting zone. Analytical solutions for the nonlinear seepage field of a subsea tunnel under dynamic water levels were derived using the complex variable method and the method of images, respectively. Furthermore, an analytical model applicable to different support conditions, such as lining, grouting zone, or no support, was established. The accuracy of the analytical solutions was verified through comparisons with numerical simulation results, other theoretical analytical solutions, and laboratory model test results, and the effects of factors such as the nonlinear parameter, dynamic water levels, and the ratio of grouting zone thickness to lining thickness on the seepage field were analyzed. The results show that as the nonlinear parameter increases, the tunnel water inflow decreases, and the grouting zone sustains greater pore water pressure, thereby reducing the pore water pressure sustained by the lining; under the action of periodic dynamic water levels, both the tunnel water inflow and pore water pressure vary periodically; the grouting zone can attenuate the influence of dynamic water levels on the lining, and as the ratio of grouting zone thickness to lining thickness increases, the tunnel water inflow further decreases and the pore water pressure sustained by the grouting zone increases, thereby reducing the pore water pressure sustained by the lining.

Abstract:To achieve accurate prediction and effective control of PM2.5 concentration in dry bulk port areas, a multivariate hybrid prediction model based on support vector regression (SVR) integrating XGBoost feature selection and particle swarm optimization (PSO) intelligent optimization was proposed, namely XGBoost-PSO-SVR model. The differences in PM2.5 formation mechanisms and diffusion processes under meteorological conditions in ports were fully considered by the model. XGBoost was employed to quantify the key influencing factors, and the SVR optimized by PSO was utilized for accurate prediction. The case verification results of typical port areas in the Nanjing section of the Yangtze River show that the XGBoost-PSO-SVR model has strong robustness in the high-concentration range; compared with the univariate STL-ARIMA-SVR model, its MAE, MAPE, and RMSE decrease by 15.6%, 14.3%, and 24.9%, respectively; compared with the conventional multivariate SVR model, they decrease by 52.5%, 57.1%, and 37.7%, respectively. The XGBoost-PSO-SVR model has good prediction performance and can provide decision support for intelligent dust suppression in dry bulk port areas.

Abstract:To quantitatively evaluate the wave attenuation performance of oyster shell bags and further investigate the influence of reef roughness parameters on wave energy dissipation, a numerical model of oyster shell bags was established based on OpenFOAM. By changing parameters including relative reef height, relative reef crest width, incident wave steepness, and roughness, the wave attenuation characteristics of oyster reefs under regular waves were analyzed. The results show that the transmission coefficient decreases with the increase in each parameter, among which the relative reef height has the most significant influence. When the relative reef height is 1.0, the influence of roughness on wave attenuation is mainly reflected in the low-value range; when the roughness increases from 0 to 2.5, the transmission coefficient decreases by 23.6%, but as the roughness continues to increase, the transmission coefficient remains almost unchanged. Based on the analytical results, a prediction formula for the transmission coefficient was fitted using regression analysis, which provides a basis for evaluating the wave attenuation capacity of oyster shell bags.

Abstract:To optimize the composition of grout materials for offshore wind suction bucket foundations and verify the recyclability of suction buckets after construction with different grouts, 18 fluidity tests, 21 unconfined compressive strength tests and 6 suction bucket recovery tests were carried out to investigate the influence mechanisms of water-solid ratio (0.75, 1, 1.1, 2.5) and bentonite content (0%, 20%, 40%, 60%, 80%, 100%) on the fluidity and compressive strength of grout materials, as well as the recyclability of suction buckets in clay with different grouts. The results show that at a fixed water-solid ratio, the fluidity and compressive strength of grout materials decrease significantly with the increase of bentonite content, and the grout basically loses fluidity when the bentonite content is no less than 60%. At a fixed bentonite content, fluidity increases with rising water-solid ratio (210-290 mm for 20% bentonite content), while compressive strength decreases accordingly. Suction buckets with grouts containing 60% and 100% bentonite can be successfully recovered by positive-pressure water injection inside the bucket. In contrast, grouts with 0% and 20% bentonite content fully solidify and completely block the water injection port, leading to recovery failure. It is recommended that the initial fluidity of grout be controlled within 250-300 mm and the fluidity after 30 min be no less than 200 mm. A bentonite content of 60% is preferred, and the water-solid ratio shall be increased until the required fluidity range is satisfied to balance the requirements of constructability, structural strength and recyclability.

Abstract:To improve the on-site stability of navigational buoys for submarine cable routes under extreme environments and optimize their motion response and mooring tension, this study takes a 2.4 m-diameter all-steel deep-water buoy as the research object, and conducts a comparative analysis of the motion responses of the buoy and mooring tension under single-point mooring (SPM) and three-point mooring (TPM) systems. Under the premise of ensuring consistent total weight and initial pretension of the mooring chains, SPM and TPM systems were designed. A time-domain coupled dynamic response calculation model for the buoy and mooring systems was established, and the buoy’s motion responses and mooring tensions were compared and analyzed under the action of different regular wave heights/periods and the extreme typhoon condition of “Rammasun”. The results show that: the motion responses amplitudes of the buoy and mooring tension are mainly affected by wave height, while influence of wave period is weak; compared with SPM system, TPM system can effectively reduce the amplitude of the buoy’s motion response and the mooring tension. TPM system layout method proposed in this study can provide a reference for the design improvement of the currently commonly used SPM buoys.

Abstract:In view of the frequent uncertain voltage fluctuations and even limit violations at buses caused by the high penetration rate of renewable energy generation and emerging loads, an analytical calculation method for voltage fluctuation intervals under uncertain power disturbances was proposed. This method employed an interval model and a non-parametric approach to characterize uncertainties and could rapidly obtain the voltage fluctuation intervals of each bus through analytical calculations using only the disturbance intervals of bus injected power. On this basis, an optimization model aimed at minimizing the adjustment cost was established to determine the power adjustment measures for mitigating voltage fluctuations, and a voltage fluctuation mitigation strategy utilizing adjustable loads during voltage limit violations was subsequently proposed to restore voltages to the allowable range. Simulation results on the IEEE 39-bus system show that the errors of the upper and lower bounds of the voltage fluctuation intervals obtained by the proposed analytical calculation method are around 1%. Furthermore, the proposed over-limit mitigation strategy is highly effective.