Second-stage Model Research Articles

Family resources, resilience beliefs, and parental adaptation: A moderated mediation analysis.

Despite the extensive body of evidence documenting how pandemic-related stressors (e.g., disruptions in daily routine) impact individuals' mental health, research examining family mechanisms through which stressors impact parental stress remains insufficient. The present study aims to address this gap by exploring a moderated mediation model that predicts parental stress resulting from the accumulation of pandemic-related stressors. Specifically, we hypothesized a second-stage moderated mediation model in which family resilience beliefs moderated the second-stage indirect paths through family relationships and marital satisfaction, resulting in conditional indirect effects. Study data were collected from American parents (n = 1386). There was no evidence that family relationships and marital satisfaction mediated the association between stressor pile-up and parent stress. In addition, family resilience beliefs did not significantly impact how marital satisfaction or family relationships affect parental stress. However, marital satisfaction mediated the relationship between stressor pile-up and parental stress across all levels of family resilience beliefs. The findings of this study carry significant implications for post-pandemic family interventions, suggesting the incorporation of resilience belief training and stress management strategies to improve intrafamilial communication.

A scalable two-stage Bayesian approach accounting for exposure measurement error in environmental epidemiology.

Accounting for exposure measurement errors has been recognized as a crucial problem in environmental epidemiology for over two decades. Bayesian hierarchical models offer a coherent probabilistic framework for evaluating associations between environmental exposures and health effects, which take into account exposure measurement errors introduced by uncertainty in the estimated exposure as well as spatial misalignment between the exposure and health outcome data. While two-stage Bayesian analyses are often regarded as a good alternative to fully Bayesian analyses when joint estimation is not feasible, there has been minimal research on how to properly propagate uncertainty from the first-stage exposure model to the second-stage health model, especially in the case of a large number of participant locations along with spatially correlated exposures. We propose a scalable two-stage Bayesian approach, called a sparse multivariate normal (sparse MVN) prior approach, based on the Vecchia approximation for assessing associations between exposure and health outcomes in environmental epidemiology. We compare its performance with existing approaches through simulation. Our sparse MVN prior approach shows comparable performance with the fully Bayesian approach, which is a gold standard but is impossible to implement in some cases. We investigate the association between source-specific exposures and pollutant (nitrogen dioxide [NO2])-specific exposures and birth weight of full-term infants born in 2012 in Harris County, Texas, using several approaches, including the newly developed method.

Degrade for upgrade: Learning degradation representations for real-world low-light image enhancement

Most existing low-light image enhancement approaches predominantly focus on directly modeling the mapping between low-light images and normal-light images, but models trained on the single fixed data set often fail to achieve satisfactory results in complex real-world scenes. To address the limitations posed by limited data, this paper proposes a joint framework to learn spatially adaptive degradation and enhancement representations of bright-to-dark images and dark-to-bright images. Firstly, we design an illumination degradation model based on cycle consistent loss to learn how to degrade normal-light images into low-light reference images. The degradation model can synthesize a large number of normal/degraded-light pairs, which is beneficial for the training of the second-stage enhancement model. Subsequently, leveraging the self-luminance information of images, we construct a self-attention-based light enhancement model. The enhancement model is trained on mixed data, which combines both real normal/low-light image pairs and synthetic normal/degraded-light image pairs. In this way, the enhancement model can learn more features from a diverse set of images, enhancing its robustness. Extensive experiments on low-light image enhancement, low-light object detection, and nighttime image segmentation have demonstrated that our proposed method outperforms existing supervised and unsupervised methods across a variety of real-world scenes.

Application of a novel nested ensemble algorithm in predicting motor function recovery in patients with traumatic cervical spinal cord injury

Traumatic cervical spinal cord injury (TCSCI) often causes varying degrees of motor dysfunction, common assessed by the International Standards for Neurological Classification of Spinal Cord Injury (ISNCSCI), in association with the American Spinal Injury Association (ASIA) Impairment Scale. Accurate prediction of motor function recovery is extremely important for formulating effective diagnosis, therapeutic and rehabilitation programs. The aim of this study is to investigate the validity of a novel nested ensemble algorithm that uses the very early ASIA motor score (AMS) of ISNCSCI examination to predict motor function recovery 6 months after injury in TCSCI patients. This retrospective study included complete data of 315 TCSCI patients. The dataset consisting of the first AMS at ≤ 24 h post-injury and follow-up AMS at 6 months post-injury was divided into a training set (80%) and a test set (20%). The nested ensemble algorithm was established in a two-stage manner. Support Vector Classification (SVC), Adaboost, Weak-learner and Dummy were used in the first stage, and Adaboost was selected as second-stage model. The prediction results of the first stage models were uploaded into second-stage model to obtain the final prediction results. The model performance was evaluated using precision, recall, accuracy, F1 score, and confusion matrix. The nested ensemble algorithm was applied to predict motor function recovery of TCSCI, achieving an accuracy of 80.6%, a F1 score of 80.6%, and balancing sensitivity and specificity. The confusion matrix showed few false-negative rate, which has crucial practical implications for prognostic prediction of TCSCI. This novel nested ensemble algorithm, simply based on very early AMS, provides a useful tool for predicting motor function recovery 6 months after TCSCI, which is graded in gradients that progressively improve the accuracy and reliability of the prediction, demonstrating a strong potential of ensemble learning to personalize and optimize the rehabilitation and care of TCSCI patients.

Two-stage evolutionary game model on complex networks for emergency logistics based on blockchain platform

Enhancing the efficiency of emergency logistics is essential to reinforce the response capacity to emergencies. It requires collaborative efforts from both the emergency management departments and logistics enterprises. However, the capability for information docking between these organizations substantially influences the efficiency of emergency materials transportation. Blockchain, as an emerging information technology, has the potential to substantially enhance the efficiency and security of information docking through its unique characteristics. Additionally, logistics enterprises share information and resources based on the blockchain platform, aiming to ensure fast, efficient, and reliable collaborative transportation of emergency materials to impacted regions. Therefore, we propose a two-stage evolutionary game analysis of emergency materials collaborative transportation based on this platform. First, we develop a first-stage evolutionary game model to analyze the challenges associated with building a blockchain platform among emergency management departments and logistics enterprises. Subsequently, a second-stage evolutionary game model is devised to bolster the willingness of logistics enterprises based on this platform for collaborative transportation of emergency materials. Third, to validate the theoretical findings of the two-stage game model, two scale-free networks are employed for numerical simulations. As those networks evolve, the edges among nodes and the strategy choices of nodes in those networks likewise change. Numerical simulations are performed based on those networks to scrutinize the sensitivity of factors influencing strategic choice among game stakeholders. Ultimately, certain management insights gleaned from the findings can assist emergency management departments and logistics enterprises in making more informed decisions in the future.

Summary-Sentence Level Hierarchical Supervision for Re-Ranking Model of Two-Stage Abstractive Summarization Framework

Fine-tuning a pre-trained sequence-to-sequence-based language model has significantly advanced the field of abstractive summarization. However, the early models of abstractive summarization were limited by the gap between training and inference, and they did not fully utilize the potential of the language model. Recent studies have introduced a two-stage framework that allows the second-stage model to re-rank the candidate summary generated by the first-stage model, to resolve these limitations. In this study, we point out that the supervision method performed in the existing re-ranking model of the two-stage abstractive summarization framework cannot learn detailed and complex information of the data. In addition, we present the problem of positional bias in the existing encoder–decoder-based re-ranking model. To address these two limitations, this study proposes a hierarchical supervision method that jointly performs summary and sentence-level supervision. For sentence-level supervision, we designed two sentence-level loss functions: intra- and inter-intra-sentence ranking losses. Compared to the existing abstractive summarization model, the proposed method exhibited a performance improvement for both the CNN/DM and XSum datasets. The proposed model outperformed the baseline model under a few-shot setting.

Detecting Eating Episodes From Wrist Motion Using Daily Pattern Analysis.

This paper presents new methods to detect eating from wrist motion. Our main novelty is that we analyze a full day of wrist motion data as a single sample so that the detection of eating occurrences can benefit from diurnal context. We develop a two-stage framework to facilitate a feasible full-day analysis. The first-stage model calculates local probabilities of eating P(Ew) within windows of data, and the second-stage model calculates enhanced probabilities of eating P(Ed) by treating all P(Ew) within a single day as one sample. The framework also incorporates an augmentation technique, which involves the iterative retraining of the first-stage model. This allows us to generate a sufficient number of day-length samples from datasets of limited size. We test our methods on the publicly available Clemson All-Day (CAD) dataset and FreeFIC dataset, and find that the inclusion of day-length analysis substantially improves accuracy in detecting eating episodes. We also benchmark our results against several state-of-the-art methods. Our approach achieved an eating episode true positive rate (TPR) of 89% with 1.4 false positives per true positive (FP/TP), and a time weighted accuracy of 84%, which are the highest accuracies reported on the CAD dataset. Our results show that the daily pattern classifier substantially improves meal detections and in particular reduces transient false detections that tend to occur when relying on shorter windows to look for individual ingestion or consumption events.

Presegmenter Cascaded Framework for Mammogram Mass Segmentation.

Accurate segmentation of breast masses in mammogram images is essential for early cancer diagnosis and treatment planning. Several deep learning (DL) models have been proposed for whole mammogram segmentation and mass patch/crop segmentation. However, current DL models for breast mammogram mass segmentation face several limitations, including false positives (FPs), false negatives (FNs), and challenges with the end-to-end approach. This paper presents a novel two-stage end-to-end cascaded breast mass segmentation framework that incorporates a saliency map of potential mass regions to guide the DL models for breast mass segmentation. The first-stage segmentation model of the cascade framework is used to generate a saliency map to establish a coarse region of interest (ROI), effectively narrowing the focus to probable mass regions. The proposed presegmenter attention (PSA) blocks are introduced in the second-stage segmentation model to enable dynamic adaptation to the most informative regions within the mammogram images based on the generated saliency map. Comparative analysis of the Attention U-net model with and without the cascade framework is provided in terms of dice scores, precision, recall, FP rates (FPRs), and FN outcomes. Experimental results consistently demonstrate enhanced breast mass segmentation performance by the proposed cascade framework across all three datasets: INbreast, CSAW-S, and DMID. The cascade framework shows superior segmentation performance by improving the dice score by about 6% for the INbreast dataset, 3% for the CSAW-S dataset, and 2% for the DMID dataset. Similarly, the FN outcomes were reduced by 10% for the INbreast dataset, 19% for the CSAW-S dataset, and 4% for the DMID dataset. Moreover, the proposed cascade framework's performance is validated with varying state-of-the-art segmentation models such as DeepLabV3+ and Swin transformer U-net. The presegmenter cascade framework has the potential to improve segmentation performance and mitigate FNs when integrated with any medical image segmentation framework, irrespective of the choice of the model.

A Cucumber Leaf Disease Severity Grading Method in Natural Environment Based on the Fusion of TRNet and U-Net

Disease severity grading is the primary decision-making basis for the amount of pesticide usage in vegetable disease prevention and control. Based on deep learning, this paper proposed an integrated framework, which automatically segments the target leaf and disease spots in cucumber images using different semantic segmentation networks and then calculates the area of disease spots and the target leaf for disease severity grading. Two independent datasets of leaves and lesions were constructed, which served as the training set for the first-stage diseased leaf segmentation and the second-stage lesion segmentation models. The leaf dataset contains 1140 images, and the lesion data set contains 405 images. The proposed TRNet was composed of a convolutional network and a Transformer network and achieved an accuracy of 93.94% by fusing local features and global features for leaf segmentation. In the second stage, U-Net (Resnet50 as the feature network) was used for lesion segmentation, and a Dice coefficient of 68.14% was obtained. After integrating TRNet and U-Net, a Dice coefficient of 68.83% was obtained. Overall, the two-stage segmentation network achieved an average accuracy of 94.49% and 94.43% in the severity grading of cucumber downy mildew and cucumber anthracnose, respectively. Compared with DUNet and BLSNet, the average accuracy of TUNet in cucumber downy mildew and cucumber anthracnose severity classification increased by 4.71% and 8.08%, respectively. The proposed model showed a strong capability in segmenting cucumber leaves and disease spots at the pixel level, providing a feasible method for evaluating the severity of cucumber downy mildew and anthracnose.

Joint operation of mobile battery, power system, and transportation system for improving the renewable energy penetration rate

Future energy system will feature in a high-share of renewable energies (REs), which poses huge challenges to obtain full utilization of renewable power generation. To solve the problem, this paper presents a joint-operation two-stage mixed integer linear programming model to coordinate the power system and train transportation system by optimizing the logistics of mobile batteries and real-time charge/discharge in cities. The full/empty batteries are transported through the train transportation system between the load side and the renewable energy station, which improves renewable energy penetration, economics, and mobilities. The first-stage model deals with the preliminary logistic optimization of batteries including routes, time and capacities of transportation, and the second-stage model optimizes real-time schedule of charge/discharge of batteries. The aim of the proposed model is to minimize the transportation cost, maximize the utilization rate of renewable energy in an energy system and smooth the daily load curve. The proposed model considers technical constraints such as railway transportation capacity, load demand satisfaction and renewable energy consumption in the power system. The optimal logistics plan and real-time charging and discharging plan can be obtained for both full and empty battery transportation. The validity of the method is verified with real data from Northeast China and Northern China, including railway routes, renewable energy output, and load profiles. The results show that the renewable energy penetration rate increases from 84.4% to 95.3% in Northeast China and from 42.7% to 78.2% in Northern China under the 2050 scenario with the proposed method. The peak-to-valley difference in the daily load curve decreases by 84% and 100% in Northeast China and Northern China, respectively. Meanwhile, the case study shows that the costs of battery transportation decrease from 0.398 CNY/kWh and 0.377 CNY/kWh to 0.252 CNY/kWh and 0.254 CNY/kWh when energy density of battery increases from 0.170 kWh/kg to 0.250 kWh/kg. This indicates that mobile energy storage has great economics. Moreover, renewable energy penetration rate is increased and peak-to-valley difference of daily load curve is decreased with no additional transmission lines.

A two-stage stochastic programming approach for dynamic OD estimation using LBSN data

Estimating origin–destination (OD) demand is essential for urban transport management and traffic control systems. With the ubiquity of smartphones, location based social networks (LBSN) data has emerged as a new rich data source with broad urban spatial and temporal coverage highly suitable for OD estimation. Its nature of confirmed trip purpose (activity) and activity chain host makes it more advantageous than other data (e.g., household travel surveys and traffic network detection). On the other hand, LBSN data is a more direct and accurate representation of demand patterns and can remove the significant burden of developing traffic models and estimating simulation-based objective functions. However, thus far, most LBSN-based estimation models only focus on static (day-level) OD estimation, making less use of those characteristics. To this end, this paper establishes a two-stage stochastic programming (TSSP) framework integrating the activity chains to model activity-level dynamic mobility flows using LBSN data. The first-stage model aims to minimize the errors introduced by the inter-zone OD flows alongside the expected errors of the check-in patterns. The second-stage model attempts to minimize the errors produced by the considered check-in pattern scenarios. Markov chain Monte Carlo (MCMC) sampling is used to generate plausible check-in scenarios. A generalized Benders decomposition (GBD) algorithm is presented to solve the two-stage stochastic programming model. We conduct the experiments on the case study of Tokyo, Japan, under the employment of the generalized least squares (GLS) estimator. The results show that algorithm convergence can be guaranteed within several iterations. The approach can provide satisfactory estimations of check-in patterns, zonal production and attraction, and OD flows. Furthermore, multiple objective function states are tested for evaluating the completeness of the proposed framework and exploring its potential for simplification and extension. Incorporating specific penalty terms into the objective function also provides a way to verify the reliability of the two-stage structure and validate the effectiveness of the model. Finally, we discuss the model enhancement from the perspectives of online OD estimation by integrating with LBSN simulations, network-wide OD extrapolation using appropriate scaling methods, and removing the user-side data requirement by leveraging activity chain modeling. The proposed framework provides a novel and effective approach to OD demand estimation using LBSN data.

A DYNAMIC SPATIAL FILTERING APPROACH TO MITIGATE UNDERESTIMATION BIAS IN FIELD CALIBRATED LOW-COST SENSOR AIR POLLUTION DATA.

Low-cost air pollution sensors, offering hyper-local characterization of pollutant concentrations, are becoming increasingly prevalent in environmental and public health research. However, low-cost air pollution data can be noisy, biased by environmental conditions, and usually need to be field-calibrated by collocating low-cost sensors with reference-grade instruments. We show, theoretically and empirically, that the common procedure of regression-based calibration using collocated data systematically underestimates high air pollution concentrations, which are critical to diagnose from a health perspective. Current calibration practices also often fail to utilize the spatial correlation in pollutant concentrations. We propose a novel spatial filtering approach to collocation-based calibration of low-cost networks that mitigates the underestimation issue by using an inverse regression. The inverse-regression also allows for incorporating spatial correlations by a second-stage model for the true pollutant concentrations using a conditional Gaussian Process. Our approach works with one or more collocated sites in the network and is dynamic, leveraging spatial correlation with the latest available reference data. Through extensive simulations, we demonstrate how the spatial filtering substantially improves estimation of pollutant concentrations, and measures peak concentrations with greater accuracy. We apply the methodology for calibration of a low-cost PM2.5 network in Baltimore, Maryland, and diagnose air pollution peaks that are missed by the regression-calibration.

A two-stage distributed optimization method for home energy management systems via multi-modal data-driven algorithm

The home energy management system (HEMS), which utilizes multi-modal data from multiple sensors to generate the knowledge about decision making, is essential to the optimization of home energy management efficiency. Load scheduling based on HEMS can improve the utilization efficiency of multi-modal data and derived knowledge, achieve power supply-demand balance, and reduce users’ electricity costs. This paper proposes a distributed load optimization scheduling method for the load scheduling problem in HEMS based on multi-modal data-driven algorithm. Additionally, a two-stage data-driven optimization method is proposed, including a first-stage optimization model based on minimizing electricity costs and a second-stage optimization model based on minimizing system load fluctuations. In the first stage, cost self-optimization is performed based on energy storage devices. In the second stage, a load optimization instruction is issued by the control center, and each user optimizes the load fluctuations based on the system load data. Compared to centralized control methods, this approach reduces the computational overhead of the control center. Finally, simulation experiments based on load scheduling in the HEMS are conducted. The results of the first optimization stage show that when the battery capacity integrated into the system increases from 3.68 kWh to 6.68 kWh, user costs can be reduced from 57.572 cents to 42.064 cents. It is not only evident that the proposed method can effectively save users on electricity costs, but the introduction of larger capacity batteries also lowers these costs. The second stage of load fluctuation optimization results show that the proposed method can effectively optimize the usage data of a group of users and decrease the absolute peak-valley difference by 8.8%.

Managing Water-Energy-Carbon Nexus for Urban Areas With Ambiguous Moment Information

The rapid growth of electric load fuels urbanization but creates unsettling environmental challenges. In that regard, the energy system is a crucial part of consuming water and emitting greenhouse gases. To support reliable and economical energy system operations, with reduced water waste and carbon emissions, we design a viable co-optimization of water-energy-carbon nexus for an integrated energy system by adequately modelling essential interdependencies of power, gas, and water systems. A two-stage distributionally robust optimization method is proposed: the first-stage model minimizes the day-ahead reserve capacity scheduling for the next day, and the second-stage model enables real-time dispatch by considering the variability in renewable power generation. The carbon emissions by power generation and distribution are incorporated in both stages to ensure low-carbon operations. We use a two-stage moment-based distributionally robust approach to capture and represent the uncertainties in renewable generation. Instead of assuming a deterministic distribution, we characterize an ambiguity set with mean vectors and covariance matrices, which produces a family set of distributions. We conduct case studies using a modified IEEE 33-bus power system that includes and links a 20-node gas system and a 10-node water system. The comparative results indicate that the proposed co-optimization of water-energy-carbon nexus is superior than several benchmarks. By considering the close interdependencies of water, energy, and carbon, we create an optimal resource allocation scheme, which is capable of minimizing operation costs, lessening carbon emissions, and reducing water waste. The current research enables effective operation schemes for urban energy systems, illustrates a viable way to curb local environmental emissions, and increases water usage efficiency in the water-energy-carbon nexus.

External Validation of Second-Stage Vaginal Delivery Prediction Model [ID: 1377356

INTRODUCTION: We sought to externally validate Gimovsky et al.’s prediction model for spontaneous vaginal delivery (SVD) in the second stage (https://www.pushprescriber.com [PUSH MODEL]) prior to using it for a quality improvement (QI) intervention at our hospital. METHODS: This was a retrospective cohort of 2,296 birthing persons delivering at a single hospital over 1 year. Inclusion criteria were similar to the PUSH MODEL: nulliparous, term, without planned cesarean, singleton, vertex, nonanomalous, epidural anesthesia. We calculated the predicted probability of SVD at every hour from the PUSH MODEL to generate receiver–operator curves and analyzed factors associated with second stage duration in our cohort. RESULTS: Overall, 1,735 (77%) delivered by SVD, similar to 74% in the PUSH MODEL. Head position had the strongest association with SVD (83% OA versus 39% OP, P<.01). The area under the curve from the PUSH MODEL at the start of the second stage was 0.64 (95% CI 0.62–0.77), as compared to 0.73 in the original population. The model had similar performance at hours 1 (n=1,513), 2 (n=917), 3 (n=522), and 4 or more (n=255). Using a cutoff of 77% (baseline rate of SVD in our population), those who “Screen Positive” at the start of the second stage had an 78.5% rate of SVD as compared to 39.3% for those who “Screen Negative” (P<.01). CONCLUSION: The PUSH MODEL performed well on external validation; we similarly found that head position and second-stage duration were strongly associated with the probability of SVD in our cohort, supporting incorporation of this tool in QI work at our hospital.

Enabling edge computing ability in view-independent vehicle model recognition

Vehicle model recognition (VMR) benefits the parking, surveillance, and tolling system by automatically identifying the exact make and model of the passing vehicles. Edge computing technology enables the roadside facilities and mobile cameras to achcieve VMR in real-time. Current work generally relies on a specific view of the vehicle or requires huge calculation capability to deploy the end-to-end deep learning network. This paper proposes a lightweight two-stage identification method based on object detection and image retrieval techniques, which empowers us the ability of recognizing the vehicle model from an arbitrary view. The first-stage model estimates the vehicle posture using object detection and similarity matching, which is cost-efficient and suitable to be programmed in the edge computing devices; the second-stage model retrieves the vehicle’s label from the dataset based on gradient boosting decision tree (GBDT) algorithm and VGGNet, which is flexible to the changing dataset. More than 8 000 vehicle images are labeled with their components’ information, such as headlights, windows, wheels, and logos. The YOLO network is employed to detect and localize the typical components of a vehicle. The vehicle postures are estimated by the spatial relationship between different segmented components. Due to the variety of the perspectives, a 7-dimensional vector is defined to represent the relative posture of the vehicle and screen out the images with a similar photographic perspective. Two algorithms are used to extract the features from each image patch: (1) the scale invariant feature transform (SIFT) combined with the bag-of-features (BoF) and (2) pre-trained deep neural network. The GBDT is applied to evaluate the weight of each component regarding its impact on VMR. The descriptors of each component are then aggregated to retrieve the best matching image from the database. The results showed its advantages in terms of accuracy (89.2%) and efficiency, demonstrating the vast potential of applying this method to large-scale vehicle model recognition.

Municipal Performance in a Network Structure of Financial Operations and Service Provision in the New South Wales Local Government

Municipal Performance in a Network Structure of Financial Operations and Service Provision in the New South Wales Local Government

Health resource allocation method at cordon sanitaire for pandemic control and prevention

<p style='text-indent:20px;'>The outbreak of COVID-19 and its variants has profoundly disrupted our normal life. Many local authorities enforced cordon sanitaires for the protection of sensitive areas. Travelers can only cross the cordon after being tested. This paper aims to propose a method to determine the optimal deployment of cordon sanitaires in terms of minimum queueing delay time with available health testing resources. A sequential two-stage model is formulated where the first-stage model describes transportation system equilibrium to predict traffic flows. The second-stage model, a nonlinear integer programming, optimizes health resource allocation along the cordon sanitaire. This optimization aims to minimize the system's total delay time among all entry gates. Note that a stochastic queueing model is used to represent the queueing phenomenon at each entry link. A heuristic algorithm is designed to solve the proposed two-stage model where the Method of Successive Averages (MSA) is adopted for the first-stage model, and a genetic algorithm (GA) with elite strategy is adopted for the second-stage model. An experimental study is conducted to demonstrate the effectiveness of the proposed method and algorithm. The results show that these methods can find a good heuristic solution, and it is not cost-effective for authorities to keep adding health resources after reaching a certain limit. These methods are useful for policymakers to determine the optimal deployment of health resources at cordon sanitaires for pandemic control and prevention.</p>

Multi-period Two-stage Robust Optimization of Radial Distribution System with Cables Considering Time-of-use Price

In the existing multi-period robust optimization methods for the optimal power flow in radial distribution systems, the capability of distributed generators (DGs) to regulate the reactive power, the operation costs of the regulation equipment, and the current of the shunt capacitor of the cables are not considered. In this paper, a multi-period two-stage robust scheduling strategy that aims to minimize the total cost of the power supply is developed. This strategy considers the time-of-use price, the capability of the DGs to regulate the active and reactive power, the action costs of the regulation equipment, and the current of the shunt capacitors of the cables in a radial distribution system. Furthermore, the numbers of variables and constraints in the first-stage model remain constant during the iteration to enhance the computation efficiency. To solve the second-stage model, only the model of each period needs to be solved. Then, their objective values are accumulated, revealing that the computation rate using the proposed method is much higher than that of existing methods. The effectiveness of the proposed method is validated by actual 4-bus, IEEE 33-bus, and PG 69-bus distribution systems.

A robust model for emergency supplies prepositioning and transportation considering road disruptions

Proper prepositioning of emergency supplies can dramatically improve the efficiency of emergency response work. However, the uncertainties of emergency demands and road conditions bring difficulties to the prepositioning of emergency supplies. This paper proposes a two-stage robust model to locate emergency supply points and preposition the corresponding storage amount of emergency supplies, in which we presented two budget sets to describe the uncertainties of demands and road conditions, respectively. The innovative use of variables in the model to limit road capacities addresses the representation of different road interruption scenarios. We proposed an algorithm based on Benders decomposition by transforming the second-stage model into a binary linear programming model. Computational experiments based on the Sioux Falls network demonstrate the validity of the model and algorithm. We conducted sensitivity analyses for some important parameters in the model, such as two uncertainty control parameters, unit transportation cost, budget for the construction of emergency supply points, etc. We find that the uncertainty of road disruptions has a greater impact on the model than the uncertainty of demands. In addition, when the control parameter of the road disruptions exceeds a certain threshold, its influence on the model remains essentially constant.