A Cost-Effective Earthquake Disaster Assessment Model for Power Systems Based on Nighttime Light Information

Abstract

The power system is one of the most important urban lifeline engineering systems. Identifying the damage to the power system is an important task in earthquake disaster assessments. Considering the importance of timeliness and accessibility, a hyperparameter optimization model is proposed to address the assessment of disaster losses in power systems on earthquakes. The power system vulnerability on earthquakes, PSVE, is assessed by the hyperparameter optimization model based on nighttime light information. Through the utilization of the computational resources provided by Google Earth Engine, the accuracy of the baseline model has been significantly improved to 87.9%; meanwhile, the cost-effectiveness in the evaluation process is maintained. The PSVE-based damage evaluation has the potential to aid in assessing earthquake damage to cities’ energy supply, power infrastructure, and lighting. Furthermore, the PSVE-based damage evaluation can provide valuable guidance for prioritizing and efficiently allocating resources for rapid repair and reconstruction efforts.

1. Introduction

The timely and accurate acquisition of disaster information is crucial for disaster emergency responses and decision-making assistance. Remote sensing technology can dynamically monitor and adapt to various harsh conditions, remaining unaffected by atmospheric conditions [1]. It offers a substantial amount of information, operates with high efficiency, and enables rapid and effective large-scale disaster monitoring and assessment. The electricity system and building infrastructure are often influenced by disasters, which can result in widespread power outages [2,3,4], and a noticeable reduction in nighttime light (NTL) intensity. Daytime imagery, used primarily for assessing surface structural failures, and NTL images are more dominant in capturing the dynamics of human activity and interruptions [5]. Specifically, NTL data are more suitable for distinguishing between damage and non-damage classes, while SAR textures features allow for us to better distinguish between different classes of damages at a block scale, such as low and heavy damage [6]. Nevertheless, the development of NTL sensors lags behind day-time sensors [7], and among the numerous studies of earthquake damage, the attenuation of light at night is often overlooked despite its significance. Larger light attenuation values indicate more severe lighting system damage. As a distinctive subset of remote sensing, NTL addresses this limitation by providing essential information during nighttime hours [8].

The research on power system performance can be roughly divided into the characterization based on network topological characteristics and the power flow analysis [9,10,11,12]. The former loses the connectivity [13] of part of the grid structure after the earthquake disaster, which will cause great errors in the evaluation. The latter are more rigorous but also more complex, involve higher-level tools, and the inputs they require are often not readily available.

Under this circumstance, as a secondary disaster of large-scale disasters, power damages cause severe outcomes and thus need to be monitored efficiently and without being costly [14]. Moreover, the correlation between city electricity power system and NTL has been verified in many studies [15,16,17] and used in disaster research [4,14,18]. For instance, NTL data have been used to model the earthquake effects on the local economies [19,20], access economic loss and recovery after natural disaster [21], detect real-time flood [22] and identify fires and power outages [23]. Therefore, predicting potential light attenuation values based on PSVE holds practical significance. Especially in disaster-stricken areas, the loss of communication with the external environment during an event underscores the significance of NTL as a proxy for human activity [24].

Therefore, we developed the PSVE model based on the following principles; the light radiation value in the same area is relatively stable and unchanged. However, the light significantly weakens when natural disasters occur. The change in the light radiation value results in a noticeable disparity in NTL levels before and after the disaster [8]. The disparity in NTL levels can serve as a quantitative measure of the impact of natural disasters on light intensity. The fundamental premise of this paper is that the calculated difference value in light brightness before and after earthquake, subject to reasonable constraints, predominantly reflects the impact of the disaster.

2. Data and Methods

2.1. Study Area and Data

This study focuses on Sichuan and Yunnan Provinces, located at the confluence of the Qinghai–Tibet Plateau and the Himalayan mountain range in the southwestern region of China. This region is well-known for its heightened seismic activity. Specifically, these provinces are situated within two seismic belts: the Dianxi Earthquake Belt in western Yunnan [25] and the Western Sichuan Earthquake Belt. Both of these regions have experienced significant seismic activity. In this study, the timeframe from 2013 to 2023 was selected and seismic events with magnitudes exceeding Ms. 4 were considered. Within this study area, the data on 639 seismic events were retrieved.

The utilized data in this study are described in

Table 1. Basic information of multisourced data.

Name	Format	Time	Resolution	Source
NPP-VIIRS	Image	2013/01/01—2023/10/31	500 m	NOAA
Earthquake catalogue	csv	2013/01/01—2023/10/31	None	USGS
Administrative division	shapefile	2022	1:4,000,000	National Basic Geographic Information Center
road	grid	2022	1000 m	Provincial official website
Human residential data	shp	2023	1 m	OpenStreetMap
LandScan dataset	TIFImage.Document	2013–2022	1000 m	Oak Ridge National Laboratory
Statistical yearbook of urban area	excel	2013–2022	None	Local government official website

. We utilized NPP-VIIRS night light imagery for our analysis. The earthquake catalogue delineates seismic events within the research domain, while administrative divisions define its geographic scope. The road network, human residential data, and LandScan dataset collectively serve as the data sources for calculating the impact factor. Specifically, they provide information on the road network, points of interest, and population values, respectively. Furthermore, the statistical yearbook of urban areas supplies city area measurements, crucial for establishing the night light threshold, as discussed in Section 2.2 (4).

2.1.1. Remote Sensing Data

NPP-VIIRS luminous remote sensing data are from the National Oceanic and Atmospheric Administration (NOAA) and compiled by Suomi NPP [26]. The data were detected by a visible infrared imaging radiation instrument.

The VIIRS/DNB presents a significant improvement over the former sensor (the DMSP/OLS), with daily images provided for free and higher spatial resolutions (740 m, instead of about 3 km for the DMSP). Additionally, there are some more important reasons for using it for this study. Firstly, it provides radiometrically calibrated data, which are sensitive to lower light levels and do not saturate in urban areas and areas with reduced overglow [27,28]. Secondly, the revisit time of NPP-VIIRS is short, so it is usually used in studying large regional scales. Thirdly, NPP-VIIRS DNB luminous remote sensing data can obtain daily data with continuity; these are suitable for the immediate assessment of disasters [4] because they can directly reflect the distribution and concentration of lights before and after disasters with high temporal resolution. Thus, they are utilized as the data source for this study.

2.1.2. Earthquake Event Data

The United States Geological Survey (USGS) provides real-time updated global earthquake catalog data, encompassing detailed information on seismic events such as occurrence time, location, magnitude, depth, and more. This dataset serves as a valuable resource from which the features for sample analysis can be directly extracted.

2.1.3. Other Data

The administrative division data used in this study are used to define the research scope, while the road data specifically refer to the three-level and higher road network data. In addition, high-precision human residential point data from OpenStreetMap, which include various categories such as town, village, hamlet, city, locality, suburb, and county, are utilized in this study. Furthermore, the LandScan dataset, provided by the Oak Ridge National Laboratory (ORNL), offers detailed information on population counts and density at a 30 arc-second (approximately 1000 m) resolution on a global scale.

2.2. Extraction of the Module Samples

The data were processed to obtain the sample; the entire extraction process is shown in Figure 1.

(1) The attributes of the earthquake event, such as depth, magnitude, location, and occurrence time from earthquake events, as well as the number of human residential points and population within the earthquake-affected zone, were obtained and used as sample attributes.

(2) The NTL image was processed to obtain the NTL value. Data noise reduction was necessary due to the influence of stray light, lightning, moonlight, and cloud cover. Firstly, cloud cover was removed using the cloud mask band of NPP-VIIRS. Next, a threshold method was used to eliminate background noise caused by factors such as fire, moonlight, and aurora. Any negative values were set to 0 to address noise-induced minima issues, followed by reassigning the maximum value to match the maximum value among the surrounding nine pixels.

(3) The distance from the earthquake epicenter to the urban area and roads were, respectively, calculated. The urban area here refers to a prefecture-level city within the earthquake’s impact zone (100 km buffer zone was made according to the coordinates of the earthquake epicenter), and the roads refer to all roads above the third level.

(4) We iteratively extracted the urban built-up area from the night light data and compared it with the urban built-up area documented in the statistical yearbook. The threshold was selected based on minimizing the disparity between the extracted area and the corresponding value from the statistical yearbook. This method was applied to analyze data from 2013 to 2022, selecting the minimum threshold from those identified. As shown in Figure 1, this is an example for the year 2021, where real-time images were used to ensure data validity during calculations.

(5) The reference comparison method was used to determine a threshold for each seismic event, through which the corresponding urban area was identified. The final urban NTL was determined using multi-temporal images. Specifically, the images from 3 days before and 3 days after each earthquake were selected based on the earthquake’s timing and the light image threshold. Then, the difference value was calculated with the average value.

At this stage, the difference results were further screened. If the result was negative (indicating an increase in light value due to the occurrence of disasters), the region was misidentified.

(6) The final sample was determined by finding the intersection between the region meeting the conditions in (4) and the buffer zone. These samples already included the properties of the light attenuation values calculated in (5).

2.3. Relevance Evaluation

As described above, after evaluating all the immediate information during the earthquake, the irrelevant variables and variables with low correlation were filtered out. Finally, seven variables were identified as predictors, and the GAM was utilized to confirm their high correlation.

(a)

Magnitude of the earthquake (mag);

(b)

Depth of the earthquake (depth);

(c)

The closest distance from the epicenter of the earthquake to the three-level road network (roadDistance);

(d)

The nearest distance from the epicenter of the earthquake to the surrounding cities (cityDistance);

(e)

The identification of whether the time of earthquake is day or night (DorN);

(f)

The population within the earthquake-affected zone (population);

(g)

The number of human residential points within the earthquake-affected zone (HR-point).

It was considered that there were multiple predictors, including both natural and anthropic, and the influence of complex environmental factors was taken into account; there may be a nonlinear relationship between them and the light attenuation value. Therefore, a Generalized Additive Model (GAM) was adopted instead of an R-squared test for correlation in this study.

The Generalized Additive Model (GAM) is a statistical model designed for modeling nonlinear relationships [29]. The fundamental concept involves modeling the relationships of predictor variables as a series of nonlinear functions, and estimating through smoothing methods. Its advantage lies in its flexibility to capture nonlinear relationships without the need for complex data transformations beforehand. Therefore, the GAM is employed to assess the selected sample features deliberately, and prevent the introduction of irrelevant variables.

In the GAM, the relationship can be accurately modeled by introducing nonlinear functions. There is a corresponding nonlinear function for each predictor variable, allowing for the adaptation of various complex models.

The basic model of GAM is:

$$g\left(E\left(Y\right)\right)={\beta }_0+f_1\left(X_1\right)+f_2\left(X_2\right)+···+f_k\left(X_k\right) ,$$

(1)

where $f_i\left(·\right)$ represents the nonlinear smoothing function associated with the predictor variable $X_i$.

Since the time of earthquake occurrence (day or night) is a Boolean variable, several other predictors are temporarily analyzed. The GAM is flexible to adapt to various data modes; hence, it is needless to normalize the data despite them having a variety of formats and scales. As shown in Figure 2, the relationship between each input feature and target variable is well identified.

It is obvious that there are varying degrees of partial dependence between each independent variable and response variable. However, the partial dependence value itself does not represent the actual output value. They are the predicted output changes, which result from changes in a single feature when all other features are held constant. As a result, these values are helpful for identifying the high-correlation variables. Other variables in the model are ignored here. For example, it is evident that earthquake magnitude (mag), earthquake depth (depth), population count (population), and distance to the city (cityDistance) have exhibited significant fluctuations, indicating a stronger correlation with the response variable. Additionally, other variables also showed fluctuations at different stages.

3. Modeling and Results

In this study, we employ NTL attenuation as the response variable, and the depth, magnitude, DorN, cityDistance, roadDistance, population and HP point as the predictor variables. The earthquake events considered for analysis span the years 2013 to 2022; following data processing and sample extraction, we obtained a dataset comprising 15,916 samples. The samples were classified utilizing machine learning techniques, with each model predicting the probability of an earthquake causing short-term irreparable damage to a city’s power system.

3.1. Development and Assessment of PSVE Model

In order to achieve optimal performance of the PSVE model, this study is conducted in two steps. Firstly, preliminary training on commonly used machine learning algorithms are performed to ensure the best fitting effect. Subsequently, we use grid search methods to find the best hyperparameters, and use 10-fold cross-validation to evaluate the performance of the model. Three machine learning models are selected: Decision Tree (DT), Random Forest (RF), K-Nearest Neighbors (KNN), and Multilayer Perceptron (MLP), which is a neural network model.

• DT is a hierarchical structure where each internal node represents an attribute-based judgment; in binary prediction tasks, the ultimate objective is to assign data points to one of two categories. The training of a decision tree specifically involves the segmentation decision of the tree. Figure 3 shows a simple decision tree model [30] consisting of a single binary target variable Y (0 or 1) and two continuous variables X1 and X2, ranging from 0 to 1. The main components of the decision tree model are nodes and branches, and the most important steps to build the model are splitting, stopping and pruning. The most important part is feature selection, which is related to the degree of “purity” of the resulting child nodes and is used to choose between different potential input variables. These features include entropy, Gini index, classification error, information gain, gain ratio, and two criteria.

Additionally, in this study, the Gini impurity method is employed for making decisions. Gini impurity is a measure of the impurity of datasets and is used in decision trees to evaluate the quality of segmentation. The lower the Gini impurity, the purer the category in the dataset. When constructing the decision tree, the goal of selecting segmentation points is to minimize the Gini impurity of the child nodes; this refers to making each child node contain a single class of data as much as possible.

$$Gini\left(T\right)=1-{{\displaystyle \sum }}_{i=1}^c{p}_i^2,$$

(2)

Here, $p_i$ represents the relative frequency of class i in dataset T, while c denotes the total number of classes.

2.

RF is an ensemble learning algorithm based on decision trees, aiming to enhance prediction accuracy by constructing multiple decision trees and aggregating their predictions [31]. As is shown in Figure 4, it achieves this by randomly selecting subsets of features from the dataset for training individual decision trees, which may yield different prediction results. For a new data point, each tree provides a prediction result. The final classification result in random forest is determined through a voting mechanism, where the category with the highest number of votes becomes the predicted result.

3.

KNN is an instance-based learning method that classifies instances by measuring distances between feature values. It does not involve explicit training but rather stores training datasets only. During prediction, given a new data point, KNN identifies the closest K points in the dataset; the classification decision is based on the distance measurement, and the formula is:

$$d\left(x,y\right)=\sqrt{{{\displaystyle \sum }}_{i=1}^n{\left(x_i-y_i\right)}^2},$$

(3)

4.

As shown in Figure 5, MLP refers to a feedforward artificial neural network comprising an input layer, one or more hidden layers, and an output layer; every layer consists of multiple neurons interconnected via weighted connections between adjacent layers [32]. Applying certain thresholds or activation functions at various nodes within MLP’s architecture determines its categorization assignment. MLP uses backpropagation and gradient descent to update the weights to implement the training process, which can be expressed as:

$${\omega }_{new}={\omega }_{new}-\mathit{ɳ}\frac{\partial L}{\partial \omega },$$

(4)

Here, ɳ is learning rate, L is loss function, $\frac{\partial L}{\partial \omega }$ is the gradient of the loss function with respect to the weight $\omega$.

Subsequently, we applied pruning to these four models by configuring appropriate hyperparameters for the grid search using a 10-fold cross-validation method. In cross-validation, the dataset is partitioned into multiple subsets, with one subset serving as the validation set in each iteration while the remainder constitutes the training set. The model’s performance metrics on the validation set are computed for each iteration. This procedure is repeated multiple times, with each iteration employing a different subset as the validation set. Precision, Recall, F1 score and ROC_AUC were selected to evaluate the performance of the model.

The equations for these indicators are provided below:

$$\mathrm{Precision}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FP}},$$

(5)

$$\mathrm{Recall}=\frac{\mathrm{TP}}{\mathrm{TP}+\mathrm{FN}},$$

(6)

$$\mathrm{F}1=2\times \frac{\mathrm{Precision}\times \mathrm{Recall}}{\mathrm{Precision}+\mathrm{Recall}},$$

(7)

ROC_AUC (Receiver Operating Characteristic Area Under Curve) is the area under the ROC curve. The ROC curve is drawn with the recall rate of the model as the ordinate and FP as the abscissa. The performance was considered poor with an ROC_AUC of <0.6, average with 0.6–0.7, good with 0.7–0.8, and very good with ≥0.8. TP (True Positive) represents the number of samples that the model correctly predicts to be positive. FP (False Positive) represents the number or proportion of negative-class samples that the model incorrectly predicts as positive-class samples. FN (False Negative) is the number of False Negatives, which represents the number of samples that the model incorrectly predicts to be negative but actually turns out to be positive.

In the grid search, according to the characteristics of each model, we designed the parameter grid, which is mainly used to control the model complexity, prevent overfitting and underfitting, and improve the model’s generalization ability. The final result is shown in

Table 2. Parameter configuration and final selection.

Parameter and Results	DT	RF	KNN	MLP
Parameter 1	Max_depth 1: [8, 10, 12, 14, 16]	Max_depth1: [8, 10, 12, 14, 16]	N_neighbors 5: [13, 14, 15, 16, 17]	Activate 7: [‘relu’, ’ tanh’]
Parameter 2	Min_samples_leaf 2: [4, 6, 8, 10, 12]	Min_samples_leaf 2: [3, 4, 5, 6, 7]	Weights 6: [‘uniform’, ‘distance’]	Hidden layer sizes 8: (10, 50, 100)
Parameter 3	Min_sample_split 3: [4, 5, 6, 7, 8]	Min_sample split 3: [4, 5, 6, 7, 8]	/	Learning rate 9: [‘constant’, ‘invscaling’, ‘adaptive’]
Parameter 4	/	N_estimators 4: [58, 60, 62, 64, 66]	/	Max iter 10: (500, 2000, 4000)
Mean deviation	0.010	0.10	0.013	0.019
Standard deviation	0.011	0.011	0.011	0.014

¹ Max_depth: the maximum depth of the tree; ² max_samples_leaf: the minimum number of samples that the final node must contain; ³ min_sample_split: the minimum number of samples divided between internal nodes; ⁴ N_estimators: the number of trees in a random forest; ⁵ N_neighbors: the number of neighbors to be considered for classification; ⁶ weights: neighbor weight during voting; ⁷ activate: introduce nonlinearity to the neural network; ⁸ hidden layer sizes: hidden layer sizes; ⁹ learning rates: invscaling indicates that the learning rate decreases with time; ¹⁰ max_iter: maximum number of iterations of the optimizer.

, with the best parameters in red and the mean and standard deviation corresponding to the best parameter model.

The baseline models before parameter tuning were put together to observe the performance improvement of the model. The final results are presented in

Table 3. Four model performance improvements; w/o HT represents the baseline model without hyperparameter tuning.

Model	Precision		Recall		F1 Score		ROC_AUC
	w/o HT	HT	w/o HT	HT	w/o HT	w/o HT	HT	w/o HT
DT	0.654	0.854	0.656	0.891	DT	0.654	0.854	0.656
RF	0.669	0.879	0.670	0.859	RF	0.669	0.879	0.670
KNN	0.633	0.838	0.632	0.884	KNN	0.633	0.838	0.632
MLP	\	0.834	\	0.816	MLP	\	0.834	\

, with the best in red and the second in blue; RF has the best performance in many indicators, but the gap between DT and it is actually very small, and KNN ranks second in Recall and F1 Score. It is worth mentioning that MLP failed to fit in the initial training; thus, it is not in the result without hyperparameter tuning (w/o HT). However, after parameter tuning, its performance has been greatly improved, as shown in Figure 6. Meanwhile, the performance improvement of other models is almost equal, so it is difficult to evaluate the advantages and disadvantages of each model from here.

Therefore, in order to further understand the fitting of the model, a learning curve is drawn, which used AUC_ROC as an evaluation indicator. AUC_ROC comprehensively considers the tradeoff between TP and FP of the classifier under different thresholds, so it can evaluate the performance of the classifier more comprehensively. At the same time, it has good robustness to unbalance problems and is not easily affected by the unbalance of sample categories, so it can evaluate the performance of the model more comprehensively and objectively. The learning curve is shown in Figure 7.

The training score of the DT is consistently higher than the validation score, which may indicate demonic overfitting. RF had a small gap in training and validation, showing excellent generalization, while KNN had a slightly larger gap; low volatility indicated that adding data did not significantly improve this, with it most likely reaching its performance bottleneck. The initial performance of MLP was low, but with the increase in training data, the performance improved significantly, indicating that the model performance required a larger amount of data. Furthermore, the training time of MLP during the training process was about ten times that of other models.

In conclusion, our evaluation highlights the superior generalization capabilities of the RandomForestClassifier, which consistently achieves high accuracy on both the training and validation datasets. Therefore, we have chosen RandomForestClassifier as the most suitable modeling algorithm for PSVE. RandomForestClassifier is an ensemble learning method that combines multiple decision trees, each trained on different subsets and aggregated for final predictions. It performs well on high-dimensional and large-scale datasets while being less prone to overfitting. Our analysis has recommended the following hyperparameters for model training: 60 trees, a minimum sample leaf of 5, minimum sample split of 7, and maximum depth of 12.

3.2. Development of the NTL Attenuation Map

PSVE plays a crucial role in guiding post-disaster reconstruction efforts by selecting specific regions of interest to predict power system damage. During verification, we chose a sample region from a historical earthquake event that aligns with the seismic characteristics of the area and exhibits relevant power attenuation. This deliberate selection ensures that the verification results offer a more accurate depiction of potential impacts. Subsequently, we have developed damage distribution maps for the power system after earthquakes at both micro and macro scales.

At the micro level, these maps are generated based on seismic event groupings and display only the spatial regions that may be affected, as depicted in Figure 8. The approximate location and estimated value of the power system damage are shown in the figure, so the PSVE can serve the emergency response after a disaster.

Taking a broad temporal and spatial perspective, we developed Figure 9, grouped by year, covering the entire study area. These maps provide valuable insights into a city’s seismic resilience and its preparedness for emergency management. A larger circular area with a lower color value indicates that the city remains relatively unscathed by higher-magnitude earthquakes. Conversely, a smaller circular area with a higher color value signifies significant light attenuation, suggesting potential economic and social consequences in the aftermath of major earthquakes. Of particular concern are the yellow dots appearing in earthquake-prone regions. These dots indicate that even in low-magnitude but high-frequency earthquakes, there may be unforeseen impacts on the city, as evidenced by the night light attenuation. In Figure 9b, it can be found that on a large spatio-temporal scale, it is necessary to focus on the seismic capability of power systems in some prefecture-level cities, such as Yuxi, Leshan, etc.

From a real-time and localized standpoint, these maps enable the city to quickly assess the extent of the potential impact based on simple parameters immediately following an earthquake. This information can serve as crucial decision support for post-earthquake response efforts.

4. Conclusions

Assessing the vulnerability of the power system after an earthquake often begins with examining its components, such as high-voltage substations, transmission towers, and power plants. In the modeling process, it is necessary to calculate parameters like peak ground acceleration, peak ground displacement, field motion spectrum energy, etc., to establish a ground motion mechanism model [33,34,35]. This model is then integrated with the vulnerability of each power system component to predict the damage state of each element. This process may necessitate a significant amount of equipment test data and historical earthquake disaster scenario records. For instance, the LADWP recovery model requires 600 initial damage and system function scenarios as inputs to evaluate and restore the power system [36,37]. Our cost savings stem from approaching this problem from a different angle, specifically examining the correlation between night light and the power system.

In the research of disaster and luminous remote sensing, case studies occupy the majority, and the research is less focused on the topic of power systems. We compared the proposed model with a few relevant studies. Zhao et al. conducted a study on selected disaster cases to assess the impact on urban of natural disasters [4], and the best result was 78%. Fan et al. proposed a method to measure the impact of earthquakes on urban brightness loss [38], which was applied to three earthquakes with magnitude 8.0 in Chile. The best result is 68.4% accuracy. The final accuracy of the model proposed in this study is 87.9%, so significant progress has been made in using luminous remote sensing to assess disaster losses.

In this study, samples of urban NTL attenuation after earthquakes based on all available NPP-VIIRS data in GEE from 2013 to 2022 were extracted, which were taken directly from city and town NTL, and the high correlation with predictors was verified in the GAM. By using the random forest method to train a large number of sample data and tuning hyperparameters, a PSVE model with high robustness was finally obtained. While PSVE may not provide all the details, and the proposed model is not intended to replace rigorous industry-specific application analysis of the power system, it can still highlight uneven damage to power systems caused by earthquakes based on night lights.

Most importantly, the predictors are very carefully selected. The predictors which can be obtained immediately when the earthquake occurs, such as magnitude, depth, distance, etc., are chosen. The whole point is to make sure that the robustness and accuracy of the model on the premise can be applied to an emergency evaluation.

The damage caused to the power system was investigated from both micro and macro spatio-temporal perspectives; the innovative value of this study is, firstly, that the prediction of the light attenuation value of the whole city after the earthquake by simple parameters is conducive to the rapid preliminary insight of the disaster damage. Secondly, on a large time scale, detailed investigation may require a lot of resources and time to fit data and build models [39]. PSVE can provide decision support under limited resources. Before conducting a more detailed investigation, the prediction of simple parameters can be preliminarily screened to determine which areas or time periods may have problems, such as cascading losses caused by earthquakes [40], so as to conduct more targeted follow-up detailed investigations.

Simple parameter models may not provide all the details of urban light attenuation after an earthquake, but they can be applied to preliminary understanding and efficient resource utilization. The best approach is to synthesize different scale and complexity models in practical applications to obtain more comprehensive information. Therefore, we also hope that this study could enhance our understanding of the multifaceted consequences of disasters and contribute to the ongoing discourse on utilizing remote sensing for effective disaster management.