# Rolling Prediction of Emergency Supplies Based on Postdisaster Multisource Time-Varying Information

Authors: Wei Li; Ming Zhang; Boquan Li; Songrui Li; Zhifeng Qiu
Journal: Complexity
 (2022)

---

## Abstract

Accurate prediction of material demands is key to ensuring the overall efficiency of emergency rescue operations. From the perspective of the prediction method, the single-material static prediction method based on the overall data has limitations. This method cannot flexibly adjust multiperiod material demands. Considering data sources, acquiring data regarding material demands in historical disasters is more difficult and has more uncertainty compared with statistical data on deaths. This study investigates a rolling prediction method for emergency supplies based on postdisaster multisource time-varying information to ensure prediction accuracy. First, the proposed method uses historical cases, real-time disasters, and time-sharing simulation data as the source data. The method implements attribute reduction of original data samples based on rough set theory and predicts cumulative death tolls in each rolling period by using the rolling time-domain as the basic framework and combining a support vector machine (SVM). Second, the proposed method estimates the material demands in the corresponding period by using the material demand model according to the prediction results in a single period. Finally, the proposed method is verified by an experiment with a general mean prediction error of 10.96%. However, the general mean prediction error of SVM reaches 17.77% in the static multistep prediction. Moreover, the general mean prediction error of the methods in the references is 14.13%. Overall, the method has high accuracy and strong timeliness. Prediction results can not only be used as a basis for material estimation, but also provide several scientific and effective references for the allocation and scheduling of emergency supplies.


---

## Body

## 1. Introduction

The timely supply of materials to people in disaster areas is vital after the occurrence of natural disasters. Such timeliness has also been a considerable concern for many experts and scholars worldwide [1–5]. Many issues regarding the distribution of emergency supplies, such as disaster relief supply chain problems [6–8], allocation and distribution problems of emergency supplies [9], inventory management problems [10], and design problems of transport paths [11], have been recently proposed. Among these issues, the accurate prediction of material demands is the key to ensuring the overall efficiency of emergency rescue. However, accurate prediction faces the following two challenges: prediction methods and data sources.Numerous methods are used to predict emergency supplies, and these methods can be divided into two types according to properties as follows: static and dynamic prediction methods. The static prediction method refers to a single gross prediction based on the overall sample data. For example, Guo and Qi [12] proposed a prediction model for emergency material demands based on a fuzzy Markov chain. In this model, emergency material demands are divided into the following five classes before material prediction: very small, small, general, high, and very high demands. Sun et al. [13] proposed a fuzzy rough set model to predict emergency materials and introduced this model in the risk decision principle in operational research to provide decision rules and computing methods for the model. They proved the validity of this model through a case study. The static prediction method is inappropriate because of the periodicity of emergency materials, especially fast-moving consumer goods (FMCGs). In this case, the effects of several multiperiod dynamic prediction methods are highlighted. Wang [14] considered the basic living needs of people in areas with snow disasters and proposed a gray prediction method based on a genetic algorithm (GA) to predict food demands in disaster areas. Sheu [15] studied emergency logistics operations under incomplete information after the occurrence of large-scale natural disasters and proposed a dynamic emergency material demand management model to predict dynamic emergency demands in each disaster area in a given period. Kopytov [16] described a real-time emergency prediction technique that was applied to scenario management systems. This technique predicted the acquired short-term sequence data through an improved Brown method, enhanced the computing model, and ensured the reliability of the emergency prediction results based on the correlation analysis method. Xue et al. [17] considered the dynamic demands of postdisaster emergency supplies and established a dynamic prediction method based on the NRS-GA-SVM algorithm. This method processed attribute indexes using NRS and optimized parameters with GA and completed predictions based on the nonlinear SVM algorithm. Mohammadi et al. [18] proposed a new radial basis neural network forecasting time sequence method based on hybrid evolution for the dynamic prediction of the time sequence of emergency material demands. In addition, Wohlgemuth et al. [19] and Najafi et al. [20] analyzed and emphasized the importance of the dynamic method in prediction.In prediction control theory, the rolling time-domain structural framework is a widely used method in dynamic studies and is mainly applied to solve problems concerning traffic and industries [21, 22]. For instance, we must make reasonable decisionsfor the aircraft scheduling problem in airport terminal areason the takeoff and landing of aircraft in a given time range. Samà et al. [23] introduced the rolling time-domain method as the basic framework to solve this problem and achieved scientific scheduling of aircraft in busy airports by combining corresponding scheduling algorithms. Zamarripa et al. studied a large-scale industrial gas supply chain [24] and proposed a rolling time-domain method based on a control system. This method not only meets the requirements for solving but also decreases the calculation quantity and solves the shortcomings of existing industrial gas supply chains. However, the rolling time-domain method has been applied in fields such as the market and materials as a response to continuous scientific development. For example, Devine et al. [25] and Silvente et al. [26] applied the rolling time-domain method as the research basis to solve the supply-demand balance in the energy market. Considerable demand uncertainty exists in global purchases, making long-term purchase plans difficult. Cao et al. [27] proposed an adaptive optimal planning method that uses the rolling time-domain method. By combining time sequence prediction and the random batch technique, this method obtained scientific and effective solutions to long-term purchase plans with demand uncertainty. Lu [28] applied the rolling time-domain method as a real-time disaster relief distribution framework to study the prediction issues of emergency material demands in disaster areas after earthquakes and accomplished prediction, allocation, and scheduling of emergency materials.Abundant disaster information is generated after the occurrence of disasters, and several sources of information continuously change [29]. Thus, making accurate predictions by combining the correlation features of disaster information is crucial. Current disaster information characteristics mainly include the following two types:Dynamic Time-Varying Characteristics of Disaster Information. With the occurrence of disasters, several sources of disaster information are in the process of real-time changes. Girard et al. [30] considered this characteristic and indicated that information in the first five days of disaster response from fast disaster evaluation to implementation of the allocation plan has characteristics of uncertainty, strong dynamics, and rapid change. Duhamel et al. [31] proposed a mathematical model considering the dynamic distribution of the victim population after the occurrence of natural disasters and solved this model using a heuristic method. They also noticed a multistage material distribution based on the dynamic population distribution. Bozorgi-Amiri et al. [32] proposed a multiobjective robust stochastic planning technique to allocate materials under uncertainty. This technique achieved an overall assessment distribution of materials under uncertainty information by minimizing the victim population and maximizing material satisfaction. Villeneuve et al. [33] introduced a demand prediction method, which can be detected to solve problems related to uncertainty and abnormal values in original data. Fabian [34] proposed an information Bayesian approach to solve prediction and assessment problems under uncertain information conditions. Liu et al. [35] presented a multigood and multistage distribution model that considered the uncertainty of data information and the timeliness of material distribution. Moreover, the rolling optimization method was applied as the basic research framework to obtain a robust allocation plan for relief goods and enabling real-time updating.Disaster Information Has Multiple Sources. Information from different pathways might differ because of the multiple channels available for disaster information acquisition. Most existing studies have mainly focused on historical data. For instance, Hu et al. [36] developed a multistage stochastic planning model that involved the influences of vehicle modes and road networks for emergency material allocation after disasters. This model was applied to the Ya’an earthquake in China to extract real case data related to earthquakes for numerical analysis. Zokaee et al. [37] analyzed the reasonable distribution of emergency goods and used available real datasets of historical cases in the Alborz region within the sphere of influence of the earthquake as data sources to verify the effectiveness of the model. They also examined the influence of uncertain parameters on the solution results in the distribution model. Cavdur et al. [38] selected historical data from the Bursa earthquake in Turkey as the data source for the analysis case in their investigation of facility allocation. During material prediction, Chen et al. [39] conducted a case study based on the Wenchuan earthquake and collected real data related to earthquakes from government websites, such as the Ministry of Civil Affairs and Seismological Bureau. Considering material demands in different regions, Sheu [15] and Lu et al. [28] obtained multiple sources of disaster information, including government organizations, in situ rescue teams, and media journalists, to predict major real-time data sources of an earthquake. Moreover, they filled in official historical data with time-sharing simulation data for comparative analysis, which verified the prediction accuracy of the proposed method.Overall, most of the existing studies emphasize single aspects. Considering the sample data, disaster information after occurrences of natural disasters have time-variant characteristics of uncertainty and dynamics. Moreover, certain limitations must be provided if only historical case data of an earthquake are considered, thus lowering the prediction accuracy. From the perspective of the prediction method, the single-material static prediction method based on overall data has strong limitations owing to the timeliness of emergency rescue. This method cannot flexibly adjust multiperiod material demands. Considering data sources, acquiring data regarding material demands in historical disasters is more difficult and has more uncertainty compared with statistical data on deaths. Therefore, ensuring the prediction accuracy of material demands in disaster areas based on historical data is complicated. The original contributions of this study can be summarized as follows:(1)
This study was compared with reference [28] in terms of multiple sources of disaster information. Reference [28] considered historical statistical data of the studied earthquake event and supplemented the missing statistical data using simulation data. These data were used as references to verify multisource real-time data from government sectors, in situ rescue teams, and media journalists. Such data quantities are also limited. However, this study is based on a set of earthquake cases. In addition to real-time data of earthquake cases, the present study also involved historical statistical and simulation data of other earthquakes. Thus, this study realizes material prediction based on data expansion through these three sources.(2)
This study considered the dynamic time-varying characteristics of disaster information and combined the rolling time-domain framework and the SVM algorithm. Moreover, the predicted value of the previous period was added into the input set of the next period as a conditional attribute in the prediction process, thus realizing dynamic material prediction.(3)
Considering the advancement of prediction methods, the prediction results in Reference [28] are interval numbers with certain fuzziness. However, this study applied the SVM algorithm to predict deaths and obtained an accurate value, ensuring accuracy to some extent.The remainder of this paper is organized as follows. Section2 describes the problems and introduces prediction methods. Section 3 establishes a prediction model for emergency material demand. Section 4 describes the design of the algorithms and solves the model. Section 5 presents the case study, comparative experimental design, and results analysis. Section 6 summarizes the study’s conclusions and prospects.


## 2. Emergency Supply Prediction Methods

### 2.1. Problem Description

A multiperiod rolling indirect prediction method based on a rolling time-domain framework with comprehensive considerations of data sources and rolling prediction methods is proposed to increase the prediction accuracy and timeliness. The proposed method not only offsets the shortcomings of previous prediction methods but also fully considers sample data sources. The main idea of the proposed method is introduced in the following text.(i)
Step 1: Multiple periods of the rolling time-domain are determined to collect historical case, simulation, and real-time disaster data.(ii)
Step 2: Attribute reduction of the original data samples is completed using rough set theory, thereby obtaining experimental datasets.(iii)
Step 3: Rolling prediction of deaths is performed by combining the rolling time-domain framework with the SVM intelligence algorithm.(iv)
Step 4: This is followed by the estimation of the aggregated relief demands needed in real time by the corresponding survivals, according to Reference [15]. Since the regional population is determined, we know the number of survivals by predicting the number of deaths. The material demands in the current period are estimated using warehouse inventory theory according to the prediction results of deaths. The flowchart is shown in Figure 1.Figure 1
Technological process.Figure1 shows that circulation flows are generated during SVM prediction based on the rolling time-domain framework. This condition is due to prediction accuracy, which is a comprehensively considered thorough practical prediction, and the addition of prediction results in the previous cycle into the input set as attribute indexes of the next cycle. Therefore, the prediction of one cycle is complete.


### 2.2. Hypotheses

Several basic hypotheses have been proposed to create a scientific and effective prediction model method because the topic background has numerous relatively complicated characteristics (e.g., uncertainty and multiple factors) in practical life.(1)
After the occurrence of earthquakes, diversified materials with unique features are required in disaster areas. As a result, different research methods for the demands of different materials are required. This study mainly focused on FMCGs (e.g., drinking water and compressed biscuits) and durable goods (mainly tents).(2)
Many trapped persons will be successfully rescued because the first seven days after the occurrence of an earthquake is the main rescue period. However, the growth rate of deaths is considerably high. Considering these factors, the first seven days after an earthquake were used as the overall planning time domain in the present study.(3)
This study only discusses problems related to the prediction of rescuing materials, but ignores those related to material supply, allocation, and scheduling.(4)
If material demands in the disaster area have weak economic efficiency after the occurrence of earthquakes and are independent of local economic development levels, then only the direct relationship between material demands and victim population is considered in this study.


### 2.3. Rolling Time-Domain Framework

The basic structural framework of the rolling time-domain method is shown in Figure2. T is the planning time domain that must be predicted and is evenly divided into M prediction stages. The black region refers to the short-term prediction of a stage. The white region represents the middle- and long-term prediction parts of a stage. The gray region refers to the part that has been predicted. Each stage M comprises L rolling periods. One stage of the plan is expressed by W, and one rolling period is expressed by P to simplify the description.Figure 2
Rolling time-domain framework.Prediction reliability generally declines with an increase in the length of the prediction scope. If the time range of the prediction is relatively long, then the reliability of the prediction results is relatively low. Each stage is divided intoL periods using the rolling time-domain method to improve the prediction reliability. In one stage, the black part refers to the effective time of the current prediction, and the white part refers to L−1 periods, where the reliability of the prediction results will be decreased.Before the first stage, the prediction results can be obtained by inputting the historical database and the acquired real-time disaster information. The reliability of the prediction results might decline over time owing to the continuous updating of disaster information. Therefore, short-term predictions are relatively reliable, whereas middle- and long-term predictions are not. The short-term prediction of theP time domain was used as the period to roll forward, and the middle- and long-term predictions were continuously updated to improve the reliability of the late prediction. This process was repeated until the end of the entire planning time domain.


### 2.4. Data Source

The relevant earthquake data in this section mainly include three types, namely, historical cases, real-time disasters, and time-sharing simulation data. The cumulative deaths in each period of the planning time domain could be predicted by combining these types of data.(1)
Historical case data cover two main aspects. One aspect is information data related to earthquakes, such as the time of occurrence, earthquake magnitude, and epicentral intensity. The other is statistical data after a certain period of earthquake accidents, such as casualties and population density. Historical case data were mainly acquired from official websites of the National Shared Center for Earthquake Science and the Statistical Bureau at the province and city levels.(2)
Real-time disaster data refer to the relevant attribute values of the research samples and are used as input values for prediction. In addition, real-time reports of research sample deaths in Reference [40] were compared with the prediction results.(3)
The simulation data mainly cover two aspects: desktop walkthrough and time-sharing simulation data. The former refers to data obtained from the simulation of an emergency rescue system and was developed by the research team in the early stage based on historical case data, which are used to supplement the data quantity of the prediction samples. The latter is proposed because this study focused on dynamic prediction and obtained the final material demands through an indirect research method. Therefore, it is necessary to determine the cumulative deaths in each interval during the study by integrating the rolling time-domain method. However, acquiring time-sharing simulation data, especially for earthquakes in the early stages, is difficult. Thus, the cumulative deaths in each interval were calculated using the time-varying functional model of earthquake-induced deaths through inverse operation. The time-varying functional model of death is described in the following section.According to [41], the variation function of cumulative deaths (N) with t can be obtained. The calculation formula for the model is as follows:(1)Nt=N01−exp−αt,where N0 and α are constants and refer to the final deaths. α is a coefficient that expresses the rescuing efficiency.Based on (1), the cumulative deaths of local earthquake cases at different moments can be calculated based on the general data of historical cases. These data can be used to simulate deaths in each historical case period.


## 2.1. Problem Description

A multiperiod rolling indirect prediction method based on a rolling time-domain framework with comprehensive considerations of data sources and rolling prediction methods is proposed to increase the prediction accuracy and timeliness. The proposed method not only offsets the shortcomings of previous prediction methods but also fully considers sample data sources. The main idea of the proposed method is introduced in the following text.(i)
Step 1: Multiple periods of the rolling time-domain are determined to collect historical case, simulation, and real-time disaster data.(ii)
Step 2: Attribute reduction of the original data samples is completed using rough set theory, thereby obtaining experimental datasets.(iii)
Step 3: Rolling prediction of deaths is performed by combining the rolling time-domain framework with the SVM intelligence algorithm.(iv)
Step 4: This is followed by the estimation of the aggregated relief demands needed in real time by the corresponding survivals, according to Reference [15]. Since the regional population is determined, we know the number of survivals by predicting the number of deaths. The material demands in the current period are estimated using warehouse inventory theory according to the prediction results of deaths. The flowchart is shown in Figure 1.Figure 1
Technological process.Figure1 shows that circulation flows are generated during SVM prediction based on the rolling time-domain framework. This condition is due to prediction accuracy, which is a comprehensively considered thorough practical prediction, and the addition of prediction results in the previous cycle into the input set as attribute indexes of the next cycle. Therefore, the prediction of one cycle is complete.


## 2.2. Hypotheses

Several basic hypotheses have been proposed to create a scientific and effective prediction model method because the topic background has numerous relatively complicated characteristics (e.g., uncertainty and multiple factors) in practical life.(1)
After the occurrence of earthquakes, diversified materials with unique features are required in disaster areas. As a result, different research methods for the demands of different materials are required. This study mainly focused on FMCGs (e.g., drinking water and compressed biscuits) and durable goods (mainly tents).(2)
Many trapped persons will be successfully rescued because the first seven days after the occurrence of an earthquake is the main rescue period. However, the growth rate of deaths is considerably high. Considering these factors, the first seven days after an earthquake were used as the overall planning time domain in the present study.(3)
This study only discusses problems related to the prediction of rescuing materials, but ignores those related to material supply, allocation, and scheduling.(4)
If material demands in the disaster area have weak economic efficiency after the occurrence of earthquakes and are independent of local economic development levels, then only the direct relationship between material demands and victim population is considered in this study.


## 2.3. Rolling Time-Domain Framework

The basic structural framework of the rolling time-domain method is shown in Figure2. T is the planning time domain that must be predicted and is evenly divided into M prediction stages. The black region refers to the short-term prediction of a stage. The white region represents the middle- and long-term prediction parts of a stage. The gray region refers to the part that has been predicted. Each stage M comprises L rolling periods. One stage of the plan is expressed by W, and one rolling period is expressed by P to simplify the description.Figure 2
Rolling time-domain framework.Prediction reliability generally declines with an increase in the length of the prediction scope. If the time range of the prediction is relatively long, then the reliability of the prediction results is relatively low. Each stage is divided intoL periods using the rolling time-domain method to improve the prediction reliability. In one stage, the black part refers to the effective time of the current prediction, and the white part refers to L−1 periods, where the reliability of the prediction results will be decreased.Before the first stage, the prediction results can be obtained by inputting the historical database and the acquired real-time disaster information. The reliability of the prediction results might decline over time owing to the continuous updating of disaster information. Therefore, short-term predictions are relatively reliable, whereas middle- and long-term predictions are not. The short-term prediction of theP time domain was used as the period to roll forward, and the middle- and long-term predictions were continuously updated to improve the reliability of the late prediction. This process was repeated until the end of the entire planning time domain.


## 2.4. Data Source

The relevant earthquake data in this section mainly include three types, namely, historical cases, real-time disasters, and time-sharing simulation data. The cumulative deaths in each period of the planning time domain could be predicted by combining these types of data.(1)
Historical case data cover two main aspects. One aspect is information data related to earthquakes, such as the time of occurrence, earthquake magnitude, and epicentral intensity. The other is statistical data after a certain period of earthquake accidents, such as casualties and population density. Historical case data were mainly acquired from official websites of the National Shared Center for Earthquake Science and the Statistical Bureau at the province and city levels.(2)
Real-time disaster data refer to the relevant attribute values of the research samples and are used as input values for prediction. In addition, real-time reports of research sample deaths in Reference [40] were compared with the prediction results.(3)
The simulation data mainly cover two aspects: desktop walkthrough and time-sharing simulation data. The former refers to data obtained from the simulation of an emergency rescue system and was developed by the research team in the early stage based on historical case data, which are used to supplement the data quantity of the prediction samples. The latter is proposed because this study focused on dynamic prediction and obtained the final material demands through an indirect research method. Therefore, it is necessary to determine the cumulative deaths in each interval during the study by integrating the rolling time-domain method. However, acquiring time-sharing simulation data, especially for earthquakes in the early stages, is difficult. Thus, the cumulative deaths in each interval were calculated using the time-varying functional model of earthquake-induced deaths through inverse operation. The time-varying functional model of death is described in the following section.According to [41], the variation function of cumulative deaths (N) with t can be obtained. The calculation formula for the model is as follows:(1)Nt=N01−exp−αt,where N0 and α are constants and refer to the final deaths. α is a coefficient that expresses the rescuing efficiency.Based on (1), the cumulative deaths of local earthquake cases at different moments can be calculated based on the general data of historical cases. These data can be used to simulate deaths in each historical case period.


## 3. Dynamic Prediction Model of Emergency Material Demands

### 3.1. Symbol Descriptions in the Model

The major symbols and marks of the follow-up models are listed in Table1.Table 1
Definitions and descriptions of model symbols.
SymbolsDescriptionstTime from the initial occurrence of earthquakekCategories of emergency materialsiNumber of condition attributes of samplesjSamples of earthquake casesnRolling period in the planning time-domainNCumulative deathsXCondition attribute setYDecision attribute setxiInputted initial attribute set for material predictionxm+nInputted attribute set atn + 1 period for material predictionNjnSimulation value of cumulative deaths inn period of earthquake case jyjnPrediction value of cumulative deaths inn period of earthquake case jakAverage demands for materialk per person in unit timeσktStandard deviation of demands for materialk in unit time in the disaster area after t (hours) from the occurrence of earthquakeD¯ktMean demands for materialk in unit time in the disaster area by the end of tRfcFMCGsRdgDurable goods


### 3.2. Attribute Reduction Model Based on Rough Set Theory

In this study, an attribute reduction model of the sample data that focuses on the original dataset of earthquake cases and the desktop simulation dataset was constructed based on the traditional rough set theory. The model construction process is illustrated in Figure3.Figure 3
Construction process of prediction attribute reduction model based on rough set.First, earthquake case samples were determined on the basis of preliminarily screened indexes, and the acquired earthquake damage dataset was used as an information system. Second, the initial information decision tableS=U,R,V,f, where U represents the domain of discourse (i.e., the set of earthquake cases), was constructed. U=u1,u2,…,uj is the set of j earthquake cases. R is the attribute set, including condition attribute X and decision attribute Y. In other words, R=X∪Y. The condition attribute mainly comprises information related to earthquakes (e.g., attribute indexes related to earthquake-induced deaths, including earthquake magnitude, focal depth, epicentral intensity, and time of occurrence) and social factors (e.g., population density, earthquake forecasting, and fortification level) X=xi,i=1,2,…,l. The decision attribute refers to the cumulative deaths in each period after the occurrence of an earthquake Y=y. V is the range set of attributes. f is an information function f:U×X⟶Y. The continuous attribute indexes in the sample data must be discretized after building the decision table because rough set processing requires discrete data. Finally, attribute reduction was achieved through a GA to obtain effective attribute samples.


### 3.3. SVM Prediction Model of Deaths Based on Rolling Time-Domain

#### 3.3.1. Construction of the Prediction Model

This study assumed thatX=xi,i=1,2,⋯,m represents m condition attributes, which were reduced and mostly related to the decision attribute. Y expresses the output quantity, that is, the predicted value of the deaths. The predicted value of the research sample in a period is yjn. From the abovementioned calculation formula of the time-sharing simulation, the cumulative deaths in each prediction period of all the samples could be obtained. Then, the cumulative deaths of sample j in the n prediction period are Njn. Based on the existing attributes of the training samples, the output prediction value yjn of the previous period of the target samples and the simulated cumulative deaths in the same period of the other samples Njn were added to the attribute set when the prediction period rolled forward continuously and were used as the input value of the next period. This process was repeated until the end of the prediction of the entire planning time domain. Therefore, the newly added input attribute set in the n+1 period is xm+n=Njn∪yjn, and the updated condition attribute set is.For the functionfx in X, the values (y) corresponding to any variable (x) can be solved through y=fx. According to the above contents, the dimension of the existing sample data is i. Therefore, the dimension of any sample can be expressed as follows: xi,y∈Ri×R.On this basis, the nonlinear regression equation of the prediction model can be established as follows:(2)fx=∑i,j=1mαi−αi∗kxi,x+b,where αi,αi∗ are Lagrangian multipliers, b is the threshold, and x is the input vector. kxi,x refers to the dot product that conforms to the Mercer condition and corresponds to any symmetric kernel function.


#### 3.3.2. Selection of Parameters

Only a few system parameters must be set because SVM has a relatively simpler structure than the other algorithms. However, the random setting of parameters may also cause problems during the model prediction. Consequently, it is difficult to ensure the prediction accuracy. Therefore, choosing the optimal parameters during prediction using SVM is crucial for ensuring the performance of the model.In this study, the parameters were determined by cross-validation and grid search, both of which are common. The former can avoid overfitting to some extent, while the latter has relatively high parallelism and performs a comprehensive and effective parameter search.During the simulation experiment, the chosen earthquake sample dataset was divided intok data subsets according to K-fold cross-validation, and different combinations of parameters c and g were tested using the grid search method. The final parameters c and g were determined by cross-validation.


#### 3.3.3. Determination of Kernel Function

The core of the SVM determines the kernel function. In the present study, a radial basis kernel function was used in the SVM prediction model for earthquake-induced deaths. The formula is as follows:(3)Kx,xi=exp−x−xi2σ2,where σ determines the kernel width of the kernel function, which controls the number of support vectors and thereby influences the prediction accuracy. Hence, the above K-fold cross-validation was used to select the numerical values of σ to increase the prediction accuracy. This process is similar to the parameter determination method described above.


#### 3.3.4. Evaluation Standards for the Prediction Results

For the predicted value of cumulative deaths in each rolling period,R2 and MSE were used as evaluation standards of the model. R2 refers to the correlation square coefficient, and MSE is the mean square error. The formula for the evaluation parameters is as follows:(4)R2=1−∑J=1jy^j−yj2∑J=1jy¯j−yj2,MSE=1j∑J=1jyj−y^j2,where J refers to the earthquake case set of the research samples, yj refers to the real value, y^j refers to the prediction value, and y¯j is the mean of the real values.In the comparison of the variation trend of cumulative deaths in all periods of the entire planning time domain of research cases with the variation trend of practical cumulative deaths, the overall prediction accuracy was evaluated by the relative errorRen in each period:(5)Ren=y^n−ynyn.


### 3.4. Material Demand Calculation Model Based on Warehouse Inventory Theory

According to Reference [42], during the modeling of material demands, if the total demand of a product is based on large-scale individual demands, then such demands can generally be viewed as conforming to normal distribution characteristics. For natural disasters, the decision-making department allocates emergency supplies based on the general prediction of demand in disaster areas. Such predictions are based on the number of individuals in affected disaster areas. Therefore, the prediction of postdisaster emergency materials is similar to that of the material demand model, in which inventory management theory was introduced.If the earthquake in a region is at 0, and this moment (unit: h) is used as the starting point of emergency rescue, then the survival numberSt in the disaster area t after the occurrence of a disaster is,(6)St=δ−Nt,where δ refers to the total population in the affected disaster areas, and N(t) is the cumulative deaths by the end of t.The necessary emergency supplies are diverse after the occurrence of natural disasters. Therefore, the calculation models of demand for FMCGs and durable goods vary. The formula to calculate the demandsDkt of disaster regions for emergency material k in disaster areas is derived according to warehouse inventory theory as follows:(7)Dkt=ak×St×LT+Z∂×σk×LTk∈Rfcak×St−Bk−∑ε=0t−1Akt−εk∈Rdg,where ∂ refers to the rate of shorts of materials and equipment resources. 1−∂ refers to the degree of satisfaction of people in the disaster area to emergency resources and conforms to a normal distribution. Z1−∂ is the coefficient corresponding to the satisfaction degree of 1−∂, and its numerical value can be obtained through a normal distribution. LT refers to the maximum interval of successful emergency supply delivery to disaster areas; that is, one rolling period was divided in this study. Bk refers to the material inventory before the occurrence of an earthquake. Akt−ε refers to material transportation in t−ε. The formula for calculating the standard deviation of demands σkt is as follows:(8)σkt=∑ε=0t−1Dkt−ε−D¯kt2t.The mean demandD¯kt of disaster areas for emergency material k per unit time by the end of t must be calculated according to (8). The calculation formula is as follows:(9)D¯kt=∑ε=0t−1Dkt−εt.Thus, the relationship between the survival rate and emergency supplies after a disaster can be derived through inventory theory. This theory was used to study the dynamic demands of victims for emergency supplies after the occurrence of earthquakes.


## 3.1. Symbol Descriptions in the Model

The major symbols and marks of the follow-up models are listed in Table1.Table 1
Definitions and descriptions of model symbols.
SymbolsDescriptionstTime from the initial occurrence of earthquakekCategories of emergency materialsiNumber of condition attributes of samplesjSamples of earthquake casesnRolling period in the planning time-domainNCumulative deathsXCondition attribute setYDecision attribute setxiInputted initial attribute set for material predictionxm+nInputted attribute set atn + 1 period for material predictionNjnSimulation value of cumulative deaths inn period of earthquake case jyjnPrediction value of cumulative deaths inn period of earthquake case jakAverage demands for materialk per person in unit timeσktStandard deviation of demands for materialk in unit time in the disaster area after t (hours) from the occurrence of earthquakeD¯ktMean demands for materialk in unit time in the disaster area by the end of tRfcFMCGsRdgDurable goods


## 3.2. Attribute Reduction Model Based on Rough Set Theory

In this study, an attribute reduction model of the sample data that focuses on the original dataset of earthquake cases and the desktop simulation dataset was constructed based on the traditional rough set theory. The model construction process is illustrated in Figure3.Figure 3
Construction process of prediction attribute reduction model based on rough set.First, earthquake case samples were determined on the basis of preliminarily screened indexes, and the acquired earthquake damage dataset was used as an information system. Second, the initial information decision tableS=U,R,V,f, where U represents the domain of discourse (i.e., the set of earthquake cases), was constructed. U=u1,u2,…,uj is the set of j earthquake cases. R is the attribute set, including condition attribute X and decision attribute Y. In other words, R=X∪Y. The condition attribute mainly comprises information related to earthquakes (e.g., attribute indexes related to earthquake-induced deaths, including earthquake magnitude, focal depth, epicentral intensity, and time of occurrence) and social factors (e.g., population density, earthquake forecasting, and fortification level) X=xi,i=1,2,…,l. The decision attribute refers to the cumulative deaths in each period after the occurrence of an earthquake Y=y. V is the range set of attributes. f is an information function f:U×X⟶Y. The continuous attribute indexes in the sample data must be discretized after building the decision table because rough set processing requires discrete data. Finally, attribute reduction was achieved through a GA to obtain effective attribute samples.


## 3.3. SVM Prediction Model of Deaths Based on Rolling Time-Domain

### 3.3.1. Construction of the Prediction Model

This study assumed thatX=xi,i=1,2,⋯,m represents m condition attributes, which were reduced and mostly related to the decision attribute. Y expresses the output quantity, that is, the predicted value of the deaths. The predicted value of the research sample in a period is yjn. From the abovementioned calculation formula of the time-sharing simulation, the cumulative deaths in each prediction period of all the samples could be obtained. Then, the cumulative deaths of sample j in the n prediction period are Njn. Based on the existing attributes of the training samples, the output prediction value yjn of the previous period of the target samples and the simulated cumulative deaths in the same period of the other samples Njn were added to the attribute set when the prediction period rolled forward continuously and were used as the input value of the next period. This process was repeated until the end of the prediction of the entire planning time domain. Therefore, the newly added input attribute set in the n+1 period is xm+n=Njn∪yjn, and the updated condition attribute set is.For the functionfx in X, the values (y) corresponding to any variable (x) can be solved through y=fx. According to the above contents, the dimension of the existing sample data is i. Therefore, the dimension of any sample can be expressed as follows: xi,y∈Ri×R.On this basis, the nonlinear regression equation of the prediction model can be established as follows:(2)fx=∑i,j=1mαi−αi∗kxi,x+b,where αi,αi∗ are Lagrangian multipliers, b is the threshold, and x is the input vector. kxi,x refers to the dot product that conforms to the Mercer condition and corresponds to any symmetric kernel function.


### 3.3.2. Selection of Parameters

Only a few system parameters must be set because SVM has a relatively simpler structure than the other algorithms. However, the random setting of parameters may also cause problems during the model prediction. Consequently, it is difficult to ensure the prediction accuracy. Therefore, choosing the optimal parameters during prediction using SVM is crucial for ensuring the performance of the model.In this study, the parameters were determined by cross-validation and grid search, both of which are common. The former can avoid overfitting to some extent, while the latter has relatively high parallelism and performs a comprehensive and effective parameter search.During the simulation experiment, the chosen earthquake sample dataset was divided intok data subsets according to K-fold cross-validation, and different combinations of parameters c and g were tested using the grid search method. The final parameters c and g were determined by cross-validation.


### 3.3.3. Determination of Kernel Function

The core of the SVM determines the kernel function. In the present study, a radial basis kernel function was used in the SVM prediction model for earthquake-induced deaths. The formula is as follows:(3)Kx,xi=exp−x−xi2σ2,where σ determines the kernel width of the kernel function, which controls the number of support vectors and thereby influences the prediction accuracy. Hence, the above K-fold cross-validation was used to select the numerical values of σ to increase the prediction accuracy. This process is similar to the parameter determination method described above.


### 3.3.4. Evaluation Standards for the Prediction Results

For the predicted value of cumulative deaths in each rolling period,R2 and MSE were used as evaluation standards of the model. R2 refers to the correlation square coefficient, and MSE is the mean square error. The formula for the evaluation parameters is as follows:(4)R2=1−∑J=1jy^j−yj2∑J=1jy¯j−yj2,MSE=1j∑J=1jyj−y^j2,where J refers to the earthquake case set of the research samples, yj refers to the real value, y^j refers to the prediction value, and y¯j is the mean of the real values.In the comparison of the variation trend of cumulative deaths in all periods of the entire planning time domain of research cases with the variation trend of practical cumulative deaths, the overall prediction accuracy was evaluated by the relative errorRen in each period:(5)Ren=y^n−ynyn.


## 3.3.1. Construction of the Prediction Model

This study assumed thatX=xi,i=1,2,⋯,m represents m condition attributes, which were reduced and mostly related to the decision attribute. Y expresses the output quantity, that is, the predicted value of the deaths. The predicted value of the research sample in a period is yjn. From the abovementioned calculation formula of the time-sharing simulation, the cumulative deaths in each prediction period of all the samples could be obtained. Then, the cumulative deaths of sample j in the n prediction period are Njn. Based on the existing attributes of the training samples, the output prediction value yjn of the previous period of the target samples and the simulated cumulative deaths in the same period of the other samples Njn were added to the attribute set when the prediction period rolled forward continuously and were used as the input value of the next period. This process was repeated until the end of the prediction of the entire planning time domain. Therefore, the newly added input attribute set in the n+1 period is xm+n=Njn∪yjn, and the updated condition attribute set is.For the functionfx in X, the values (y) corresponding to any variable (x) can be solved through y=fx. According to the above contents, the dimension of the existing sample data is i. Therefore, the dimension of any sample can be expressed as follows: xi,y∈Ri×R.On this basis, the nonlinear regression equation of the prediction model can be established as follows:(2)fx=∑i,j=1mαi−αi∗kxi,x+b,where αi,αi∗ are Lagrangian multipliers, b is the threshold, and x is the input vector. kxi,x refers to the dot product that conforms to the Mercer condition and corresponds to any symmetric kernel function.


## 3.3.2. Selection of Parameters

Only a few system parameters must be set because SVM has a relatively simpler structure than the other algorithms. However, the random setting of parameters may also cause problems during the model prediction. Consequently, it is difficult to ensure the prediction accuracy. Therefore, choosing the optimal parameters during prediction using SVM is crucial for ensuring the performance of the model.In this study, the parameters were determined by cross-validation and grid search, both of which are common. The former can avoid overfitting to some extent, while the latter has relatively high parallelism and performs a comprehensive and effective parameter search.During the simulation experiment, the chosen earthquake sample dataset was divided intok data subsets according to K-fold cross-validation, and different combinations of parameters c and g were tested using the grid search method. The final parameters c and g were determined by cross-validation.


## 3.3.3. Determination of Kernel Function

The core of the SVM determines the kernel function. In the present study, a radial basis kernel function was used in the SVM prediction model for earthquake-induced deaths. The formula is as follows:(3)Kx,xi=exp−x−xi2σ2,where σ determines the kernel width of the kernel function, which controls the number of support vectors and thereby influences the prediction accuracy. Hence, the above K-fold cross-validation was used to select the numerical values of σ to increase the prediction accuracy. This process is similar to the parameter determination method described above.


## 3.3.4. Evaluation Standards for the Prediction Results

For the predicted value of cumulative deaths in each rolling period,R2 and MSE were used as evaluation standards of the model. R2 refers to the correlation square coefficient, and MSE is the mean square error. The formula for the evaluation parameters is as follows:(4)R2=1−∑J=1jy^j−yj2∑J=1jy¯j−yj2,MSE=1j∑J=1jyj−y^j2,where J refers to the earthquake case set of the research samples, yj refers to the real value, y^j refers to the prediction value, and y¯j is the mean of the real values.In the comparison of the variation trend of cumulative deaths in all periods of the entire planning time domain of research cases with the variation trend of practical cumulative deaths, the overall prediction accuracy was evaluated by the relative errorRen in each period:(5)Ren=y^n−ynyn.


## 3.4. Material Demand Calculation Model Based on Warehouse Inventory Theory

According to Reference [42], during the modeling of material demands, if the total demand of a product is based on large-scale individual demands, then such demands can generally be viewed as conforming to normal distribution characteristics. For natural disasters, the decision-making department allocates emergency supplies based on the general prediction of demand in disaster areas. Such predictions are based on the number of individuals in affected disaster areas. Therefore, the prediction of postdisaster emergency materials is similar to that of the material demand model, in which inventory management theory was introduced.If the earthquake in a region is at 0, and this moment (unit: h) is used as the starting point of emergency rescue, then the survival numberSt in the disaster area t after the occurrence of a disaster is,(6)St=δ−Nt,where δ refers to the total population in the affected disaster areas, and N(t) is the cumulative deaths by the end of t.The necessary emergency supplies are diverse after the occurrence of natural disasters. Therefore, the calculation models of demand for FMCGs and durable goods vary. The formula to calculate the demandsDkt of disaster regions for emergency material k in disaster areas is derived according to warehouse inventory theory as follows:(7)Dkt=ak×St×LT+Z∂×σk×LTk∈Rfcak×St−Bk−∑ε=0t−1Akt−εk∈Rdg,where ∂ refers to the rate of shorts of materials and equipment resources. 1−∂ refers to the degree of satisfaction of people in the disaster area to emergency resources and conforms to a normal distribution. Z1−∂ is the coefficient corresponding to the satisfaction degree of 1−∂, and its numerical value can be obtained through a normal distribution. LT refers to the maximum interval of successful emergency supply delivery to disaster areas; that is, one rolling period was divided in this study. Bk refers to the material inventory before the occurrence of an earthquake. Akt−ε refers to material transportation in t−ε. The formula for calculating the standard deviation of demands σkt is as follows:(8)σkt=∑ε=0t−1Dkt−ε−D¯kt2t.The mean demandD¯kt of disaster areas for emergency material k per unit time by the end of t must be calculated according to (8). The calculation formula is as follows:(9)D¯kt=∑ε=0t−1Dkt−εt.Thus, the relationship between the survival rate and emergency supplies after a disaster can be derived through inventory theory. This theory was used to study the dynamic demands of victims for emergency supplies after the occurrence of earthquakes.


## 4. Algorithm Design

According to the above rough set reduction model and the SVM prediction model based on the rolling time-domain framework, the steps and pseudocodes of the main algorithms of the two models are presented in Tables2 and 3, respectively.Table 2
Steps and pseudocodes of reduction algorithms.
Algorithm 1: Attribute reduction algorithm based on rough setInput: given the data decision tableS=U,X,Y,V,fU: domain of discourse, earthquake cases;X: condition attribute set, including epicenter position, earthquake magnitude, time of occurrence, and other initial index attributes;Y: decision attribute set, that is, earthquake-induced deaths;V: domain set of attributes; f: Information function;Output: Reduction set of important index attribute set.Steps:Step 1: Determine the reduction core CORE to calculate the condition attribute of earthquake cases;Step 2: Calculate reduction sets of the condition attribute of earthquake cases;Step 3: Combine the calculated reduction sets;Step 4: Generate condition attribute reduction sets. End.Pseudocodes:The condition sets are assigned toCORE;Fori = 0: l−1Calculate the importance of indicatorl in condition attribute sets in earthquake cases;Individually judge the necessity of condition attribute indexes;If the condition attribute is necessary;The intersection between this condition attribute and the kernel set is selected;End ifThe reduction kernel of the condition attribute is obtained;End forwhile the kernel set that deaths rely on is not equal to the dependent condition attribute set;If the step kernel set of condition attribute i, it is added into the kernel set;Implementi = i + 1;Recalculate the dependence of decision attributes on the kernel set;Else if implement i = i + 1;End ifEnd whileTable 3
Steps and pseudocodes of prediction algorithms.
Algorithm 2: SVM prediction algorithm based on rolling time-domain frameworkInput: Index attribute set in each periodOutput: Prediction value of deaths in the current periodSteps:Step 1: Determine the overall planning time-domain (T) and rolling period (n);Step 2: Determine the input attribute set X=xi, the output attribute set Y, and the training and testing samples;Step 3: Data normalization. The original data are mapped to the interval [−1, 1] by using the mapminmax function to finish linear transformation of the original sample data. The transformation model isy=ymax−ymin×x−xmin/xmax−xmin+ymin.Step 4: Determine the kernel function and relevant parameters; the RBF kernel function is chosen as the kernel function of the prediction model, and the value of σ is searched by the K-fold cross-validation method. It is combined with the grid search method to determine the optimal values of parameters c and g.Step 5: Generate the prediction function: The abovementioned nonlinear regression model is applied for training and prediction. Thus, the prediction results are obtained.Step 6: Update the input condition attribute set. If the prediction in all periods is not finished, then proceed to Step 3; else, the process is completed.Updating pseudocodes of the input attribute set:If the prediction period is smaller than the preset rolling period n;Then the input attribute index set is xi+n. The condition attribute i+n is the combination of the output prediction value yn of the target sample in the previous period and the simulation results Njn of cumulative deaths of the other samples in the same period:x1+n=Njn∪yn;Else if the prediction period is higher than or equal to the preset rolling period n;Finish the prediction of deaths in all periods of the entire plan time-domain;End if


## 5. Case Study

The codes for the proposed model were compiled using the MATLAB software platform through a case study on dynamic material demands in disaster areas after the Wenchuan earthquake. The encoded model was used to predict material demands and was proven to be scientific and effective. The proposed model can quickly predict the emergency material demands of victims after the occurrence of natural disasters. This model can also provide references for decision-making departments to adopt emergency relief work in a timely manner.


### 5.1. Determination of Rolling Time-Domain Framework

In determining the rolling time-domain structural framework, the first seven days (168 h) after the occurrence of the Wenchuan earthquake were chosen as the planning time domain. A rolling period was determined every 8 h, and the prediction stage was set every 24 h. Considering this case study, a total of 21 rolling periods were divided (Figure4).Figure 4
Division of periods of rolling time-domain in the case study.


### 5.2. Data Source

#### 5.2.1. Historical Case Data

Considering the practical significance of the studies, great earthquakes (>6 magnitudes), which have caused considerable life and property losses in the last 50 years in China, were chosen as the research samples of historical cases (30). The index attributes, which were chosen preliminarily, include epicenter position, magnitudes, time of occurrence, focal depth, epicentral intensity, population density, fortification level, earthquake forecasting, and deaths. The details are presented in Table4.Table 4
Sample data of historical earthquake cases.
Sample no.PlaceMagnitudesTimeFocal depthEpicentral intensityFortification levelPopulation densityEarthquake forecastingDeaths1Tangshan, Hebei Province7.803:42231151100002427692Min county, Gansu Province6.607:4520971461953Haicheng, Liaoning Province7.319:361695670120414Xintai, Hebei Province7.216:1910105462080645Longlin, Yunnan Province7.320:23127526891986Wuding, Yunnan Province6.506:461596551527Lijiang, Yunnan Province719:14101065813098Payzawat County, Xinjiang Autonomous Region6.617:0312865812629Shangyi, Hebei Province6.211:50108611504910Yushu, Qinhai Province7.107:49149770269811Daguan, Yunnan Province7.103:2589511061142312Lancang, Yunnan Province7.421:03139766074813Luhuo, Yunnan Province7.918:3714105610217514Jiuzhaigou, Sichuan Province721:1920961513015Ludian, Yunnan Province6.516:401287287061716Horinger, Neimenggu6.300:5418852204217Zhaosu, Xinjiang Autonomous Region6.09:3818751101018Songpan, Sichuan Province7.222:06159537075519Wuqia, Xinjiang Autonomous Region6.823:522776417020Damxung County, Tibet6.616:30885901021Minle, Gansu Province6.120:4118752801622Marabishi, Xinjiang Autonomous Region6.810:03168510025823Gonghe, Qinhai Province7.017:3715857011924Liyang, Jiangsu Province6.018:57137533704125Dayao, Yunnan Province6.223:1667610111026Nantou, Taiwan Province7.61:478762160241527Lushan, Guizhou Province708:02139792119628Tonghai, Yunnan Province7.701:001010526701562129Huili, Sichuan Province6.116:30127710114130Wenchuan, Sichuan Province814:2814117237069227


#### 5.2.2. Simulation Data

The simulation data cover the desktop walkthrough and time-sharing simulation data. The data size must be expanded to improve prediction accuracy because of the considerably limited statistical data of historical disasters. Considering the data attributes of the epicenter position and time factors, a desktop walkthrough was performed on the historical data. Herein, the data of the two indexes were simulated on the basis of the abovementioned discretization rule of attribute indexes, finally obtaining 970 desktop walkthrough data. Some of the simulation data are listed in Table5.Table 5
Some desktop walkthrough data.
Sample no.PlaceMagnitudesTimeFocal depthEpicentral intensityFortification levelPopulation densityEarthquake forecastingDeaths107.401295417134466217.301496124513808338.211811713704018426.711495710538506.2020958211097637.411610572004023737.10117726079827.3128116771384937.1114761016098481007.4119859703861..............................96636.8025955918596736.302096904796837.401896282501156496927.4126853560149097016.511197950662In addition, the time-sharing simulation data in a single period were generated through (1) using 30 historical case data and 970 desktop walkthrough data. Given the large data size, only 30 historical case data points are listed in the following tables. The time-sharing simulation data for the first eight periods are listed in Table 6.Table 6
Time-sharing simulation data.
SamplePeriods12345678...1548410844160832120426209311013588240556...22543566673798386...385165242316387455521583...42575057459781203142116321837...5815212732374246...648111417192224...72343628096111125139...817334861748698108...947101316182123...10220421607777933107612081329...1167131192250305358408456...124995137177214249282312...1318435451065578991310271132...141320242728293030...15189319410474517548569584...163681113151718...1713445667...1855106153197237275310342...19510141822252831...2012344566...21235678910...222140587489103115127...23713182429343943...243691113151719...2522445556...26148286416539653761862957...271320242728293030...28189319410474517548569584...2973119148166177184189192...306281231180923642897340838994370.................................In this study, historical case and desktop walkthrough data were integrated to produce 1000 data points as the general samples. Twenty subsets were set. Among the 1000 data, 950 data were used as training samples and 50 data were used as testing samples, covering 27–30 historical case samples. Furthermore, the 50th test sample was set as the 30# historical case sample, that is, the data of the Wenchuan earthquake. The test sample was used as the sample for analysis in this case study. The codes were compiled in the MATLAB2016A software platform using the above algorithm. Finally, the program orders were implemented for attribute reduction of the dataset and the prediction of deaths in all periods, thus completing the experiment.


### 5.3. Attribute Reduction

In the sample data of the initial attribute indexes, the conditional attributes areX = {x1, x2, x3, x4, x5, x6, x7, x8}, which indicate the epicenter position, time of occurrence, focal depth, magnitude, epicentral intensity, fortification level, population density, and earthquake forecasting. The decision attribute is Y = {death}. According to the initial decision table, the discretization of continuous attributes is realized by natural division. The discretization rules are presented in Table 7.Table 7
Discretization rule of index attributes.
v01234c1North ChinaEast ChinaNorthwestSouthwestOthersc2[6.0, 6.9][7.0, 7.9][8.0, 8.9]——c3[20:00, 8:00)[8:00, 20:00)———c4(0, 10)[10, 20)[20, 30)——c57891011c6567——c7(0, 99)[100, 999)[1000, 9999)[10000, +∞)-c801———d(0, 99)[100, 999)[1000, 9999)[10000, 100000)[100000, +∞)The discretization results based on the above discretization rule are shown in Table8.Table 8
Discretization results of attributes.
uc1c2c3c4c5c6c7c8d101024030422002221103111120112401113010253101002106300121010731113101182011110119001111100102101220021131002021212310122001133111300021431022101015301112101161001100001730110000018210120001192002010102030101000021200100000222011100012321111000124401100100253000011102641000110227311122011283101301032930110211030321142103..............................GA was chosen as the basic algorithm for attribute reduction of the sample data in the present study. The discretized decision table represents the input. The coding result of attribute reduction was 01101111 when the crossover and mutation probabilities werePc=0.7 and Pm=0.01, respectively. This result indicates that the condition attributes after the final reduction were {x2, x3, x5, x6, x7, x8}, which denote magnitudes, time of occurrence, epicentral intensity, fortification level, population density, and earthquake forecasting, respectively. The reduced attributes were used as design references for the SVM, and the relevant reduced attribute dataset was used as the initial attribute value of the input.


### 5.4. Prediction Experiment

According to the abovementioned prediction experimental steps, SVM type, loss function, judgment references for ending iteration, and number of cross-validations were set to e-SVR, 0.1, 0.001, and 5, respectively. The optimal parametersc and g were selected through cross-validation. Finally, the experimental data for 21 rolling periods were obtained. In the following text, the prediction results of the first, second, and last rolling periods are analyzed.During the prediction of deaths in the first rolling period, the input attributes included magnitude, time of occurrence, epicentral intensity, fortification level, population density, and earthquake forecasting. The output result was cumulative deaths within 8 h after the earthquake. According to the cross-validation of the training sample set, the optimal parameters werec = 541 and g = 0.0587. The prediction results were obtained by introducing c = 541 and g = 0.0587 into the test sample set (Figure 5).Figure 5
Prediction results in the first rolling period.The prediction results of the testing samples in the first rolling period are shown in Figure5, where the MSE and R2 are 0.1347 and 91.04%, respectively. At this moment, the output value of the predicted cumulative deaths in the first period of earthquake case samples and the simulation values of cumulative deaths in the first period of other earthquake cases were used as the condition attribute set. These indexes were added to the input attribute of the first period, which was used as the input attribute of the second period. Cumulative deaths at 16 h after the occurrence of earthquakes were recorded. Moreover, the optimal values of parameters c and g change with the input attribute set. Hence, cross-validation must be performed. Finally, c = 619 and g = 0.0472 were determined. The two parameters were introduced into the testing samples to obtain the prediction results of the cumulative deaths in the second period (Figure 6).Figure 6
Prediction results of the second period.The prediction results of the testing samples in the second rolling period are shown in Figure6, where the MSE and R2 are 0.1135 and 93.86%, respectively. In addition, MSE and R2 are lower and higher, respectively, than those of the first period. This finding indicates a higher prediction accuracy for the second period than that of the first period. Similarly, the input attributes of the last period included 26 attributes, which were six original indexes and cumulative deaths of the first 20 periods. The output value is the predicted death of the 21st period. The values of c and g were 1173 and 0.0849, respectively, according to cross-validation. These values were introduced into the testing samples to obtain the prediction results of the cumulative deaths in the last period (Figure 7).Figure 7
Prediction results of the last rolling period.The prediction results of the testing samples in the last rolling period are shown in Figure7, where the MSE and R2 are 0.0519 and 99.23%, respectively. By combining Figures 5–7, the MSE of the last period is lower, but R2 is higher than those of the first and second periods. The MSE decreases while R2 continuously increases when the period rolls forward (Table 9).Table 9
Prediction accuracy of testing samples in the planning time-domain.
PeriodsMSER210.13470.910420.11350.938630.10970.947840.10160.954350.09530.956160.09740.961270.09160.96380.08680.963790.08210.9682100.08190.9723110.07520.9754120.07640.9716130.07150.9815140.06890.9726150.06470.9779160.06380.9782170.06210.9764180.05470.9791190.05830.9803200.05340.9808210.05190.9819The variation curve of death prediction was drawn according to the prediction data from the Wenchuan earthquake (50th sample) in each period. Meanwhile, real-time report data of media after the occurrence of the Wenchuan earthquake were obtained, and data at the missing time points were generated by the time-sharing simulation model to ensure the complete real-time statistical data of the 21 divided periods. The real variation trend of cumulative deaths was drawn. A comparison diagram of the predicted and real values is shown in Figure8.Figure 8
Comparison between predicted and real values of cumulative deaths.In Figure8, the black solid line is the variation curve of the real cumulative deaths with time after the occurrence of earthquakes, while the red solid line is the variation curve of the prediction results. A considerable error was observed in the first 48 h after the occurrence of an earthquake because this was the period with a sharp increase in deaths. The prediction result is a decision attribute and is generated by the time-sharing simulation based on the gross data of historical earthquake cases. However, the error between the real value and prediction results gradually decreased with the forward roll of the period. The average relative error is 10.96%.


### 5.5. Comparative Analysis

Three groups of comparative experiments were performed to reflect the scientificity and effectiveness of the proposed SVM prediction method intuitively based on the rolling time domain. The first group is an experiment for selecting the prediction algorithm, a comparative experiment on prediction performances between the BP neural network based on general data and no period division and SVM. The second group is a comparative experiment of SVM, that is, the comparison between dynamic and multiperiod static predictions based on the rolling time-domain framework. The third group is a comparative experiment among the different methods. Thus, the proposed method was compared with the interval data fusion (IDF) prediction method based on the rolling time-domain framework in Reference [28].


#### 5.5.1. Comparison between BP and SVM Methods

This comparison is an advanced experiment conducted to reveal that the SVM method is more applicable to this study than the BP neural network. The prediction results of the testing samples based on the BP neural network are shown in Figure9(a). The prediction results of the testing samples based on SVM are shown in Figure 9(b). This experiment is a general prediction based on the sample data.Figure 9
Prediction results of the two methods. (a) Prediction results based on the BP neural network and (b) prediction results based on SVM.
(a)(b)Figure9 indicates that the prediction results based on the BP neural network fluctuate more evidently than the real values, while the prediction results based on SVM fluctuate less than the real values. The prediction errors of the four historical cases in the testing set were analyzed to compare the prediction results intuitively. The results are listed in Table 10.Table 10
Comparison of prediction results based on BP neural network and SVM.
No. of historical casesReal valuesPrediction results based on BP neural networkPrediction results based on SVMPrediction resultsPrediction errorPrediction resultsPrediction error161962470.26022330.18881715621200310.2823179620.14761841540.3171480.17071969227526950.2388791150.1428According to the above figures and tables, SVM has a smaller prediction error than that of the BP neural network in terms of sample points and general data. Overall, SVM is applicable to the prediction of this study.


#### 5.5.2. Static Prediction Method for SVM

The static prediction of the SVM involves no rolling. That is, the input prediction results of the previous period were not used as the input value for the next period. Furthermore, the input attribute index was fixed, and no input attribute was added with the rolling forward of periods. This highlights the high accuracy of the rolling prediction method. An experimental comparison of the various trends of deaths over time is shown in Figure10.Figure 10
Comparison between rolling and static predictions.Figure10 shows that the solid blue line is a static prediction. The rolling prediction is closer to the variation trend of the real-time numerical value of earthquakes than the static prediction.


#### 5.5.3. IDF Prediction Method

This comparative experiment compared the effectiveness of the proposed method. The IDF was proposed by Lu in [28] to predict the cumulative deaths in multiple periods after the occurrence of earthquakes based on the rolling time domain. The prediction results of the IDF method are presented at intervals. In this study, the IDF method was used as the major comparative method for predicting deaths during the Wenchuan earthquake. The prediction results were compared with those obtained using the proposed method.Reference [28] had limited data sources. The prediction of an earthquake is mainly based on real-time data sources from government sections, in situ rescues, and media journalists. Time-sharing simulation data were used to fill in the missing official historical data and were then used as the real values for comparative analysis. This study had access to relatively comprehensive data sources based on historical statistical and simulation data and real-time disaster information after the occurrence of multiple earthquakes.This case was predicted using the method described in Reference [28]. The prediction results were compared with those obtained using the proposed method (Figure 11).Figure 11
Variation trend of prediction results of IDF method.Figure11 shows that the blue dotted line represents the prediction intervals of each period. If the real value falls in the prediction interval, then the prediction is successful; otherwise, the prediction is invalid. This prediction method has certain fuzziness and cannot accurately reflect the practical prediction accuracy. For the convenience of comparison with the proposed method, the midvalue of the prediction intervals in each period was chosen as the control group. On this basis, the variation curve of the prediction results was drawn, as denoted by the cyan solid line in Figure 11.The fitting degree of the IDF and the proposed methods was satisfactory in the first 120 h, with a small difference. However, the width of the prediction intervals in the IDF method gradually increased over time. This phenomenon raises the uncertainty of the prediction results. Moreover, the prediction error of the midvalue of the intervals relative to the real values gradually increased. The prediction results of the proposed method are fixed and single, resulting in the absence of error growth with the rolling of the prediction period. Overall, the dynamic prediction error of the SVM is even small.The relative errors of the BP, IDF, and dynamic SVM methods in a single period are compared in the following text. The results are presented in Figure12 and Table 11.Figure 12
Comparison of prediction errors of three methods.Table 11
Comparison of period-based prediction error.
Period1234567Static prediction error0.6110.47940.38420.23070.17930.11770.0765IDF prediction error0.59610.44070.39990.22840.1570.10640.0562Dynamic prediction error0.6110.39940.32690.22130.12790.08860.0162Period891011121314Static prediction error0.03820.00390.06890.03660.07560.11390.142IDF prediction error0.02140.02730.05050.02370.04640.07540.0613Dynamic prediction error0.00510.05270.04720.01650.02780.04140.058Period15161718192021Static prediction error0.14240.15850.14870.1570.17880.18210.2055IDF prediction error0.06550.06490.06710.09040.11540.12420.1489Dynamic prediction error0.04040.03360.03240.03720.03950.03220.0466According to the above error changes and the statistical table, a single static prediction was performed by SVM, and the prediction error was 17.77%. The prediction error of the IDF method is 14.13%. The prediction error of the SVM based on the rolling time-domain framework is 10.96%. The overall prediction accuracy is approximately 90%. This finding reveals that the SVM prediction method based on the rolling time domain can effectively improve prediction accuracy.


### 5.6. Calculation of Emergency Material Dynamic Demands

After predicting the cumulative deaths in each period in disaster areas, the demand for research materials in each period was estimated according to the prediction results of the 19# samples (Wenchuan earthquake) using warehouse inventory theory. In this study, the parameters of the calculation formula of warehouse inventory theory were set, as shown in Table12.Table 12
Settings of relevant parameters.
Parameters (unit)∂1−∂Z1−∂LT (h)a1 (ml/h)a2 (g/h)a3Numerical values0.050.951.658120300.25In Table12, a1 denotes drinking water, a2 is the compressed biscuit, and a3 is the tent. Meanwhile, the stock-out rate (∂) is 0.05, such that the satisfaction degree of victims to materials is 95%. The normal distribution of the numerical value table shows that the corresponding coefficient is 1.65, and the value of the continuous maximum interval period (LT) for emergency supplies to the disaster areas is the setting value of the rolling period.According to Reference [39], the total victim population of the Wenchuan earthquake was 104,870,000. The survivors were zoomed 1000 times for convenient material estimation due to the considerable losses and large victim population base. If the victim population was 104,870, then the survival quantity in each rolling period could be calculated from (8) according to the total survival. Specific information is shown in Table 13.Table 13
Survivals in each period.
Rolling periods1234567Survivals102736994339698194832927239131688885Within seven days after the occurrence of the Wenchuan earthquake, the dynamic demands for drinking water and compressed biscuit in the disaster area in each period could be estimated from Equations (9), (11), and (12). The first period is the initial moment after the earthquake; therefore, σk0=0. The estimation results of the FMCG demands for each period are shown in Table 14.Table 14
Estimations of dynamic material demands in each rolling period.
Rolling periodTime after earthquakeDemands for drinking water (ml)Demands for compressed biscuit (g)18131502080246566402161272742402386392032412413568023275440432121384960227596805401186854402225352064811688448021915840756113772800213324008641111731202084496097210799744020249520108010603520019881600118810370944019445520129610177408019082640131049958528018672240141129718272018221760151209575424017953920161289453824017725920171369257216017357280181449111168017083440191529030400016932000201608947456016776480211688864768016621440The tent is a durable good. The demand for tents during the first rolling period was 25,684. Unlike FMCGs, the demand for durable goods in the latter stage is slightly influenced by time in practical situations, resulting in small differences among different stages. Considering practical significance, the demands for FMCGs in multiple periods were estimated, while those for durable goods in a single period were estimated globally.


## 5.1. Determination of Rolling Time-Domain Framework

In determining the rolling time-domain structural framework, the first seven days (168 h) after the occurrence of the Wenchuan earthquake were chosen as the planning time domain. A rolling period was determined every 8 h, and the prediction stage was set every 24 h. Considering this case study, a total of 21 rolling periods were divided (Figure4).Figure 4
Division of periods of rolling time-domain in the case study.


## 5.2. Data Source

### 5.2.1. Historical Case Data

Considering the practical significance of the studies, great earthquakes (>6 magnitudes), which have caused considerable life and property losses in the last 50 years in China, were chosen as the research samples of historical cases (30). The index attributes, which were chosen preliminarily, include epicenter position, magnitudes, time of occurrence, focal depth, epicentral intensity, population density, fortification level, earthquake forecasting, and deaths. The details are presented in Table4.Table 4
Sample data of historical earthquake cases.
Sample no.PlaceMagnitudesTimeFocal depthEpicentral intensityFortification levelPopulation densityEarthquake forecastingDeaths1Tangshan, Hebei Province7.803:42231151100002427692Min county, Gansu Province6.607:4520971461953Haicheng, Liaoning Province7.319:361695670120414Xintai, Hebei Province7.216:1910105462080645Longlin, Yunnan Province7.320:23127526891986Wuding, Yunnan Province6.506:461596551527Lijiang, Yunnan Province719:14101065813098Payzawat County, Xinjiang Autonomous Region6.617:0312865812629Shangyi, Hebei Province6.211:50108611504910Yushu, Qinhai Province7.107:49149770269811Daguan, Yunnan Province7.103:2589511061142312Lancang, Yunnan Province7.421:03139766074813Luhuo, Yunnan Province7.918:3714105610217514Jiuzhaigou, Sichuan Province721:1920961513015Ludian, Yunnan Province6.516:401287287061716Horinger, Neimenggu6.300:5418852204217Zhaosu, Xinjiang Autonomous Region6.09:3818751101018Songpan, Sichuan Province7.222:06159537075519Wuqia, Xinjiang Autonomous Region6.823:522776417020Damxung County, Tibet6.616:30885901021Minle, Gansu Province6.120:4118752801622Marabishi, Xinjiang Autonomous Region6.810:03168510025823Gonghe, Qinhai Province7.017:3715857011924Liyang, Jiangsu Province6.018:57137533704125Dayao, Yunnan Province6.223:1667610111026Nantou, Taiwan Province7.61:478762160241527Lushan, Guizhou Province708:02139792119628Tonghai, Yunnan Province7.701:001010526701562129Huili, Sichuan Province6.116:30127710114130Wenchuan, Sichuan Province814:2814117237069227


### 5.2.2. Simulation Data

The simulation data cover the desktop walkthrough and time-sharing simulation data. The data size must be expanded to improve prediction accuracy because of the considerably limited statistical data of historical disasters. Considering the data attributes of the epicenter position and time factors, a desktop walkthrough was performed on the historical data. Herein, the data of the two indexes were simulated on the basis of the abovementioned discretization rule of attribute indexes, finally obtaining 970 desktop walkthrough data. Some of the simulation data are listed in Table5.Table 5
Some desktop walkthrough data.
Sample no.PlaceMagnitudesTimeFocal depthEpicentral intensityFortification levelPopulation densityEarthquake forecastingDeaths107.401295417134466217.301496124513808338.211811713704018426.711495710538506.2020958211097637.411610572004023737.10117726079827.3128116771384937.1114761016098481007.4119859703861..............................96636.8025955918596736.302096904796837.401896282501156496927.4126853560149097016.511197950662In addition, the time-sharing simulation data in a single period were generated through (1) using 30 historical case data and 970 desktop walkthrough data. Given the large data size, only 30 historical case data points are listed in the following tables. The time-sharing simulation data for the first eight periods are listed in Table 6.Table 6
Time-sharing simulation data.
SamplePeriods12345678...1548410844160832120426209311013588240556...22543566673798386...385165242316387455521583...42575057459781203142116321837...5815212732374246...648111417192224...72343628096111125139...817334861748698108...947101316182123...10220421607777933107612081329...1167131192250305358408456...124995137177214249282312...1318435451065578991310271132...141320242728293030...15189319410474517548569584...163681113151718...1713445667...1855106153197237275310342...19510141822252831...2012344566...21235678910...222140587489103115127...23713182429343943...243691113151719...2522445556...26148286416539653761862957...271320242728293030...28189319410474517548569584...2973119148166177184189192...306281231180923642897340838994370.................................In this study, historical case and desktop walkthrough data were integrated to produce 1000 data points as the general samples. Twenty subsets were set. Among the 1000 data, 950 data were used as training samples and 50 data were used as testing samples, covering 27–30 historical case samples. Furthermore, the 50th test sample was set as the 30# historical case sample, that is, the data of the Wenchuan earthquake. The test sample was used as the sample for analysis in this case study. The codes were compiled in the MATLAB2016A software platform using the above algorithm. Finally, the program orders were implemented for attribute reduction of the dataset and the prediction of deaths in all periods, thus completing the experiment.


## 5.2.1. Historical Case Data

Considering the practical significance of the studies, great earthquakes (>6 magnitudes), which have caused considerable life and property losses in the last 50 years in China, were chosen as the research samples of historical cases (30). The index attributes, which were chosen preliminarily, include epicenter position, magnitudes, time of occurrence, focal depth, epicentral intensity, population density, fortification level, earthquake forecasting, and deaths. The details are presented in Table4.Table 4
Sample data of historical earthquake cases.
Sample no.PlaceMagnitudesTimeFocal depthEpicentral intensityFortification levelPopulation densityEarthquake forecastingDeaths1Tangshan, Hebei Province7.803:42231151100002427692Min county, Gansu Province6.607:4520971461953Haicheng, Liaoning Province7.319:361695670120414Xintai, Hebei Province7.216:1910105462080645Longlin, Yunnan Province7.320:23127526891986Wuding, Yunnan Province6.506:461596551527Lijiang, Yunnan Province719:14101065813098Payzawat County, Xinjiang Autonomous Region6.617:0312865812629Shangyi, Hebei Province6.211:50108611504910Yushu, Qinhai Province7.107:49149770269811Daguan, Yunnan Province7.103:2589511061142312Lancang, Yunnan Province7.421:03139766074813Luhuo, Yunnan Province7.918:3714105610217514Jiuzhaigou, Sichuan Province721:1920961513015Ludian, Yunnan Province6.516:401287287061716Horinger, Neimenggu6.300:5418852204217Zhaosu, Xinjiang Autonomous Region6.09:3818751101018Songpan, Sichuan Province7.222:06159537075519Wuqia, Xinjiang Autonomous Region6.823:522776417020Damxung County, Tibet6.616:30885901021Minle, Gansu Province6.120:4118752801622Marabishi, Xinjiang Autonomous Region6.810:03168510025823Gonghe, Qinhai Province7.017:3715857011924Liyang, Jiangsu Province6.018:57137533704125Dayao, Yunnan Province6.223:1667610111026Nantou, Taiwan Province7.61:478762160241527Lushan, Guizhou Province708:02139792119628Tonghai, Yunnan Province7.701:001010526701562129Huili, Sichuan Province6.116:30127710114130Wenchuan, Sichuan Province814:2814117237069227


## 5.2.2. Simulation Data

The simulation data cover the desktop walkthrough and time-sharing simulation data. The data size must be expanded to improve prediction accuracy because of the considerably limited statistical data of historical disasters. Considering the data attributes of the epicenter position and time factors, a desktop walkthrough was performed on the historical data. Herein, the data of the two indexes were simulated on the basis of the abovementioned discretization rule of attribute indexes, finally obtaining 970 desktop walkthrough data. Some of the simulation data are listed in Table5.Table 5
Some desktop walkthrough data.
Sample no.PlaceMagnitudesTimeFocal depthEpicentral intensityFortification levelPopulation densityEarthquake forecastingDeaths107.401295417134466217.301496124513808338.211811713704018426.711495710538506.2020958211097637.411610572004023737.10117726079827.3128116771384937.1114761016098481007.4119859703861..............................96636.8025955918596736.302096904796837.401896282501156496927.4126853560149097016.511197950662In addition, the time-sharing simulation data in a single period were generated through (1) using 30 historical case data and 970 desktop walkthrough data. Given the large data size, only 30 historical case data points are listed in the following tables. The time-sharing simulation data for the first eight periods are listed in Table 6.Table 6
Time-sharing simulation data.
SamplePeriods12345678...1548410844160832120426209311013588240556...22543566673798386...385165242316387455521583...42575057459781203142116321837...5815212732374246...648111417192224...72343628096111125139...817334861748698108...947101316182123...10220421607777933107612081329...1167131192250305358408456...124995137177214249282312...1318435451065578991310271132...141320242728293030...15189319410474517548569584...163681113151718...1713445667...1855106153197237275310342...19510141822252831...2012344566...21235678910...222140587489103115127...23713182429343943...243691113151719...2522445556...26148286416539653761862957...271320242728293030...28189319410474517548569584...2973119148166177184189192...306281231180923642897340838994370.................................In this study, historical case and desktop walkthrough data were integrated to produce 1000 data points as the general samples. Twenty subsets were set. Among the 1000 data, 950 data were used as training samples and 50 data were used as testing samples, covering 27–30 historical case samples. Furthermore, the 50th test sample was set as the 30# historical case sample, that is, the data of the Wenchuan earthquake. The test sample was used as the sample for analysis in this case study. The codes were compiled in the MATLAB2016A software platform using the above algorithm. Finally, the program orders were implemented for attribute reduction of the dataset and the prediction of deaths in all periods, thus completing the experiment.


## 5.3. Attribute Reduction

In the sample data of the initial attribute indexes, the conditional attributes areX = {x1, x2, x3, x4, x5, x6, x7, x8}, which indicate the epicenter position, time of occurrence, focal depth, magnitude, epicentral intensity, fortification level, population density, and earthquake forecasting. The decision attribute is Y = {death}. According to the initial decision table, the discretization of continuous attributes is realized by natural division. The discretization rules are presented in Table 7.Table 7
Discretization rule of index attributes.
v01234c1North ChinaEast ChinaNorthwestSouthwestOthersc2[6.0, 6.9][7.0, 7.9][8.0, 8.9]——c3[20:00, 8:00)[8:00, 20:00)———c4(0, 10)[10, 20)[20, 30)——c57891011c6567——c7(0, 99)[100, 999)[1000, 9999)[10000, +∞)-c801———d(0, 99)[100, 999)[1000, 9999)[10000, 100000)[100000, +∞)The discretization results based on the above discretization rule are shown in Table8.Table 8
Discretization results of attributes.
uc1c2c3c4c5c6c7c8d101024030422002221103111120112401113010253101002106300121010731113101182011110119001111100102101220021131002021212310122001133111300021431022101015301112101161001100001730110000018210120001192002010102030101000021200100000222011100012321111000124401100100253000011102641000110227311122011283101301032930110211030321142103..............................GA was chosen as the basic algorithm for attribute reduction of the sample data in the present study. The discretized decision table represents the input. The coding result of attribute reduction was 01101111 when the crossover and mutation probabilities werePc=0.7 and Pm=0.01, respectively. This result indicates that the condition attributes after the final reduction were {x2, x3, x5, x6, x7, x8}, which denote magnitudes, time of occurrence, epicentral intensity, fortification level, population density, and earthquake forecasting, respectively. The reduced attributes were used as design references for the SVM, and the relevant reduced attribute dataset was used as the initial attribute value of the input.


## 5.4. Prediction Experiment

According to the abovementioned prediction experimental steps, SVM type, loss function, judgment references for ending iteration, and number of cross-validations were set to e-SVR, 0.1, 0.001, and 5, respectively. The optimal parametersc and g were selected through cross-validation. Finally, the experimental data for 21 rolling periods were obtained. In the following text, the prediction results of the first, second, and last rolling periods are analyzed.During the prediction of deaths in the first rolling period, the input attributes included magnitude, time of occurrence, epicentral intensity, fortification level, population density, and earthquake forecasting. The output result was cumulative deaths within 8 h after the earthquake. According to the cross-validation of the training sample set, the optimal parameters werec = 541 and g = 0.0587. The prediction results were obtained by introducing c = 541 and g = 0.0587 into the test sample set (Figure 5).Figure 5
Prediction results in the first rolling period.The prediction results of the testing samples in the first rolling period are shown in Figure5, where the MSE and R2 are 0.1347 and 91.04%, respectively. At this moment, the output value of the predicted cumulative deaths in the first period of earthquake case samples and the simulation values of cumulative deaths in the first period of other earthquake cases were used as the condition attribute set. These indexes were added to the input attribute of the first period, which was used as the input attribute of the second period. Cumulative deaths at 16 h after the occurrence of earthquakes were recorded. Moreover, the optimal values of parameters c and g change with the input attribute set. Hence, cross-validation must be performed. Finally, c = 619 and g = 0.0472 were determined. The two parameters were introduced into the testing samples to obtain the prediction results of the cumulative deaths in the second period (Figure 6).Figure 6
Prediction results of the second period.The prediction results of the testing samples in the second rolling period are shown in Figure6, where the MSE and R2 are 0.1135 and 93.86%, respectively. In addition, MSE and R2 are lower and higher, respectively, than those of the first period. This finding indicates a higher prediction accuracy for the second period than that of the first period. Similarly, the input attributes of the last period included 26 attributes, which were six original indexes and cumulative deaths of the first 20 periods. The output value is the predicted death of the 21st period. The values of c and g were 1173 and 0.0849, respectively, according to cross-validation. These values were introduced into the testing samples to obtain the prediction results of the cumulative deaths in the last period (Figure 7).Figure 7
Prediction results of the last rolling period.The prediction results of the testing samples in the last rolling period are shown in Figure7, where the MSE and R2 are 0.0519 and 99.23%, respectively. By combining Figures 5–7, the MSE of the last period is lower, but R2 is higher than those of the first and second periods. The MSE decreases while R2 continuously increases when the period rolls forward (Table 9).Table 9
Prediction accuracy of testing samples in the planning time-domain.
PeriodsMSER210.13470.910420.11350.938630.10970.947840.10160.954350.09530.956160.09740.961270.09160.96380.08680.963790.08210.9682100.08190.9723110.07520.9754120.07640.9716130.07150.9815140.06890.9726150.06470.9779160.06380.9782170.06210.9764180.05470.9791190.05830.9803200.05340.9808210.05190.9819The variation curve of death prediction was drawn according to the prediction data from the Wenchuan earthquake (50th sample) in each period. Meanwhile, real-time report data of media after the occurrence of the Wenchuan earthquake were obtained, and data at the missing time points were generated by the time-sharing simulation model to ensure the complete real-time statistical data of the 21 divided periods. The real variation trend of cumulative deaths was drawn. A comparison diagram of the predicted and real values is shown in Figure8.Figure 8
Comparison between predicted and real values of cumulative deaths.In Figure8, the black solid line is the variation curve of the real cumulative deaths with time after the occurrence of earthquakes, while the red solid line is the variation curve of the prediction results. A considerable error was observed in the first 48 h after the occurrence of an earthquake because this was the period with a sharp increase in deaths. The prediction result is a decision attribute and is generated by the time-sharing simulation based on the gross data of historical earthquake cases. However, the error between the real value and prediction results gradually decreased with the forward roll of the period. The average relative error is 10.96%.


## 5.5. Comparative Analysis

Three groups of comparative experiments were performed to reflect the scientificity and effectiveness of the proposed SVM prediction method intuitively based on the rolling time domain. The first group is an experiment for selecting the prediction algorithm, a comparative experiment on prediction performances between the BP neural network based on general data and no period division and SVM. The second group is a comparative experiment of SVM, that is, the comparison between dynamic and multiperiod static predictions based on the rolling time-domain framework. The third group is a comparative experiment among the different methods. Thus, the proposed method was compared with the interval data fusion (IDF) prediction method based on the rolling time-domain framework in Reference [28].


### 5.5.1. Comparison between BP and SVM Methods

This comparison is an advanced experiment conducted to reveal that the SVM method is more applicable to this study than the BP neural network. The prediction results of the testing samples based on the BP neural network are shown in Figure9(a). The prediction results of the testing samples based on SVM are shown in Figure 9(b). This experiment is a general prediction based on the sample data.Figure 9
Prediction results of the two methods. (a) Prediction results based on the BP neural network and (b) prediction results based on SVM.
(a)(b)Figure9 indicates that the prediction results based on the BP neural network fluctuate more evidently than the real values, while the prediction results based on SVM fluctuate less than the real values. The prediction errors of the four historical cases in the testing set were analyzed to compare the prediction results intuitively. The results are listed in Table 10.Table 10
Comparison of prediction results based on BP neural network and SVM.
No. of historical casesReal valuesPrediction results based on BP neural networkPrediction results based on SVMPrediction resultsPrediction errorPrediction resultsPrediction error161962470.26022330.18881715621200310.2823179620.14761841540.3171480.17071969227526950.2388791150.1428According to the above figures and tables, SVM has a smaller prediction error than that of the BP neural network in terms of sample points and general data. Overall, SVM is applicable to the prediction of this study.


### 5.5.2. Static Prediction Method for SVM

The static prediction of the SVM involves no rolling. That is, the input prediction results of the previous period were not used as the input value for the next period. Furthermore, the input attribute index was fixed, and no input attribute was added with the rolling forward of periods. This highlights the high accuracy of the rolling prediction method. An experimental comparison of the various trends of deaths over time is shown in Figure10.Figure 10
Comparison between rolling and static predictions.Figure10 shows that the solid blue line is a static prediction. The rolling prediction is closer to the variation trend of the real-time numerical value of earthquakes than the static prediction.


### 5.5.3. IDF Prediction Method

This comparative experiment compared the effectiveness of the proposed method. The IDF was proposed by Lu in [28] to predict the cumulative deaths in multiple periods after the occurrence of earthquakes based on the rolling time domain. The prediction results of the IDF method are presented at intervals. In this study, the IDF method was used as the major comparative method for predicting deaths during the Wenchuan earthquake. The prediction results were compared with those obtained using the proposed method.Reference [28] had limited data sources. The prediction of an earthquake is mainly based on real-time data sources from government sections, in situ rescues, and media journalists. Time-sharing simulation data were used to fill in the missing official historical data and were then used as the real values for comparative analysis. This study had access to relatively comprehensive data sources based on historical statistical and simulation data and real-time disaster information after the occurrence of multiple earthquakes.This case was predicted using the method described in Reference [28]. The prediction results were compared with those obtained using the proposed method (Figure 11).Figure 11
Variation trend of prediction results of IDF method.Figure11 shows that the blue dotted line represents the prediction intervals of each period. If the real value falls in the prediction interval, then the prediction is successful; otherwise, the prediction is invalid. This prediction method has certain fuzziness and cannot accurately reflect the practical prediction accuracy. For the convenience of comparison with the proposed method, the midvalue of the prediction intervals in each period was chosen as the control group. On this basis, the variation curve of the prediction results was drawn, as denoted by the cyan solid line in Figure 11.The fitting degree of the IDF and the proposed methods was satisfactory in the first 120 h, with a small difference. However, the width of the prediction intervals in the IDF method gradually increased over time. This phenomenon raises the uncertainty of the prediction results. Moreover, the prediction error of the midvalue of the intervals relative to the real values gradually increased. The prediction results of the proposed method are fixed and single, resulting in the absence of error growth with the rolling of the prediction period. Overall, the dynamic prediction error of the SVM is even small.The relative errors of the BP, IDF, and dynamic SVM methods in a single period are compared in the following text. The results are presented in Figure12 and Table 11.Figure 12
Comparison of prediction errors of three methods.Table 11
Comparison of period-based prediction error.
Period1234567Static prediction error0.6110.47940.38420.23070.17930.11770.0765IDF prediction error0.59610.44070.39990.22840.1570.10640.0562Dynamic prediction error0.6110.39940.32690.22130.12790.08860.0162Period891011121314Static prediction error0.03820.00390.06890.03660.07560.11390.142IDF prediction error0.02140.02730.05050.02370.04640.07540.0613Dynamic prediction error0.00510.05270.04720.01650.02780.04140.058Period15161718192021Static prediction error0.14240.15850.14870.1570.17880.18210.2055IDF prediction error0.06550.06490.06710.09040.11540.12420.1489Dynamic prediction error0.04040.03360.03240.03720.03950.03220.0466According to the above error changes and the statistical table, a single static prediction was performed by SVM, and the prediction error was 17.77%. The prediction error of the IDF method is 14.13%. The prediction error of the SVM based on the rolling time-domain framework is 10.96%. The overall prediction accuracy is approximately 90%. This finding reveals that the SVM prediction method based on the rolling time domain can effectively improve prediction accuracy.


## 5.5.1. Comparison between BP and SVM Methods

This comparison is an advanced experiment conducted to reveal that the SVM method is more applicable to this study than the BP neural network. The prediction results of the testing samples based on the BP neural network are shown in Figure9(a). The prediction results of the testing samples based on SVM are shown in Figure 9(b). This experiment is a general prediction based on the sample data.Figure 9
Prediction results of the two methods. (a) Prediction results based on the BP neural network and (b) prediction results based on SVM.
(a)(b)Figure9 indicates that the prediction results based on the BP neural network fluctuate more evidently than the real values, while the prediction results based on SVM fluctuate less than the real values. The prediction errors of the four historical cases in the testing set were analyzed to compare the prediction results intuitively. The results are listed in Table 10.Table 10
Comparison of prediction results based on BP neural network and SVM.
No. of historical casesReal valuesPrediction results based on BP neural networkPrediction results based on SVMPrediction resultsPrediction errorPrediction resultsPrediction error161962470.26022330.18881715621200310.2823179620.14761841540.3171480.17071969227526950.2388791150.1428According to the above figures and tables, SVM has a smaller prediction error than that of the BP neural network in terms of sample points and general data. Overall, SVM is applicable to the prediction of this study.


## 5.5.2. Static Prediction Method for SVM

The static prediction of the SVM involves no rolling. That is, the input prediction results of the previous period were not used as the input value for the next period. Furthermore, the input attribute index was fixed, and no input attribute was added with the rolling forward of periods. This highlights the high accuracy of the rolling prediction method. An experimental comparison of the various trends of deaths over time is shown in Figure10.Figure 10
Comparison between rolling and static predictions.Figure10 shows that the solid blue line is a static prediction. The rolling prediction is closer to the variation trend of the real-time numerical value of earthquakes than the static prediction.


## 5.5.3. IDF Prediction Method

This comparative experiment compared the effectiveness of the proposed method. The IDF was proposed by Lu in [28] to predict the cumulative deaths in multiple periods after the occurrence of earthquakes based on the rolling time domain. The prediction results of the IDF method are presented at intervals. In this study, the IDF method was used as the major comparative method for predicting deaths during the Wenchuan earthquake. The prediction results were compared with those obtained using the proposed method.Reference [28] had limited data sources. The prediction of an earthquake is mainly based on real-time data sources from government sections, in situ rescues, and media journalists. Time-sharing simulation data were used to fill in the missing official historical data and were then used as the real values for comparative analysis. This study had access to relatively comprehensive data sources based on historical statistical and simulation data and real-time disaster information after the occurrence of multiple earthquakes.This case was predicted using the method described in Reference [28]. The prediction results were compared with those obtained using the proposed method (Figure 11).Figure 11
Variation trend of prediction results of IDF method.Figure11 shows that the blue dotted line represents the prediction intervals of each period. If the real value falls in the prediction interval, then the prediction is successful; otherwise, the prediction is invalid. This prediction method has certain fuzziness and cannot accurately reflect the practical prediction accuracy. For the convenience of comparison with the proposed method, the midvalue of the prediction intervals in each period was chosen as the control group. On this basis, the variation curve of the prediction results was drawn, as denoted by the cyan solid line in Figure 11.The fitting degree of the IDF and the proposed methods was satisfactory in the first 120 h, with a small difference. However, the width of the prediction intervals in the IDF method gradually increased over time. This phenomenon raises the uncertainty of the prediction results. Moreover, the prediction error of the midvalue of the intervals relative to the real values gradually increased. The prediction results of the proposed method are fixed and single, resulting in the absence of error growth with the rolling of the prediction period. Overall, the dynamic prediction error of the SVM is even small.The relative errors of the BP, IDF, and dynamic SVM methods in a single period are compared in the following text. The results are presented in Figure12 and Table 11.Figure 12
Comparison of prediction errors of three methods.Table 11
Comparison of period-based prediction error.
Period1234567Static prediction error0.6110.47940.38420.23070.17930.11770.0765IDF prediction error0.59610.44070.39990.22840.1570.10640.0562Dynamic prediction error0.6110.39940.32690.22130.12790.08860.0162Period891011121314Static prediction error0.03820.00390.06890.03660.07560.11390.142IDF prediction error0.02140.02730.05050.02370.04640.07540.0613Dynamic prediction error0.00510.05270.04720.01650.02780.04140.058Period15161718192021Static prediction error0.14240.15850.14870.1570.17880.18210.2055IDF prediction error0.06550.06490.06710.09040.11540.12420.1489Dynamic prediction error0.04040.03360.03240.03720.03950.03220.0466According to the above error changes and the statistical table, a single static prediction was performed by SVM, and the prediction error was 17.77%. The prediction error of the IDF method is 14.13%. The prediction error of the SVM based on the rolling time-domain framework is 10.96%. The overall prediction accuracy is approximately 90%. This finding reveals that the SVM prediction method based on the rolling time domain can effectively improve prediction accuracy.


## 5.6. Calculation of Emergency Material Dynamic Demands

After predicting the cumulative deaths in each period in disaster areas, the demand for research materials in each period was estimated according to the prediction results of the 19# samples (Wenchuan earthquake) using warehouse inventory theory. In this study, the parameters of the calculation formula of warehouse inventory theory were set, as shown in Table12.Table 12
Settings of relevant parameters.
Parameters (unit)∂1−∂Z1−∂LT (h)a1 (ml/h)a2 (g/h)a3Numerical values0.050.951.658120300.25In Table12, a1 denotes drinking water, a2 is the compressed biscuit, and a3 is the tent. Meanwhile, the stock-out rate (∂) is 0.05, such that the satisfaction degree of victims to materials is 95%. The normal distribution of the numerical value table shows that the corresponding coefficient is 1.65, and the value of the continuous maximum interval period (LT) for emergency supplies to the disaster areas is the setting value of the rolling period.According to Reference [39], the total victim population of the Wenchuan earthquake was 104,870,000. The survivors were zoomed 1000 times for convenient material estimation due to the considerable losses and large victim population base. If the victim population was 104,870, then the survival quantity in each rolling period could be calculated from (8) according to the total survival. Specific information is shown in Table 13.Table 13
Survivals in each period.
Rolling periods1234567Survivals102736994339698194832927239131688885Within seven days after the occurrence of the Wenchuan earthquake, the dynamic demands for drinking water and compressed biscuit in the disaster area in each period could be estimated from Equations (9), (11), and (12). The first period is the initial moment after the earthquake; therefore, σk0=0. The estimation results of the FMCG demands for each period are shown in Table 14.Table 14
Estimations of dynamic material demands in each rolling period.
Rolling periodTime after earthquakeDemands for drinking water (ml)Demands for compressed biscuit (g)18131502080246566402161272742402386392032412413568023275440432121384960227596805401186854402225352064811688448021915840756113772800213324008641111731202084496097210799744020249520108010603520019881600118810370944019445520129610177408019082640131049958528018672240141129718272018221760151209575424017953920161289453824017725920171369257216017357280181449111168017083440191529030400016932000201608947456016776480211688864768016621440The tent is a durable good. The demand for tents during the first rolling period was 25,684. Unlike FMCGs, the demand for durable goods in the latter stage is slightly influenced by time in practical situations, resulting in small differences among different stages. Considering practical significance, the demands for FMCGs in multiple periods were estimated, while those for durable goods in a single period were estimated globally.


## 6. Conclusions

The actual disaster information in areas affected by natural disasters is subject to real-time updating because of the influences of natural and social environmental factors. Consequently, some static prediction methods cannot ensure the accuracy of the prediction results, thereby influencing the efficiency of emergency rescue. A rolling prediction method based on dynamic time-varying information is proposed. First, historical statistical and real-time disaster data were collected. The time-sharing simulation data were generated by the previous time-sharing formula of cumulative deaths because acquiring time-sharing statistical data after disasters is difficult. Second, the attribute reduction of the initial dataset was performed using the rough set theory. Third, a rolling prediction model of cumulative deaths in each period was formed by combining the rolling time-domain method and the SVM-based regression intelligence algorithm. Finally, a postdisaster emergency material demand model was constructed based on the prediction of deaths and the unknown model in warehouse inventory management theory. This model was used to estimate the emergency material demands in the current period. In the simulation experiment, an SVM prediction method based on the rolling time domain was developed using the MATLAB 2016a platform and a libsvm tool kit. The prediction error of the SVM prediction method in the experiments was 10.96% and continuously decreased with the rolling forward of periods. The proposed method was compared with static prediction and IDF methods to increase its reliability. The prediction errors of the static prediction and IDF methods are 17.77% and 14.13%, respectively. Finally, the period-based prediction over material demands for drinking water and compressed biscuit in disaster areas after the Wenchuan earthquake was conducted according to warehouse inventory management theory and prediction data. The results demonstrate that the proposed method has certain scientificity and can provide reliable decision references for decision-making departments after the occurrence of natural disasters.Future research directions should be explored. The case study indicates that the prediction error in the first several periods is relatively large, and the prediction accuracy in a single period must be increased. This trend could be the main direction for improvement in future studies. Furthermore, this study only considered two types of materials, namely FMCGs and durable goods. Future studies can predict other types of emergency supplies, such as emergency medical services.



---

*Source: 2431611-2022-08-25.xml*