CN112001565A - Earthquake disaster loss prediction and evaluation method and system based on Softmax regression model - Google Patents

Earthquake disaster loss prediction and evaluation method and system based on Softmax regression model Download PDF

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CN112001565A
CN112001565A CN202010937250.3A CN202010937250A CN112001565A CN 112001565 A CN112001565 A CN 112001565A CN 202010937250 A CN202010937250 A CN 202010937250A CN 112001565 A CN112001565 A CN 112001565A
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李云飞
池招招
许才顺
张飞
许令顺
胡浩然
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Anhui Zeone Safety Technology Co ltd
Hefei City Lifeline Engineering Safety Operation Monitoring Center
Hefei Institute for Public Safety Research Tsinghua University
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Hefei City Lifeline Engineering Safety Operation Monitoring Center
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Abstract

A seismic disaster damage prediction and evaluation method and system based on a Softmax regression model relate to the technical field of seismic disaster damage prediction and evaluation, solve the problem of how to improve the accuracy of seismic disaster damage prediction and the training speed, use different seismic disaster damage degree grades as classification labels of the Softmax regression classification model, select past seismic disaster characteristic data for training, and predict the past seismic disaster damage by using the Softmax regression classification model; inputting new earthquake disaster characteristic data and classification labels in a Softmax regression classification model; judging the classification weight of the input data belonging to each earthquake disaster damage degree grade; determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster; compared with a Back Propagation (BP) neural network and a Support Vector Machine (SVM), the method has the advantages of stronger capability of distinguishing the earthquake disaster loss, high test precision and short test time.

Description

Earthquake disaster loss prediction and evaluation method and system based on Softmax regression model
Technical Field
The invention relates to the technical field of earthquake disaster loss prediction and evaluation, in particular to a method and a system for predicting and evaluating earthquake disaster loss based on a Softmax regression model.
Background
Earthquake is one of natural disasters difficult to predict accurately, and is the biggest security threat of human society. China is one of the countries with the strongest earthquake activities and the most serious earthquake disaster loss in the world, and the personal and property economic losses caused by earthquakes are huge every year, so that the earthquake-resistant method has great impact on the sustainable development of economy, society and environment. Therefore, the method can be used for rapidly and accurately evaluating, predicting and analyzing the earthquake disaster damage, and is a key link for disaster risk management, particularly emergency management.
In the prior art, Liu jin Long and so on in the literature, "earthquake casualty assessment method research based on earthquake intensity", use earthquake intensity as a main parameter, and magnitude and population density as auxiliary parameters to provide a casualty prediction model for correction through function fitting and regression analysis.
Chua Younjun and the like construct a Bayesian model-based rapid evaluation method by combining a seismic intensity-seismic intensity joint distribution law on the basis of a regression function in 'Bayesian model-based rapid evaluation method for earthquake direct economic loss' in a document, taking the influences of seismic intensity and seismic intensity on direct economic loss into consideration.
However, an earthquake disaster and the resulting consequences thereof are a complex process, the occurrence of earthquake disaster loss is usually formed by interactive influence of multiple factors such as a disaster-pregnant environment, a disaster-causing factor and a disaster-bearing body, the economic loss assessment after the earthquake disaster also faces a quite complex technical problem, nonlinear interactive influence among multiple influencing factors needs to be considered, and the factors have complex uncertainty, discreteness, randomness and mutual correlation, so that the prediction of the earthquake disaster risk loss is challenging. Therefore, researchers begin to introduce nonlinear modeling methods such as artificial neural networks and the like in practice to construct earthquake disaster damage models.
Mayajie et al, in the document "artificial neural network-based earthquake economic loss evaluation", adopt a multi-level-based index system to establish a three-layer BP neural network earthquake disaster economic evaluation model suitable for rapid evaluation of economic loss after an earthquake.
The random weight neural network is respectively adopted in the literature 'earthquake multi-occurrence region damage degree estimation model design based on big data' of the Chenglan and the literature 'earthquake disaster economic loss evaluation and prediction based on the random weight neural network' of the Xijiazhi to realize the rapid evaluation of the earthquake disaster damage degree under the big data environment.
The research further enriches the theoretical methods of earthquake disaster damage assessment and prediction work. However, due to the complexity of secondary derivative disasters caused by earthquake disasters, accurate numerical values of direct and indirect losses are difficult to evaluate and predict. Compared with the prior art, the method has the advantages that the classification, evaluation and prediction of the earthquake disaster damage level are more feasible and operable. Common algorithms for solving the multi-classification problem are various, such as decision trees, naive bayes, Back Propagation (BP) neural networks, Support Vector Machines (SVMs), and the like; the disadvantage of the BP neural network is that it is locally minimized; the convergence speed of the algorithm is low; network structure selection is not easy to determine; the approaching and popularizing capability of the network model is closely related to the typicality of the learning sample, and the problem of selecting typical sample examples from problems to form a training set is a difficult problem; the SVM has the defects that the classic SVM algorithm only provides a two-class classification algorithm and cannot predict multi-level disasters, so that the problems are solved by combining a plurality of two-class SVM algorithms, and the calculation complexity is increased.
In recent years, Softmax regression models in machine learning, which is an extension of linear regression on multi-class problems, have been increasingly emphasized as a method of constructing multi-class models, and Softmax can give a probability of belonging to each class, mainly for dealing with multi-class problems. Therefore, it is urgent to construct a fused earthquake disaster damage level prediction model based on Softmax regression and to improve the accuracy and calculation speed of earthquake disaster damage prediction.
Disclosure of Invention
The invention aims to improve the accuracy and the calculation speed of earthquake disaster damage prediction.
The invention solves the technical problems through the following technical scheme.
The earthquake disaster damage prediction and evaluation method based on the Softmax regression model comprises the following steps:
step one, taking different earthquake disaster damage degree grades as classification labels of a Softmax regression classification model, selecting past earthquake disaster characteristic data for training, and predicting the past earthquake disaster damage by using the Softmax regression classification model;
inputting new earthquake disaster characteristic data and classification labels in the trained Softmax regression classification model;
step three, judging the classification weight of the input data belonging to each earthquake disaster damage degree grade;
and step four, determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster.
In the Softmax regression classification model, different earthquake disaster damage degree grades are used as classification labels of the Softmax regression classification model, past earthquake disaster characteristic data is selected for training, and the Softmax regression classification model is used for predicting the loss of the past earthquake disasters so as to establish a classification model suitable for disaster grade evaluation; inputting new earthquake disaster characteristic data and classification labels in the trained Softmax regression classification model; judging the classification weight of the input data belonging to each earthquake disaster damage degree grade; determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster; the prediction model constructed in the training time and the prediction precision is superior to a BP neural network and an SVM, and compared with the BP neural network and the SVM, the prediction model has stronger capability of distinguishing the earthquake disaster loss, high test precision and short test time.
As a further improvement of the technical scheme of the invention, the earthquake disaster damage degree grade is divided into m grades, the number of classification labels of the corresponding Softmax regression classification model is m, and the training samples are as follows:
A＝{(x(1)，y(i))，(x(2)，y(i))，...，(x(n)，y(i))} (1)
where A is the sample of training, x(1)、x(2)...x(n)For the input seismic disaster characteristic data, n is the number of seismic disaster characteristic data, y(i)To classify the tag parameter, y(i)∈{1,2,...,m}。
As a further improvement of the technical solution of the present invention, the calculation formula for estimating the probability of the classification label to which each sample belongs is as follows:
P(y＝j|x)(j＝1,2,...,m) (2)
wherein x represents seismic disaster characteristic data, and y represents the seismic disaster damage degree grade; p represents the probability; j is a counting factor;
according to the generalized linear model theory, the prediction function of the sample can be obtained as follows:
Figure BDA0002672392910000041
wherein the content of the first and second substances,
Figure BDA0002672392910000051
hw(x(i)) Representing the prediction function of the ith sample, estimating the probability of occurrence of each classification result of x, x(i)For the input seismic disaster characteristic data, hw(x(i)) The output m-dimensional vector represents probability values estimated for m classification labels;
Figure BDA0002672392910000052
the effect of (1) is to normalize the probability distribution so that x(i)The sum of the probabilities belonging to each category is 1; w is aiIs x(i)The classification weight, W, is an m × k matrix.
As a further improvement of the technical solution of the present invention, the training method is to use a loss function of a Softmax regression model to evaluate the maximum likelihood, and the formula of the loss function j (w) is as follows:
Figure BDA0002672392910000053
wherein, I (y)(i))jTo indicate the function, I (y)(i))jTo indicate the function, when y(i)Class j time I (y)(i))j1, otherwise 0;
Figure BDA0002672392910000054
represents x(i)Probability of classification into category j; the loss function measures the similarity of the true class to the predicted class, and the goal of the training is to minimize j (w).
As a further improvement of the technical solution of the present invention, the method for solving the loss is as follows:
retaining all weight parameters (w)1，w2，...，wm) In the case of (2), a weighted attenuation term is added to the loss function
Figure BDA0002672392910000055
Then the loss function becomes:
Figure BDA0002672392910000056
at this time, the loss function becomes a convex function, a unique solution is provided, the Hessian matrix is reversible, and the partial derivative of J (W) is obtained by adopting a gradient descent method, which is as follows:
Figure BDA0002672392910000057
combining training data to weights wjUpdate to obtain wjThe optimal solution of (a) is as follows:
Figure BDA0002672392910000061
wherein α is the learning rate; and after the training is finished, carrying out forward propagation on the test data by using W, obtaining m values for each test data, and selecting the class corresponding to the maximum value as the optimal class of model prediction.
The system for predicting and evaluating the loss of earthquake disasters based on the Softmax regression model comprises:
a model training module: taking different earthquake disaster damage degree grades as classification labels of a Softmax regression classification model, selecting past earthquake disaster characteristic data for training, and predicting the loss of the past earthquake disasters by using the Softmax regression classification model;
the new earthquake prediction and evaluation module comprises: inputting new earthquake disaster characteristic data and classification labels in a Softmax regression classification model after training; judging the classification weight of the input data belonging to each earthquake disaster damage degree grade; and determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster.
As a further improvement of the technical scheme of the invention, the earthquake disaster damage degree grade is divided into m grades, the number of classification labels of the corresponding Softmax regression classification model is m, and the training samples are as follows:
A＝{(x(1)，y(i))，(x(2)，y(i))，...，(x(n)，y(i))} (1)
where A is the sample of training, x(1)、x(2)...x(n)For the input seismic disaster characteristic data, n is the number of seismic disaster characteristic data, y(i)To classify the tag parameter, y(i)∈{1,2,...,m}。
As a further improvement of the technical solution of the present invention, the calculation formula for estimating the probability of the classification label to which each sample belongs is as follows:
P(y＝j|x)(j＝1,2,...,m) (2)
wherein x represents seismic disaster characteristic data, and y represents the seismic disaster damage degree grade; p represents the probability; j is a counting factor;
according to the generalized linear model theory, the prediction function of the sample can be obtained as follows:
Figure BDA0002672392910000071
wherein the content of the first and second substances,
Figure BDA0002672392910000072
wherein h isw(x(i)) Representing the prediction function of the ith sample, estimating the probability of occurrence of each classification result of x, x(i)For the input seismic disaster characteristic data, hw(x(i)) The output m-dimensional vector represents probability values estimated for m classification labels;
Figure BDA0002672392910000073
the effect of (1) is to normalize the probability distribution so that x(i)The sum of the probabilities belonging to each category is 1; w is aiIs x(i)The classification weight, W, is an m × k matrix.
As a further improvement of the technical solution of the present invention, the training method is to use a loss function of a Softmax regression model to evaluate the maximum likelihood, and the formula of the loss function j (w) is as follows:
Figure BDA0002672392910000074
wherein, I (y)(i))jTo indicate the function, I (y)(i))jTo indicate the function, when y(i)Class j time I (y)(i))j1, otherwise 0;
Figure BDA0002672392910000075
represents x(i)Probability of classification into category j; the loss function measures the similarity of the true class to the predicted class, and the goal of the training is to minimize j (w).
As a further improvement of the technical solution of the present invention, the method for solving the loss is as follows:
retaining all weight parameters (w)1，w2，...，wm) In the case of (2), a weighted attenuation term is added to the loss function
Figure BDA0002672392910000081
Then the loss function becomes:
Figure BDA0002672392910000082
at this time, the loss function becomes a convex function, a unique solution is provided, the Hessian matrix is reversible, and the partial derivative of J (W) is obtained by adopting a gradient descent method, which is as follows:
Figure BDA0002672392910000083
combining training data to weights wjUpdate to obtain wjThe optimal solution of (a) is as follows:
Figure BDA0002672392910000084
wherein α is the learning rate; and after the training is finished, carrying out forward propagation on the test data by using W, obtaining m values for each test data, and selecting the class corresponding to the maximum value as the optimal class of model prediction.
The invention has the advantages that:
(1) in the Softmax regression classification model, different earthquake disaster damage degree grades are used as classification labels of the Softmax regression classification model, past earthquake disaster characteristic data is selected for training, and the Softmax regression classification model is used for predicting the loss of the past earthquake disasters so as to establish a classification model suitable for disaster grade evaluation; inputting new earthquake disaster characteristic data and classification labels in the trained Softmax regression classification model; judging the classification weight of the input data belonging to each earthquake disaster damage degree grade; determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster; the prediction model constructed in the training time and the prediction precision is superior to a BP neural network and an SVM, and compared with the BP neural network and the SVM, the prediction model has stronger capability of distinguishing the earthquake disaster loss, high test precision and short test time.
Drawings
Fig. 1 is a schematic diagram of a seismic disaster direct economic loss index system of a seismic disaster loss prediction and evaluation method and system based on a Softmax regression model according to an embodiment of the present invention;
fig. 2 is a loss function graph of Softmax for seismic data prediction in the method and system for predicting and evaluating seismic disaster loss based on the Softmax regression model according to the embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present invention clearer, the technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the embodiments of the present invention. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present invention.
The technical scheme of the invention is further described by combining the drawings and the specific embodiments in the specification:
example one
The earthquake disaster damage prediction and evaluation method based on the Softmax regression model comprises the following steps:
1. earthquake disaster prediction based on Softmax regression model
And (3) taking different earthquake disaster damage degree grades as classification categories, taking earthquake disaster related parameters as characteristics for training, and predicting the damage of the past earthquake disasters by using a Softmax regression classification model.
1.1 establishing Softmax regression-based Classification
And if the earthquake disaster damage degree is divided into m levels, the corresponding Softmax classification labels are m. Assuming n training samples, the sample set is:
A＝{(x(1)，y(1))，(x(2)，y(2))，...，(x(n)，y(n))}
wherein x is(i)Inputting earthquake disaster characteristics, wherein if the number of earthquake disaster characteristic parameters is k, the earthquake disaster characteristic parameters are one-dimensional vectors with the number of elements being k, and i is {1, 2.. multidot.k }; y is(i)E {1, 2.
Each sample estimates its class probability of belonging to P (y ═ j | x) (j ═ 1, 2. According to the theory of the generalized linear model, the assumed function can be obtained as follows:
Figure BDA0002672392910000101
wherein h isw(x(i)) Representing the prediction function for the ith sample, estimates the probability of occurrence of each classification result for x. h isw(x(i)) The output m-dimensional vector represents probability values estimated for m class labels;
Figure BDA0002672392910000102
the effect of (1) is to normalize the probability distribution so that x(i)The sum of the probabilities belonging to each category is 1; w is aiIs a characteristic x(i)And (4) classifying weight. W is an m × k matrix, as follows:
Figure BDA0002672392910000103
1.2Softmax regression solution
During training, the Softmax regression algorithm is used for solving the maximum likelihood estimation of the loss function of the Softmax regression algorithm, and a gradient descent method or a Newton method can be used for solving the maximum likelihood estimation. The loss function of the Softmax regression algorithm is as follows:
Figure BDA0002672392910000104
the loss function measures the similarity of the true class to the predicted class, and the goal of training the model parameters is to minimize J (W). In the above formula I (y)(i))jTo indicate the function, when y(i)Class j time I (y)(i))jOtherwise, it is 0.
Figure BDA0002672392910000105
Represents x(i)Probability of classification into category j.
The first step in the operation of the Softmax model is to input the data of the training set into the model, where the data of the training set includes the disaster level. The training process of the model is equivalent to gradually constructing a function, and the earthquake disaster characteristics and the disaster grade are connected to obtain a relational expression between the earthquake disaster characteristics and the disaster grade. The loss function has the effect that the model is closer to the real earthquake disaster grading model, and the smaller the loss function value is, the better the model training result is.
Since the Softmax regression has parameter redundancy problem, that is, for any one hypothesis function used for fitting data, multiple sets of parameter values can be obtained, and the parameters obtain the same hypothesis function hw(x(i)). At this time, the local optimal solution cannot be obtained by adopting a gradient descent method, and the Newton method cannot ensure the convergence of the algorithm because the Hessian matrix of the loss function is irreversible. In order to solve the numerical problem caused by parameter redundancy and make the algorithm simpler, all weight parameters (w) are reserved1，w2，...，wm) In the case of (2), a weighted attenuation term is added to the loss function
Figure BDA0002672392910000111
Then the loss function becomes:
Figure BDA0002672392910000112
at the moment, the loss function is changed into a convex function, a unique solution is provided, the Hessian matrix is reversible, and a gradient descent method or a Newton method can be adopted for solving. The partial derivatives of J (W) are calculated as follows:
Figure BDA0002672392910000113
the gradient descent method is adopted here, and training data is combined with the weight wjUpdate to obtain wjThe optimal solution of (a) is as follows:
Figure BDA0002672392910000114
wherein α is the learning rate; and after the training is finished, carrying out forward propagation on the test data by using W, obtaining m values for each test data, and selecting the class corresponding to the maximum value as the optimal class of model prediction.
2. Earthquake disaster index system construction and characteristic parameter design
Constructing an earthquake disaster loss index system, quantizing earthquake disaster characteristic indexes, and selecting the earthquake disaster characteristic indexes;
as earthquake disasters are products of social and natural combined actions, the disasters act on human society to generate disasters, and the disaster condition of the disasters depends on the stability of pregnant disaster environments, the dangerousness of disaster-causing factors and the fragility of disaster-bearing bodies. Therefore, the direct economic loss of earthquake disaster is regarded as a function of the pregnant disaster environment, the disaster causing factor and the disaster bearing body. There are complex non-linearity, uncertainty and discreteness between them, and the interaction results in a loss that is difficult to estimate. The natural disaster loss evaluation refers to the analysis and evaluation of the damage and destruction of disaster-causing factors to the survival and development of human society, and is embodied in three aspects of casualties, direct economic loss and indirect economic loss. In general, a disaster damage assessment system is composed of an index system for disaster damage assessment and a disaster damage assessment method (qualitative or quantitative). The direct damage of natural disasters is embodied in two aspects of property loss and casualties. In disaster damage calculation, casualties and economic losses are usually calculated respectively, and due to the fact that the evaluation methods of the casualties and the economic losses are different and the calculation calibers are inconsistent, the casualties and the economic losses are unified into a comprehensive result to be evaluated by few researches, and a dual index system is adopted. The other aspect of the natural disaster damage is realized in the aspects of people, property, objects and the like which are invested in the post-disaster rescue. In order to evaluate and predict earthquake economic loss more objectively, comprehensively, reasonably and effectively, an earthquake disaster direct economic loss index system is established in the text, as shown in fig. 1. In the practical process, however, a plurality of representative indexes are further selected based on the following principles for experimental verification.
As can be seen from FIG. 1, the magnitude, the depth of the seismic source and the intensity of the seismic center are selected as the quantitative indexes of the disaster-causing factors. The quantitative indexes of the pregnant disaster environment comprise earthquake fortification intensity, design earthquake basic acceleration, medical technology degree, planning of earthquake zones and road and evacuation site area. As the medical technical degree is difficult to quantify, the earthquake zone planning is difficult to operate, and the areas of roads and evacuation places are difficult to count, only the earthquake fortification intensity and the designed earthquake basic acceleration are selected as experimental simulation indexes of the pregnant disaster environment. The quantitative indexes of the disaster-bearing body are disaster-stricken population, disaster-stricken area, average GDP of people in disaster areas, building earthquake fortification standard and building type and proportion. The value of the disaster-bearing body relates to the economic development degree, the wealth distribution condition and the disaster area of the disaster-bearing area. The degree of economic development can be measured by GDP. Considering that earthquake disasters sometimes occur at the junction of two areas or a plurality of areas are involved, so that GDP in a disaster area is difficult to count, the average value of GDP in two areas is adopted for counting. Therefore, the economic development degree and the wealth condition of people in the earthquake-stricken area are reasonably reflected, and the earthquake-stricken area is easy and convenient to operate. In addition, the size of the area of suffering from a disaster becomes positive correlation with the direct economic loss of earthquake, under the prerequisite that other conditions are unchangeable, the area of suffering from a disaster is big more, the social wealth that involves just also more, the direct economic loss that suffers after the earthquake takes place will be big more. According to the building earthquake-proof design specification (GB50011-2010), the building earthquake-proof fortification standard is related to earthquake fortification intensity, so that the earthquake fortification intensity is only selected as one of indexes reflecting direct economic loss of an earthquake, and the type and proportion of the building are difficult to measure and calculate in a short time. The actual selection index of the disaster bearing body is the disaster area. The earthquake and the seismic fortification intensity which occur at the junction of two areas are involved, the basic earthquake acceleration and the GDP are designed to be inconsistent in the two areas, and the mean value of the two areas is taken.
3 model building and result analysis
3.1 data Source and data processing
The earthquake magnitude, the earthquake focus depth, the earthquake intensity, the disaster population, the disaster area and the direct economic loss of the used data are from China mainland earthquake disaster loss evaluation and review (2005-2017), the corresponding earthquake fortification intensity and the design basic earthquake acceleration refer to building earthquake design Specification GB50011-2010(2016 year edition), the per capita GDP is obtained by the inquiry of the national statistical office, and the inquiry condition is the per capita GDP of the year of the local province. Definition of the population suffering from the earthquake (reference: all round of sunshine, hairy swallow, Shiweihua, evaluation of earthquake population suffering from the earthquake and economic loss [ J ] earthquake research, 2004,27(001):88-93.) in Yunnan area, wherein the earthquake disaster area refers to an area with social and economic damage, and the area with intensity more than or equal to VI degree is generally taken; the population in the disaster area is called the disaster population.
Table 12005-2017 Chinese continent earthquake disaster loss data set
Figure BDA0002672392910000141
Since the parameter values of each training sample are distributed differently, the obtained sample interval difference is large, and therefore, a large deviation may occur in the model when the data is fitted. Even if the fitting effect of the model on the training set is good, the model does not have generalization capability, so that the training sample data needs to be subjected to normalization processing. For each attribute parameter in all training samples, normalization was performed using the following formula:
Figure BDA0002672392910000142
wherein, ymaxAnd yminIs a set value which is 1 and 0 respectively; x is the number ofmaxIs the maximum value in the x-series, xminThe maximum value of the attribute parameter in all training samples.
3.2 seismic disaster loss grading
The measure of natural disaster damage can be absolute or relative. The concept of disaster degree is given by Zhao Axing et al based on the absolute measure of disaster loss, and natural disasters are divided into five grades (A-grade huge disaster, B-grade huge disaster, C-grade medium disaster, D-grade disaster elimination and E-grade micro disaster) by taking the disaster degree as a standard. The relative measure of disaster damage can be measured by the rate of disaster damage. Table 2 is a natural disaster ranking based on disaster severity and disaster damage rate. In 2005-2017 earthquake disaster statistical data, there was only one level E of disaster, so the subsequent model prediction did not count the level. The disaster damage classification proposed by Zhao Axing et al lacks property loss of 109～1010In between, thus in itModified on the basis of classification, 109～1010The seismic data in between are defined as B-level disasters, and the classification table is shown in table 2.
TABLE 2 disaster loss grading
Figure BDA0002672392910000151
3.3 model parameter setting and training
As can be seen from table 1, the values of the 8 features are very different, and if such data is input to the Softmax model (of course, the BP neural network and the SVM are also included), the calculation accuracy is easily reduced. Therefore, the data are normalized before being input into the Softmax model, so that the range of the data is between (0, 1); after the data are processed (including the division of disaster damage grades and the normalization of 8 characteristics), 105 groups of seismic data are used, 105 groups of data are divided into two parts, one part is a training set, the other part is a testing set, and the number of the corresponding data in each grade is shown in a table 3.
TABLE 3 training set and test set grouping
Figure BDA0002672392910000152
The Softmax, SVM and BP neural networks all adopt the same data structure: the earthquake magnitude, the earthquake focus depth, the earthquake mid-earthquake intensity, the earthquake fortification intensity, the earthquake acceleration, the per-capita GDP, the disaster population and the disaster area are used as input earthquake disaster characteristics; the earthquake disaster grade is used as a label. The more important parameter settings in the Softmax model are shown in table 4.
Table 4 parameter values for Softmax model
Figure BDA0002672392910000161
When using an SVM model, the SVM selects the radial basis function as the kernel function since the number of samples is much higher than the number of eigenvalues. Using a one-to-one modeThere are multiple classes of identification, and thus there are k (k-1)/2 classifiers. Calculating the optimal value of the parameter array by using a cross-validation method, wherein the penalty factor c and the parameter value 9.766 x 10 of the nuclear parameter g-4。
Setting parameters of the BP neural network: the method comprises the steps of establishing a three-layer neural network according to the actual situation of a disaster, wherein an input layer is 8 nodes of earthquake disaster characteristics, the number of hidden nodes is 8, the earthquake disaster grade is graded into 5 nodes in a mode of single-hot coding and serves as an output layer, meanwhile, the hidden layer takes a tanh function as an activation function, and the output layer takes a sigmoid function as an activation function. And in the selection of the loss function, a cross entropy loss function is adopted to replace a quadratic loss function. Parameters were set according to a conventional BP neural network model (refer: wang wei. MATLAB from foundation to mastery [ M ]. beijing: electronics industry press, 2012:388.) as shown in table 5.
TABLE 5 BP neural network parameter settings
Figure BDA0002672392910000162
The trend of the loss function in the iterative process when the regression was performed using Softmax is shown in fig. 2.
The loss function value gradually decreases with the increase of the number of iterations, and after 120 iterations, the value becomes stable and does not change any more. After the model training is finished, the data of the test set are input into the model after training, and the disaster grade of the earthquake is predicted by the model after training according to 8 characteristics of the earthquake each time. Comparing the predicted result with the real grade to obtain the precision of the model (the test precision corresponds to the model precision obtained by the test set data); and taking the calculated precision under the iteration times. Meanwhile, the BP neural network and the SVM are used for classification, and the comparison of the obtained prediction results is shown in Table 6.
TABLE 6 comparison of results for three prediction models
Figure BDA0002672392910000171
3.4 analysis of results
The training time of the SVM is the shortest in the data set, but the precision is relatively low, and the earthquake disaster grade cannot be accurately predicted; the BP neural network and Softmax can achieve small precision difference, the prediction result of the earthquake disaster grade is accurate, and Softmax is more efficient in the aspect of computing time. Thus, for seismic data sets, relatively speaking, using Softmax can achieve higher prediction accuracy in a shorter time.
By carrying out grading evaluation and prediction on earthquake disasters, the method has important significance on post-disaster economic construction. After the characteristics of the seismic data of the past years are extracted, a reasonable classification model is found to carry out grading classification on the seismic disaster loss. The earthquake disaster loss is evaluated and predicted by applying a Softmax regression model, and compared with the traditional BP neural network, the Softmax regression model has the advantages of being low in convergence speed, inconsistent in structure selection, local minimization and difficult to implement on large-scale training samples by an SVM algorithm, the iteration times are fewer, and convergence can be achieved preferentially. After experiments, when the Softmax regression model, the traditional BP neural network and the SVM are used for predicting the seismic disaster of China in 2017 with 2005 + materials, the results show that the prediction and evaluation of the seismic disaster loss by using the Softmax regression model have better practicability, and the application prospect of the Softmax regression model in the seismic disaster is shown.
In practical applications, there may be a need for more accurate classification, and optimization may be performed by increasing influence factors such as geological conditions of the seismic site and readjusting the Softmax parameter.
The above examples are only intended to illustrate the technical solution of the present invention, but not to limit it; although the present invention has been described in detail with reference to the foregoing embodiments, it will be understood by those of ordinary skill in the art that: the technical solutions described in the foregoing embodiments may still be modified, or some technical features may be equivalently replaced; and such modifications or substitutions do not depart from the spirit and scope of the corresponding technical solutions of the embodiments of the present invention.

Claims (10)

1. The earthquake disaster damage prediction and evaluation method based on the Softmax regression model is characterized by comprising the following steps of:
step one, taking different earthquake disaster damage degree grades as classification labels of a Softmax regression classification model, selecting past earthquake disaster characteristic data for training, and predicting the past earthquake disaster damage by using the Softmax regression classification model;
inputting new earthquake disaster characteristic data and classification labels in the trained Softmax regression classification model;
step three, judging the classification weight of the input data belonging to each earthquake disaster damage degree grade;
and step four, determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster.
2. The method for predicting and evaluating earthquake disaster damage based on Softmax regression model according to claim 1, wherein the earthquake disaster damage degree is classified into m levels, the classification labels of the corresponding Softmax regression classification models are m, the trained samples are:
A＝{(x(1)，y(i))，(x(2)，y(i))，...，(x(n)，y(i))} (1)
where A is the sample of training, x(1)、x(2)...x(n)For the input seismic disaster characteristic data, n is the number of seismic disaster characteristic data, y(i)To classify the tag parameter, y(i)∈{1,2,...,m}。
3. The method for predicting and evaluating earthquake disaster damage based on Softmax regression model of claim 1, wherein the probability of each sample being evaluated for the class label to which it belongs is calculated by the formula:
P(y＝j|x)(j＝1,2,...,m) (2)
wherein x represents seismic disaster characteristic data, and y represents the seismic disaster damage degree grade; p represents the probability; j is a counting factor;
according to the generalized linear model theory, the prediction function of the sample can be obtained as follows:
Figure FDA0002672392900000021
wherein the content of the first and second substances,
Figure FDA0002672392900000022
hw(x(i)) Representing the prediction function of the ith sample, estimating the probability of occurrence of each classification result of x, x(i)For the input seismic disaster characteristic data, hw(x(i)) The output m-dimensional vector represents probability values estimated for m classification labels;
Figure FDA0002672392900000023
the effect of (1) is to normalize the probability distribution so that x(i)The sum of the probabilities belonging to each category is 1; w is aiIs x(i)The classification weight, W, is an m × k matrix.
4. The method for predicting and evaluating earthquake disaster damage based on Softmax regression model of claim 1, wherein the training method is maximum likelihood estimation by using a loss function of Softmax regression model, and the loss function J (W) is expressed as follows:
Figure FDA0002672392900000024
wherein, I (y)(i))jTo indicate the function, I (y)(i))jTo indicate the function, when y(i)Class j time I (y)(i))j1, otherwiseIs 0;
Figure FDA0002672392900000025
represents x(i)Probability of classification into category j; the loss function measures the similarity of the true class to the predicted class, and the goal of the training is to minimize j (w).
5. The method for predicting and evaluating the damage of a seismic disaster based on Softmax regression model according to claim 1, wherein the method for solving the damage is as follows:
retaining all weight parameters (w)1，w2，...，wm) In the case of (2), a weighted attenuation term is added to the loss function
Figure FDA0002672392900000031
Then the loss function becomes:
Figure FDA0002672392900000032
at this time, the loss function becomes a convex function, a unique solution is provided, the Hessian matrix is reversible, and the partial derivative of J (W) is obtained by adopting a gradient descent method, which is as follows:
Figure FDA0002672392900000033
combining training data to weights wjUpdate to obtain wjThe optimal solution of (a) is as follows:
Figure FDA0002672392900000034
wherein α is the learning rate; and after the training is finished, carrying out forward propagation on the test data by using W, obtaining m values for each test data, and selecting the class corresponding to the maximum value as the optimal class of model prediction.
6. The system for predicting and evaluating the loss of earthquake disasters based on the Softmax regression model is characterized by comprising the following steps:
a model training module: taking different earthquake disaster damage degree grades as classification labels of a Softmax regression classification model, selecting past earthquake disaster characteristic data for training, and predicting the past earthquake disaster damage by using the Softmax regression classification model;
the new earthquake prediction and evaluation module comprises: inputting new earthquake disaster characteristic data and classification labels in a Softmax regression classification model after training; judging the classification weight of the input data belonging to each earthquake disaster damage degree grade; and determining a classification label corresponding to the input data according to the classification weight, thereby determining the damage degree grade of the new earthquake disaster.
7. The system for predicting and evaluating earthquake disaster damage based on Softmax regression model of claim 6, wherein the earthquake disaster damage degree is classified into m levels, the classification labels of the corresponding Softmax regression classification models are m, the trained samples are:
A＝{(x(1)，y(i))，(x(2)，y(i))，...，(x(n)，y(i))} (1)
where A is the sample of training, x(1)、x(2)...x(n)For the input seismic disaster characteristic data, n is the number of seismic disaster characteristic data, y(i)To classify the tag parameter, y(i)∈{1,2,...,m}。
8. The system for seismic disaster damage prediction and evaluation based on Softmax regression model of claim 6, wherein the formula for calculating the probability of each sample estimating the class label to which it belongs is:
P(y＝j|x)(j＝1,2,...,m) (2)
wherein x represents seismic disaster characteristic data, and y represents the seismic disaster damage degree grade; p represents the probability; j is a counting factor;
according to the generalized linear model theory, the prediction function of the sample can be obtained as follows:
Figure FDA0002672392900000041
wherein the content of the first and second substances,
Figure FDA0002672392900000042
hw(x(i)) Representing the prediction function of the ith sample, estimating the probability of occurrence of each classification result of x, x(i)For the input seismic disaster characteristic data, hw(x(i)) The output m-dimensional vector represents probability values estimated for m classification labels;
Figure FDA0002672392900000043
the effect of (1) is to normalize the probability distribution so that x(i)The sum of the probabilities belonging to each category is 1; w is aiIs x(i)The classification weight, W, is an m × k matrix.
9. The system for predicting and evaluating earthquake disaster damage based on Softmax regression model of claim 6, wherein the training method is maximum likelihood estimation by using a loss function of Softmax regression model, and the loss function J (W) is expressed as follows:
Figure FDA0002672392900000051
wherein, I (y)(i))jTo indicate the function, I (y)(i))jTo indicate the function, when y(i)Class j time I (y)(i))j1, otherwise 0;
Figure FDA0002672392900000052
represents x(i)Probability of classification into category j; the loss function measures the similarity of the true class to the predicted class, and the goal of the training is to minimize j (w).
10. The system for predicting and evaluating loss of seismic disaster based on Softmax regression model of claim 6, wherein said method for solving loss is as follows:
retaining all weight parameters (w)1，w2，...，wm) In the case of (2), a weighted attenuation term is added to the loss function
Figure FDA0002672392900000053
Then the loss function becomes:
Figure FDA0002672392900000054
at this time, the loss function becomes a convex function, a unique solution is provided, the Hessian matrix is reversible, and the partial derivative of J (W) is obtained by adopting a gradient descent method, which is as follows:
Figure FDA0002672392900000055
combining training data to weights wjUpdate to obtain wjThe optimal solution of (a) is as follows:
Figure FDA0002672392900000056
wherein α is the learning rate; and after the training is finished, carrying out forward propagation on the test data by using W, obtaining m values for each test data, and selecting the class corresponding to the maximum value as the optimal class of model prediction.
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