CN112036493A - Forest fire early warning method based on principal component analysis and fuzzy C-means - Google Patents

Forest fire early warning method based on principal component analysis and fuzzy C-means Download PDF

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CN112036493A
CN112036493A CN202010907980.9A CN202010907980A CN112036493A CN 112036493 A CN112036493 A CN 112036493A CN 202010907980 A CN202010907980 A CN 202010907980A CN 112036493 A CN112036493 A CN 112036493A
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sample
principal component
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高德民
孙权
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Nanjing Forestry University
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    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/21—Design or setup of recognition systems or techniques; Extraction of features in feature space; Blind source separation
    • G06F18/213—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods
    • G06F18/2135—Feature extraction, e.g. by transforming the feature space; Summarisation; Mappings, e.g. subspace methods based on approximation criteria, e.g. principal component analysis
    • G—PHYSICS
    • G06—COMPUTING; CALCULATING OR COUNTING
    • G06F—ELECTRIC DIGITAL DATA PROCESSING
    • G06F18/00—Pattern recognition
    • G06F18/20—Analysing
    • G06F18/23—Clustering techniques
    • G06F18/232—Non-hierarchical techniques
    • G06F18/2321—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions
    • G06F18/23213—Non-hierarchical techniques using statistics or function optimisation, e.g. modelling of probability density functions with fixed number of clusters, e.g. K-means clustering
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    • G06—COMPUTING; CALCULATING OR COUNTING
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    • G—PHYSICS
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    • G06Q—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES; SYSTEMS OR METHODS SPECIALLY ADAPTED FOR ADMINISTRATIVE, COMMERCIAL, FINANCIAL, MANAGERIAL OR SUPERVISORY PURPOSES, NOT OTHERWISE PROVIDED FOR
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    • G06Q50/02—Agriculture; Fishing; Mining
    • G—PHYSICS
    • G08—SIGNALLING
    • G08B—SIGNALLING OR CALLING SYSTEMS; ORDER TELEGRAPHS; ALARM SYSTEMS
    • G08B17/00—Fire alarms; Alarms responsive to explosion
    • G08B17/005—Fire alarms; Alarms responsive to explosion for forest fires, e.g. detecting fires spread over a large or outdoors area
    • G—PHYSICS
    • G16—INFORMATION AND COMMUNICATION TECHNOLOGY [ICT] SPECIALLY ADAPTED FOR SPECIFIC APPLICATION FIELDS
    • G16Y—INFORMATION AND COMMUNICATION TECHNOLOGY SPECIALLY ADAPTED FOR THE INTERNET OF THINGS [IoT]
    • G16Y10/00—Economic sectors
    • G16Y10/10—Forestry
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    • G16Y—INFORMATION AND COMMUNICATION TECHNOLOGY SPECIALLY ADAPTED FOR THE INTERNET OF THINGS [IoT]
    • G16Y20/00—Information sensed or collected by the things
    • G16Y20/10—Information sensed or collected by the things relating to the environment, e.g. temperature; relating to location
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    • G16Y40/00—IoT characterised by the purpose of the information processing
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    • G16Y40/00—IoT characterised by the purpose of the information processing
    • G16Y40/50—Safety; Security of things, users, data or systems

Abstract

The invention provides a forest fire early warning method based on principal component analysis and fuzzy C mean value, which comprises the following steps: step 1, collecting meteorological data and performing PCA (principal component analysis) dimension reduction processing on the characteristics; step 2, establishing a target function according to the new features after dimension reduction; and 3, solving the objective function. According to the invention, through the collection of meteorological data and the dimension reduction processing of characteristics, an objective function is established, and through the solution of the objective function, the distribution of each sample is obtained, so that the target function is divided into clusters with different forest fire risk levels, and the method has a positive effect on early warning of forest monitoring environment and forest fire.

Description

Forest fire early warning method based on principal component analysis and fuzzy C-means
Technical Field
The invention relates to a forest fire early warning method based on principal component analysis and fuzzy C mean value.
Background
Forest fires are frequently caused by current climate abnormality, and are still one of the major threat factors for human survival. In 11 months 2018, 78 people died from forest fires in california, usa, which was the forest fire with the largest number of deaths in california historically. In 2017, in 5 months, the forest fire of Bilahe 502 in Mongolia in China can be successfully extinguished under the condition that more than 1 million armed police officers and soldiers and fire fighters put out the fire. Researchers including developed countries such as the united states are still stranded in the days of advanced information technology, before serious casualties due to forest fires occur. In recent years, forest fires have been increasingly developed, and the research on forest fires is still one of the important issues in forestry research. From 2018 onwards, the Chinese forestry academy has developed forest fire research as an independent topic in parallel with other topics in forestry.
The high development and destructiveness of forest fire determine the importance of forest fire prevention and control, and countries in the world have no residual force for the reason. The factors causing the forest fire are numerous, the reasons are complex, accurate quantification is difficult, and the factors are also the main reasons that although the forest fire research lasts for nearly one hundred years, the forest fire does not fall and reversely rises. The applicant provides a forest fire model based on principal component analysis and fuzzy C-means, the model belongs to a forest fire occurrence prediction model, and the model is theoretically used for uncertain analysis of multiple factors in causal relationship and accords with a forest fire cause analysis model. In the process of acquiring forest fire parameters, the high-efficiency prevention and control and automatic monitoring of forest fire are realized by means of the current advanced internet of things technology, and the national forestry administration also explicitly provides a struggle target of accelerating forestry informatization and driving forestry modernization. The method has the advantages that the forest fire is scientifically and effectively pre-warned and forecasted, the loss caused by the forest fire is reduced to the maximum extent, the problem which is very concerned by the management department and the scientific research department of the forestry in China is always solved, the rise and the development of the wireless sensor network technology provide opportunities for the realization of the pre-warning and forecasting of the fire in the modern forestry, the modern information technology is actively applied in the development of the forestry, and the Internet of things of the modern forestry is built.
Disclosure of Invention
The purpose of the invention is as follows: in order to solve the technical problems in the background art, the invention provides a forest fire early warning method based on principal component analysis and fuzzy C mean value, which comprises the following steps:
step 1, collecting meteorological data and performing dimensionality reduction processing on characteristics to obtain a first principal component and a second principal component;
step 2, establishing an objective function according to the first principal component and the second principal component;
and 3, solving the objective function, and outputting the fire early warning level according to the obtained result.
The step 1 comprises the following steps: based on the wireless sensor network, x 'is taken as each original sample'j＝(x′1j，x′2j，…，x′nj)TCollecting meteorological parameters, namely features, wherein j is a sample serial number, n is the category total number of the features, x'njRepresenting the nth feature of the jth original sample; for different types of features, a PCA dimension reduction technology is adopted to compress the features and form a first principal component and a second principal component, and for an original data set, the specific dimension reduction process is as follows:
Figure BDA0002662184090000021
x′nNan nth feature representing an nth sample, which is raw data, i.e., data before dimensionality reduction;
the sample variance calculation formula is as follows:
Figure BDA0002662184090000026
where Var represents the variance of the features, N is the number of samples, xiRepresents the value of the ith sample in a feature,
Figure BDA0002662184090000022
represents the mean of the column of samples, and X' represents the matrix after dimensionality reduction; this column represents a feature column, and each column of matrix X' represents a feature column.
By solving a covariance matrix
Figure BDA0002662184090000023
The characteristic equation | S- λ I | ═ 0, and the corresponding characteristic value λ is obtainediI is 1, 2, …, n, where I is the identity matrix. λ represents a characteristic value, and there are several characteristic values for several characteristics.
The step 2 comprises the following steps: cluster c for different forest fire risk classesiAnd each reduced sample xjThe following objective function user is established:
Figure BDA0002662184090000024
Figure BDA0002662184090000025
the target function is established according to the samples, but the original parameters of one sample are temperature, humidity, wind speed and rainfall, and the parameters of the sample after dimensionality reduction are a first principal component and a second principal component. j takes on a value from 1-N, N is the number of samples (3648), and each sample xj＝(x1j，x2j)T，x1jRepresenting the first principal component, x, of the jth sample2jRepresenting the second principal component of the jth sample.
||xj-ci||2Is the square of the Euclidean distance and is the distance between the jth reduced sample and the ith cluster center. x is the number ofjAnd ciIn the same dimension, both are in the form of vectors. The FCM algorithm is an iterative and constantly updated membership value uijAnd cluster center ciFor c, foriRandomly appointing K cluster centers during initialization, wherein K is the total number of clusters and is represented by ciCalculate uijThen is further prepared byuijUpdate ciBy analogy, finally make | Pnew-PoldI <, convergence ends and a clustering result is obtained, where it is a sufficiently small number.
Wherein the member function uijRepresenting the reduced dimension sample xjAnd cluster center ciM is a blurring factor greater than 1, and K is the total number of clusters.
The step 3 comprises the following steps:
step 3-1, constructing a Lagrangian function L based on a Lagrangian multiplier method, wherein the Lagrangian function L is expressed as:
Figure BDA0002662184090000031
wherein λ isjA Lagrange multiplier of the jth dimensionality reduced sample;
step 3-2, for Lagrangian function L, for uijDifferentiating and letting the result be 0, then:
Figure BDA0002662184090000032
wherein m is a blurring factor;
step 3-3, according to the formula (2),
Figure BDA0002662184090000033
uijthe rewrite is:
Figure BDA0002662184090000034
formula (5) is uijFor the lagrange function L, for ciDifferentiating to obtain:
Figure BDA0002662184090000035
according to the formula (6), ciExpressed as:
Figure BDA0002662184090000041
ciis a cluster center, and finally there are 4 cluster centers, each cluster center is a coordinate, i.e. the abscissa is the first principal component and the ordinate is the second principal component. And adding the abscissa and the ordinate of each cluster center to obtain 4 values, wherein the 4 values correspond to the high fire risk grade, the medium fire risk grade and the low fire risk grade respectively.
The invention has the following beneficial effects: the invention provides a forest fire early warning method based on principal component analysis and fuzzy C-means, which comprises the steps of collecting meteorological data, carrying out dimensionality reduction processing on characteristics, establishing an objective function, solving the objective function to obtain the distribution of each sample, dividing the distribution into clusters with different forest fire risk levels, and having positive effects on early warning of forest fire and forest fire monitoring environment.
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The foregoing and/or other advantages of the invention will become further apparent from the following detailed description of the invention when taken in conjunction with the accompanying drawings.
Fig. 1 is a schematic diagram of clustering samples.
Detailed Description
The invention provides a forest fire early warning method based on principal component analysis and Fuzzy C-means, which compresses high-dimensional characteristics through the principal component analysis and explains the information content contained in the original characteristics by using different principal components, wherein the Fuzzy C-means (Fuzzy C-means) algorithm is called FCM algorithm for short, is a Fuzzy clustering algorithm based on an objective function, is mainly used for data clustering analysis, and is an excellent clustering algorithm. For big data multivariate time series feature extraction and similarity measurement analysis of a forestry monitoring environment and forest fires, relevant meteorological factors and other unstructured data in a period of time before and after the occurrence of the forest fires are taken as a time segment, information redundancy and noise are removed through multivariate data analysis, similarity measurement analysis is carried out on the time segments of the forest fires, common characteristics of the time segments are extracted, and the relation of each multivariate time series, the relation of multivariate time series observed values and the correlation among component attributes can be analyzed from the overall view angles of the whole multivariate time series database and the like. The characteristics of the multivariate time series data such as the characteristics and large data quantity of the multivariate time series data cause the design of a time series data mining algorithm to need to consider more factors. The feature representation and the similarity measurement are used as the basic work of the mining of the multivariate time series data, and the design of the algorithm and the model of the feature representation and the similarity measurement also accords with the characteristics of the multivariate time series.
Based on a wireless sensor network, meteorological data of ten stations (Kunshan, tin-free, Liyang, Nanjing, Nantong, high post, east station, Huaian, Shuyang, Xuzhou) in Jiangsu province are collected, the meteorological data comprise the temperature, the humidity, the rainfall and the wind speed of 2019 year all the year, and 3648 samples are collected after data are cleaned. X 'for each original sample'j＝(x′1j，x′2j，x′3j，x′4j)TCollecting meteorological data and carrying out PCA (principal component analysis) dimension reduction processing on 4 characteristics, wherein j is a sample serial number, and for an original data set, the specific dimension reduction process is as follows:
Figure BDA0002662184090000051
the sample variance calculation formula is as follows:
Figure BDA0002662184090000052
where Var represents the variance of the feature, xiRepresenting the value of each sample in a feature,
Figure BDA0002662184090000056
represents the mean of this column of samples.
By solving a covariance matrix
Figure BDA0002662184090000053
The characteristic equation | S- λ I | ═ 0, and the corresponding characteristic value λ is obtainediI is 1, 2, …, 4, where I is the identity matrix, the eigenvalues of the solution are shown in table 1 below:
TABLE 1
Figure BDA0002662184090000054
Variance contribution ratio:
Figure BDA0002662184090000055
the first two principal components after dimensionality reduction contain 88% of the original 4 features, so that an ideal effect is achieved, and the first two principal components, namely x, are reserved after dimensionality reduction1jIs a first main component, x2jThe second principal component is the entire dimensionality-reduced dataset, which is assumed to be X ═ X (X)1，x2，，...，xj，...，x3648). As shown below, Table 2 is the original sample data, and Table 3 is the reduced-dimension sample data.
TABLE 2
Figure BDA0002662184090000061
TABLE 3
Figure BDA0002662184090000062
The meteorological parameters are related to forest fire risks which are respectively a low fire risk grade, a medium fire risk grade and a high fire risk grade, and the forest fire risks are divided according to clustering results. Therefore, the problem is to determine which risk level area the sample belongs to, i.e. to determine the cluster it belongs to, for clusters c of different forest fire risk levelsiAnd each reduced sample xjThe following objective function P is established:
Figure BDA0002662184090000063
Figure BDA0002662184090000071
wherein the member function uijRepresenting the reduced dimension sample xjAnd cluster center ciM is a fuzzy factor larger than 1, K is the total number of clusters, and m is 2 and K is 4. Based on the Lagrange multiplier method, a Lagrange function L is constructed and expressed as:
Figure BDA0002662184090000077
wherein λ isjA Lagrange multiplier of the jth dimensionality reduced sample;
now, if equation (3) is to be solved, u is found out using the differentialijAnd ci。
Figure BDA0002662184090000072
Carrying out parametric separation on the formula (4) to obtain
Figure BDA0002662184090000073
Then according to the formula (2),
Figure BDA0002662184090000074
uijthe rewrite is:
Figure BDA0002662184090000075
formula (5) is uijThe final iterative formula of (2). Now, solve for c by differentiationiObtaining:
Figure BDA0002662184090000076
according to the formula (6), ciExpressed as:
Figure BDA0002662184090000081
after iteration is completed, respectively calculating 4 cluster centers according to the divided 4 clusters, then weighting the 4 cluster centers, taking the weighted result as an index for comprehensively evaluating the fire risk grade, and as shown in table 4, the method is a clustering result and a fire risk grade evaluation table thereof:
TABLE 4
Figure BDA0002662184090000082
Equations (5) and (7) are the final results of the machine learning FCM algorithm solution. From these two formulae, u is observedijAnd ciAre interrelated. However, there is a problem in that when the algorithm starts, there is no u eitherijAlso has no value of ciThe value of (c). So, u is initialized randomly at the beginningijOr ciThis is necessary to satisfy the assumption. The FCM algorithm selects an initialization cluster center ciThe corresponding membership value u is obtained from the result of the initialization according to equation (5)ijThen u is further calculated byijUpdate ciBy analogy, finally make | Pnew-PoldI <, convergence ends and a clustering result is obtained, where it is a sufficiently small number.
The fuzzy C-means algorithm is applied to fire prediction in forests, and the method is taken as an example in figure 1. FIG. 1 is a schematic diagram of clustering samples, i.e., the abscissa represents a first principal component, the ordinate represents a second principal component, xjRepresenting the sample number u after dimensionality reduction1j、u2jFor reduced dimension sample xjMembership values to different cluster centers for reduced-dimension sample xjBy calculating u1j、u2jIf it is closer to c1The Euclidean distance is relatively small, and instead the membership value u1jRelatively large, which is also a benefit of the FCM algorithm to balance the weights.
Through the collection and dimension reduction processing of meteorological data and a fuzzy C-means method, the meteorological data of each station are clustered, and finally 4 clusters can be divided into a low fire risk grade, a medium fire risk grade and a high fire risk grade according to a clustering model, wherein the 4 clusters correspond to the forest fire risk grade.
In brief, 4 cluster centers are given during initialization, a membership value matrix of each reduced-dimension sample to the 4 cluster centers is solved, the 4 cluster centers are updated once by the membership matrix, iteration is performed in sequence until convergence is achieved, the obtained membership value matrix after convergence is the final dividing basis, and finally division is completed and 4 cluster areas are obtained. The weighted result of 4 cluster center coordinates is used as an index for measuring the fire risk level, and the higher the weighted value is, the higher the fire risk level is, which uses the principle of fuzzy C-means algorithm to predict the occurrence of forest fire.
The invention provides a forest fire early warning method based on principal component analysis and fuzzy C mean value, and a plurality of methods and ways for implementing the technical scheme are provided, the above description is only a preferred embodiment of the invention, and it should be noted that, for a person skilled in the art, a plurality of improvements and embellishments can be made without departing from the principle of the invention, and the improvements and embellishments should also be regarded as the protection scope of the invention. All the components not specified in the present embodiment can be realized by the prior art.

Claims (4)

1. A forest fire early warning method based on principal component analysis and fuzzy C-means is characterized by comprising the following steps:
step 1, collecting meteorological data and performing dimensionality reduction processing on characteristics to obtain a first principal component and a second principal component;
step 2, establishing an objective function according to the first principal component and the second principal component;
and 3, solving the objective function, and outputting the fire early warning level according to the obtained result.
2. The method of claim 1, wherein step 1 comprises: based on the wireless sensor network, x 'is taken as each original sample'j＝(x′1j，x′2j，…，x′nj)TCollecting meteorological parameters, namely features, wherein j is a sample serial number, n is the category total number of the features, x'njRepresenting the nth feature of the jth original sample; for different types of features, a PCA dimension reduction technology is adopted to compress the features and form a first principal component and a second principal component, and for an original data set, the specific dimension reduction process is as follows:
Figure FDA0002662184080000011
x′nNan nth feature representing an nth sample, which is raw data, i.e., data before dimensionality reduction;
the sample variance calculation formula is as follows:
Figure FDA0002662184080000012
where Var represents the variance of the features, N is the number of samples, xiRepresents the value of the ith sample in a feature,
Figure FDA0002662184080000013
represents the mean of this column of samples; this column represents a feature column, each column of matrix X' representing a feature column;
by solving a covariance matrix
Figure FDA0002662184080000014
The characteristic equation | S- λ I | ═ 0, and the corresponding characteristic value λ is obtainediI is 1, 2, …, n, where I is the identity matrix and λ represents the eigenvalue.
3. The method of claim 2, step 2 comprising: cluster c for different forest fire risk classesiAnd each reduced sample xjThe following objective function P is established:
Figure FDA0002662184080000015
Figure FDA0002662184080000016
wherein the member function uijRepresenting the reduced dimension sample xjAnd cluster center ciMembership value between, m is a blurring factor greater than 1, K is the total number of clusters, x is the number of samples per samplej＝(x1j，x2j)T，x1jRepresenting the first principal component, x, of the jth sample2jRepresenting the second principal component of the jth sample.
4. The method of claim 3, step 3 comprising:
step 3-1, constructing a Lagrangian function L based on a Lagrangian multiplier method, wherein the Lagrangian function L is expressed as:
Figure FDA0002662184080000021
wherein λ isjLagrange multiplier for jth sample;
step 3-2, for Lagrangian function L, for uijDifferentiating and letting the result be 0, then:
Figure FDA0002662184080000022
wherein m is a blurring factor;
step 3-3, according to the formula (2),
Figure FDA0002662184080000023
uijthe rewrite is:
Figure FDA0002662184080000024
formula (5) is uijFor the lagrange function L, for ciDifferentiating to obtain:
Figure FDA0002662184080000025
according to the formula (6), ciExpressed as:
Figure FDA0002662184080000026
cithe cluster centers are the cluster centers, 4 cluster centers exist finally, each cluster center is a coordinate, namely the abscissa is a first main component, the ordinate is a second main component, the abscissa and the ordinate of each cluster center are added to obtain 4 values in total, and the 4 values respectively correspond to a high fire risk level, a medium fire risk level and a low fire risk level.
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