Study on the Wildfires Occurring Risk Based on Fuzzy FTA

The serious consequences of wildfire urges scholars to pay more attention to control the occurrence of wildfire. Wildfire occurring is considered to be the result of satisfying comprehensive conditions including sufficient forest fuel, high forest fire-danger weather ratings and ignition source in this paper. In order to further study the causes and potential risks of wildfires. An assessment algorithm used for wildfires occurring risk is proposed by combining trapezoidal fuzzy theory and FTA. Furthermore, Xiangxi was chosen as application example, and the result shows that the top five dangerous BEs are ‘High average temperatures (X1)’, ‘illegal sacrifices (burning) (X23)’, ‘large underground humics (X7)’, ‘large weeds and dwarf shrubs (X11)’, ‘luxuriant tree branches (X14)’ exist highly risk. Finally, based on the evaluation results, suggestions are provided for the above basic events with greater risks.


Introduction
Wildfires have been a common occurrence since the appearance of forests on earth. On average, more than 200,000 wildfires occur every year in the world, accounting for more than 1‰ of the total forest area of the world. China has an average of more than 10,000 wildfires every year, burning hundreds of thousands to millions of hectares of forest, accounting for 5-8 per thousand of the country's forest area. These accidents will seriously affect the normal life of the residents and cause an enormous economic cost [1][2][3][4].
Many researches have been done about the adverse effects of wildfires. The coupling effect of vegetation, topography, surface availability, season, region and other factors on the severity and the occurrence probability of wildfires is considered from the aspect of natural factors and human factors [5; 6]. Furthermore, many research methods are adopted to evaluate the hazards of wildfires, such as logistic regression model [6], cellular automata theory [7], dynamic heat balance equation [8], artificial neural network [9], spectral analysis [10] et al. In addition, related prediction algorithms and methods of wildfires are taken into consideration. Michael C. et al [11] proposed a prediction method for wildfires in south-central America based on the downscaled climate projections and physical chemistry fire frequency algorithm (PC2FM). Zhang H. et al [12] established the binary logistic regression model to study the probability of occurrence on wildfires in Northeast China. Although ESMA 2019 IOP Conf. Series: Earth and Environmental Science 440 (2020) 052100 IOP Publishing doi:10.1088/1755-1315/440/5/052100 2 some achievements have been made in this field, the prediction and prevention of wildfires still needs to be further improved due to complex properties of coupled multi-factors on wildfires [13].
Unlike the perspectives of previous research, wildfire occurring is considered to be the result of satisfying comprehensive conditions including sufficient forest fuel, high forest fire-danger weather ratings and ignition source. Furthermore, the risk assessment algorithm consisting above factors is established by using the fuzzy FTA in the paper. Finally, the potential risks are found and the safety suggestions are put forward.

Establishing fault tree
Wildfires occurring is regarded as the top event (TE) in the fault tree. Wildfires will happen easily in case of sufficient forest fuel [14], high forest fire-danger weather ratings [15] and ignition source [16]. Therefore, these three factors are considered as intermediate events in the fault tree, then various factors associated with above events is further analyzed. Wildfires occurring fault tree is shown in Fig.  1 and Table 1 presents the meanings of basic events (BEs).  = , , , , , P X X X X X X ;   2  7  8  9  10  11  12  13  14  15 = , , , , , , , , There are 486 minimum cut sets and 3 minimum path sets in the fault tree. The minimum cut sets indicate the number of paths for wildfires occurring and wildfires will happen when one of the paths links. In addition, the minimum path sets represents the means of avoiding wildfires occurring. Therefore, the minimum path sets are selected to calculate the probability of the TE by comparing the numbers of the two sets.

The calculation process of fuzzy fault tree
2.2.1. Expert evaluation. Each expert often evaluates BEs according to the previous work experience and common sense, so there would be errors. Therefore, three experts in related fields are invited to evaluate the probabilities of fuzzy events for the more accurate assessment, and weights for each experts are determined according to Table 2. Table 3 , and the larger ( , ) DA A B represents the stronger similarity of fuzzy number A and B , which means that the agreement degree of two expert's opinion is higher.
(2) Calculating the average of agreement ( ) AA of each expert Where n is the sum of experts, and ( ) i AA E indicates the average agreement degree between an expert and all experts opinion.
(3) Calculating the relative of agreement ( ) RA of each expert Where ( ) i RA E is the weight of the average agreement degree for the opinion of an expert. (4) Estimating the consensus coefficient ( ) CC degree of each expert Here,  is relaxation factor and (5) Finally, the aggregated results of expert judgment AG R can be obtained as follows: Here, AG R is the fuzzy number of BEs after aggregating, and i R is the trapezoid fuzzy probability given by an expert.

Defuzzification process.
In order to make the results more accurate, the fuzzy probability of TE needs to be defuzzified, which is shown as follows: Where i x I is the importance degree of a BE; and 0 i x TE P  is the probability of TE when the occurrence probability of specific BE is zero.
3. An illustrative case for the assessment algorithm of wildfire Located in the south of the Yangtze River, Xiangxi has a low dimension and is a subtropical monsoon humid climate with obvious continental characteristics which leads to a high forest coverage up to 70.24%. In addition, this area mainly including 11 ethnic minorities such as Tujia, Miao, Yi, Yao, Bai, and Hui, etc. has rich cultural customs.  Table 4. 6 degree (AA), relative agreement degree (RA), etc. The aggregating calculation process of basic events X 1 is shown in Table 5 and the calculations for other BEs are the same, so they are omitted.
According to the calculation results, the probability of wildfire occurring (IE) is 2.570%, which indicates that potential risks exist.

Analysis for importance degree of BEs
The importance degree of BEs is determined by eq. (9), and the importance degree of all BEs in wildfire occurring is calculated and sorted. Through sequencing, the key factors affecting the wildfire occurring are discovered. The result is presented in Table 7.