Fire risk assessment and factor analysis of buildings based on multi-target decision and fuzzy mathematical model

Abstract

Reasonable fire risk assessment system can demonstrate the occurrence of fire and ensure the safe evacuation of fire. The selected indicators of the evaluation system play a fundamental role in the establishment of the system. In the evaluation model, the general problem is transformed into a specific mathematical model by using the method of fuzzy information processing, which makes the evaluation result more direct and measurable. This paper uses a measure of feature attributes to measure the contribution of clusters, that is, the method of calculating the weight of features. When the value of the equilibrium discriminant function reaches the minimum value, the clustering result under the optimal condition can be obtained. Then, the author analyzes the fire risk assessment and factor analysis of buildings based on multi-target decision and fuzzy mathematical model. The simulation results show that the improved fuzzy model proposed in this paper makes the calculation results more accurate. The fire risk analysis and control system based on the theory of fuzzy information processing can be widely used in various high-rise buildings to ensure safety.

Keywords

Multi-objective decision high-rise building fire risk fuzzy mathematics

1. Introduction

The high-rise building in city usually has large number of floors and huge volume that leads to extremely concentrated population, so the consequence of fire disaster is more serious in high-rise building than other typologies [1]. The fire disaster including high-rise building fire disaster rate are increased in a rapid speed that draw national attention from public and relevant government department [2]. How to complete fire protection and fire fighting system becomes a national issue, and effective solutions are required urgent [3]. A reasonable fire risk evaluation system could proof the fire disaster happening and ensure the safe evacuation, while the indexes selected for the evaluation system plays a foundation role in system establishment. Whether those indexes are selected fully considerate with the real requirement has a close relationship with the final performance of evaluation system [4, 5]. The high-rise building fire risk analysis and control system presents the connection between potential fire disaster factors as well as the possible solution to form a organic entity.

With the increasing attention to high-rise building safety, more and more research has been done for following topics [6]. The fire protection standard and the fire risk evaluation is one of the most popular issue. To go further about the risk evaluation, the fire disaster situation and the fire protection zone must be indicated [7]. Meanwhile, the building structure character and the fire proofing material selection plays the important role in high-rise building fire safety as well. In addition, the fire sprawl prediction and smoke flow study is a key evidence during the fire fightingprocess [8]. The equipment located in high rise building such as fire alarm system and automatic spray system could improve the fire protection and fire fighting ability of the building itself [9]. The following paper will highlight the establishment of fire rise analysis and control system in city high rise building from the setting of fire situation, the division of different fire disaster stage, and the relative action and solution for different stage [10]. In terms of the evaluation model, the fuzzy information process method applied as the transition between general issue into a specific mathematics model, then the evaluation outcome is more direct and measurable. The key evaluation factors for the fire risk analysis and control system includes the fire protection ability, fire fight ability, evacuation system and management level. The outcome is calculated by fuzzy model from the above four aspects.

2. Related work

The establishment of accurate, comprehensive and effective high-rise building fire risk evaluation system is the key point to the fire risk assessment, so particular attention should be paid when selecting evaluation index, which is supposed to fully consider with the applicable and measurable [11]. The fire risk evaluation of high-rise building should combine the situation that few fire disaster happens as well as the evacuation and fighting measurement after fire disasters happen [12]. Therefore, fire risk analysis and control system is a multiple layer system that will be influenced by multiple factors, and those factors are interlocked with each other accompanying with extremely completed relationship [13, 14]. The following paragraphs attempt to assume possible fire disaster situation in order to identify the potential reasons for fire disaster happen. The potential threat analysis could contribute to the establishment of fire risk analysis and control system.

Fire disaster situation means the description about the process of some particular fire disasters from the very beginning of burning to the increasing period and ended in the peak [15]. Meanwhile, the fire disaster refers to the instruction of architecture structure as well as the expected damage that caused by fire disaster. The sitting of fire disaster situation should fully consider about the surrounding before fire disaster happens, ignition source, burning material and the possibility of extension [16]. The setting of fire disaster situation could expect the consequence of fire disaster such as human death, architectural structure damage and the property loss, which means that the fire disaster situation is the key step of fire risk evaluation and property analysis [17]. In the fire disaster situation, all the relevant factors of fire disaster happened in high-rise building are exposed to protection and fighting system. The beginning time and location of fire disaster are not limited in those situations, only the fire protection zone divisions are supposed to be assumed. The vertical and horizontal broken of fire will damage the whole building, which will cause a serious consequence especially for human injury or death and the property loss.

The fire disaster should be recognized from the fire protection plan, generally, should be understood from the unit space influenced by fire disaster and the actions for different stages [18]. Based on this concept, the fire disaster could be divided into several stages with different situation, and the time factors should be included as well. When the fire disaster happens and develops, human will have a great influence on the fire disaster, because the action human take will change the consequence totally [19]. The partition of fire disaster could assist fireman to figure out the most effective fire protection strategy. Those theories could benefit the following research and study for high-rise building fire protection.

The functions of high-rise building and its politic or economic position have a significant influence on the fire load capacity and design standard [20]. The evacuation plans and fire fighting strategies could determine the quantity and location of the relevant equipment and fire fighting installation, which have continuous influence on the partition of fire disaster. Therefore, those following two assumptions should be made before stage division [21]. Firstly, It is possible that some mistake behavior will happen for building user [22]. Although, there is only a little situation that those mistake behavior will cause fire disaster, this necessary and sufficient condition should be fully considered. Meanwhile, the fire protection infrastructure located in building will be ineffective randomly [23]. No matter how low the possibility for the broken machine, the above situation is the other necessary and sufficient condition.

Based on the above assumption, the fire disaster develops process from primary beginning to completed statue could be divided into five different stages with the consideration of dangerous degree and fire protection measurement.

When the fire disaster happens, the open flame appears because of the fire source touch the burning material.

The heat release rate is slower during the primary stage, so the fire disaster could be fought by fire extinguisher or automatic spraying system.

During the third stage, the fire disaster developed with further step. A large quantity toxic gas will be released because of high temperature. The fire extinguisher and automatic spraying system could not control the fire disaster situation. The fire hydrant should be applied to control the fire disaster situation and organize person evacuation.

The forth stage means all fire hydrant damaged, and the fire extended to all horizontal fire proof zone, which could cause the explosion.

After the horizontal proof zone has been broken, the vertical proofing zone will be broken sooner or later. The fire could extend into other floors that will cause significant loss of property. Meanwhile, the toxic smoke is the main reason for human death. Part of the building will the demolished by fire disaster.

3. Theoretical analysis

3.1. Feature selection method

When the feature attributes of the data set are very large, the irrelevant and redundant feature attributes will greatly affect the accuracy of the calculation, and thus affect the performance of the algorithm, which may cause dimensionality problems. In general, the method of feature selection can be used to solve the dimensionality problem. This paper uses a measure of feature attributes to measure the contribution of clusters, that is, the method of calculating the weight of features. The method measures the distinguishing ability of a feature by examining the difference between a neighboring data object of the same category and a neighboring data object of a different category. If the difference between the data objects of the same category is small, and the difference between the data objects of different data categories is large, it indicates that the feature has strong distinguishing ability.

The data set S ={ s₁, s₂, ⋯ s_m } is set, each data object contains P features, that is, s_i = { s_i1, s_i2, ⋯ s_ip }, 1 ≤ i ≤ m. Category c_i∈ C, C = { c₁, c₂, ⋯ c_K } of s_i is a collection of K number categories. The method first randomly selects a data object S_i from the data set. In the data object of each category, the d number of data object closest to the distance s_i is selected to combined with the d number of data objects of the same category as s_i to form a collection H (c).Data objects of different categories from s_i form a collection m (c) according to their category. The weight vector W = (w₁, w₂, ⋯ w_p) of the feature is updated according to the set m (c) and H (c), and the weight of the feature t (1 ≤ t ≤ p) is calculated as shown in the formula (1): $w_{t}^{l + 1} = \begin{matrix} w_{t}^{l} - \sum_{x \in H (C)} \frac{diff (t, s_{l}, x)}{(n \times d)} + \\ \sum_{c \notin class (s_{l})} [\begin{matrix} \frac{p (c)}{1 - p (class (s_{l}))} \\ \sum_{x \in M (C)} diff (t, s_{l}, x) \end{matrix}] \end{matrix} / (n \times d)$ (1)

Among them, n is the number of samples, and the diff (t, s_l, s_j) function is the difference function of the data objects s_l and s_j on the feature t. The specific formula is shown in Equations (2) and (3).

If the feature t is continuous, $min_{t}$ and $max_{t}$ are the minimum and maximum values of the feature t in the data set, then $diff (t, s_{l}, s_{j}) = | \frac{s_{lt} - s_{jt}}{{max}_{t} - {min}_{t}} |$ (2)

If the feature t is discrete, then $diff (t, s_{l}, s_{j}) = {\begin{matrix} 0 \\ 1 \end{matrix} \begin{matrix} s_{lt} = s_{jt} \\ s_{lt} \neq s_{jt} \end{matrix}$ (3)

The method equalizes d number of data objects in data object s_l and category c (c ≠ class (s_l)) that are close to s_l distance on the feature t. After that, the proportion of the C-type data objects in all the data objects of different categories of s_l is multiplied. The above operation is performed once in all categories of the same category as s_l.Using the results obtained to obtain the mean, the difference between all the different types of data objects on the feature t is obtained. This can evaluate the ability of the feature to distinguish between close-range data objects. The processing of this method is shown in Table 1.

Table 1

Feature selection method

Feature selection method
Input: data set S
Begin:
for : i← to p do
w_i = 0;
for : i← to n do
Randomly select a data object from S
Among all the data objects of the same category as s_i, the d number of data objects of the nearest neighbor are selected to constitute a set H (c).
for (eachc ∈ C ∩ c ≠ class (s_i))
From category C, the d number of data objects closest to s_i are selected to form a set M (c).
Calculating the weight vector of the feature W ={ w₁, w₂,. . . , w_p }
End

The weight vector W of the feature is calculated according to Table 1 and is arranged in descending order of the weight value, and the feature vectors of the first m numbers with the largest weight value are selected to form the final feature subset. The method uses the distance between data objects to select the nearest neighbor of a feature. The feature attributes involved in the calculation process have an effect on the relative distance between the data objects and in turn affect the selection of the nearest neighbors so that it can act on the weight values of the feature attributes. The greater the weight value of the feature attribute, the stronger the ability of the feature to distinguish the data object and the greater the contribution to the cluster. Otherwise, the feature has weaker ability to distinguish the data object and the contribution to the cluster is less.

3.2. Optimized selection of the initial cluster center

We assume that there are data sets x ={ x₁, x₂, ⋯ , x_n } of n number of objects, each data object contains p features, ie x_l ={ x_l1, x_l2, ⋯ , x_lp }.Data set X is now planned to be divided into K number of clusters c_j = (j = 1, 2, ⋯ k, k < n), and the feature attributes of the j (1 ≤ j ≤ p)-th data object can be defined as X_lj.

The Euclidean distance between arbitrary data objects X_l and (1 ≤ i ≠ j ≤ n) is defined as: $d (x_{l}, x_{j}) = \sqrt{\sum_{a = 1}^{p} {(x_{la} - x_{ja})}^{2}}$ (4)

The distance density function density (x_l) corresponding to the data object (1 ≤ i ≤ n) in the data set is defined as: $density (x_{l}) = \sum_{j = 1}^{n} \frac{d (x_{l}, x_{j})}{\sum_{l = 1}^{n} d (x_{l}, x_{j})}$ (5)

The neighborhood radius R_l of data object X_l, (1 ≤ i ≤ n) in the dataset is defined as: $R_{i} = n^{cR} \times \frac{1}{n} \sum_{i = 1}^{n} e^{- density (x_{l})}$ (6)

Among them, cR (0 < cR < 1) is the neighborhood radius adjustment coefficient. It is shown by experience that there is a better clustering effect when cR = 0.13.

Assuming that there is a data object X_l, (1 ≤ i ≤ n) in the data set X, the number of data objects contained in the spherical domain with X_l as the center and the radius R_l of the neighborhood radiuses defined as the point density of X_l, which is denoted as D (x_l). The larger the value of D (x_l), the higher the density of the spherical area where the data object is located, ie: $D (x_{l}) = | p | {d (x_{l}, p) \leq R_{l}, p \in X}$ (7)

The density average MD (x) of all data objects in data set X is:

$MD (x) = \frac{1}{n} \sum_{x \in X} D (x)$ (8)

The step of optimizing the selection of the initial cluster center is shown in Fig. 3.

Fig. 1

Fire risk degree.

Fig. 2

clustering algorithm.

Fig. 3

Flowchart for selecting the initial cluster center.

3.3. Equilibrium discriminant function

When clustering a data set, the general reference function is used to discriminate and determine whether similar data objects exist in the data set are classified as one class. The criterion function is also called the objective function. The clustering algorithm determines whether the similarity within the cluster is maximized by calculating the objective function, and whether the degree of dissimilarity between the clusters tends to be maximized. Based on this idea, this paper chooses an equilibrium discriminant function as the criterion to detect the intra-cluster differences and cluster-to-cluster differences of cluster C, which effectively balances the inconsistency between intra-cluster differences and cluster-like differences and improves the overall quality of clustering. At the same time, when the value of the equalization discriminant function reaches a minimum, the clustering result and the optimal cluster number in the optimal case can be obtained.

Data set X ={ x₁, x₂, ⋯ , x_n } and set C ={ c₁, c₂, ⋯ c_K } are assumed to be a set of K categories. Among them, c_l (1 ≤ i ≤ n) is the center of the i category.

The intraclass cluster difference is a measure of the compactness inside the cluster. The sum of the squares of the distances of each data object in the cluster to the cluster center of the cluster to which it belongs is calculated as shown in Equation (9). $w (c) = \sum_{l = 1}^{k} w (c_{l}) = \sum_{l = 1}^{k} {\sum_{x \in c_{l}} d (x, c_{l})}^{2}$ (9)

The difference between clusters is to measure the difference between clusters by calculating and discriminating the Euclidean distance from the cluster to the center of the cluster.c_l and c_j are the centers of the i-th cluster and the j-th cluster, respectively, and the difference b (c) between the clusters is as shown in formula (10). $b (c) \sum_{1 \leq j \leq l \leq k} d (c_{j}, c_{l})$ (10)

The equilibrium discriminant function is shown in Equation (11). Among them, the difference between the class cluster w (c) and the class cluster b (c) needs to be normalized first, and K is the number of clusters. $W (c, k) = \frac{1}{1 + e^{b (c) - w (c)}}$ (11)

3.4. Description of the optimization algorithm

The steps of the K. Means feature selection algorithm are mainly divided into three phases: First, using the feature selection method to select the top m number of feature attributes with the largest weight (i.e., the greatest contribution to the cluster);Second, the optimal initial center is selected using an optimization selection algorithm of the initial cluster center; Third, the equilibrium number is used to select the optimal number of clusters. When the number of clusters k is chosen to be different, the function value and the number of clusters when the equalization discriminant function converges are recorded using an array. Then, the number of clusters corresponding to the minimum function value is the optimal number of clusters. A detailed description of the K. Means feature selection algorithm is shown in Fig. 4.

Fig. 4

K-Means feature selection algorithm.

4. Factors influence high rise building fire protection

4.1. Analysis of fire disaster in different stage

During the first stage, the reason of fire disaster is the touching between fire source and burning material, as a consequence, well manage the fire source is the best solution to avoid fire disaster (Fig. 1). To achieve the well management, the fire load of the building should be calculated carefully during design stage, and the decoration material should be selected with the limitation of fire load. In order to reduce the influence from surrounding, the functional plan should be designed with more consideration of fire protection, which means each building should keep safe distance. The main fire source inside building includes human and machine. For the high-rise building, normally equipped with large quantity of electricity machine, which is easier to become the fire source should be carefully located. For the other fire source, it is difficult to control for high-rise building itself, the only way to solve this is management for example forbidden smoking inside high-rise building.

When the fire disaster stay in the primary stage, the fire could be fought by fire extinguisher or automatic spraying system. Therefore, whether the open fire could be observed in time is the key point to control fire disaster during this stage. With the development of fire disaster, the fire hydrant should work for fire fighting. The main influenced factors of fire fighting during this stage is the work capacity of hydrant and situation of smoke emission. With the increasing high temperature, a lot of toxic smoke are generated by burning decoration material, which has negative influence on the fire hydrant using. Therefore, the effective performance of the smoke emission system is the guarantee for the using of fire hydrant. If the smoke emission and fire hydrant systems are broken by fire disaster, the fire disaster will developed into the other stage. The fire disaster will sprawl into other rooms in the same fire protection zone. To proof the further sprawl of fire disaster, the fire screen should be closed in time. Therefore, the influence factors during this stage include fire zone division, smoke proofing, and the urban fireman ability. Fire hazard GIS Map as shown in Fig. 5.

Fig. 5

Fire Hazard GIS Map.

4.2. The fire protection ability of building

Generally, people is used to describe things by fuzzy language, and the fuzzy judgement is the brief expression of thing that described by fuzzy language. The evaluation of management personnel performance could be judged by the fire protection knowledge and fire protection training. The class of this evaluation could be classified into five different degree, which is excellent, good, average, acceptable, bad. Therefore, the sub-system of management personnel fire protection performance includes V=(excellent, good, average, acceptable, bad). The information for this sub-system would be collected in the form of questionnaire. The professor who is good at fire protection knowledge will be invited to mark the performance for each individual factors, and all the date will be calculated with weight to generate the single factor evaluation subset R = (R₁, R₂, R₃, R₄, R₅), and the single factor matrix with collection mark could be expressed as following: $R_{mj} = \begin{matrix} R_{11} & R_{12} & . . . & R_{1 j} \\ R_{21} & R_{21} & . . . & R_{2 j} \\ . . . & . . . & . . . & . . . \\ R_{m 1} & R_{m 2} & . . . & R_{mj} \end{matrix}$

The high-rise building fire safety are influenced by several factors, and those factors plays different role in the fire risk proofing, which determines that the evaluation outcome should not be simply added (Mahdipour & Dadkhah, 2014). The weight index could be used to represented different importance on high-rise building safety to form the fuzzy subset of weight that A_im = (a₁, a₂, a₃, a₄, a₅). The weight index for different fire safety factor will be provided by relevant department and professor based on their experience. With the fuzzy mathematical matrix generation principle, the comprehensive evaluation outcome could be: C = A_im × R_mj, in where C is the comprehensive outcome for high-rise building fire proofing factors U=(Fire Protection Ability, Fire Fighting Ability, Safe Evacuation Ability, Safety Management Level). To present more directly, based on the single belonging principle, the single evaluation outcome could be μ₀ (x) = max(c_j)

The fire protection ability for high-rise building itself is the main factor that determine the fire protection ability, which is the foundation of high-rise building safety. The fire protection ability has close relationship with fire resistance class, inside and outside decoration material, inertial furniture quantity and distribution, function fire proofing zone as well as the architectural plan. Those factors construct the sub-system of building fire protection that U₁=(plan, fire resistance, fire load, fire proofing zone).

The fire fighting ability of building: The fire fighting ability for high rise building refer to the capacity that building equipment could stifle the fire automatically. This capacity mainly includes following factors, such as the ability of management people, the advanced fire protection equipment, the operation and maintain of equipment, and the ability to emission toxic smoke. The sub-system factors for fire fighting ability U₂=(artificial fire protection ability, fire equipment advance, situation of fire equipment, smoke emission ability)

The safe evacuation ability of building: It is impossible to ensure that no fire disaster happens in any high-rise building, therefore ensure that building user could escape from building quickly and effectively is very important. High-rise building must equip sufficient and advanced fire protection equipment to proved escape approach when fire disaster happens. Meanwhile, the evacuation ability of building has close relationship with user’s behaviour. All those factor compose the sub-system of safe evacuation ability that U₃=(evacuation equipment, design of fire proofing shelter, human behavior).

Safety management level: The safety management is a important guarantee for fire disaster proofing, which has a significant contribution in fire fighting. Safety management level mainly influenced by management policy, the fire protection knowledge of building user, the electronic operation situation, and the professional ability of fireman. The above factors compose the sub-system of safety management level that U₄=(safety management policy, user’s fire protection knowledge, electronic equipment operation situation, professional ability of fireman).

4.3. Fuzzy information model and specific calcula-tion process

The evaluation model for high-rise building fire risk evaluation system is established based on the advantages of fuzzy information recognition and fuzzy formula identification. The specific establishment process could refer to Fig. 6 and the general calculate process is as following:

Fig. 6

The Diagram for Specific Calculation Process.

Doing research and survey for target object to obtain the original material and organize some professors mark for those target object. The relevant indexes for sub-system (k) is the matrix collect all fuzzy information, which is the character matrix as well.

The character matrix for each fire protection proposal could be achieved by fire disaster statistics material. After that, the corresponding index and corresponding matrix could be calculated.

All the weight index and sub-system (k) could be applied for the best corresponding matrix.

The relative situation value of sub-system (k) could be calculated through correct formula.

Combined with the fuzzy evaluation method and indicated weight index, the secondary fuzzy evaluation could be done.

Repeat the step (5), multiple layer evaluation could be completed.

The building fire risk evaluation system has l = 4 sub-system totally, and any of those sub-system (k) contain more than one factors (n). Hence, the indicated character vector could be expressed as follow: $_{k} X = (_{k} X_{1},_{k} X_{2} . . .,_{k} X_{n})$ (12)

In where the _kX_n is the factor m in sub-system (k), while the k = l = 4.

If the factor n in sub-system (k)could be identified by several class s, then the standard character matrix for s class could be expressed as follow: $\begin{matrix} _{k} Y = \begin{matrix} _{k} Y_{11} & _{k} Y_{12} & . . . & _{k} Y_{1 s} \\ _{k} Y_{21} & _{k} Y_{22} & . . . & _{k} Y_{2 s} \\ . . . & . . . & . . . & . . . \\ _{k} Y_{n 1} & _{k} Y_{n 2} & . . . & _{k} Y_{ns} \end{matrix} = (_{k} Y_{ig}) \\ g = 1, 2 . . ., s; i = 1, 2, . . . m \end{matrix}$ (13)

In where _kY_ig means the character value for i factor in g class for sub-system (k).

Based on the fuzzy character of safety evaluation, the relative corresponding degree could be used for describe the safety degree, in where the class 1 is very safety while class s is extremely dangerous and the relative corresponding degree is 0 and 1 respectively. 2 and s-1 are two in middle situation between safety and extremely dangerous. The relative corresponding degree _kr_i of Sub-system (k) and relative corresponding degree s_ih of character index could be calculated as following: $\begin{matrix} _{k} r_{i} = 1 (_{k} r_{i} \leq_{k} r_{i 1} or_{k} r_{i} \geq_{k} r_{i 1}) \\ _{k} r_{i} = \frac{_{k} r_{ic} -_{k} r_{i}}{_{k} r_{ic} -_{k} r_{i 1}} (y_{i 1} <_{k} r_{i} <_{k} y_{ic} {ory}_{i 1} >_{k} r_{i} >_{k} y_{ic}) \\ _{k} r_{i} = 0 (x_{i} \geq_{k} y_{ic}) \end{matrix}$ (14)

In where _kr_i means the relative corresponding degree of index i of sub-system (k) under safe situation, and _kx_i is the indicated character value of sub-system (k). $\begin{matrix} _{k} s_{ih} = 1 (_{k} y_{ih} =_{k} y_{i 1}) \\ _{k} s_{ih} = \frac{_{k} y_{ic} -_{k} y_{ih}}{_{k} y_{ic} -_{k} y_{i 1}} (_{k} y_{i 1} <_{k} y_{ih} <_{k} y_{ic} or_{k} y_{i 1} >_{k} y_{ih} >_{k} y_{ic}) \\ _{k} s_{ih} = 0 (_{k} y_{ih} =_{k} y_{ic}) \end{matrix}$ (15)

In where _ks_ih means the relative corresponding degree for i class h standard of sub-system (k) under safe situation, and _ky_ih is the indicated class for h standard in sub-system (k).

The above formula could transform the _kX and _kY into corresponding relative matrix $k R = (k r_{1}, k r_{2} . . ., k r_{m})$ ${_{k}}^{s} = \begin{matrix} _{k} s_{11} & _{k} s_{12} & . . . & _{k} s_{1 s} \\ _{k} s_{21} & _{k} s_{22} & . . . & _{k} s_{2 s} \\ . . . & . . . & . . . & . . . \\ _{k} s_{m 1} & _{k} s_{m 2} & . . . & _{k} s_{mc} \end{matrix} = (_{k} s_{ih})$ (16)

Compare the relative corresponding degree _kr_1,_kr_2, . . . , _kr_m in m index of the sub-system (k) under safety situation with the 1, 2,. . . , m respectively could get the maximal and minimal class value of sub-system (k) the a_min, a_max.

Assume that relative corresponding degree matrix for sub-system (k) under safety situation could be expressed as following: $_{k} U = (_{k} u_{1},_{k} u_{2} . . .,_{k} u_{e})$ (17)

In where _kU_e is the relative corresponding degree for class c under safety situation, and the above formula should satisfied the following condition: $\sum_{_{k} = 1}^{e} u_{h} - 1 = 0; (0 \leq u_{h} \leq 1)$ (18)

The weight index of m factors in sub-system (k) for the target evaluation building is: $\begin{matrix} _{k} W = (_{k} W_{1},_{k} W_{2}, . . .,_{k} W_{m}) \\ \sum_{i = 1}^{m}_{k} W_{i} = 1 \end{matrix}$ (19)

Therefore, the fuzzy model is established as following: $\begin{matrix} _{k} U_{h} = 1; (h = a_{min} = a_{max}) \\ _{k} U_{h} = \frac{1}{\sum_{a_{min}}^{a_{max}} {[\frac{\sum_{i = 1}^{m} {(_{k} W_{i} |_{k} y_{i} -_{k} s_{ih} |)}^{p}}{\sum_{i = 1}^{m} {(_{k} W_{i} |_{k} y_{i} -_{k} s_{i 1} |)}^{p}}]}^{\frac{p}{2}}} (a_{min} < h < a_{max}) \\ _{k} U_{h} = 0 (h < a_{min} orh > a_{max}) \end{matrix}$ (20)

In where p is the distance parameter, and p = 1 means Hamming distance, while p = 2 means Euclidean distance. Based on the above fuzzy model, the most excellent relative corresponding matrix of sub-system (k) could be expressed as following: $_{k} U^{e} = (_{k} U_{1}^{e},_{k} U_{2}^{e}, . . .,_{k} U_{c}^{e})$ (21)

With the application of special character formula value $H (μ) = \sum_{h = 1}^{e} μ_{Ah} (μ) \times h$ could get $_{k} H = (1, 2, . . ., c) \times k {(_{k} u_{1}^{e},_{k} u_{2}^{e}, . . .,_{k} u_{c}^{e})}^{r}$

In where, _KH is the special character value for sub-system (k) under the safety situation, which could be used to measure the safety degree of 4 sub-system.

Assume that the weight vector for the target evaluation building is $\begin{matrix} W = (_{1} w,_{2} w, . . ._{i} w) \\ \sum_{k = 1}^{i}_{k} w = 1 \end{matrix}$ (22)

The safety class character value of targeted evaluation system is: $H = (_{1} w,_{2} w, . . ._{l} w) \times {(_{k} H 1,_{k} H 2, . . .,_{k} H n)}^{T}$ (23)

In where H is the safety class character value for targeted evaluation system. Because of the 1 ≤ H ≤ c, when H = 1, the system is existing in a safety situation, while when H = c, the system is in a extremely dangerous situation. When the value of H is located between 1 and c, the system situation is between safety and extremely dangerous situation.

5. Model simulation analysis

When the training samples and test samples are constructed, it is necessary to emphasize the typical and representative samples, which can fully represent the characteristics of the Building construction risk in the study area and time. In view of this, we will study the object is locked in the 20 of the project. Risk index score for: 0.1, 0.3, 0.5, 0.7, and 0.9 five levels in the, followed by the corresponding risk level: low, in general, high and higher. Building construction the overall level of risk value set to between 0 and 1, retained two decimal places, by Building construction risk reviews set as: [very low, low, in general, high and higher], risk interval [0, 1].

The last 5 samples were used as the test sample input system. The overall mean square error of the model is obtained by testing: MSE = 1.13225e-5, the smaller MSE value shows that the model has higher prediction accuracy. The error of the predicted value and the true value of the system is shown in Table 2.

Table 2
Test results and relative errors of SA-SVM

Test sample	16	17	18	19	20
Expert evaluation value	0.42	0.44	0.37	0.42	0.28
SA-SVM output value	0.4087	0.4106	0.3934	0.4089	0.3008
Error	2.7%	6.7%	6.3%	2.6%	6.9%

The relative error of each test sample is very small, which indicates that the evaluation model has good generalization performance. It can be seen from Table 3 that the evaluation results of the output of the simulated annealing support vector machine model are in agreement with the expert evaluation results. Therefore, the model can be applied to the Building construction risk assessment, and provides the decision basis for the Building construction risk management.

Table 3

Evaluation results of SA-SVM and experts

Test sample	SA-SVM output value	Risk level	Expert evaluation level	Risk level
16	0.4087	higher	0.42	Low
17	0.4106	General	0.44	General
18	0.3934	General	0.37	Low
19	0.4089	General	0.42	General
20	0.3008	Low	0.28	Low

In the risk factors affecting the normal operation of the Building construction, each factor has different effects on the size and the probability of the risk of the system. The sensitivity of each risk factor is analyzed by using the simulated annealing and support vector machine model, and the key risk factors that affect the operation of the supply chain can be found. Specific approach is in the same proportion from both positive and negative direction change index for each risk factor value, then the change after the index value of input into the model for risk prediction. The prediction results and original evaluation values are compared, value at risk, more changes of risk factors more sensitive. All the risk evaluation index values in positive and negative direction were changes in 15%. The changes of data input into the trained simulated annealing - support vector machine model for a new level of risk value, and compared with the original evaluation value, large differences in the risk factors is the key risk factors. The results of the analysis are shown in Table 4.

Table 4

Risk factors sensitivity analysis form

index	Index Value	Risk Value	Variation range (%)	New index Value	New risk Value	Deviation	Difference degree	Mean degree
U11	0.5	0.23	+15–15	0.5750.425	0.28730.1903	0.05730.0397	24.917.3	21.1
U12	0.5	0.23	+15–15	0.5750.425	0.24970.1998	0.01970.0302	8.513.1	10.8
U21	0.3	0.23	+15–15	0.3450.255	0.27420.1812	0.04420.0488	19.221.2	20.2
U31	0.3	0.23	+15–15	0.3450.255	0.31290.1534	0.08290.0336	36.033.3	34.7
U32	0.3	0.23	+15–15	0.3450.355	0.24910.1988	0.01910.0312	8.313.6	11.0
U41	0.5	0.23	+15–15	0.5750.425	0.32920.1486	0.09920.0814	43.135.4	39.3
U42	0.7	0.23	+15–15	0.8050.595	0.31840.1359	0.08840.0941	38.440.0	39.7
U51	0.3	0.23	+15–15	0.3450.255	0.32120.1623	0.09120.0677	40.929.4	34.7
U52	0.3	0.23	+15–15	0.3450.255	0.25330.1992	0.02330.0308	10.113.4	11.8
U53	0.5	0.23	+15–15	0.5750.425	0.26710.1916	0.03710.0384	16.116.7	16.4
U61	0.1	0.23	+15–15	0.1150.085	0.25720.2109	0.02720.0191	11.88.3	10.1
U62	0.7	0.23	+15–15	0.8050.595	0.33750.1584	0.09250.0716	40.231.1	35.7
U71	0.1	0.23	+15–15	0.8050.595	0.26310.1978	0.03310.0322	14.414.0	14.2
U72	0.7	0.23	+15–15	0.1150.085	0.26870.1876	0.03870.0424	16.818.4	17.6
U81	0.5	0.23	+15–15	0.8050.595	0.16180.2968	0.06820.0668	30.029.0	28.0
U82	0.3	0.23	+15–15	0.5750.425	0.26570.1793	0.03570.0507	15.522.0	18.8

6. Conclusion

In terms of the characters of fire disaster in city high-rise building, the above fuzzy model based on fuzzy identity formula has been established to analysis and control the fire risk. The fuzzy comprehensive evaluation method could assist to transit the information which is described in an object language into a accurate mathematics outcome which is measurable. Hence, the evaluation outcome in the form of number is easier to compare, as its more persuasive, acceptable and more objective. Given that the fire rise analysis and control system is a multiple influence factors system, this method is more suitable to setting up a reasonable standard. The traditional fuzzy model define the excellent corresponding degree by the fuzzy information directly, the comprehensive evaluation system attempt to avoid the mistake caused by character value and safety class, which means the outcome is more accurate and scientific. This fire risk analysis and control system based on fuzzy information process theory could be applied widely in all kind of high-rise building to ensure the safety. It could guide the dairy management of high-rise building as well. With the development of national fire protection, fire fighting and fire rise evaluation system, the fuzzy information collected by the above model will be more accurate. The improvement of the fuzzy model will benefit the more accurate calculation outcome. The fire rise analysis and control system could move forward into another new stage.

Footnotes

Acknowledgments

This research is supported by the National Natural Science Foundation of China (No. 71573252).

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