2.1.1 Classification on Uncertainty Type

(1) Aleatory uncertainty

Aleatory uncertainty represents the intrinsic, inherent and fundamental uncertainty of basic variables. It refers to the natural randomness of physical quantities and cannot be eliminated. Aleatory uncertainty is a type of objective uncertainty, which is determined by internal factors and external conditions, such as the uncertainty of load, material properties and geometric dimensions.

(2) Epistemic uncertainty

Epistemic uncertainty is a type of uncertainty arising from limited information and understanding. It can be further divided into statistical uncertainty, model uncertainty and measurement uncertainty. The first is caused by limited observations and depends on the sum of sample data and any existing knowledge; model uncertainty is caused by the defects and idealization of the physical model; measurement uncertainty is caused by the inaccuracy of the methods and tools used to evaluate a variable. Generally, knowledge uncertainty can be reduced by collecting more information in a more careful manner, or by adopting a more sophisticated model.

2.1.2 Classification on Uncertainty Characteristics

(1) Objective uncertainty

Objective uncertainty refers to all countable information from an event. It is random and can be described mathematically, involving only variables.

(2) Subjective uncertainty

Subjective uncertainty refers to all uncountable information from an event, caused by human activities. It is characterized by fuzziness, ignorance and incomplete knowledge. Often expressed by the Fuzzy theory, it involves not only variables, but also system processes.

2.1.3 Classification on Form of Manifestation

(1) Random uncertainty

The concept of random uncertainty means that the result of an event is uncertain because the conditions for its occurrence are out of control, but the result still has a clearly defined range of variation. Random uncertainty (called randomness for short) boasts a certain category of items, and the concept of randomness has a certain extension, but its connotation is uncertain. It can be expressed by a mathematical expression. For example, variable uncertainty obeys normal distribution. In general, the reliability uncertainty analysis method, which is a probability method, can be used.

(2) Fuzzy uncertainty

Fuzzy uncertainty (called fuzziness for short) is caused by the boundary uncertainty of variables, characterized by “fuzziness”. Fuzzy things fall under an uncertain category. The concept of fuzziness has a clear connotation, but its extension is unclear. It is usually described in fuzzy words. From a philosophical point of view, fuzzy uncertainty is a higher form of random uncertainty. In general, the fuzzy random structural reliability theory based on fuzzy set theory can be used.

(3) Incompleteness

Incompleteness is caused by a lack of knowledge. Its concept has a clear yet unclear connotation, i.e., “some information is known, whereas some is unknown”. Normally, it can be described by means of the gray theory, by the neural network theory and turbidity, and by the bifurcation theory. In general, reliability uncertainty analysis methods, such as gray theory and information theory, can be adopted.

2.1.4 Classification on Uncertainty Attributes

(1) Parameter uncertainty^[2-5]

Parameter uncertainty is caused by the uncertain knowledge of basic variables or events. As a fuzzy random problem, it arises from the randomness, fuzziness and incompleteness of variables.

(2) System uncertainty ^[2-5]

System uncertainty is caused by the inadequacy of the theoretical model or failure probability. It is the rest (in the sense of remainder) of parameter uncertainty. It is primarily caused by human activities and incompleteness.

2.2.1 Classical Probability Analysis Method

If the joint probability density function f(x) of random variables of a structure is known, then the failure probability P_f of the structure can be expressed as:

(2.1)

where D_f represents the structural failure zone. This kind of method is commonly used in the traditional structural reliability method based on the probability characteristics of variables[2-6]. Subjective judgment is completely ruled out because objective probability is adopted as part of classical probability theory and reliability is calculated based strictly on assumed objective distribution. It is usually very difficult to establish a total probability distribution function. In general, the first and second moments of distribution parameters are used to approximately describe the uncertainty of basic variables.

2.2.2 Bayes Probability Method

Subjective judgment is expressed by the rule of objective probability. The new formula obtained from conditional probability is as follows:

(2.2)

(2.3)

(2.4)

Fuzzy mathematical analysis is primarily used to solve uncertainty problems with an inexact definition and unclear boundaries. Zedeh[2-7] was the first person to introduce the concept of fuzzy subsets into the idea that basic variables are not taken as deterministic values or stochastic variables, but rather represented by discrete feature points. This means that the fuzzy subset A can be represented as

(2.5)

(2.6)

(2.7)

(2.8)

The common representations of a membership function are as follows in Table 2.1:

In where, if [L] = μ_L, then

(2.9)

2.3.2 Mode of Expression

The subjective uncertainty of a basic variable A can be expressed by the following steps.

Let subjective uncertainty be E_i. The measurement criteria are as follows: (i) M_i is the level of E_i; (ii) G_i is the importance of E_i. So

(2.10)

(2.11)

(2.12)

(2.13)

(2.14)

(2.15)

2.4.1 Basic Concept

The gray theory is characterized by information incompleteness and the non-uniqueness of results obtained. Therefore, theories have been devised including the principle of information incompleteness and the principle of process non-uniqueness. The solving process for non-uniqueness is a combination of qualitative and quantitative analyses. By supplementing information, qualitative analysis can be used to determine one or several satisfactory solutions. That is how the gray system is solved.

System information incompleteness is divided into four types: (1) incomplete element information; (2) incomplete structural information; (3) incomplete boundary information; and (4) incomplete information on operating behavior.

If the connotation and extension of an object are completely certain, it is white; if it has an uncertain connotation and a certain extension, it is gray; if it has a certain connotation and an uncertain extension, it is fuzzy; if both connotation and extension are uncertain, it is gray fuzzy.

For the basic variable z, its value changes at interval h, making it a gray variable, denoted by ⊗(z).

(2.16)

For the carbonized depth in concrete[2-9], this can be represented by a gray area, and a region can be set for β.

(2.17)

where i = 0, 1, 2, ……, N, N +1. A is the factor of carbon velocity. B is a parameter of concrete carbonization, is about 0.4 to 0.6. Given the concrete carbonization qualification index d_o, the failure probability of concrete carbonation durability P_f = P(d_o ≤ d) and . Table 2.2 shows the list of digital reperesentation of gray scale.

Because the corresponding carbonized depth in concrete is a weighted interval number at time t, β also has a weighted average. The specific calculation process is as follows:

1. Given time are taken in proper order at the interval of ,
   

   The weight corresponding to each value is calculated and denoted as

   
   

   . (Normally, N should not be too small).

   
   
2. The formula for is as follows
   
   (2.18)
   
   

   where i = 0, 1, 2, ……, N, N +1.

   
   
3. It is assumed that both d₀ and are random variables which obey normal distribution. So
   
   (2.19)
   
   

   where i = 0, 1, 2, ……, N, N +1

   
   
4. A curve of is drawn, and the weighted average is calculated
   
   (2.20)

An ANN (Artificial Neural Network) is a theoretical mathematical model of the human brain and its activities. Composed of a great many processing units properly interconnected, an ANN is a large-scale nonlinear adaptive system[2-14]. Featuring excellent nonlinear mapping and associative memory capabilities, ANNs are widely used for function fitting under various complex relations, and show both great flexibility and good adaptability. ANNs helps to provide more accurate calculation results without the aid of explicit mathematical and physical models. Moreover, they can boast good fault tolerance and adaptability. These characteristics make ANNs suitable for the time-variant reliability evaluation of structures.

Among neural network algorithms, the most widely used is a multi-layered feed forward neural network based on error back propagation, the BP (Back Propagation) neural network. The BP learning algorithm is adopted in the BP neural network, which is composed of both forward propagation and back propagation. Forward propagation means transmitting the input signal from the input layer to the output layer via the hidden layer. If the signal is properly output from the output layer, the learning algorithm will end; otherwise, back propagation will be enabled. Back propagation involves reversely calculating the error signal (the difference between sample output and network output) along the original connection route, with the gradient-descent algorithm used to adjust the weight and threshold of neurons in each layer to reduce the 4error signal. BP is a widely used neural network characterized by high operability, low computational complexity and low parallelism.

Structurally, the BP neural network consists of an input layer, an output layer and one or more hidden layers. The neural network is a process of mapping from the input surface to the output surface. This type of mapping is realized by means of the transfer function. There are two kinds of transfer functions commonly used in the BP neural network: purelin and sigmoid. Sigmoid functions include the symmetric tansig function and the asymmetric logsig function. See Figure 2.1.

If there are enough elements in the hidden layer, two layers can approximate any continuous function. Figure 2.2 shows a typical BP neural network containing two hidden layers. P represents the input parameter; IW_i represents the set of weights in the i-th layer; F₁ and F₂ are transfer functions tansig and purelin in the first and second hidden layers, respectively; a¹ is the intermediate variable generated after the input parameter is transmitted through the first hidden layer, and also the input parameter of the second hidden layer; the output parameter a² is obtained after a¹ is transmitted through the second hidden layer.

The following is the specific process by which the BP responding surface method is used for structural reliability analysis:

1. The number and statistical characteristics of random structural variables, and their corresponding sampling points, are randomly generated.
   
2. A structural finite element model is used to calculate the structural response at the sampling point to solve the structural limit state function. The function value and random variables constitute neural network learning samples.
   
3. The BP neural network model is used to determine structural parameters of the neural network, with learning samples applied to neural network training.
   
4. The weight and threshold of the trained neural network are substituted into the response function to establish an explicit expression for the limit state function.
   
5. FORM is used to calculate the structural failure probability and complete the structural reliability analysis.

2.6.2 Support Vector Machine

SVM (Support Vector Machine) is a general machine learning method based on the statistical learning theory. Its idea originated from the support vector method proposed by Vapnik et al.^[2-15] in 1963 to solve the pattern recognition problem. SVM maps the original space of the problem to a higher-dimensional feature space, where the classification problem can then be solved. When the classification problem is solved, it is considered that only the vectors on the classification boundary play a role in classification; these vectors are called support vectors. In Figure 2.3, a, b, c, d and e are support vectors. This is where the method gets its name.

The principle of structural risk minimization is applied to SVM, enhancing the generalization ability of the learning machine. This means that a small error is still bound to be generated even if a solution is obtained from limited training samples. There is a strict theoretical basis for SVM, capable of solving practical problems featuring a small sample size, nonlinearity, high number of dimensions and a local minimum. Considering this, the implicit limit state equation can be reconstructed in a new manner for structural reliability analysis.

For response surface reconstruction by SVM, it is essentially a process of building a regression support vector machine (RSM)^[2-16]. For SVM, regression is the same as pattern recognition, because it is also a process of mapping the input vectors in the original space to a higher-dimensional feature space, where a classification problem is taken into consideration. The mapping from the original space to a higher-dimensional feature space is realized by using the inner product in the feature space described by the kernel that meets the Mercer condition. Figure 2.4 shows the basic process of how RSM is implemented.

(1) SVM response surface reconstruction

A quantitative method that makes a trade-off between approximation precision and approximate function complexity for a given set of sample data is adopted for RSM. A set of feature subsets is selected from the training set so that the linear division of the feature subsets are equivalent to the segmentation of the entire dataset. For RSM in linear loss functions, the following optimization problem needs to be solved

(2.30)

where vector w and scalar b control the position of the optimal classification plane; (x_i, y_i) is a training point set; C is a penalty function, reflecting the coordination between structural and empirical risk; ε is the error insensitivity coefficient; ξ and ξ^* are slack variables.

Under Kuhn-Trucker conditions, Equation (2.30) is transformed into the following dual problem:

(2.31)

where α^* and α are Lagrange multipliers; l represents the number of support vectors.

Equation (2.31) is a convex set programming problem and has a unique solution. In other words, there is an obvious theoretical basis for the determination of the network topology of SVM. This is also one of its advantages over neural networks. The complexity of the process of solving Equation (2.31) is determined by the number of samples with a nonzero weight, i.e., the support vectors. During the development of its solving algorithms, SMO (Sequential Minimal Optimization) ^[2-17] was gradually developed on the basis of the Chunking and Osuna algorithms. SMO can decompose a large-scale QP (Quadratic Programming) problem into a series of smaller QP problems containing 2 Lagrange multipliers only, making it possible to solve the primal problem by a semi-analytical method.

After Equation (2.31) is solved, the optimal regression function of RSM is as follows:

(2.32)

The training point set in Equation (2.32) is composed of the empirical points corresponding to the input and the response obtained by the structural finite element method. It is the structural limit state equation reconstructed by SVM. Different kernel functions can be used to obtain different response surface equations. Commonly used kernel functions include linear kernel, polynomial kernel, RBF (radial basis function, or Gaussian) kernel and two-layer neural network kernel. However, there is no satisfactory method for choosing an appropriate kernel function, meaning they need to be selected based on experience.

(2) Deduction of partial derivative for SVM regression function

The FORM/SORM for reliability calculation requires the use of a partial derivative of the limit state equation. A first-order partial derivative is required if FORM method is used for calculation. For the reconstruction of the response surface Equation (2.32), let support vector , and input vector . In this way, the first-order partial derivative of the response surface equation constructed by linear kernel, polynomial kernel, RBF kernel and two-layer neural network (Sigmoid) kernel can be deduced. Examples are as follows:

(i) Linear kernel

Kernel function

(2.33)

(2.34)

(2.35)

(ii) Polynomial kernel

Kernel function

(2.36)

(2.37)

(2.38)

(2.39)

(2.40)

(2.41)

(2.42)

(2.43)

(2.44)

Where v(X·X_i)is a linear kernel, but S[•] is function of v(X · X_i). c and b is a constant, respectively.

(3) Calculation steps for SVM-based responding surface method

The traditional responding surface method for structural reliability analysis consists of two processes: the reconstruction of a local response surface near the expansion point and the search for the design point. For the SVM-based responding surface method, SVM is used to reconstruct the response surface, while the geometric reliability method is used to calculate the design point and structural reliability. The steps are as follows:

1. Let the initial expansion center point be X(1)=(x₁(1), x₂(1), …, x_n(1)), with the average point taken normally;
   
2. Use FEM or another method to calculate the function value at the current expansion point and each subsequent expansion point: g(x₁(k), x₂(k), …, x_n(k)) and g(x₁(k), x₂(k), …, x_i(k)±f_σi, …, x_n(k)), where the value range of f is generally set to 1∼3, and k represents the number of iteration rounds;
   
3. Normalize the data of the above empirical points;
   
4. Substitute normalized 2N +1 sample points into Equation (2.31) to solve the quadratic programming problem, obtaining the value of a*, α and b, thus establishing SVM response surface Equation (2.32);
   
5. Use the geometric reliability calculation method to calculate the checking and reliability index β, with the partial derivative deduced according to Equations (2.35) ∼(2.44);
   
6. Check whether the reliability index |β(k)-β(k-1)| and checking point function value |g(x_k)| meet the given accuracy requirements. If the conditions are met, finish iteration to obtain the reliability index; if the conditions are not met, calculate a new expansion point, and return to step 2 to restart iterative computation.

2.7.1 Basic Information of the Formwork Support Structure

A 10-storey beamless floor structure with a storey height of 3m, column grid size 6,000mm×6,000mm, column size 550mm×550mm, and slab thickness of 200 mm; concrete strength of the concrete slab and column: C30; reinforcement in positive and negative moment field: HPB235 steel and HRB335 steel. Area of reinforcement at support: 1,214 mm²/m; area of reinforcement at midspan: 808 mm²/m. Fastener-type steel pipe formwork is used for support. Steel pipe φ48 mm×3.5 mm; vertical rod spacing 750 mm; step distance 1,700 mm. Section stiffness of the bracing system is 6.4×103 kN, determined after considering the influence of wood keel on bracing stiffness and the depreciation effect of steel uprights.

In particular, the length is calculated together with the stable bearing capacity of the formwork support system, according to the code.

(2.45)

In order to evaluate the construction risk of fastener-type steel pipe formwork, it is necessary to first establish a risk evaluation system. The construction safety of the fastener-type steel pipe formwork is affected by a variety of factors, which can generally be divided into two categories, the first of which is on-site construction. Throughout the entire process, from scaffold design to dismantling, each link directly affects formwork safety. The second category is safety management, which must be underlined throughout the whole construction process, and which exerts a significant influence on formwork safety. Both of these can be further divided into sub-indices. Scaffold collapse is the main type of safety accident that occurs, with every link in the formwork erection process affecting safety. Design scheme, materials and erection, inspection and acceptance, and loading and dismantling all fall under key influential indices, so the construction indices are divided into these six aspects. Safety management and site construction are closely related and interact with each other. Effective auxiliary safety management is entailed in the whole formwork construction process. A multi-index and multi-level risk evaluation system[2-18] was duly established based on the above analysis, and after soliciting advice from numerous design and construction experts for fastener-type steel pipe formwork.

The evaluation system includes a total of five levels:

• Level A: Overall objective of evaluation (formwork construction risk)
  
• Level B: Evaluation index set (safety management and construction safety)
  
• Level C: Subset of evaluation indices (safety education, personnel ability, safety protection, design scheme, inspection and acceptance, dismantling, materials, loads and erection)
  
• Level D: Subset of evaluation indices (dismantling time, component dismantling, steel pipe quality, fastener quality, dynamic load, stacking load, support, bottom horizontal tube, scissor support, fastener installation and vertical rods)
  
• Level E: Bottom evaluation index set (position selection, proper torque, aspect, step distance, verticality and connection mode)

Table 2.3 shows indices and weights of a risk evaluation system for fastener-type steel pipe formwork support construction.

2.7.4 Index Weighting

In the evaluation system shown in Table 2.3, the importance of each index varies, making it necessary to determine the weighting of each index. This index weighting can be determined by such methods as the Analytic Hierarchy Process (AHP) ^[2-19], expert scoring method, or others. To be specific, an expert scoring method is adopted to determine the appropriate weighting by means of a questionnaire, the respondents to which are construction site managers. To reflect the influence of the respondents’ educational background μ1, age μ2, working years μ3, and safety education μ4 on the weighting judgment, the questionnaire also contains some questions regarding these aspects.

The importance of the indices in the questionnaire is further divided into 10 grades, from 1 (no influence) to 10 (most important). See Table 2.4 for details of this classification. A total of 84 questionnaires were collected for the 10 projects investigated.

The calculation formula for the importance of each index can be expressed as:

(2.46)

(2.47)

Where, μ_i1, μ_i2, μ_i3 and μ_i4 represent the weighting of educational background, age, working years and safety education, respectively. Their values are determined as shown in Table 2.5; R_i is the specific score of indices in a single questionnaire received. See Table 2.4 for the scoring standard; n is the number of questionnaires collected; S_i is the importance of each index in the same level index; W_i is the relative weight of each index in the same level index. See Table 2.5 for the importance and relative weights of each index after processing.

2.7.5 Expert Scoring Results and Risk Evaluation Grades

The score value x(x ∈ [0,10]) of each evaluation index indicates the actual implementation status. Questionnaires were distributed to managers, who were required to score all grades of the indices according to the realities on site, in order to determine the score for each index.

A total of 120 questionnaires were collected from the 10 projects investigated. Respondents were asked to evaluate the risk of formwork construction in the industry using a 10-point system. See Table 2.6 for the averaged results of the experts’ scores. Uncertainties in the scoring of various evaluation indices of the formwork support system are inevitable, since they reflect the inherent features of the framework support system. When using random statistical methods, only the random uncertainty of the index score value can be considered, not its own fuzzy uncertainty. Therefore, the score value of each index was fuzzed, as shown in Figure 2.5. In Figure 2.5, the score was . After introducing the λ horizontal truncation set, let , and the fuzzy interval that can obtain the score value can be expressed as:

(2.48)

Where, the value of c reflects the fuzzy boundary range of random variables, which is determined according to project realities; in general, . If the fuzzy interval of the score value does not belong to [0, 10], then any interval lower than 0 is treated as 0, and any interval higher than 10 as 10.

According to the realities of construction risk evaluation for fastenertype steel pipe formwork, the evaluation grade was divided into five grades. V={v1, v2, v3, v4, v5}={Grade 1, Grade 2, Grade 3, Grade 4, Grade 5}={Least safe, unsafe, relatively safe, safe, and safest}, represented by a fuzzy function in Figure 2.6.

2.7.6 Evaluation of a Fastener-Type Steel Pipe Scaffold

Taking the actual data collected as an example, the fuzzy grey correlation method and the traditional multilevel grey correlation analysis method were used, respectively, to describe the step-by-step data flow process in the risk evaluation system for formwork construction, and to explain the calculation method of multi-index multilevel grey correlation analysis. Superscript (1), (2) and (3) in the following table (Table 2.7 and Table 2.8) show the calculation results for the fuzzy grey correlation analysis method as represented by plane distance, lattice distance, and traditional multilevel grey correlation analysis, respectively.

Fastener installation	W10
Position selection	0.43	0.41, 0.49, 0.68, 1.00, 0.79	0.34, 0.34, 0.45, 1.00, 0.48	0.40, 0.53, 0.78, 1.00, 0.62
Proper torque	0.57	0.41, 0.49, 0.69, 1.00, 0.77	0.34, 0.34, 0.46, 0.94, 0.47	0.41, 0.54, 0.80, 0.97, 0.61
Vertical rod	W11
Aspect	0.28	0.41, 0.48, 0.63, 0.94, 0.95	0.39, 0.39, 0.43, 0.78, 0.81	0.34, 0.43, 0.58, 0.90, 0.67
Step distance	0.29	0.40, 0.47, 0.62, 0.91, 0.98	0.39, 0.39, 0.42, 0.73, 0.90	0.33, 0.42, 0.56, 0.86, 0.69
Verticality	0.21	0.43, 0.50, 0.68, 1.00, 0.86	0.39, 0.39, 0.48, 1.00, 0.63	0.36, 0.46, 0.65, 0.94, 0.60
Connection mode	0.22	0.42, 0.49, 0.66, 0.98, 0.89	0.39, 0.39, 0.46, 0.91, 0.69	0.35, 0.45, 0.62, 1.00, 0.62

Then the correlation matrix for the fastener installation indices D10

The correlation matrix for the vertical rod indices D11

Material	W7
Steel pipe quality	0.48	0.46, 0.57, 0.84, 1.00, 0.73	0.51, 0.51, 0.81, 1.00, 0.56	0.36, 0.50, 0.83, 0.67, 0.44
Fastener quality	0.52	0.49, 0.61, 0.92, 0.91, 0.68	0.51, 0.51, 0.94, 0.82, 0.51	0.38, 0.55, 1.00, 0.59, 0.40
Erection	W9
Support	0.15	0.42, 0.50, 0.71, 1.00, 0.76	0.40, 0.40, 0.54, 1.00, 0.51	0.44, 0.59, 0.90, 1.00, 0.63
Bottom horizontal tube	0.18	0.49, 0.64, 1.00, 0.77, 0.57	0.43, 0.43, 1.00, 0.56, 0.43	0.48, 0.73, 1.00, 0.58, 0.41
Scissor support	0.12	0.462 0.57, 0.84, 1.00, 0.73	0.51, 0.51, 0.81, 1.00, 0.56	0.43, 0.60, 1.00, 0.81, 0.52
Fastener installation	0.27
Vertical rod	0.28

2) Correlation degree matrix for each index in level C

Then the correlation matrix for the material index C₇

The correlation degree matrix for the erection index C₉

The calculation for dismantling and load index is the same as above.

3) Calculation of correlation degree matrix for each index in Level B

The calculation method is the same as that for Level C and Level D, so the detailed calculation process can be omitted. The result is shown in Table 2.9.

Correlation degree matrix for safety management index B₁

Correlation degree matrix of field construction index B₂

Construction risk of formwork support	W	B(1)	B(2)	B(3)
Safety management	0.45
Onsite construction	0.55

4) Calculation of correlation degree matrix for each index in Level A

The correlation degree matrix for construction risk of a fastener-type steel pipe formwork can be expressed as:

5) Determining the construction risk of fastener-type steel pipe formwork

The correlation degree is a numerical representation of the close relationship between sequences. When studying the correlation between reference sequences and compared sequences of a system, special attention should be paid to the order of the correlation degree between reference sequences and compared sequences, that is, the ranking of the correlation degree, rather than the magnitude of the correlation degree in numerical terms^[2-21]. According to the principle of maximum correlation degree identification, the results of the three methods are consistent, and the construction risk grade for fastener-type steel pipe formwork investigated on site is Grade 4, which falls within the safety scope. The ranking for the correlation degree obtained by the first two methods where fuzziness is considered is completely consistent, but slightly different from that obtained by the traditional method of multilevel grey correlation analysis. In the former two methods, where the fuzzification of standard index values and score values are considered, the ranking of the correlation degree better complies with the objective requirements.

2.7.7 Discussion and Summary Analysis

In this paper, fuzzy numbers were introduced into grey relational multilevel and multi-index analysis theory, and a grey comprehensive evaluation method based on fuzzy numbers was proposed. The distance of the fuzzy numbers is represented by plane distance and grid distance. Regarding the standard index value and the index score value as fuzzy numbers enables the complexity and inherent fuzzy uncertainty of objective items to be considered more easily, thus making multilevel grey correlation analysis more scientific and bringing it closer to reality. This method is applied to the construction risk evaluation of fastener-type steel pipe formwork. The results show that the grey correlation ranking obtained via the improved grey correlation analysis method (based on two fuzzy number distances) is completely consistent, but slightly different from the traditional grey correlation analysis method. This method can facilitate the comprehensive quantitative evaluation of fastener-type steel pipe formwork safety, avoid subjective randomness during risk evaluation, and help managers understand and master site safety in a timely manner, thus improving enterprises’ ability to carry out proper accident control.