Multi-risk coupling model considering coupling effect and cascade transfer

Abstract

The invention belongs to the field of engineering risk coupling effect analysis, and particularly relates to a multi-risk coupling model considering a coupling effect and cascade transfer, and a design method comprises the following steps: 1, determining a plurality of multi-risks of a certain risk assessment unit; 2, determining a representative risk of the risk assessment unit according to a priority order and a risk level of the plurality of risks; 3, determining a coupling coefficient and a transfer coefficient; 4, determining an effective risk transmission path; 5, determining the probability proportion of each effective risk transmission path; 6, substituting into a multi-risk coupling model for calculation; and 7, determining a final risk level. According to the method, the amplification effect and the cascade transfer effect after multi-risk coupling can be scientifically revealed and considered from the perspective of multi-risk coupling, and a theoretical reference is provided for multi-risk coupling and even generalized multi-factor coupling analysis in the future.

Description

Technical Field

[0001] The invention belongs to the field of engineering risk coupling effect analysis, and in particular relates to a multiple risk coupling model that takes coupling effects and cascade transmission into consideration. Background Art

[0002] Civil engineering, especially tunnel and underground engineering, involves many uncertainties and uncertainties. There are great and numerous risks in the construction and operation stages. The necessity of risk assessment and management is obvious (Huang Hongwei, 2006). With the vigorous development of underground engineering, the utilization of underground space has received more and more attention. The current construction of tunnels and underground engineering shows a trend of large-scale, complex and high requirements (Yi Guoliang et al., 2024). In such a complex and uncertain environment, the construction of tunnels and underground engineering will inevitably be coupled due to the mutual influence of multiple risks such as safety risks, quality risks, progress risks, and investment risks. Under the coupling of multiple risks, engineering risks may be amplified to a large extent, bringing unacceptable risks. Therefore, it is particularly important to study how to quantitatively evaluate the coupling effect of multiple risks and reveal the coupling mechanism of multiple risks.

[0003] However, the current risk assessment and control are mostly based on a single risk event, and rarely consider the impact of multiple complex coupling effects on engineering risks (Ming et al., 2013). This approach ignores the risk amplification effect that may be brought about by the coupling of multiple risks, which will result in dangerous design and construction organization. Some scholars have also used NK models (Fang Jun et al., 2022), Bayesian networks (Tao Ruoyi et al., 2024) or digital twin technology (Guo Feng, 2024) to try to reveal the mechanism of multiple risk coupling. However, these studies either simply migrate existing models in other fields, ignoring the physical characteristics of civil engineering itself; or simply start from a probability perspective and ignore risk losses. Moreover, most models abstract a new comprehensive risk based on existing risks, and do not clarify the attributes of the comprehensive risk, which is not conducive to risk control and management.

[0004] In summary, the main problems currently exist are: in the study of multiple risk coupling effects, (1) it is difficult to reveal the mechanism of multiple risk coupling in complex environments; and (2) the multiple risk coupling effects are difficult to quantitatively evaluate through scientific models. Summary of the invention

[0005] The purpose of the present invention is to overcome the shortcomings of the prior art, consider the coupling amplification and cascade transmission effects between complex multiple risks, and propose a multiple risk coupling model that considers coupling effects and cascade transmission. The gradient change method and the upper tail correlation method are used to quantitatively calculate the coupling amplification effect and cascade transmission effect. This method can scientifically reveal the mechanism of multiple risk coupling effects and cascade transmission from the perspective of consequences and probability, and provide a theoretical reference for future related multiple risk coupling analysis and generalized multi-factor coupling mechanism research.

[0006] The present invention adopts the following technical solutions:

[0007] The multiple risk coupling model considering coupling effects and cascade transmission is designed by the following method, which mainly includes the following steps:

[0008] Step 1: Identify a number of multiple risks for a risk assessment unit.

[0009] Multiple project risks include ten major risks: safety risk, quality risk, schedule risk, investment risk, contract risk, technical risk, management risk, environmental risk, social stability and other risks.

[0010] Step 2: Determine the representative risk of the risk assessment unit based on the priority ranking and risk level of multiple risks.

[0011] The multiple risks of a project are usually prioritized as follows: safety risk > quality risk > schedule risk > investment risk > contract risk > technical risk > management risk > environmental risk > social stability and other risks.

[0012] Step 3: Determine the coupling coefficient (c ij ) and the transfer coefficient (t ij The coupling coefficient and transmission coefficient between each risk in the assessment unit are determined by the gradient change method and the upper tail correlation method, and finally the coupling coefficient matrix (C n×n ) and the transfer coefficient matrix (T n×n ). Where n is the number of risks in the risk assessment unit.

[0013] Coupling coefficient (c ij ) reflects the coupled amplification (reduction) effect of risk i on risk j, that is, the amplification (reduction) multiple of risk j when risk i exists.

[0014] Transfer coefficient (t ij ) reflects the cascading effect of risk i on risk j, that is, the probability of risk j being amplified (reduced) by risk i.

[0015] The n×n coupling coefficients (c ij ) and the transfer coefficient (t ij) is summarized into an n×n matrix form, that is, the coupling coefficient matrix (C n×n ) and the transfer coefficient matrix (T n×n ), which is convenient for using the coupling coefficient (c ij ) and the transfer coefficient (t ij ), and possible matrix operations in the future.

[0016]

[0017] Among them, 1 to 10 are numbered from high to low according to the top ten risk priorities, including safety risk, quality risk, schedule risk, investment risk, contract risk, technical risk, management risk, environmental risk, social stability and other risks.

[0018] Step 4: Determine the effective risk transfer path. First, all risk transfer paths are obtained based on multiple risks. The probability of the i-th risk transfer path (assuming it is j→k→m→…→p→q) occurring is the product of the transfer coefficients between adjacent risks on the path:

[0019] T i =t jk ×t km ×...×t pq

[0020] Among them, t jk ,t km ,t pq are the transmission coefficients between adjacent risks on the i-th risk transmission path. Set the relevant threshold T 0 , the risk path greater than the threshold is the effective risk transfer path and is considered in the weight calculation of the effective risk transfer path in step 5.

[0021] Step 5: Determine the probability proportion p of each effective risk transfer path i The probability of occurrence of each effective risk transfer path is summed up, and the probability proportion of each path, i.e., the weight, is calculated:

[0022]

[0023] Among them, T i is the occurrence probability of the i-th effective risk transfer path.

[0024] Step 6: Substitute the current level of representative risks, the probability of occurrence of each effective risk transmission path, and the coupling coefficient between risks into the calculation formula of the multiple risk coupling model:

[0025]

[0026] in, R is the representative risk level value after considering multiple risk coupling. 1 is the representative risk level without considering multiple risk coupling, p i is the weight of the i-th effective risk transfer path, c jk 、c km 、c pq are the coupling coefficients of adjacent risks on the i-th effective risk transmission path.

[0027] Step 7: Determine the final risk level. If the value of the level is less than or equal to the average of the current level and the level one level higher:

[0028]

[0029] If the level is higher, it is considered that the level has been upgraded to a higher level and requires special attention; otherwise, it remains at the current level, but a reminder is required to pay attention.

[0030] Beneficial effects: The present invention provides a new calculation paradigm for multiple risk coupling effects in the field of engineering risk coupling effect analysis. It quantitatively characterizes the coupling amplification and cascade transmission effects in multiple risk coupling from the perspectives of consequence and probability through the pioneering gradient change method and upper tail correlation method, and intuitively depicts the internal mechanism of multiple risk coupling transmission by establishing risk transmission paths and thresholds. The invention can quantitatively calculate the coupling effects of multiple risks in a certain risk assessment unit, and provide a theoretical reference for future related multiple risk coupling analysis and generalized multi-factor coupling mechanism research.

[0031] Compared with other analytical methods, the present invention has the following characteristics:

[0032] (1) This invention is the first to split the complex coupling effect into two effects: coupling effect and cascade transfer effect for model construction, and characterizes them respectively through coupling coefficient (matrix) and transfer coefficient (matrix);

[0033] (2) A gradient variation method was proposed to calculate the coupling coefficient, and an upper tail correlation method was proposed to calculate the transfer coefficient;

[0034] (3) By introducing the threshold, the concept of effective risk transmission path is proposed, which makes the abstract and complex risk coupling effect visualized and concrete.

[0035] (4) The invention can scientifically consider the coupling and transmission mechanism among multiple risks, which has positive significance for quantitatively evaluating the coupling effect of multiple risks. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flow chart of a multiple risk coupling model considering coupling effects and cascade transmission in the present invention;

[0037] Figure 2 A flow chart of determining the coupling coefficient using the gradient variation method of the present invention;

[0038] Figure 3 The flow chart of determining the transfer coefficient by the upper tail correlation method of the present invention;

[0039] Figure 4 Schematic diagram of risk transfer path with security risk as representative risk in an embodiment of the present invention. DETAILED DESCRIPTION

[0040] The technical solution provided by the present application will be further described below in conjunction with specific embodiments and accompanying drawings. The advantages and features of the present application will become more apparent with the following description.

[0041] This paper proposes a multiple risk coupling model that takes into account coupling effects and cascade transmission, and establishes an engineering risk analysis process under multiple risk coupling to reveal the mechanism of multiple risk coupling amplification and cascade transmission effects in complex civil engineering environments. This method can scientifically analyze the effects of complex multiple risk coupling and conduct quantitative evaluation from the perspective of consequences and probability, which is of great significance for future related engineering risk assessment and multiple risk coupling effect evaluation.

[0042] The implementation process of the present invention is described in detail below. Figure 1 , the specific implementation steps are as follows:

[0043] (1) Determine the multiple risks of a certain risk assessment unit. The multiple risks of the project include ten major risks, namely safety risk, quality risk, schedule risk, investment risk, contract risk, technical risk, management risk, environmental risk, social stability and other risks. (The ten major risks are selected from the risk assessment unit division, risk source identification, risk confirmation, risk level evaluation and other links)

[0044] (2) Determine the representative risk of the risk assessment unit based on the priority ranking and risk level evaluation of multiple risks. The priority ranking of multiple risks in a project is usually: safety risk > quality risk > schedule risk > investment risk > contract risk > technical risk > management risk > environmental risk > social stability and other risks. If there is a risk with the highest risk level among multiple risks, then this risk is the representative risk; if there are multiple risks with the same level, then the one with the highest priority level is selected as the representative risk according to the priority ranking.

[0045] (3) Determine the coupling coefficient (c ij ) and the transfer coefficient (t ij ). By gradient change method (see the process for details) Figure 2 ) and upper tail correlation method (see the process Figure 3) determines the coupling coefficient and transmission coefficient between the risks in the assessment unit, and finally forms a coupling coefficient matrix (C n×n ) and the transfer coefficient matrix (T n×n ). Where n is the number of risks in the risk assessment unit.

[0046] Coupling coefficient (c ij ) reflects the coupling amplification (reduction) effect of risk i on risk j, that is, the amplification (reduction) multiple of risk j when risk i exists. Its calculation method, that is, the specific steps of the gradient change method are as follows:

[0047] ① Determine the distribution and numerical characteristics of the characterization parameters of risk i and risk j through statistical analysis.

[0048] ② When only risk j exists, generate a series of sample points of the characterization parameter n of risk j. Substitute these sample points into the numerical calculation model in turn to calculate the value of the corresponding response evaluation index a.

[0049] ③ According to this series of sample points and their corresponding response indicators, fit the functional relationship A(n) between the response evaluation index A and the characterization parameter n of risk j. Then the response sensitivity coefficient under the action of single risk j is

[0050]

[0051] ④ When risks i and j exist at the same time, generate a series of sample points of the characterization parameters m and n of risks i and j. Substitute these sample points into the numerical calculation model in turn and calculate the value of the corresponding response evaluation index a again.

[0052] ⑤ According to this series of sample points and their corresponding response indicators, fit the functional relationship A(m,n) between the response evaluation index A and the characterization parameters m and n of risks i and j. Then the response sensitivity coefficient of risk j under the coupling effect of risk i is

[0053]

[0054] ⑥ Therefore, the coupling coefficient of risk i to risk j is

[0055]

[0056] Transfer coefficient (t ij ) reflects the cascading effect of risk i on risk j, that is, the probability of risk j being amplified (reduced) by risk i. Its calculation method, namely the upper tail correlation method, has the following specific steps:

[0057] ① Collect a large amount of observational data (no less than 20 groups) on the characterization parameters m and n of risks i and j.

[0058] ② Establish the marginal probability density functions of the characterization parameters m and n of risk i and risk j respectively.

[0059] ③ Calculate the Kendall rank correlation parameter by the following formula:

[0060]

[0061] Among them, τ K is the Kendall rank correlation parameter of m and n observation data, N is the number of observation data groups, sgn is the sign function, when [(m i -m j )(n i -n j )]>0, sgn(·)=1, otherwise sgn(·)=-1.

[0062] ④Use the Kendall rank correlation parameter τ through the following formula K Calculate the Copula correlation parameter θ:

[0063]

[0064] Among them, C(u 1 ,u 2 ; θ) is the Copula function, u 1 =F 1 (m),u 2 =F 2 (n) are the marginal distribution functions of m and n respectively.

[0065] ⑤Use the AIC criterion to identify the Copula function that best reflects the correlation between risk i and risk j, thereby obtaining the joint probability density function of the characterization parameters m and n of risk i and risk j.

[0066] ⑥ Therefore, the transmission coefficient of risk i to risk j is

[0067]

[0068] The n×n coupling coefficients (c ij ) and the transfer coefficient (t ij ) is summarized into an n×n matrix form, that is, the coupling coefficient matrix (C n×n ) and the transfer coefficient matrix (T n×n ), which is convenient for using the coupling coefficient (c ij ) and the transfer coefficient (t ij ), and possible matrix operations in the future.

[0069]

[0070]

[0071] Among them, 1 to 10 are numbered from high to low according to the top ten risk priorities, including safety risk, quality risk, schedule risk, investment risk, contract risk, technical risk, management risk, environmental risk, social stability and other risks.

[0072] (4) Determine the effective risk transmission path. First, obtain all the The probability of a risk transmission path is the product of the transmission coefficients of adjacent risks on the path, and the relevant threshold T is set. 0 , the risk path greater than the threshold is an effective risk transfer path and is considered in the weight calculation of the effective risk transfer path in step 5. If the i-th risk transfer path (assuming it is j→k→m→…→p→q) is an effective risk transfer path, its judgment formula is:

[0073] T i =t jk ×t km ×...×t pq ≥T 0

[0074] Among them, t jk ,t km ,t pq are the transmission coefficients of adjacent risks on the i-th risk transmission path.

[0075] (5) Determine the probability proportion p of each effective risk transfer path i The probability of occurrence of each effective risk transfer path is summed up, and the probability proportion of each path, i.e., the weight, is calculated:

[0076]

[0077] Among them, T i is the occurrence probability of the i-th effective risk transfer path.

[0078] (6) Substitute the current level of the representative risk, the probability of occurrence of each effective risk transmission path, and the coupling coefficient between each risk into the calculation formula of the multiple risk coupling model:

[0079]

[0080] in, R is the representative risk level value after considering multiple risk coupling. 1 is the representative risk level without considering multiple risk coupling, p i is the weight of the i-th effective risk transfer path, c jk 、c km、c pq are the coupling coefficients between adjacent risks on the i-th effective risk transmission path.

[0081] (7) Determine the final risk level. If the value of the level is less than or equal to the average of the current level and the level one level higher:

[0082]

[0083] If the level is higher, it is considered that the level has been upgraded to a higher level and requires special attention; otherwise, it remains at the current level, but a reminder is required to pay attention.

[0084] The present invention is further described below by way of examples.

[0085] Taking a tunnel construction project in Qingdao as an example, there are safety risks (level III), quality risks (level III), and progress risks (level III) in a certain risk assessment unit. The following is a calculation of the coupling risk of the assessment unit in combination with this multiple risk coupling model. Figure 4 shown.

[0086] Since the three risks (safety risk, quality risk and schedule risk) have the same level and are the highest, according to the priority ranking of multiple risks, safety risk is selected as the representative risk to bear and reflect the multiple risk coupling effect. Through the gradient change method, the coupling coefficient of quality risk to safety risk is 1.2, and the coupling coefficient to schedule risk is 1.05; the coupling coefficient of schedule risk to safety risk is 1.2, and the coupling coefficient to quality risk is 1.1. Through the upper tail correlation method, the transfer coefficient of quality risk to safety risk is 0.5, and the transfer coefficient to schedule risk is 0.15; the transfer coefficient of schedule risk to safety risk is 0.4, and the transfer coefficient to quality risk is 0.3. Set the correlation threshold T 0 =0.05. In this example, there are 4 risk transfer paths, with probabilities of: schedule risk → safety risk (0.4), quality risk → safety risk (0.5), schedule risk → quality risk → safety risk (0.3×0.5=0.15), quality risk → schedule risk → safety risk (0.15×0.4=0.06), all of which are greater than the threshold of 0.05 and need to be considered. The sum of the probabilities of the 4 risk transfer paths in this example is 0.4+0.5+0.15+0.06=1.11, and the proportions of the probabilities of each risk transfer path are 0.4 / 1.11=0.360, 0.5 / 1.11=0.450, 0.15 / 1.11=0.135, and 0.06 / 1.11=0.055, which are the weights of each effective risk transfer path.

[0087] Finally, substitute it into the model calculation. 1 , the probability of occurrence of each effective risk transfer path p i , the coupling coefficient c between each riskmn Substitute into the formula The representative risk level after considering multiple risk coupling is calculated

[0088]

[0089] While the original safety risk level is III, it is noted that the overall risk level of 2.46 is less than (2+3) / 2=2.5. Therefore, it is considered that after considering the coupling of multiple risks, the representative risk (safety risk) level is one level higher than the original level, which is II, and requires special attention.

[0090] The above description is only a description of the preferred embodiments of the present application, and is not intended to limit the scope of the present application. Any changes or modifications made by any person skilled in the art based on the above disclosed technical contents shall be deemed as equivalent effective embodiments and shall fall within the scope of protection of the technical solution of the present application.

Claims

1. A multiple risk coupling model considering coupling effects and cascade transmission, characterized by: The method is designed by the following steps: Step 1: Identify a number of multiple risks for a risk assessment unit; The multiple risks of the project include safety risk, quality risk, schedule risk, investment risk, contract risk, technical risk, management risk, environmental risk, social stability and other risks, a total of ten risks; Step 2: Determine the representative risk of the risk assessment unit based on the priority ranking and risk level of multiple risks; Step 3: Determine the coupling coefficient c ij and the transfer coefficient t ij ; The coupling coefficient and transmission coefficient between each risk in the assessment unit are determined by the gradient change method and the upper tail correlation method, and finally the coupling coefficient matrix (C n×n ) and the transfer coefficient matrix (T n×n ). Where n is the number of risks existing in the risk assessment unit; Coupling coefficient (c ij ) reflects the coupling amplification (reduction) effect of risk i on risk j, that is, the amplification (reduction) multiple of risk j when risk i exists; Transfer coefficient (t ij ) reflects the cascading effect of risk i on risk j, that is, the probability of risk j being amplified (reduced) by risk i; The n×n coupling coefficients (c ij ) and the transfer coefficient (t ij ) is summarized into an n×n matrix form, that is, the coupling coefficient matrix (C n×n ) and the transfer coefficient matrix (T n×n ); Among them, 1 to 10 are numbered from high to low according to the priority of the top ten risks, including safety risk, quality risk, schedule risk, investment risk, contract risk, technical risk, management risk, environmental risk, social stability and other risks; Step 4: Determine the effective risk transfer path; first, obtain all risk transfer paths based on multiple risks. The probability of the i-th risk transfer path (assuming it is j→k→m→…→p→q) occurring is the product of the transfer coefficients between adjacent risks on the path: T i =t jk ×t km ×...×t pq Among them, t jk ,t km ,t pq are the transmission coefficients between adjacent risks on the ith risk transmission path respectively; a relevant threshold T0 is set, and the risk path greater than the threshold is the effective risk transmission path, which is considered in the weight calculation of the effective risk transmission path in step 5; Step 5: Determine the probability proportion p of each effective risk transfer path i ; Sum the probability of occurrence of each effective risk transmission path and calculate the probability proportion of each path, i.e., the weight: Among them, T i is the probability of occurrence of the i-th effective risk transfer path; Step 6: Substitute the current level of representative risks, the probability of occurrence of each effective risk transmission path, and the coupling coefficient between risks into the calculation formula of the multiple risk coupling model: Among them, R1 c is the representative risk level value after considering multiple risk coupling, R1 is the representative risk level without considering multiple risk coupling, and p i is the weight of the i-th effective risk transfer path, c jk 、c km 、c pq are the coupling coefficients of adjacent risks on the i-th effective risk transmission path; Step 7: Determine the final risk level; if the level value is less than or equal to the average of the current level and its next higher level: If the level is higher, it is considered that the level has been upgraded to a higher level and requires special attention; otherwise, it remains at the current level, but a reminder is required to pay attention.

2. The multiple risk coupling model considering coupling effects and cascade transmission as claimed in claim 1, characterized in that: In step 2, the priority order of multiple project risks is: safety risk > quality risk > schedule risk > investment risk > contract risk > technical risk > management risk > environmental risk > social stability and other risks.

3. The multiple risk coupling model considering coupling effects and cascade transmission as claimed in claim 1, characterized in that: The coupling coefficient between risks in the assessment unit is determined by the gradient change method. The specific process is as follows: ① Determine the distribution and numerical characteristics of the characterization parameters of risk i and risk j respectively through statistical analysis; ② When only risk j exists, generate a series of sample points of the characterization parameter n of risk j; Substitute these sample points into the numerical calculation model in turn to calculate the corresponding response evaluation index a; ③ According to this series of sample points and their corresponding response indicators, fit the functional relationship A(n) between the response evaluation index A and the characterization parameter n of risk j; then the response sensitivity coefficient under the action of single risk j is ④ When risks i and j exist at the same time, generate a series of sample points of the characterization parameters m and n of risks i and j; Substitute these sample points into the numerical calculation model in turn and calculate again to obtain the value of the corresponding response evaluation index a; ⑤ According to this series of sample points and their corresponding response indicators, fit the functional relationship A(m,n) between the response evaluation index A and the characterization parameters m and n of risks i and j; then the response sensitivity coefficient of risk j under the coupling effect of risk i is ⑥ Therefore, the coupling coefficient of risk i to risk j is 4. The multiple risk coupling model considering coupling effects and cascade transmission as claimed in claim 1, characterized in that: The upper tail correlation method is used to determine the transmission coefficient between each risk in the assessment unit. The specific process is as follows: ① Collect a large amount of observation data (no less than 20 groups) of the characterization parameters m and n of risk i and risk j; ② Establish the marginal probability density functions of the characterization parameters m and n of risk i and risk j respectively; ③ Calculate the Kendall rank correlation parameter by the following formula: Among them, τ K is the Kendall rank correlation parameter of m and n observation data, N is the number of observation data groups, sgn is the sign function, when [(m i -m j )(n i -n j )]>0, sgn(·)=1, otherwise sgn(·)=-1; ④Use the Kendall rank correlation parameter τ through the following formula K Calculate the Copula correlation parameter θ: Where, C(u1,u2;θ) is the Copula function, u1=F1(m), u2=F2(n) are the marginal distribution functions of m and n respectively; ⑤ Identify the Copula function that best reflects the correlation between risk i and risk j through the AIC criterion, thereby obtaining the joint probability density function of the characterization parameters m and n of risk i and risk j; ⑥ Therefore, the transmission coefficient of risk i to risk j is

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