Multiple risk coupling model considering coupling effects and cascade transmission

Abstract

The present invention belongs to the field of engineering risk coupling effect analysis, specifically relating to a multiple risk coupling model that considers coupling effects and cascade transmission. The design method includes the following steps: Step 1: Determine a number of multiple risks for a risk assessment unit; Step 2: Determine the representative risk of the risk assessment unit based on the priority ranking and risk level of the multiple risks; Step 3: Determine the coupling coefficient and transmission coefficient; Step 4: Determine the effective risk transmission path; Step 5: Determine the probability proportion of each effective risk transmission path; Step 6: Substitute the results into the multiple risk coupling model for calculation; Step 7: Determine the final risk level. This method can scientifically reveal the amplification effect and cascade transmission effect after considering multiple risk coupling from the perspective of multiple risk coupling, providing a theoretical reference for future multiple risk coupling and even generalized multi-factor coupling analysis.

Description

Technical Field

[0001] The present 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 numerous uncertainties and uncertainties, presenting significant and numerous risks during the construction and operation phases. 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 increasing attention. Current tunnel and underground engineering construction is trending towards larger scale, greater complexity, and higher requirements (Yi Guoliang et al., 2024). In such a complex and uncertain environment, tunnel and underground engineering construction involves the interaction of multiple risks, such as safety risks, quality risks, schedule risks, and investment risks, which inevitably lead to coupling effects. Under the coupling of multiple risks, engineering risks may be significantly amplified, resulting in unacceptable risks. Therefore, it is crucial to study how to quantitatively evaluate the effects of multiple risk coupling and reveal the mechanisms of multiple risk coupling.

[0003] However, current risk assessment and control efforts are mostly based on single risk events, rarely considering the impact of multiple, complex coupling effects on engineering risk (Ming et al., 2013). This approach ignores the potential risk amplification effects of multiple risk coupling, which can lead to riskier designs and construction organizations. Some researchers have employed the NK model (Fang Jun et al., 2022), Bayesian networks (Tao Ruoyi et al., 2024), or digital twin technology (Guo Feng, 2024) to attempt to uncover the mechanisms of multiple risk coupling. However, these studies either simply transfer existing models from other fields, disregarding the inherent physical characteristics of civil engineering, or operate solely from a probabilistic perspective, ignoring risk losses. Furthermore, most models abstract a new, integrated risk from existing risks without clearly defining the attributes of the integrated risk, hindering 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] This invention aims to overcome the shortcomings of existing technologies by considering the coupling amplification and cascade transmission effects between complex multiple risks and proposing a multi-risk coupling model that accounts for these effects. Using the gradient variation method and upper-tail correlation method to quantitatively calculate the coupling amplification and cascade transmission effects, this method can scientifically reveal the mechanisms of multi-risk coupling and cascade transmission from the perspectives of consequences and probability, providing a theoretical reference for future research on related multi-risk coupling analysis and generalized multi-factor coupling mechanisms.

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

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

[0008] Step 1: Identify several 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 priority order of multiple project risks is usually: 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 gradient change method and upper tail correlation method respectively, 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 transmission 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 ), so that 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 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.

[0018] 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:

[0019] T i =t jk ×t km ×...×t pq

[0020] Among them, t jk , t km , t pq are the transfer coefficients between adjacent risks on the ith risk transfer path. A relevant threshold T0 is set. Risk paths greater than the threshold are considered valid risk transfer paths and are considered in the weight calculation of valid risk transfer paths in step 5.

[0021] 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:

[0022]

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

[0024] Step 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:

[0025]

[0026] in, 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 transmission 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 level value is less than or equal to the average of the current level and the next higher level:

[0028]

[0029] If the level is raised to a higher level, it is considered that the level has been raised 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: This invention provides a new computational paradigm for multiple risk coupling effects in the field of engineering risk coupling effect analysis. Through the pioneering gradient variation method and upper-tail correlation method, it quantitatively characterizes the coupling amplification and cascade transmission effects of multiple risk coupling from the perspectives of consequences and probability, respectively. By establishing risk transmission paths and thresholds, it intuitively depicts the inherent mechanism of multiple risk coupling transmission. This invention can quantitatively calculate the coupling effects of multiple risks within a risk assessment unit and provide a theoretical reference for future research on related multiple risk coupling analysis and generalized multi-factor coupling mechanisms.

[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 transmission effect for model construction, and characterize them respectively through coupling coefficient (matrix) and transmission 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 effects visual and concrete.

[0035] (4) This invention can scientifically consider the coupling and transmission mechanism between multiple risks, which has positive significance for the quantitative evaluation of the coupling effect of multiple risks. BRIEF DESCRIPTION OF THE DRAWINGS

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

[0037] Figure 2Flowchart for determining 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 transmission path with security risk as representative risk in an embodiment of the present invention. DETAILED DESCRIPTION

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

[0041] This paper proposes a multi-risk coupling model that considers coupling effects and cascade transmission, establishing an engineering risk analysis process under the influence of multi-risk coupling. This approach aims to reveal the mechanisms of multi-risk coupling amplification and cascade transmission in complex civil engineering environments. This method enables scientific analysis and quantitative assessment of the effects of complex multi-risk coupling from the perspective of consequences and probability, and is of great significance for future engineering risk assessment and the evaluation of multi-risk coupling effects.

[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 a project 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. (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 project risks is usually as follows: 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 Figure 2 ) and upper tail correlation method (see the process Figure 3 ) determines the coupling coefficient and transmission coefficient between each risk in the assessment unit, and finally forms the coupling coefficient matrix (Cn×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 coupled amplification (reduction) effect of risk i on risk j, that is, the amplification (reduction) factor of risk j when risk i exists. Its calculation method, namely the gradient change method, has the following specific steps:

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

[0048] ② For the case where only risk j exists, generate a series of sample points representing the parameter n of risk j. Substitute these sample points into the numerical calculation model in sequence to calculate 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 simultaneously, generate a series of sample points representing the parameters m and n of risks i and j. Substitute these sample points sequentially into the numerical calculation model and recalculate the corresponding response evaluation index a.

[0052] ⑤ Based on 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 that risk j is amplified (or 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 observation data (no less than 20 groups) on the characterization parameters m and n of risk i and risk 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 using 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] ④ Using the Kendall rank correlation parameter τ K Calculate the Copula correlation parameter θ:

[0063]

[0064] 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.

[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 ), so that 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 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.

[0072] (4) Determine the effective risk transmission path. First, obtain all the The probability of a risk transmission path occurring is the product of the transmission coefficients of adjacent risks on the path. A relevant threshold T0 is set. Risk paths greater than the threshold are considered valid risk transmission paths and are then considered in the weight calculation of valid risk transmission paths in step 5. If the i-th risk transmission path (assuming it is j→k→m→…→p→q) is a valid risk transmission path, its judgment formula is:

[0073] T i =t jk ×t km ×...×t pq ≥T0

[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 Sum the probability of occurrence of each effective risk transmission path and calculate the probability proportion of each path, i.e., the weight:

[0076]

[0077] Among them, T i is the probability of occurrence 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, 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 transmission 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 next higher level:

[0082]

[0083] If the level is raised to a higher level, it is considered that the level has been raised 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 coupled risk of this assessment unit using this multiple risk coupling model. Figure 4 shown.

[0086] Since the three risks (safety risk, quality risk, and schedule risk) have the same and highest levels, safety risk is selected as the representative risk based on the priority ranking of multiple risks and reflects the multiple risk coupling effect. Using the gradient change method, the coupling coefficients of quality risk to safety risk are 1.2 and 1.05 for schedule risk; the coupling coefficients of schedule risk to safety risk are 1.2 and 1.1 for quality risk. Using the upper-tail correlation method, the transfer coefficients of quality risk to safety risk are 0.5 and 0.15 for schedule risk; the transfer coefficients of schedule risk to safety risk are 0.4 and 0.3 for quality risk. Setting the correlation threshold T0 to 0.05, there are four risk transfer paths in this example, with probabilities: schedule risk → safety risk (0.4), quality risk → safety risk (0.5), schedule risk → quality risk → safety risk (0.3 × 0.5 = 0.15), and quality risk → schedule risk → safety risk (0.15 × 0.4 = 0.06). All of these paths are greater than the threshold of 0.05 and need to be considered. In this example, the total probability of the four risk transfer paths is 0.4+0.5+0.15+0.06=1.11, and the probability proportions 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 the model for calculation. The current level of representative risk R1, the probability of occurrence of each effective risk transmission path p i , the coupling coefficient c between each risk mn 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 believed 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 does not 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 content should be regarded as equivalent valid embodiments and fall within the scope of protection of the technical solution of the present application.

Claims

1. A multi-risk coupling model considering coupling effects and cascade transmission, characterized by: It is designed by the following method, including the following steps: Step 1: Identify multiple risks for a risk assessment unit; Multiple project risks 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 major 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 gradient change method and upper tail correlation method respectively, 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; 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 that risk j is 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 transfer coefficients between adjacent risks on the i-th risk transfer path respectively; a relevant threshold T0 is set, and the risk path greater than the threshold is considered as a valid risk transfer path and is considered in the calculation of the weight of the valid risk transfer 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 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: 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 transmission 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 the next higher level: If the level is raised to a higher level, it is considered that the level has been raised 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 ranking 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 each risk 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) on 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 using 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; ④ Using the Kendall rank correlation parameter τ 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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