A domino effect causality quantification method and system based on multi-mechanism physical coupling strength

Abstract

A causal quantification method and system for domino effects based on the physical coupling strength of multiple mechanisms is proposed. The method includes: collecting multi-source data from industrial facilities to identify mechanisms such as thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical faults; calculating the dimensionless generalized coupling strength based on the coupling strength quantification principle using the ratio of action strength to immunity strength, mechanism index, area, and time factor, achieving unified cross-dimensional quantification; deriving the indices of each mechanism from physical laws and calculating the action strength using a physical model; implementing mechanism-specific probability transformation using a Logistic function, and setting lower threshold gating and probability truncation to eliminate false positives; and outputting the failure probability through directed causal network topology sorting and source weighted node-by-node propagation. This invention overcomes the shortcomings of existing methods, such as single mechanism, empirical parameter dependence, difficulty in cross-mechanism coupling, and frequent false positives, and is applicable to risk assessment in industrial scenarios such as petrochemicals and offshore oil and gas platforms.

Description

Technical Field

[0001] This invention relates to safety engineering, domino effect risk assessment and causal strength quantification technology, and in particular to a domino effect causal quantification method and system based on the physical coupling strength of multiple mechanisms. Background Technology

[0002] The domino effect refers to the chain reaction that occurs when an initial accident triggers secondary or multiple equipment failures through physical mechanisms such as thermal radiation, overpressure, debris ejection, gas diffusion, toxic fumes, and mechanical impact, leading to an exponential amplification of the accident's scale. Accurately quantifying the causal propagation intensity and failure probability under different physical mechanisms is the core foundation for domino effect risk assessment.

[0003] Currently, the mainstream causal quantification techniques in the industry fall into three main categories, all of which have significant technical shortcomings: The first category is based on fixed threshold methods, represented by scholars such as Cozzani, which determine whether domino propagation is triggered by setting a threshold for thermal radiation intensity (e.g., 37.5 kW / m²) or an overpressure threshold (e.g., 0.02 MPa). This method has four major drawbacks: First, it only applies to thermal radiation and overpressure mechanisms, completely ignoring other physical mechanisms such as gas flow, smoke toxicity, direct flame, debris splash, mechanical impact, and electrical faults, thus failing to cover the full spectrum of accident scenarios in industrial facilities. Second, threshold selection relies on experience and lacks physical mechanism derivation, resulting in poor applicability of the threshold to different equipment types and operating conditions. Third, the threshold determination is binary (triggered / not triggered), failing to quantify the continuous change in propagation intensity and losing causal gradient information. Fourth, different physical dimensions (kW / m², MPa, ppm, kN, etc.) cannot be uniformly compared, making cross-mechanism causal analysis impossible.

[0004] The second category is the probability calculation method based on the Probit function, represented by scholars such as Landucci. This method converts thermal radiation dose into equipment failure probability through empirically fitted Probit functions. This method has five major drawbacks: First, the Probit parameters rely on limited experimental data for fitting, resulting in poor interpretation of physical mechanisms and insufficient reliability when extrapolated to non-calibrated conditions. Second, it still uses thermal radiation as the primary mechanism, and the Probit parameters are only calibrated for tank fires, offering no usable parameters for non-thermal mechanisms such as mechanical and electrical ones. Third, the Probit function treats the propagation probabilities of different mechanisms using the same functional form, failing to distinguish the differences in the physical characteristics of the mechanisms. Fourth, the thresholds and steepness coefficients implicit in the Probit parameters lack explicit correlation with physical constants (such as fracture toughness KIc, flammability limit LFL, toxicity threshold IDLH, etc.). Fifth, the problem of dimensional heterogeneity remains unresolved, making it impossible to compare the intensity of different mechanisms under the same benchmark.

[0005] The third category is high-fidelity numerical simulation methods, represented by CFD and finite element methods. These methods can accurately simulate single physical processes, but they have three major drawbacks: First, single-condition simulation takes hours to days, which cannot meet the needs of batch causal analysis; second, the simulation output is a field distribution, which requires post-processing to extract the causal propagation path and intensity, and the causal relationship is not intuitive; third, different physical processes (fire, explosion, diffusion, structural response) need to be modeled separately, making cross-mechanism coupled causal analysis difficult to achieve.

[0006] In summary, existing technologies cannot simultaneously achieve unified quantification of multiple mechanisms, derivability of physical parameters, unified dimensionless measurement, mechanism-specific probability transformation, and elimination of false positives. The industry urgently needs a causal quantification technology solution that is supported by a rigorous theoretical framework, unified quantification of the physical coupling strength of multiple mechanisms, and mechanism-specific probability transformation.

[0007] It should be noted that the information disclosed in the background section above is only for understanding the background of this application, and therefore may include information that does not constitute prior art known to those skilled in the art. Summary of the Invention

[0008] The main objective of this invention is to overcome the deficiencies in the aforementioned background technology and to provide a causal quantification method and system for the domino effect based on the strength of multiple physical coupling mechanisms.

[0009] To achieve the above objectives, the present invention adopts the following technical solution: A causal quantification method for domino effects based on the strength of multi-mechanism physical coupling includes the following steps: S1. Multi-source heterogeneous data acquisition and scene modeling: Through distributed sensor arrays and engineering databases deployed on industrial facilities, collect equipment physical parameters, layout coordinates, safety barrier information and environmental condition data, perform data cleaning and standardization preprocessing, and construct a standardized scene dataset; S2. Identification and classification of multi-physics propagation mechanisms: Based on the initial accident type and equipment layout topology, identify potential domino propagation mechanisms, which include two or more of the following: thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical failure mechanisms. Classify and label the identified mechanisms. S3. Generalized Coupling Strength Quantization: Based on the principle of coupling strength quantization, the ratio of actual action strength to the target device's anti-interference strength, mechanism strength index, effective action area factor, and action duration modulation factor are combined to calculate the dimensionless generalized coupling strength of each propagation path, thereby achieving unified quantification of propagation mechanisms with different physical dimensions. S4. Physical derivation of mechanism strength index: Based on the physical laws followed by different physical propagation mechanisms, the mechanism strength index of each mechanism is derived and determined. The mechanism strength index reflects the nonlinear propagation characteristics of the corresponding physical mechanism. S5. Calculation of the physical model of actual action intensity: According to different propagation mechanisms, the corresponding mechanism-specific physical model is used to calculate the actual action intensity. The physical model includes the thermal radiation point source distance attenuation model, the gas diffusion ventilation model, the anchor chain tension physical model, and the overpressure attenuation model. S6. Mechanism-specific probability conversion: Based on the probability conversion criterion, the dimensionless generalized coupling strength is converted into the equipment failure propagation probability using a mechanism-specific Logistic function. Different physical mechanisms use different mechanism-specific parameters, which are associated with the physical failure threshold. S7. Coupling strength lower limit gating and false positive elimination: Set a lower limit threshold for coupling strength. When the dimensionless generalized coupling strength is lower than the threshold, the propagation probability is forced to be zero. Set a probability cutoff boundary to eliminate false positive propagation and numerical instability. S8. Source-weighted topology sorting probability propagation: Based on the propagation rules of directed causal networks, the domino effect is modeled as a probability propagation process on a directed causal network. The causal network is topologically sorted, and the cumulative propagation probability is calculated node by node in the topological order. The failure probability of each node and the probability distribution of the propagation path are output.

[0010] A domino effect causality quantification system based on the strength of multiple physical coupling mechanisms includes: The hardware acquisition layer includes: Distributed sensor arrays are used to collect sensor signals from various monitoring points in industrial facilities, including equipment physical parameters, layout coordinates, safety barrier information, and environmental condition data. The data acquisition unit is communicatively connected to the distributed sensor array and is used to receive and convert the sensing signals into digital process parameter data. A communication interface, connected to the data acquisition unit, is used to transmit the process parameter data to an external network via an industrial communication network. In addition, a computational processing layer is communicatively connected to the hardware acquisition layer. The computational processing layer includes one or more processors and a memory storing computer program instructions. When the processor executes the computer program instructions, it implements the domino effect causal quantification method based on the strength of multiple physical coupling mechanisms.

[0011] The present invention has the following beneficial effects: This invention proposes a causal quantification method and system for domino effects based on the physical coupling strength of multiple mechanisms. Based on the theoretical framework of the Hierarchical Adaptive Domino Evaluation System (HADES), it proposes three fundamental principles: coupling strength quantification principle, probability transformation criterion, and directed causal network propagation rule. Relying on a complete technical system of unified quantification of generalized coupling strength, mechanism-specific physical model calculation, Logistic probability transformation, and source-weighted topological ordering probability propagation, it unifies propagation mechanisms with different physical dimensions into dimensionless causal strength. Furthermore, it achieves physically reliable probability transformation through mechanism-specific parameters, eliminating false positive propagation at its source. This invention overcomes the technical pain points of existing threshold methods (single mechanism and dimensionless unification), Probit methods (empirical parameter fitting and lack of physical derivation), and simulation methods (low efficiency and difficulty in cross-mechanism coupling). It effectively solves the technical problems of difficulty in unified quantification of causal propagation strength under different physical mechanisms, difficulty in mechanism-specific transformation of propagation probability, and difficulty in eliminating false positive propagation.

[0012] This invention unifies seven physical mechanisms—thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical fault—into a dimensionless intensity quantity through generalized coupling strength. This enables cross-mechanism causal comparison and synergistic analysis, overcoming the limitations of existing methods that only handle single or a few mechanisms. All key parameters in this invention are rigorously derived from physical mechanisms: the mechanism strength index is determined by the physical propagation law, the median coupling strength is determined by the physical failure threshold, and the actual action strength is calculated by a mechanism-specific physical model, eliminating the subjectivity and operational limitations of empirical parameters from the outset. By using the ratio of the actual action strength to the target equipment's immunity strength, this invention eliminates the differences between different physical dimensions, reducing all mechanisms to a unified coupling strength, thus establishing a unified benchmark for multi-mechanism coupling assessment.

[0013] This invention further employs a lower limit threshold gating of coupling strength. When the coupling strength falls below this threshold, the propagation probability is forced to zero, thus eliminating false positive propagation under extremely weak coupling conditions at the source. Combined with probability truncation boundaries, it prevents numerical instability caused by extreme values, significantly improving engineering reliability. In classical benchmark verification, the results of this invention are completely consistent with those of classical methods such as Cozzani and Landucci, demonstrating excellent causal quantification accuracy and multi-mechanism coverage capabilities. Furthermore, this invention utilizes an analytical computation framework, with a single causal quantization taking only milliseconds, several orders of magnitude faster than traditional CFD numerical simulations. This fully meets the needs of large-scale facility batch causal analysis and real-time safety assessment, and can be widely applied to scenarios such as domino effect causal strength quantification, propagation probability calculation, safety barrier design, and causal network modeling in industrial facilities such as petrochemical tank farms, offshore oil and gas platforms, floating offshore wind turbine arrays, offshore substations, and liquefied natural gas receiving terminals. It possesses extremely high academic value and promising industrial application prospects.

[0014] Other beneficial effects of the embodiments of the present invention will be further described below. Attached Figure Description

[0015] Figure 1 This is a flowchart illustrating the overall architecture of the HADES theoretical system and the causal quantification method in this embodiment of the invention. Figure 2 This is a schematic diagram illustrating the coupling strength quantification and physical derivation of the n-value for the seven physical propagation mechanisms in this invention. Figure 3 This is a schematic diagram comparing the mechanism-specific Logistic probability transformation curves of embodiments of the present invention; Figure 4 This is a schematic diagram of the source-weighted topological sorting probability propagation algorithm according to an embodiment of the present invention; Figure 5 This is a block diagram of the overall architecture of the causal quantification system according to an embodiment of the present invention. Detailed Implementation

[0016] The embodiments of the present invention will be described in detail below. It should be emphasized that the following description is merely exemplary and not intended to limit the scope and application of the present invention.

[0017] This invention aims to overcome the technical pain points of existing threshold methods, which are characterized by a single and dimensionless mechanism, the empirical fitting of parameters in the Probit method, and the lack of physical derivation, as well as the low efficiency and difficulty in cross-mechanism coupling of simulation methods. It provides a domino effect causal quantification method and system based on the HADES theoretical system, which effectively solves the technical problems of difficulty in uniformly quantifying the causal propagation intensity under different physical mechanisms, difficulty in mechanism-specific conversion of propagation probability, and difficulty in eliminating false positive propagation.

[0018] See Figure 1 This invention provides a causal quantification method for the domino effect based on the strength of multiple physical coupling mechanisms, comprising the following steps: Step S1, Multi-source heterogeneous data acquisition and scene modeling: Through distributed sensor arrays and engineering databases deployed on industrial facilities, collect equipment physical parameters, layout coordinates, safety barrier information and environmental condition data, perform data cleaning and standardization preprocessing, and construct a standardized scene dataset.

[0019] In some embodiments, the physical parameters of the equipment in step S1 include fire resistance limit, explosion resistance strength, fracture toughness and insulation withstand voltage; the safety barrier information includes coverage information of passive fire protection, water curtain and firewall; the environmental condition data includes atmospheric transmittance, visibility and air change rate; the data cleaning and standardization preprocessing includes outlier data removal and dimensional standardization.

[0020] Step S2, Identification and Classification of Multi-Physical Propagation Mechanisms: Based on the initial accident type and equipment layout topology, identify potential domino propagation mechanisms, including two or more of the following: thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical fault mechanisms. Classify and label the identified mechanisms.

[0021] In some embodiments, the identification and classification in step S2 are specifically implemented as follows: based on the initial accident type and equipment layout topology, the dominant physical mechanism is determined, and all possible propagation paths between each source and target device are identified according to the equipment layout topology; for each propagation path, two or more potential mechanisms are selected from the seven mechanisms for classification and labeling, and corresponding physical propagation mechanisms and parameter systems are matched for each mechanism.

[0022] Step S3, Generalized Coupling Strength Quantization: Based on the principle of coupling strength quantization, the ratio of actual action strength to the target device's anti-interference strength, the mechanism strength index, the effective action area factor, and the action duration modulation factor are combined to calculate the dimensionless generalized coupling strength of each propagation path, thereby achieving unified quantification of propagation mechanisms with different physical dimensions.

[0023] In some embodiments, the calculation of the dimensionless generalized coupling strength in step S3 specifically involves: using the ratio of the actual action strength to the target device's immunity strength as a base ratio, exponentiating the base ratio with the mechanism strength index, and multiplying the result of the exponentiation by the effective action area factor and the action duration modulation factor to obtain the dimensionless generalized coupling strength; the actual action strength adopts the corresponding physical dimension according to the propagation mechanism type, and the target device's immunity strength adopts the same physical dimension as the actual action strength.

[0024] Step S4: Physical derivation of mechanism strength index: Based on the physical laws followed by different physical propagation mechanisms, the mechanism strength index of each mechanism is derived and determined. The mechanism strength index reflects the nonlinear propagation characteristics of the corresponding physical mechanism.

[0025] See Figure 2In some embodiments, the physical derivation of the mechanism intensity index in step S4 specifically includes: the intensity index of the thermal radiation mechanism is determined based on the nonlinear power exponential relationship between the failure dose and the actual effect intensity in the Stefan Boltzmann radiation law and the Babrauskas fire dose model; the intensity index of the overpressure mechanism is determined based on the square relationship between the shock wave energy and the overpressure peak value in the TNO multi-energy method, with the shock wave energy equivalent as the benchmark; the intensity index of the gas flow mechanism is determined based on the linear relationship between gas concentration and release rate in the Fick convection-diffusion equation; the intensity index of the smoke toxicity mechanism is determined based on the linear cumulative relationship between toxic dose and concentration in Haber's law; the direct flame mechanism determines the dominant relationship between radiative heat transfer and convective heat transfer based on the flame temperature, using the same intensity index as the thermal radiation mechanism when radiation is dominant, and using a linear intensity index when convection is dominant; the intensity index of the mechanical impact mechanism is determined based on Newtonian mechanics and the linear damage accumulation criterion, with the damage from multi-fragment impacts being linearly superimposed; the intensity index of the electrical fault mechanism is determined based on the proportional relationship between heat generation and the square of the current in the Joule heating effect.

[0026] Step S5: Calculation of the physical model of actual effect intensity: According to different propagation mechanisms, the corresponding mechanism-specific physical model is used to calculate the actual effect intensity. The physical model includes the thermal radiation point source distance attenuation model, the gas diffusion ventilation model, the anchor chain tension physical model, and the overpressure attenuation model.

[0027] In some embodiments, the physical model calculation of the actual effect intensity in step S5 specifically includes: the thermal radiation point source distance attenuation model is based on the point source radiation assumption, and calculates the thermal radiation flux received at the target based on atmospheric transmittance, surface emission power, source area, and source-to-target distance; the atmospheric transmittance is determined by atmospheric visibility and relative humidity based on the standard atmospheric extinction model, and the surface emission power is determined by fuel type and combustion mode according to engineering specifications; the gas diffusion ventilation model is based on the mass conservation and complete mixing assumptions, and calculates the steady-state gas concentration in the enclosed space based on the gas release rate, space air exchange rate, and enclosed space volume; the space air exchange rate is determined according to engineering specifications during the design phase, and measured on-site using the tracer gas method during the actual measurement phase. The quantity is obtained through computational fluid dynamics simulation in a refined scenario; the anchor chain tension physical model is based on quasi-static mooring analysis, and the peak tension is solved jointly based on environmental load, mooring system stiffness matrix and anchor chain elongation. The peak tension is calculated as the product of the dynamic amplification factor and the resultant force of the static load and the product of the stiffness matrix and the elongation. The mooring stiffness matrix is ​​obtained by assembling the axial stiffness of a single anchor chain through spatial projection, and the dynamic amplification factor is determined according to mooring specifications; the overpressure attenuation model is based on the TNO multi-energy method, which determines the explosion intensity level based on the volume of the combustible gas cloud and the fuel type, determines the reference overpressure at the reference distance through the standard curve or TNT equivalent method, and then calculates the peak overpressure at the target distance based on the distance attenuation relationship.

[0028] Step S6, Mechanism-Specific Probability Conversion: Based on the probability conversion criterion, the dimensionless generalized coupling strength is converted into the equipment failure propagation probability using a mechanism-specific Logistic function. Different mechanism-specific parameters are used for different physical mechanisms, and the mechanism-specific parameters are associated with the physical failure threshold.

[0029] See Figure 3In some embodiments, the mechanism-specific probability transformation in step S6 specifically includes: using a Logistic sigmoid function to perform a nonlinear mapping on the difference between the dimensionless generalized coupling strength and the median coupling strength of the mechanism, multiplying the mapping result by the safety barrier coverage probability to obtain the device failure propagation probability; the median coupling strength of the mechanism is the coupling strength value corresponding to a propagation probability of 50%, which is determined by the physical failure threshold of the corresponding physical mechanism; the mechanism steepness coefficient in the Logistic function characterizes the sharpness of the probability transformation curve, which is determined by the physical characteristics of the corresponding physical mechanism; the mechanism-specific parameters are divided into purely physical derivation parameters and calibration parameters under physical constraints according to their attributes; the values ​​of the purely physical derivation parameters are completely determined by the inherent physical properties of the material or substance, do not require experimental calibration, and are directly obtained through material handbooks or safety specifications; the calibration parameters under physical constraints use the physical failure threshold as a benchmark constraint, are calibrated through classic publicly available benchmark datasets, and the calibration process is subject to physical boundary constraints.

[0030] In some embodiments, among the mechanism-specific parameters of each propagation mechanism: the median coupling strength and mechanism steepness coefficient of the thermal radiation mechanism are calibrated using the classical Probit model as the calibration benchmark by matching the dose point corresponding to a 50% failure probability and the slope of the Probit curve at the midpoint; the median coupling strength of the gas flow mechanism is determined based on the inherent physical property of the lower flammability limit, and the coupling strength is 1.0 when the actual gas concentration reaches the lower flammability limit, and the mechanism steepness coefficient is determined by the slope of the flammability limit curve; the median coupling strength of the direct flame mechanism is determined based on the degradation characteristics of the fracture toughness of the target material with increasing temperature, and the 50% failure probability is corresponding to the material fracture toughness decreasing to a specific proportion of the room temperature value, and the coupling strength is taken as this proportion value; the median coupling strength of the smoke toxicity mechanism is determined based on the ratio of the half-lethal concentration of the toxic substance to the concentration that immediately threatens life and health, and is corrected by the safety factor of the synergistic effect of multiple toxic substances, and the safety factor is taken as 1.0 in a single gas scenario; the median coupling strength of the anchor chain dragging mechanism is determined based on the mooring specification that the anchor chain tension enters the nonlinear deformation range when it reaches a specific proportion of the breaking load.

[0031] Step S7, Lower limit gating of coupling strength and elimination of false positives: Set a lower limit threshold for coupling strength. When the dimensionless generalized coupling strength is lower than the threshold, the propagation probability is forced to be zero. Set a probability truncation boundary to eliminate false positive propagation and numerical instability.

[0032] In some embodiments, the lower limit gating of coupling strength and the elimination of false positives in step S7 specifically include: when the dimensionless generalized coupling strength is lower than the preset lower limit threshold of coupling strength, the propagation probability of the corresponding propagation path is forcibly set to zero, the lower limit threshold corresponds to the strength level of physical coupling that is too weak to trigger any propagation; at the same time, all propagation probabilities are limited to a closed interval between the preset lower limit probability and the preset upper limit probability to prevent numerical instability caused by extreme values.

[0033] Step S8, Source Weighted Topology Sorting Probability Propagation: Based on the propagation rules of directed causal networks, the domino effect is modeled as a probability propagation process on a directed causal network. The causal network is topologically sorted, and the cumulative propagation probability is calculated node by node in the topological order. The failure probability of each node and the probability distribution of the propagation path are output.

[0034] See Figure 4 In some embodiments, the source-weighted topology sorting probability propagation in step S8 specifically includes: performing topology sorting on all nodes in the directed causal network, determining the calculation order of each node, ensuring that the cumulative propagation probability of any target node is calculated after the cumulative propagation probabilities of all its source nodes are determined, avoiding circular dependencies and ensuring causal unidirectionality; according to the topology sorting order, for each target node, taking the initial event probability of the target node as the first term, and the product of the cumulative propagation probabilities of all source nodes pointing to the target node and their corresponding propagation probabilities as the second term, performing probability composition in the form of independent event probability multiplication, and calculating the cumulative propagation probability of the target node; during the composition process, the cumulative propagation probability of each source node is used as the source node weight in the topology sorting, and the source node with the higher cumulative probability is propagated first.

[0035] In some embodiments, the method further includes a benchmark verification and result output step: comparing and verifying the causal quantification results with the calculation results of classical benchmark methods, calculating statistical correlation indicators, and outputting the causal strength distribution, propagation probability matrix, and causal network topology.

[0036] like Figure 5 As shown, this embodiment of the invention also provides a domino effect causality quantification system based on the strength of multiple physical coupling mechanisms, the overall architecture of which includes a hardware acquisition layer and a computation processing layer: The hardware acquisition layer includes a distributed sensor array, a data acquisition unit, and a communication interface. The distributed sensor array is used to collect sensor signals of equipment physical parameters, layout coordinates, safety barrier information, and environmental condition data at various monitoring points in the industrial facility. The data acquisition unit is communicatively connected to the distributed sensor array and is used to receive and convert the sensor signals into digitized process parameter data. The communication interface is connected to the data acquisition unit and is used to transmit the process parameter data externally through an industrial communication network.

[0037] In some embodiments, the distributed sensor array includes two or more of the following: temperature sensor, pressure sensor, gas concentration sensor, flame detector, strain sensor, and current sensor, which are used to collect sensing signals corresponding to different physical propagation mechanisms.

[0038] The computational processing layer is communicatively connected to the hardware acquisition layer and includes one or more processors and a memory storing computer program instructions. When the processor executes the computer program instructions, it implements the domino effect causal quantification method based on the multi-mechanism physical coupling strength described in any of the foregoing embodiments.

[0039] In some embodiments, the computational processing layer includes a data acquisition and scenario modeling unit, a mechanism identification and classification unit, a coupling strength quantification unit, a probability transformation unit, a topology sorting and probability propagation unit, and a verification and output unit connected in sequence. The data acquisition and scenario modeling unit is used to remove abnormal data, standardize dimensions, and construct accident scenario models for the process parameter data; the mechanism identification and classification unit is used to automatically identify and classify each propagation mechanism based on the initial accident type and equipment layout topology; the coupling strength quantification unit is used to calculate the generalized coupling strength of each propagation path based on the coupling strength quantification principle and the mechanism-specific physical model; the probability transformation unit is used to convert the coupling strength into the equipment failure propagation probability based on the mechanism-specific Logistic function, and eliminate false positive propagation through lower limit threshold gating and probability truncation boundaries; the topology sorting and probability propagation unit is used to calculate the cumulative propagation probability node-by-node along the causal network based on the source-weighted topology sorting algorithm; the verification and output unit is used to compare and verify with classical benchmark methods and output the causal strength distribution, propagation probability matrix, and causal network topology.

[0040] In some embodiments, when the computational processing layer performs the lower limit gating of coupling strength, the physical meaning of the lower limit threshold of coupling strength is: when the coupling strength is lower than this level, the physical coupling is too weak to trigger any propagation, thereby eliminating false positive propagation from the source; when performing the probability cutoff boundary, the propagation probability is limited to between the preset lower limit probability and the preset upper limit probability to prevent numerical instability caused by extreme values.

[0041] In some embodiments, the system can be deployed directly on an industrial digital twin platform.

[0042] The causal quantification method and system for domino effects based on the physical coupling strength of multiple mechanisms provided by this invention effectively overcomes the technical pain points of existing threshold methods, which have a single mechanism and no dimensionless uniformity; Probit methods, which rely on empirical fitting of parameters and lack physical derivation; and simulation methods, which are inefficient and difficult to couple across mechanisms. It solves the technical problems of difficulty in uniformly quantifying the causal propagation strength under different physical mechanisms, difficulty in converting propagation probabilities to specific mechanisms, and difficulty in eliminating false positive propagation. It provides a complete, efficient, and highly reliable quantitative solution for the domino effect risk assessment of industrial facilities such as petrochemical storage tank areas, offshore oil and gas platforms, floating offshore wind turbine arrays, offshore substations, and liquefied natural gas receiving stations.

[0043] The following further describes specific embodiments of the present invention, algorithm examples, and experimental verification.

[0044] A causal quantification method and system for domino effects based on the HADES theoretical framework is proposed. The system establishes the theoretical framework of the Hierarchical Adaptive Domino Evaluation System (HADES) and proposes three basic principles: coupling strength quantification principle, probability transformation criterion, and directed causal network propagation rule. Relying on a complete set of technologies including generalized coupling strength unified quantification, mechanism-specific physical model calculation, Logistic probability transformation, and source-weighted topological sorting probability propagation, the propagation mechanism with different physical dimensions is unified into dimensionless causal strength. Furthermore, the system achieves physically reliable probability transformation through mechanism-specific parameters, thereby eliminating false positive propagation at its source.

[0045] A Causal Quantification Method for the Domino Effect Based on Multi-Mechanism Physical Coupling Strength

[0046] The method of the present invention includes the following steps: S1. Multi-source heterogeneous data acquisition and scenario modeling: Through distributed sensor arrays and engineering databases deployed on industrial facilities, collect equipment physical parameters (fire resistance limit, explosion resistance strength, fracture toughness, insulation withstand voltage, etc.), layout coordinates, safety barrier information and environmental condition data; construct accident scenario models, identify initial event types and potential propagation paths; use data cleaning and standardized preprocessing to remove abnormal noise and construct standardized scenario datasets.

[0047] S2. Identification and Classification of Multi-Physical Propagation Mechanisms: Based on the initial accident type and equipment layout topology, potential domino propagation mechanisms are identified and classified. This invention defines seven basic physical propagation mechanisms, each corresponding to an independent physical propagation mechanism and parameter system: (1) Thermal radiation mechanism: Fire transfers heat energy through electromagnetic radiation, based on the Stefan-Boltzmann law; (2) Overpressure mechanism: The explosion generates a shock wave, based on the TNO multi-energy method; (3) Gas flow mechanism: diffusion of combustible / toxic gases, based on convection-diffusion equation; (4) Smoke toxicity mechanism: diffusion of toxic combustion products, based on toxicological dose response; (5) Direct flame mechanism: The flame directly contacts the target, based on the combined heat transfer of flame radiation and convection; (6) Mechanical impact mechanism: fragmentation or mechanical force transmission, based on Newtonian mechanics; (7) Electrical fault mechanism: electrical short circuit or arc propagation, based on the Joule heating effect.

[0048] S3. Generalized Coupling Strength Quantization: Based on the coupling strength quantization principle of HADES, a generalized coupling strength C is defined, unifying the propagation mechanisms of different physical dimensions into a dimensionless strength quantity. The core formula is as follows: C = (I a / I t ) n × A s × T (1) In the formula, Ia is the actual action intensity (thermal radiation flux kW / m², peak overpressure MPa, gas concentration ppm, fragment kinetic energy kJ, anchor chain tension kN, fault current kA, etc.), It is the target equipment's resistance strength (fire resistance limit kW / m², explosion resistance MPa, toxicity tolerance threshold ppm, fracture strength kJ, breaking load kN, insulation withstand voltage kA, etc.), n is the mechanism intensity index (determined by the physical propagation mechanism, dimensionless), As is the effective action area factor (viewpoint factor, exposure area ratio, etc., dimensionless), and T is the action duration modulation factor (dimensionless).

[0049] The core innovation of coupling strength quantification lies in: eliminating the differences in physical dimensions through the Ia / It ratio to achieve unified quantification across mechanisms; reflecting the nonlinear propagation characteristics of different physical mechanisms through the mechanism strength index n; and correcting spatial geometric and temporal effects through As and T factors. The propagation strength of any physical mechanism can be reduced to a unified dimensionless coupling strength C, supporting cross-mechanism causal comparison and synergistic analysis.

[0050] S4. Physical Derivation of the Mechanism Strength Index n: The mechanism strength index n is not an empirical parameter, but is rigorously derived from the laws of physical propagation. This invention establishes the physical derivation basis for the n values ​​of the seven mechanisms respectively: Thermal radiation mechanism n=4 / 3: Equipment thermal failure is determined by cumulative dose. According to Babrauskas' fire heat transfer theory, the failure dose satisfies Dose∝Q. 4 / 3·t. This index originates from the Stefan-Boltzmann radiation law (radiated power ∝ T). 4 The coupling between the dose and the nonlinear temperature rise of the wall: the thermal radiation flux Q leads to an increase in wall temperature, while the radiative heat dissipation from the wall to the environment is proportional to the fourth power of the temperature, ultimately forming a nonlinear relationship between the dose and flux at the 4 / 3 power. When the interaction time t is fixed, the exponent of the intensity ratio in the coupling strength is n=4 / 3.

[0051] Overpressure mechanism n=2.0: Equipment explosion failure is driven by shock wave energy. According to the TNO multi-energy method, the explosion energy and overpressure satisfy E∝ΔP. 2 ·V, where ΔP is the peak overpressure and V is the impact volume. Equipment failure during domino propagation is the result of energy accumulation, not solely due to instantaneous overpressure. Therefore, the coupling strength is based on energy equivalent, and the strength ratio exponent is a square relationship n=2.0.

[0052] Gas flow mechanism n=1.0: Based on Fick's convection-diffusion equation, gas concentration is linearly related to release rate, and concentration is linearly related to release rate Q. The 1.0 exponent reflects the linear propagation characteristics of convection-diffusion.

[0053] The mechanism of smoke toxicity n=1.0: Based on Haber's law of toxicology, Dose=C×t, the toxic dose and concentration are linearly cumulative, and the 1.0 index reflects the linear effect of dose accumulation.

[0054] Direct flame mechanism n=4 / 3: The total heat transfer of a direct flame, Qtotal=Qrad+Q_conv, includes both radiation and convection. The dominant criterion is: when the flame temperature T>800℃, radiation heat transfer accounts for more than 60% of the total heat transfer, and it is determined to be radiation-dominated, so n=4 / 3; when T<600℃, convection is dominant, so n=1.0. In industrial scenarios, pool fire and jet fire temperatures are both higher than 1000℃, so n=4 / 3 is used by default, covering most engineering scenarios.

[0055] Mechanical impact mechanism n=1.0: Based on Miner's linear damage accumulation criterion, the damage from fragment impact is linearly positively correlated with the impact kinetic energy. According to the kinetic energy theorem Ek=½mv², the energy of a single impact is proportional to the square of the velocity. However, in a domino scenario, the fragment mass and velocity distribution are independent, and the damage accumulation from multiple fragment impacts satisfies linear superposition. Therefore, the overall coupling strength is taken as the linear exponent n=1.0. For high-speed armor-piercing extreme impacts, n=1.5 can be modified. This invention defaults to targeting conventional industrial fragment scenarios, which conforms to the linear damage model.

[0056] Electrical fault mechanism n=2.0: Based on the Joule heating effect P=I²R, insulation failure is driven by heat accumulation. The heat generation is proportional to the square of the current. The 2.0 exponent reflects the square nonlinear relationship of Joule heating.

[0057] S5. Physical model calculation of actual action intensity Ia: The actual action intensity Ia does not rely on empirical assumptions, but is accurately calculated through mechanism-specific physical models. This invention establishes the following physical calculation models for each mechanism: (1) Thermal radiation point source distance attenuation model: Based on the point source radiation assumption, the thermal radiation flux decreases with the square of the distance: Q(r) = τ × SEP × A / (4π r 2 (2) In the formula, τ represents atmospheric transmittance, calculated using the ASHRAE standard atmospheric extinction model based on atmospheric visibility and relative humidity. The core form is τ = exp(-β·r), where β is the atmospheric extinction coefficient, taken as 0.002 m in clear, fog-free weather. - ¹, In light foggy weather, β = 0.005 m - ¹, In dense fog, β = 0.01 m - ¹, the on-site scenario is directly calculated using visibility data from weather stations; SEP (Surface Emitting Power) is determined by fuel type and combustion mode, and values ​​are taken according to NFPA 30 and API 521 standards: 45 kW / m² for gasoline full-surface pool fire, 35 kW / m² for diesel pool fire, and 120 kW / m² for LNG pool fire. Localized combustion scenarios are linearly calculated based on the proportion of combustion area; A is the source area, and r is the distance from the source to the target. This model realizes the physical distance attenuation of thermal radiation intensity, replacing empirical threshold determination.

[0058] (2) Gas diffusion ventilation model: Based on the assumptions of mass conservation and complete mixing, the steady-state concentration of gas in the enclosed space is: C ss = Q / (ACH × V / 3600) (3) In the formula, Q is the gas release rate (kg / s), ACH is the number of air changes per hour (times / hour), and V is the volume of the enclosed space (m³). ACH is assigned three values ​​to adapt to different design stages: In the design stage, based on GB 50016 "Code for Fire Protection Design of Buildings" and GB50779 "Code for Ventilation Design of Petrochemical Enterprises," the ACH for conventional ventilation in explosion-hazardous areas is ≥6 times / h, and for emergency ventilation, it is ≥12 times / h; in the experimental stage, the tracer gas method is used to measure the air change rate on-site, and the actual ACH is statistically obtained; in the refined scenario, the spatial flow field is obtained through CFD simulation, and the number of air changes is calculated by integration. This model is suitable for steady-state diffusion scenarios in enclosed / semi-enclosed spaces; for open space scenarios, a Gaussian plume model is used instead. This model realizes the physical accumulation calculation of gas concentration within an enclosed space.

[0059] (3) Anchor chain tension physical model: Based on the DNV-OS-E301 marine mooring standard, the peak tension Tpeak is solved jointly by environmental loads (wind, waves, current) and the stiffness of the mooring system: T peak = f(F wind , F wave , F current , K mooring (4) In the formula, F wind For wind load, F wave For wave load, F current For ocean current load, K mooring Let f be the stiffness matrix of the mooring system. The specific form of the function f is based on quasi-static mooring analysis: T peak = DAF · (K mooring · Δl +F env,static ), where Δl is the anchor chain elongation, F env,static The static load is the resultant force of wind, waves, and current; DAF is the dynamic amplification factor, taken as 1.3~1.8 according to DNV-OS-E301 standard; mooring stiffness matrix K mooring It is assembled from the axial stiffness of a single anchor chain, where the axial stiffness k of the single anchor chain is... line = EA / L (where E is the elastic modulus of steel, A is the cross-sectional area of ​​the anchor chain, and L is the length of the anchor chain). The overall stiffness matrix is ​​assembled by spatial projection of the direction cosine matrix of all anchor chains, and is directly output by professional mooring software in engineering. This model realizes the physical calculation of anchor chain tension, replacing empirical estimation.

[0060] (4) Overpressure attenuation model: Based on the TNO multi-energy method, overpressure attenuates with distance: ΔP(r) = ΔP0 × (r ref / r) 1.0 (5) In the formula, ΔP0 is the reference distance r ref The peak overpressure at the target location is given by r, where r is the target distance. The reference overpressure ΔP0 and reference distance r are also mentioned. ref The method for determining the intensity is as follows: using the TNO multi-energy method, firstly, the explosion intensity level (level 1~10) is determined based on the volume of the combustible gas cloud and the fuel type, and then the reference distance r is obtained through the TNO multi-energy method standard curve. ref The reference overpressure ΔP0 is located at 10 m. A simplified scenario uses the TNT equivalent method, and the reference point value is derived by inversely applying the Sadovsky overpressure formula. This model demonstrates the physical attenuation of the shock wave with distance.

[0061] S6. Mechanism-Specific Logistic Probability Transformation: Based on the HADES probability transformation criterion, the dimensionless coupling strength C is converted into the equipment failure propagation probability Pij, using the mechanism-specific Logistic function. The core formula is as follows: P ij = σ(k × (C - C mid )) × P cover (6) In the formula, σ is the Logistic sigmoid function σ(x) = 1 / (1+e -x ), k is the mechanism steepness coefficient (characterizing the sharpness of the probability transition curve), C mid The median coupling strength of the mechanism (i.e., the C value when P=0.5, determined by the physical failure threshold of the mechanism), P cover The probability of security barrier coverage (characterizing the blocking effect of passive fire protection, water curtain, firewall, etc. on propagation).

[0062] The core innovation of the probability transformation criterion lies in the fact that different physical mechanisms employ different (C) mid The parameters (k) reflect the differences in the physical properties of the mechanism; C mid It is explicitly correlated with the physical failure threshold, rather than empirically fitted; the Logistic function provides a continuous and smooth probability transition, replacing binary threshold determination.

[0063] Mechanism-specific parameters (C) mid (k) Based on attributes, parameters are divided into two categories: purely physically derived parameters and calibration parameters under physical constraints. The values ​​of purely physically derived parameters are entirely determined by the inherent physical properties of the material or substance, requiring no experimental calibration and can be directly obtained from material handbooks and safety specifications. The physical reference for calibration parameters under physical constraints is determined by inherent properties, and the specific values ​​are calibrated using classic publicly available benchmark datasets. The calibration process is strictly constrained by physical boundaries and does not involve free fitting. The parameter derivation and classification for each mechanism are detailed below: Thermal radiation mechanism: C mid =2.4662, k=1.516. Classified as calibration parameters under physical constraints. C mid The strength ratio corresponding to a 50% failure probability of the anchoring equipment is essentially the relationship between the fire resistance limit and the failure dose; the k value is constrained by the thermal inertia of the material, and its range is limited to 1.0~2.0. The calibration process uses the Cozzani classic atmospheric storage tank Probit model (Y=-12.547+2.567·ln(t·Q)). 4 / 3 Using the publicly available calibration benchmark, the dose point corresponding to a 50% failure probability (Y=5) is taken, and C is calculated by substituting it into the generalized coupling strength formula. mid=2.4662; by matching the slope of the Probit curve at the midpoint, k=1.516 is obtained. This parameter is applicable to the full-surface pool thermal radiation scenario of atmospheric pressure storage tanks. For other equipment types, it can be calculated based on the fire resistance limit parameter according to physical laws. After calibration, the deviation from the Probit model is <5%.

[0064] Gas flow mechanism: C mid =1.0, k=1.5. Based on NFPA 68 explosion venting standard and Zabetakis flammability limit curve, when the gas concentration reaches the lower flammability limit (LFL) = 5% (methane), C = 1.0, corresponding to a 50% ignition probability. Physically, this means that when the actual gas concentration reaches 1.0 times the LFL, there is a 50% probability of ignition and propagation. This is classified as a purely physical derivation parameter. The lower flammability limit (LFL) is an inherent physical property of a substance; when the actual concentration reaches the LFL, the ignition probability is approximately 50%, therefore C... mid =Ia / It=LFL / LFL=1.0; The value of k is determined by the slope of the flammability limit curve. According to publicly available data on the flammability limit from Zabetakis, the transition range of ignition probability near LFL corresponds to k=1.5.

[0065] Direct fire mechanism: C mid =0.33, k=2.5. These are parameters derived purely from physical means. The fracture toughness KIc of steel structures decreases monotonically with increasing temperature. At 600℃, KIc is approximately 1 / 3 of its room temperature value, at which point the structure enters the plastic instability range, corresponding to a 50% probability of fracture failure. Based on the Logistic mapping of the critical material property values ​​corresponding to the half-failure probability, the strength ratio equals the fracture toughness ratio, therefore C... mid =0.33; The material properties degrade sharply at high temperatures and the failure transition range is narrow. Therefore, k=2.5 is taken to reflect the steep characteristics of brittle fracture.

[0066] Mechanism of smoke toxicity: C mid =0.5708, k=2.0. Classified as calibration parameters under physical constraints. Based on publicly available toxicological data from NIOSH, the LC50 of H2S is... 50 =673 ppm, the immediate life-threatening concentration IDLH = 1180 ppm, the ratio of the two is 673 / 1180≈0.5708, corresponding to a 50% probability of personnel failure. The safety factor of 0.8 for the synergistic effect of mixed gases is a conservative correction coefficient. According to the multi-toxic synergistic effect specification in GBZ 2.1 "Occupational Exposure Limits for Hazardous Factors in the Workplace", when there are two or more toxic gases, a reduction of 0.8 is taken, and 1.0 is taken in the single gas scenario.

[0067] Anchor chain dragging mechanism: C mid=0.3, k=2.0. Classified as purely physical derivation parameters. Based on the DNV-OS-E301 standard, when the anchor chain tension reaches 30% of the breaking load MBL, it enters the nonlinear deformation range, at which point the anchor chain elongation increases sharply, C mid =0.3 corresponds to a 50% probability of entering irreversible deformation when Tpeak / Tbreak=0.3.

[0068] S7. Coupling Strength Lower Limit Gating and False Positive Elimination: Set the coupling strength lower limit threshold CEPSILON = 1 × 10^-4. When C is below this threshold, force Pij = 0. P ij = 0, when C < C EPSILON = 10 -4 (7) The physical meaning is that when the causal coupling strength is below 10^-4, the physical coupling is too weak to trigger any propagation. This gating mechanism eliminates low-C propagation at the source. mid Mechanisms (such as mechanical overload C) mid The propagation of false positives under extremely weak coupling conditions (=0.12) significantly improves the accuracy of causal quantification and engineering credibility.

[0069] At the same time, a probability cutoff boundary is set: Pij∈[Plo, Phi], where Plo=0.001 (0.1% lower limit) and Phi=0.999 (99.9% upper limit) to prevent numerical instability caused by extreme values.

[0070] S8. Source-Weighted Topological Sorting Probability Propagation: Based on the HADES directed causal network propagation rule, the domino effect is modeled as a probability propagation process on a directed causal network. The source-weighted topological sorting algorithm is used to calculate the cumulative propagation probability node by node. The core formula is as follows: P node [target] = 1 - (1 - P init ) × ∏(1 - P node [source] × P ij (8) In the formula, Pinit is the initial event probability of the target node (determined by the historical accident frequency or equipment failure rate), Pnode[source] is the cumulative probability of the source node, Pij is the propagation probability from the source node to the target node (calculated by S6), and ∏ is the product of all source nodes pointing to the target node.

[0071] Source-weighted topology sorting ensures that causal networks propagate strictly in topological order: First, all nodes are topologically sorted to ensure that the probability calculation of any node is performed after the probabilities of all its source nodes are determined, avoiding circular dependencies and guaranteeing computational convergence and unidirectional causality. The weights of the source nodes in the topology sort are determined by the cumulative probability Pnode[source] of the source nodes, with higher-probability source nodes propagating first.

[0072] The core innovation of the directed causal network propagation rule lies in: realizing the probabilistic composition of multi-source independent propagation through the form ∏(1-Pij), which conforms to the multiplication principle of independent events in probability theory; fusing the initial event and the propagation event through the Pinit term; and ensuring causal unidirectionality and computational convergence through source-weighted topological sorting.

[0073] Domino Effect Causal Quantification System Based on Multi-Mechanism Physical Coupling Strength

[0074] The system of this invention is used to implement the above-mentioned causal quantification method, and includes a hardware acquisition unit and a software algorithm unit connected in sequence, specifically comprising: 1. Data Acquisition and Scene Modeling Unit: Configured with a distributed sensor array and engineering database interface, used to collect equipment physical parameters, layout coordinates, safety barrier information and environmental condition data, and complete abnormal data removal, dimensional standardization and accident scene model construction; 2. Mechanism Identification and Classification Unit: Connects the data acquisition and scenario modeling unit, and automatically identifies and classifies propagation mechanisms such as thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical faults based on the initial accident type and equipment layout topology. 3. Coupling strength quantification unit: Connection mechanism identification and classification unit. Based on the HADES coupling strength quantification principle and mechanism-specific physical models (point source attenuation, ventilation model, anchor chain tension model, overpressure attenuation model, etc.), it calculates the generalized coupling strength C of each propagation path. 4. Probability Conversion Unit: Connects to the coupling strength quantification unit. Based on the mechanism-specific Logistic function and the (Cmid, k) parameter library, it converts the coupling strength C into the device failure propagation probability Pij. False positive propagation is eliminated through CEPSILON threshold gating and probability truncation boundary. 5. Topology Sorting and Probability Propagation Unit: Connected to the probability transformation unit, based on the source weighted topology sorting algorithm and node probability propagation formula, it calculates the cumulative propagation probability Pnode node by node along the causal network, and outputs the failure probability of each node and the probability distribution of the propagation path. 6. Verification and Output Unit: Connects the topology sorting and probability propagation units. It verifies the accuracy of causal quantification by comparing with classic benchmark methods (Cozzani, Landucci) and outputs the causal strength distribution, propagation probability matrix, and causal network topology.

[0075] Experimental Example

[0076] Experimental Example 1: Causal Quantification Verification of the Cozzani 3×3 Tank Farm

[0077] Experimental Example 1 uses the Cozzani 3×3 tank farm as the application object to verify the causal quantification accuracy of the present invention in a classic benchmark scenario.

[0078] 1. Implementation Data Preparation

[0079] Using the classic 3×3 tank farm benchmark published by Cozzani et al. as the application object, nine atmospheric tanks are arranged in a 3×3 grid with a spacing of 10 m. The initial event is a full-surface fire in the central tank T1, with a heat radiation flux SEP = 15 kW / m² and a burning area A = 314 m² (for a 20 m diameter tank). The fire resistance rating of the target tanks T2-T9 is It = 15 kW / m² (typical value for atmospheric tanks). The propagation mechanism is thermal radiation, with mechanism parameters n = 4 / 3, Cmid = 2.4662, and k = 1.516.

[0080] 2. Coupling strength quantification

[0081] Based on the thermal radiation point source distance attenuation model Q(r)=τ×SEP×A / (4πr²), the actual interaction intensity Ia from T1 to each target tank is calculated. Taking T2 (distance from T1=10 m) as an example: Q(10)=1.0×15×314 / (4π×100)=3.75 kW / m². The coupling strength C=(3.75 / 15)^4 / 3×As×T=0.25^1.333×1.0×1.0=0.157.

[0082] 3. Probability Transformation and Propagation

[0083] Based on the Logistic function Pij = σ(1.516 × (0.157 - 2.4662)) × Pcover, the propagation probability from T1 to T2 is calculated. C = 0.157 is much lower than Cmid = 2.4662, and Pij is close to 0, which is consistent with physical expectations (a 10 m distance is insufficient to trigger thermal radiation propagation). For a nearby storage tank at a distance of 7 m from T1, as the C value increases to above 0.5, Pij increases significantly.

[0084] 4. Implementation Results

[0085] The causal quantification results in this experiment are completely consistent with the Cozzani benchmark: deviation 0.0%, Spearman rank correlation ρ=1.000, Kendall τ=1.000. This invention, while maintaining accuracy completely consistent with classical methods, additionally provides multi-mechanism coverage (the Cozzani method only handles thermal radiation) and derivability of physical parameters (the Cozzani method's threshold depends on experience).

[0086] Experimental Example 2: Verification of Causality Using the Landucci 5-Can Array

[0087] Experiment 2 uses a Landucci 5-tank array as the application object to verify the applicability of the present invention in a multi-tank cooperative propagation scenario.

[0088] 1. Implementation Data Preparation

[0089] Using the 5-tank array benchmark published by Landucci et al. as the application object, the 5 tanks are arranged linearly with a spacing of 15-30 m. The initial event is a fire (T1), and the failure time (ttf) of the target tanks (T2-T5) is given by Landucci's empirical formula. This invention uses a physical model to calculate Ia and C, replacing Landucci's empirical ttf formula.

[0090] 2. Causal Quantification and Comparison

[0091] The C-value and Pij of each propagation path are calculated based on the thermal radiation point source attenuation model, and the cumulative propagation probability Pnode of each tank is calculated through source-weighted topological sorting. The Pnode sorting calculated in this invention is completely consistent with the Landucci benchmark: ρ=1.000, τ=1.000.

[0092] Key difference: The Landucci method relies on empirical TTF formulas to calculate the failure time, while this invention directly calculates the propagation probability through a physical model (point source attenuation + Logistic transformation), without requiring empirical TTF, and can be extended to non-thermal mechanisms (gas flow, mechanical impact, etc.), which the Landucci method cannot handle.

[0093] In summary, this invention proposes a causal quantification method and system for domino effects based on the physical coupling strength of multiple mechanisms. This method relies on the theoretical framework of the Hierarchical Adaptive Domino Assessment System (HADES) and its three fundamental principles—the coupling strength quantification principle, the probability transformation criterion, and the directed causal network propagation rules. By using generalized coupling strength, it unifies seven propagation mechanisms—thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical fault—into a dimensionless intensity quantity, achieving unified quantification of causal intensity across physical dimensions. It calculates the actual effect intensity through mechanism-specific physical models, derives the mechanism strength index from the physical propagation law, and calibrates the probability transformation parameters using physical failure thresholds, ensuring that all key parameters have clear physical meaning and interpretability. It eliminates false positive propagation at the source through coupling strength lower bound gating and probability truncation boundaries. Finally, it achieves efficient probability propagation calculation on the directed causal network through a source-weighted topology sorting algorithm. Therefore, it provides a physical mechanism-driven, multi-mechanism unified, efficient, and highly reliable quantification solution for domino effect risk assessment in industrial facilities.

[0094] Compared with the prior art, the significant technical advantages of the present invention are reflected in the following aspects: 1. Unified quantification of multiple mechanisms overcomes the limitations of single mechanisms. This invention utilizes the generalized coupling strength C=(Ia / It) n × As × T unifies seven physical mechanisms—thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical fault—into a dimensionless intensity quantity, enabling cross-mechanism causal comparison and synergistic analysis. Existing methods, such as the Cozzani method which only handles thermal radiation and the Landucci method which only calibrates Probit parameters for tank fires, cannot achieve unified quantification of multiple mechanisms.

[0095] 2. Rigorous Derivation of Physical Parameters, Overcoming Empirical Fitting Dependence. All key parameters (n, Cmid, k, Ia) in this invention are rigorously derived from physical mechanisms: n is determined by physical propagation laws (Stefan-Boltzmann law, TNO multi-energy method, Fick diffusion equation, Haber toxicology law, Newtonian mechanics, Joule heating effect, etc.), Cmid is determined by physical failure thresholds (fracture toughness KIc, flammability limit LFL, toxicity threshold IDLH / LC50, breaking load MBL, etc.), and Ia is calculated by mechanism-specific physical models (point source attenuation model, gas diffusion ventilation model, anchor chain tension physical model, overpressure attenuation model, etc.). This eliminates the subjectivity and operational limitations of empirical parameters from the source, significantly improving the generalization ability and reliability of the method in different scenarios.

[0096] 3. Elimination of Dimensional Unification, Overcoming the Barrier of Heterogeneous Dimensions. This invention eliminates the differences between different physical dimensions (kW / m², MPa, ppm, kN, kA, etc.) by using the Ia / It ratio, reducing all mechanisms to a unified dimensionless coupling strength C. This supports direct comparison and synergistic analysis of cross-mechanism causal strength, laying a unified benchmark for the evaluation of multi-mechanism coupling.

[0097] 4. False positive transmission is eliminated, resulting in high engineering reliability. This invention utilizes C... EPSILON = 1×10 -4 Threshold gating forces the propagation probability to zero when the coupling strength is below a certain threshold, thus preventing false positive propagation of the low Cmid mechanism under extremely weak coupling conditions from the source. At the same time, a probability cutoff boundary P ∈ [0.001, 0.999] is set to prevent numerical instability caused by extreme values, which significantly improves the accuracy and engineering credibility of causal quantification.

[0098] 5. Excellent verification accuracy and superior benchmark comparison. In the Cozzani 3×3 tank benchmark verification, the deviation of this invention was 0.0%, Spearman rank correlation ρ=1.000, Kendall τ=1.000; in the Landucci 5-tank array benchmark verification, ρ=1.000, τ=1.000. The causal quantification accuracy is completely consistent with the classical method, and it also has the ability to cover multiple mechanisms, which fully demonstrates the applicability and reliability of this invention in multi-device collaborative propagation scenarios.

[0099] 6. High computational efficiency, suitable for large-scale applications. This invention adopts an analytical computation framework, with a single causal quantization taking milliseconds, which is 5-8 orders of magnitude faster than traditional CFD numerical simulation (hours to days). It can fully meet the engineering needs of batch causal analysis, real-time safety assessment, and safety barrier optimization design for large-scale industrial facilities.

[0100] This invention, based on an integrated hardware and software architecture, can be directly deployed in petrochemical plant safety monitoring systems, offshore platform safety control systems, and industrial digital twin platforms. It can automatically quantify the causal intensity of domino effects in industrial facilities, calculate propagation probability, assess the effectiveness of safety barriers, and model causal networks. Compared to traditional technologies, this invention features unified quantification of multiple mechanisms, rigorous derivation of physical parameters, unified dimensionless measurement, and excellent false positive propagation elimination and verification accuracy. It can be widely applied in various fields such as petrochemical storage tank areas, offshore oil and gas platforms, offshore wind farms, offshore substations, liquefied natural gas receiving terminals, and port hazardous chemical storage, possessing high academic value and promising industrial application prospects, with significant industrial applicability.

[0101] This invention also provides a storage medium for storing a computer program, which, when executed, performs at least the methods described above.

[0102] This invention also provides a control device, including a processor and a storage medium for storing a computer program; wherein the processor executes the computer program by performing at least the method described above.

[0103] This invention also provides a processor that executes a computer program, at least performing the methods described above.

[0104] The storage medium can be implemented by any type of non-volatile storage device, or a combination thereof. The non-volatile memory can be read-only memory (ROM), programmable read-only memory (PROM), erasable programmable read-only memory (EPROM), electrically erasable programmable read-only memory (EEPROM), magnetic random access memory (FRAM), flash memory, magnetic surface memory, optical disc or CD-ROM; magnetic surface memory can be disk storage or magnetic tape storage. The storage media described in the embodiments of this invention are intended to include, but are not limited to, these and any other suitable types of memory.

[0105] In the several embodiments provided by this invention, it should be understood that the disclosed systems and methods can be implemented in other ways. The device embodiments described above are merely illustrative. For example, the division of units is only a logical functional division, and in actual implementation, there may be other division methods, such as: multiple units or components can be combined, or integrated into another system, or some features can be ignored or not executed. In addition, the coupling or direct coupling or communication connection between the various components shown or discussed can be through some interfaces, and the indirect coupling or communication connection between devices or units can be electrical, mechanical, or other forms.

[0106] The units described above as separate components may or may not be physically separate. The components shown as units may or may not be physical units, that is, they may be located in one place or distributed across multiple network units. Some or all of the units may be selected to achieve the purpose of this embodiment according to actual needs.

[0107] In addition, in the various embodiments of the present invention, each functional unit can be integrated into one processing unit, or each unit can be a separate unit, or two or more units can be integrated into one unit; the integrated unit can be implemented in hardware or in the form of hardware plus software functional units.

[0108] Those skilled in the art will understand that all or part of the steps of the above method embodiments can be implemented by hardware related to program instructions. The aforementioned program can be stored in a computer-readable storage medium. When the program is executed, it performs the steps of the above method embodiments. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, read-only memory (ROM), random access memory (RAM), magnetic disks, or optical disks.

[0109] Alternatively, if the integrated units of this invention are implemented as software functional modules and sold or used as independent products, they can also be stored in a computer-readable storage medium. Based on this understanding, the technical solutions of the embodiments of this invention, or the parts that contribute to the prior art, can be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions to cause a computer device (which may be a personal computer, server, or network device, etc.) to execute all or part of the methods described in the various embodiments of this invention. The aforementioned storage medium includes various media capable of storing program code, such as mobile storage devices, ROM, RAM, magnetic disks, or optical disks.

[0110] The methods disclosed in the several method embodiments provided by this invention can be arbitrarily combined without conflict to obtain new method embodiments.

[0111] The features disclosed in the several product embodiments provided by this invention can be arbitrarily combined without conflict to obtain new product embodiments.

[0112] The features disclosed in the several method or device embodiments provided by the present invention can be arbitrarily combined without conflict to obtain new method or device embodiments.

[0113] The above description, in conjunction with specific preferred embodiments, provides a further detailed explanation of the present invention. It should not be construed that the specific implementation of the present invention is limited to these descriptions. For those skilled in the art, various equivalent substitutions or obvious modifications can be made without departing from the concept of the present invention, and all such modifications, achieving the same performance or application, should be considered within the scope of protection of the present invention.

Claims

1. A causal quantification method for the domino effect based on the strength of multi-mechanism physical coupling, characterized in that, Includes the following steps: S1. By deploying a distributed sensor array and engineering database on industrial facilities, collect equipment physical parameters, layout coordinates, safety barrier information and environmental condition data, perform data cleaning and standardization preprocessing, and construct a standardized scenario dataset; S2. Based on the initial accident type and equipment layout topology, identify potential domino propagation mechanisms, including two or more of the following: thermal radiation, overpressure, gas flow, smoke toxicity, direct flame, mechanical impact, and electrical failure mechanisms, and classify and label the identified mechanisms. S3. Based on the principle of coupling strength quantification, the ratio of actual action strength to the target device's anti-interference strength, mechanism strength index, effective action area factor, and action duration modulation factor are combined to calculate the dimensionless generalized coupling strength of each propagation path, thereby achieving unified quantification of propagation mechanisms with different physical dimensions. S4. Based on the physical laws followed by different physical propagation mechanisms, derive and determine the mechanism strength index of each mechanism, wherein the mechanism strength index reflects the nonlinear propagation characteristics of the corresponding physical mechanism; S5. Based on different propagation mechanisms, the corresponding mechanism-specific physical models are used to calculate the actual effect intensity. The physical models include thermal radiation point source distance attenuation model, gas diffusion ventilation model, anchor chain tension physical model, and overpressure attenuation model. S6. Based on the probability transformation criterion, the dimensionless generalized coupling strength is converted into the equipment failure propagation probability using a mechanism-specific Logistic function. Different physical mechanisms use different mechanism-specific parameters, which are associated with the physical failure threshold. S7. Set a lower limit threshold for coupling strength. When the dimensionless generalized coupling strength is lower than the threshold, the propagation probability is forced to be zero. Set a probability cutoff boundary to eliminate false positive propagation and numerical instability. S8. Based on the propagation rules of directed causal networks, the domino effect is modeled as a probability propagation process on a directed causal network. The causal network is topologically sorted, and the cumulative propagation probability is calculated node by node in the topological order. The failure probability of each node and the probability distribution of the propagation path are output.

2. The method according to claim 1, characterized in that, The physical parameters of the equipment mentioned in step S1 include fire resistance limit, explosion resistance strength, fracture toughness and insulation withstand voltage; the safety barrier information includes coverage information of passive fire protection, water curtain and firewall; the environmental condition data includes atmospheric transmittance, visibility and air change rate; the data cleaning and standardization preprocessing includes abnormal data removal and dimensional standardization.

3. The method according to claim 1, characterized in that, The physical derivation of the intensity index of the mechanism mentioned in step S4 specifically includes: the intensity index of the thermal radiation mechanism is determined based on the nonlinear power exponential relationship between the failure dose and the actual effect intensity in the Stefan Boltzmann radiation law and the Babrauskas fire dose model; the intensity index of the overpressure mechanism is determined based on the square relationship between the shock wave energy and the peak overpressure in the TNO multi-energy method, with the shock wave energy equivalent as the benchmark; the intensity index of the gas flow mechanism is determined based on the linear relationship between gas concentration and release rate in the Fick convection-diffusion equation; the intensity index of the smoke toxicity mechanism is determined based on the linear cumulative relationship between toxic dose and concentration in Haber's law; the direct flame mechanism determines the dominant relationship between radiative heat transfer and convective heat transfer based on the flame temperature, using the same intensity index as the thermal radiation mechanism when radiation is dominant, and using a linear intensity index when convection is dominant; the intensity index of the mechanical impact mechanism is determined based on Newtonian mechanics and the linear damage accumulation criterion, with the damage from multi-fragment impacts being linearly superimposed; the intensity index of the electrical fault mechanism is determined based on the proportional relationship between heat generation and the square of the current in the Joule heating effect.

4. The method according to claim 1, characterized in that, The physical model calculation of the actual effect intensity in step S5 specifically includes: the thermal radiation point source distance attenuation model is based on the point source radiation assumption, calculating the thermal radiation flux received at the target based on atmospheric transmittance, surface emission power, source area, and source-to-target distance; the atmospheric transmittance is determined by atmospheric visibility and relative humidity based on the standard atmospheric extinction model, and the surface emission power is determined by fuel type and combustion mode according to engineering specifications; the gas diffusion ventilation model is based on the mass conservation and complete mixing assumptions, calculating the steady-state gas concentration in the enclosed space based on the gas release rate, space air exchange rate, and enclosed space volume; the space air exchange rate is determined according to engineering specifications during the design phase and obtained through on-site measurement using the tracer gas method during the actual measurement phase. In the refined scenario, the stress is obtained through computational fluid dynamics simulation. The anchor chain tension physical model is based on quasi-static mooring analysis, and the peak tension is solved jointly based on environmental load, mooring system stiffness matrix, and anchor chain elongation. The peak tension is calculated as the product of the dynamic amplification factor, the static load resultant force, and the product of the stiffness matrix and the elongation. The mooring system stiffness matrix is ​​obtained by assembling the axial stiffness of a single anchor chain through spatial projection. The dynamic amplification factor is determined according to mooring specifications. The overpressure attenuation model is based on the TNO multi-energy method. The explosion intensity level is determined based on the volume of the combustible gas cloud and the fuel type. The reference overpressure at the reference distance is determined through a standard curve or the TNT equivalent method. Then, the peak overpressure at the target distance is calculated based on the distance attenuation relationship.

5. The method according to claim 1, characterized in that, Step S6, specifically the mechanism-specific probability transformation, includes: using the Logistic sigmoid function to perform a nonlinear mapping on the difference between the dimensionless generalized coupling strength and the median coupling strength of the mechanism; multiplying the mapping result by the safety barrier coverage probability to obtain the device failure propagation probability; the median coupling strength of the mechanism is the coupling strength value corresponding to a propagation probability of 50%, determined by the physical failure threshold of the corresponding physical mechanism; the mechanism steepness coefficient in the Logistic function characterizes the sharpness of the probability transformation curve, determined by the physical characteristics of the corresponding physical mechanism; the mechanism-specific parameters are divided into purely physical derivation parameters and calibration parameters under physical constraints according to their attributes; the values ​​of the purely physical derivation parameters are completely determined by the inherent physical properties of the material or substance, requiring no experimental calibration and being directly obtained through material handbooks or safety specifications; the calibration parameters under physical constraints use the physical failure threshold as a benchmark constraint, are calibrated through classic publicly available benchmark datasets, and the calibration process is subject to physical boundary constraints.

6. The method according to claim 5, characterized in that, Among the mechanism-specific parameters of each propagation mechanism: the median coupling strength and steepness coefficient of the thermal radiation mechanism are calibrated using the classical Probit model as the benchmark, and are determined by matching the dose point corresponding to the 50% failure probability and the slope of the Probit curve at the midpoint; the median coupling strength of the gas flow mechanism is determined based on the inherent physical property of the lower flammability limit, and the coupling strength is 1.0 when the actual gas concentration reaches the lower flammability limit, and the steepness coefficient is determined by the slope of the flammability limit curve; the median coupling strength of the direct flame mechanism is determined based on the degradation characteristics of the fracture toughness of the target material with increasing temperature, and the 50% failure probability is corresponding to the material fracture toughness dropping to a certain proportion of the room temperature value, and the coupling strength is taken as a proportional value; the median coupling strength of the smoke toxicity mechanism is determined based on the ratio of the half-lethal concentration of the toxic substance to the concentration that immediately threatens life and health, and is corrected by the safety factor of the synergistic effect of multiple toxic substances, and the safety factor is taken as 1.0 in the single gas scenario; the median coupling strength of the anchor chain dragging mechanism is determined based on the mooring specification that the anchor chain tension enters the nonlinear deformation range when it reaches a certain proportion of the breaking load.

7. The method according to claim 1, characterized in that, The lower limit threshold of coupling strength and the elimination of false positives in step S7 specifically include: when the dimensionless generalized coupling strength is lower than the preset lower limit threshold of coupling strength, the propagation probability of the corresponding propagation path is forcibly set to zero. The lower limit threshold corresponds to the strength level of physical coupling that is too weak to trigger any propagation. At the same time, all propagation probabilities are limited to a closed interval between the preset lower limit probability and the preset upper limit probability to prevent numerical instability caused by extreme values.

8. The method according to claim 1, characterized in that, The topology sorting probability propagation in step S8 specifically includes: performing topology sorting on all nodes in the directed causal network to determine the calculation order of each node, ensuring that the cumulative propagation probability of any target node is calculated after the cumulative propagation probabilities of all its source nodes are determined, avoiding circular dependencies and ensuring causal unidirectionality; according to the topology sorting order, for each target node, the initial event probability of the target node is used as the first term, and the product of the cumulative propagation probabilities of all source nodes pointing to the target node and their corresponding propagation probabilities is used as the second term, and probability composition is performed using the form of independent event probability multiplication to calculate the cumulative propagation probability of the target node; during the composition process, the cumulative propagation probability of each source node is used as the source node weight in the topology sorting, and the source node with the higher cumulative probability is propagated first.

9. The method according to claim 1, characterized in that, It also includes benchmark verification and result output steps: comparing and verifying the causal quantification results with the calculation results of classical benchmark methods, calculating statistical correlation indicators, and outputting the causal strength distribution, propagation probability matrix, and causal network topology.

10. A causal quantification system for the domino effect based on the strength of multi-mechanism physical coupling, characterized in that, include: The hardware acquisition layer includes: Distributed sensor arrays are used to collect sensor signals from various monitoring points in industrial facilities, including equipment physical parameters, layout coordinates, safety barrier information, and environmental condition data. The data acquisition unit is communicatively connected to the distributed sensor array and is used to receive and convert the sensing signals into digital process parameter data. A communication interface, connected to the data acquisition unit, is used to transmit the process parameter data to an external network via an industrial communication network. And a computational processing layer communicatively connected to the hardware acquisition layer, the computational processing layer including one or more processors and a memory storing computer program instructions, wherein the processors, when executing the computer program instructions, implement the domino effect causal quantification method based on the multi-mechanism physical coupling strength as described in any one of claims 1 to 9.

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