Parameter simulation optimization method for thickness of fireproof coating on bridge tunnel fire surface

Abstract

This invention belongs to the field of bridge and tunnel material optimization, and particularly relates to a parameter simulation optimization method and system for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels. The method includes: acquiring a parameter set containing the substrate's critical temperature, fire temperature rise curve, coating thermal conductivity and expansion ratio, application rate, and curing temperature threshold; building a thickness-insulation performance simulation model and setting the optimization interval and step size; simulating the thickness values ​​to obtain the substrate temperature rise time history and carbonized layer thermal barrier efficiency at each thickness; determining the insulation performance index based on this, and combining it with construction parameters to determine engineering suitability indicators; constructing a multi-objective optimization function, assigning weights to insulation, cost, and process, and calculating the comprehensive evaluation value for each thickness; verifying whether performance and engineering constraints are met, selecting the optimal thickness, and outputting the corresponding construction parameters. This invention achieves synergistic optimization of fire safety and construction economy through dynamic simulation of the entire coating expansion process and adaptive step-size traversal.

Description

Technical Field

[0001] This invention belongs to the field of bridge and tunnel material optimization, and in particular relates to a parameter simulation optimization method and system for the thickness of fireproof coatings on fire-exposed surfaces of bridges and tunnels. Background Technology

[0002] With the rapid development of high-risk industries such as bridges, oil, natural gas, petrochemicals, and power, steel structures and bridge cables, as core load-bearing structures, rely heavily on fire-retardant coatings. The thickness design of these coatings on their fire-exposed surfaces forms the cornerstone of the fire protection system, and its rationality and precision directly determine the structure's fire resistance limit and safe operation capability. In complex fire application scenarios, the thickness of fire-retardant coatings exhibits a high degree of scenario dependence, performance coupling, and engineering constraints. For example, in the protection of bridge main cables, the coating thickness needs to match the temperature rise pattern of a 100MW-scale hydrocarbon combustion fire while also considering the critical temperature threshold of 300℃ for the main cable steel wires. In the protection of petrochemical steel structures, the coating thickness needs to cope with the temperature gradients of different fire types, such as hydrocarbon pool fires and jet fires, achieving thermal insulation protection for a specified duration at temperatures above 1050℃. In actual construction scenarios, the coating thickness design also needs to combine different construction techniques such as layered application and airless spraying to balance the engineering requirements of coating rate, loss coefficient, and curing time. The above factors mean that thickness design needs to handle coating thickness gradients from millimeters to substrate temperature control at the hundred-degree Celsius level, while taking into account the correlation between the thermal properties of the coating (such as thermal conductivity and expansion ratio) and fire scenario parameters (such as flame temperature and burning time). Furthermore, the nonlinear relationship between coating thickness and substrate temperature rise and fire resistance limit may be dynamically reconstructed as the fire type and construction environment change.

[0003] In existing technologies, a common approach is to design the thickness of fire-retardant coatings based on empirical values ​​or general regulatory requirements. This involves directly determining the dry film thickness of the coating on the fire-exposed surface by referring to general standards for fire-retardant coatings on steel structures or similar engineering cases. This method is effective in applications with simple fire scenarios and structures. However, when facing high-risk and complex fire-exposed surfaces, the static fixed thickness cannot match the insulation requirements under different fire temperatures and combustion durations. The empirical design approach ignores the quantitative coupling law between coating thickness and substrate temperature rise, and does not consider the impact of construction technology and ambient temperature on the actual coating thickness. This results in either excessive redundancy in coating thickness design, leading to waste of materials and construction costs, or insufficient thickness to meet fire resistance requirements, making it difficult to effectively cope with sudden and high-intensity fire scenarios such as hydrocarbon jet fires and bridge main cable fires.

[0004] Another approach involves a trial-and-error design of coating thickness using real fire tests. By preparing coating samples of different thicknesses, the temperature rise and fire resistance time of the substrate are tested under simulated fire conditions to select the thickness value that meets the protection requirements. While these methods have improved the matching between thickness design and actual fire protection requirements to some extent, existing real-fire testing methods still have significant drawbacks in thickness optimization: multiple physical tests conducted to cover different thickness gradients result in long testing cycles and high manpower and material costs, making it difficult to achieve refined and multi-dimensional optimization of thickness parameters; physical tests are limited by testing equipment and the accuracy of working condition simulation, making it impossible to fully reproduce the dynamic temperature rise curves of different fire scenarios and the constraints of complex construction environments, leading to adaptation deviations in the thickness parameters obtained from the tests in actual engineering applications; during the test, only discrete thickness-performance data points can be obtained, making it impossible to explore the continuous nonlinear relationship between coating thickness and multiple parameters such as thermal conductivity, expansion ratio, and substrate temperature rise, and it is difficult to take into account the impact of engineering constraints such as application rate, curing time, and diluent addition on thickness design, resulting in problems such as high construction difficulty and poor coating quality when the designed thickness parameters are implemented in engineering projects.

[0005] Therefore, the urgent technical problem to be solved by existing technologies is how to balance the quantitative coupling relationship between coating thickness and fire resistance performance, the dynamic characteristics of fire scenarios and the actual constraints of engineering construction, and achieve accurate simulation and optimization of the thickness of fire-resistant coatings on fire-exposed surfaces from microscopic thermal parameters to macroscopic engineering applications. This would fundamentally solve the problems of low design accuracy, high testing costs and poor engineering adaptability of existing fire-resistant coating thickness designs when facing complex fire scenarios and diverse engineering constraints. Summary of the Invention

[0006] To address the shortcomings of existing technologies, this invention proposes a parameter simulation optimization method and system for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels. The method includes: acquiring a parameter set containing the substrate's critical temperature, fire temperature rise curve, coating thermal conductivity and expansion ratio, application rate, and curing temperature threshold; building a thickness-insulation performance simulation model and setting the optimization interval and step size; simulating the thickness values ​​to obtain the substrate temperature rise time history and carbonized layer thermal barrier efficiency at each thickness; determining the insulation performance index based on this, and combining it with construction parameters to determine engineering suitability indicators; constructing a multi-objective optimization function, assigning weights to insulation, cost, and process, and calculating the comprehensive evaluation value for each thickness; verifying whether performance and engineering constraints are met, selecting the optimal thickness, and outputting the corresponding construction parameters. This invention solves the problems of low accuracy and poor efficiency of traditional static models by dynamically simulating the entire coating expansion process and using adaptive step size traversal, achieving synergistic optimization of fire safety and construction economy.

[0007] To achieve the above objectives, the present invention provides the following technical solution:

[0008] A parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels includes:

[0009] Obtain the set of parameters related to the protection of the fire-exposed surface, build a thickness-thermal insulation performance simulation model based on the set of parameters, set the value range and iteration step size of the coating thickness optimization variable, and configure performance constraints and engineering constraints.

[0010] The associated parameter set is input into the thickness-thermal insulation performance simulation model. All values ​​of the coating thickness optimization variable are traversed according to the iteration step size and simulation is performed to obtain the real-time temperature rise time history data of the substrate on the fire-exposed surface and the thermal barrier efficiency of the coating expansion carbonization layer under each thickness value.

[0011] Based on the temperature rise time history data and thermal barrier efficiency, the thermal insulation performance index corresponding to each thickness is determined, and the engineering adaptability index corresponding to each thickness is determined based on the construction coating rate and curing temperature threshold.

[0012] A multi-objective optimization judgment function is constructed, and preset weight coefficients are assigned to thermal insulation performance, construction cost and process adaptability respectively. The thermal insulation performance index and engineering adaptability index corresponding to each thickness value are substituted into the multi-objective optimization judgment function to calculate the comprehensive quantitative evaluation value corresponding to each thickness value.

[0013] Verify whether the comprehensive quantitative evaluation value corresponding to each thickness value simultaneously satisfies the performance constraints and engineering constraints. Select the coating thickness value that satisfies all constraints and has the best comprehensive quantitative evaluation value, and generate an optimization result that includes the optimal coating thickness and matching construction parameters.

[0014] Specifically, the parameter set includes the substrate critical temperature, the fire scenario temperature rise curve, the coating thermal conductivity, the coating expansion ratio, the application rate, and the curing temperature threshold. The performance constraints are that the temperature rise of the fire-exposed substrate is ≤ the substrate critical temperature and the fire resistance time is ≥ the preset design threshold. The engineering constraints are that the coating loss coefficient is ≤ the preset loss value and the application temperature is not lower than the curing temperature threshold. The fire scenario temperature rise curve is a simulated hydrocarbon combustion HC temperature rise curve, which includes a sequentially connected heating stage, a stabilization stage, and a decay stage. The heating stage is when the temperature linearly rises from the initial temperature to 1100℃ within 10 minutes. The stabilization stage is when the temperature remains constant at 1100℃ for 60 minutes. The decay stage is when the temperature linearly drops from 1100℃ to the initial temperature for 20 minutes.

[0015] Specifically, a thickness-thermal insulation performance simulation model is built based on the aforementioned parameter set, including:

[0016] Obtain the expansion trigger temperature, stable carbonization temperature, initial thermal conductivity of the coating, thermal conductivity of the carbonized layer, minimum expansion ratio, and maximum expansion ratio from the parameter set.

[0017] Based on the expansion trigger temperature and the stable carbonization temperature, the temperature range during the fire temperature rise process is divided into an unexpanded zone, an expansion transition zone, and a fully carbonized zone. A piecewise function of the expansion ratio with respect to temperature is established. In the expansion transition zone, the expansion ratio monotonically increases from the minimum expansion ratio to the maximum expansion ratio according to a preset interpolation model. In the unexpanded zone and the fully carbonized zone, the expansion ratio is always equal to the minimum expansion ratio and the maximum expansion ratio, respectively.

[0018] Based on the initial thermal conductivity of the coating and the thermal conductivity of the carbonized layer, a piecewise function of the equivalent thermal conductivity with respect to temperature is established. In the unexpanded region, the equivalent thermal conductivity is equal to the initial thermal conductivity of the coating; in the fully carbonized region, the equivalent thermal conductivity is equal to the thermal conductivity of the carbonized layer; and in the expansion transition region, the equivalent thermal conductivity transitions from the initial thermal conductivity of the coating to the thermal conductivity of the carbonized layer according to the degree of carbonization function.

[0019] Specifically, building a thickness-thermal insulation performance simulation model based on the aforementioned parameter set also includes:

[0020] Within each iteration time step of the simulation model, the current coating temperature is obtained, the current expansion ratio is determined according to the piecewise function of the expansion ratio with respect to temperature, and the current equivalent thermal conductivity is determined according to the piecewise function of the equivalent thermal conductivity with respect to temperature.

[0021] The current carbonized layer thickness is calculated by multiplying the initial coating thickness by the current expansion ratio.

[0022] Calculate the thermal resistance of the current carbonized layer based on the ratio of the current carbonized layer thickness to the current equivalent thermal conductivity.

[0023] Substitute the current thermal resistance of the carbonized layer into the heat transfer control equation of the substrate to obtain the temperature value of the substrate on the fire-exposed surface at the current time step, and update the temperature rise time history data of the substrate on the fire-exposed surface.

[0024] Specifically, real-time temperature rise time history data of the substrate exposed to fire and the thermal barrier efficiency of the coating expansion and carbonization layer are obtained for various thickness values, including:

[0025] Set the initial iteration step size, set the step size adjustment threshold, and set the minimum iteration step size;

[0026] Starting from the lower limit of the value range, the current thickness value is selected with the initial iteration step size. For the current thickness value, based on the thickness-thermal insulation performance simulation model, the current expansion ratio, current equivalent thermal conductivity, current carbonized layer thickness and current carbonized layer thermal resistance are dynamically calculated according to the current coating temperature within each iteration time step.

[0027] Substitute the current thermal resistance of the carbonized layer into the heat transfer control equation of the substrate, and combine the flame temperature at the current moment as the boundary condition to solve for the temperature value of the substrate at the current time step. Iterate to the total time corresponding to the temperature rise curve of the fire scene to obtain the substrate temperature rise time history data and carbonized layer thermal barrier efficiency time history data corresponding to the thickness value.

[0028] Extract the fire resistance time and extreme temperature rise value of the substrate corresponding to the current thickness value from the substrate temperature rise time history data. The fire resistance time refers to the moment when the substrate temperature first reaches the substrate critical temperature. If it does not reach the critical temperature throughout the entire process, the total fire duration is taken.

[0029] The current thickness value is compared with the fire resistance time and the extreme temperature rise of the substrate corresponding to the previous thickness value. The change rate of fire resistance time and the change rate of extreme temperature rise of the substrate are calculated. The change rate refers to the absolute value of the difference between the current thickness value and the corresponding index of the previous thickness value divided by the corresponding index of the previous thickness value.

[0030] Specifically, obtaining real-time temperature rise time history data of the substrate exposed to fire and the thermal barrier efficiency of the coating expansion and carbonization layer for various thickness values ​​also includes:

[0031] Determine whether the rate of change of the fire resistance time or the rate of change of the extreme value of the substrate temperature rise is greater than the step size adjustment threshold.

[0032] For the current adjacent thickness value pairs, compare the rate of change of the fire resistance time with the rate of change of the extreme temperature rise of the substrate; if either rate of change is greater than the step size adjustment threshold, insert an intermediate thickness value between the thickness pairs, complete the simulation of the intermediate thickness value with half of the current iteration step size and insert the sequence, and backtrack to the beginning position of the thickness pair to re-execute the comparison and insertion operation; if the rate of change of all adjacent thickness value pairs is not greater than the step size adjustment threshold, or the current iteration step size is less than the minimum iteration step size, then terminate the iteration.

[0033] Repeat the above comparison and insertion steps until the rate of change of fire resistance time and the rate of change of extreme temperature rise of the substrate between all adjacent thickness values ​​are not greater than the step size adjustment threshold, or the current iteration step size is less than the minimum iteration step size.

[0034] The final thickness values, along with their corresponding substrate temperature rise time history data and carbonized layer thermal barrier efficiency time history data, are output as the traversal results.

[0035] Specifically, the process of obtaining thermal insulation performance indicators and engineering compatibility indicators includes:

[0036] For each thickness value, the fire resistance time and the extreme value of the substrate temperature rise are extracted from the substrate temperature rise time history data corresponding to that thickness as thermal insulation performance indicators. The fire resistance time refers to the moment when the substrate temperature first reaches the substrate critical temperature. If it does not reach the critical temperature throughout the process, the total time corresponding to the temperature rise curve of the fire scenario is taken. The extreme value of the substrate temperature rise refers to the highest temperature value in the substrate temperature rise time history data.

[0037] The amount of paint used per unit area is calculated by multiplying the thickness value by the application rate, which serves as the first engineering compatibility index. The construction temperature margin is calculated based on the difference between the construction ambient temperature and the curing temperature threshold, which serves as the second engineering compatibility index.

[0038] Specifically, the comprehensive quantitative evaluation value corresponding to each thickness value is calculated, including:

[0039] For each thickness value d, the comprehensive thermal insulation performance index I_th(d) is calculated based on its fire resistance time t_crit(d) and the extreme temperature rise of the substrate T_max(d). The calculation formula is I_th(d) = ω_t (t_crit(d) t_total)+ω_T (1-T_max(d) T_limit), where t_total is the total duration corresponding to the temperature rise curve of the fire scenario, T_limit is the critical temperature of the substrate, ω_t and ω_T are preset thermal insulation performance sub-weight coefficients and ω_t+ω_T=1;

[0040] The construction cost index I_co(d) is calculated based on the amount of paint used per unit area M(d) for each thickness value d. The calculation formula is I_co(d) = 1 - M(d). M_max, where M_max is the preset maximum allowable amount of paint;

[0041] The process adaptability index I_pr(d) is calculated based on the construction temperature margin ΔT(d) corresponding to the thickness value d. The calculation formula is I_pr(d) = ΔT(d). ΔT_max, where ΔT_max is the preset maximum allowable temperature margin;

[0042] Construct a multi-objective optimization decision function F(d)=α I_th(d)+β I_co(d)+γ I_pr(d), where α, β, and γ are preset weighting coefficients and α+β+γ=1;

[0043] Substitute I_th(d), I_co(d), and I_pr(d) corresponding to each thickness value into the multi-objective optimization judgment function to calculate the comprehensive quantitative evaluation value F(d) corresponding to each thickness value.

[0044] Specifically, the comprehensive quantitative evaluation value corresponding to each thickness value is calculated, and also includes:

[0045] The thickness values ​​and their corresponding fire resistance time, substrate temperature rise extreme value, coating amount per unit area, construction temperature margin, and comprehensive quantitative evaluation value are associated and stored to form a comprehensive evaluation dataset of thickness-performance-cost-process.

[0046] For each thickness value in the comprehensive evaluation dataset, determine whether it simultaneously meets the performance constraints of fire resistance time not less than the preset design threshold and substrate temperature rise extreme value not exceeding substrate critical temperature, and the engineering constraints of coating amount per unit area not exceeding the maximum allowable coating amount corresponding to construction loss constraint and construction temperature margin not less than zero.

[0047] The thickness values ​​that satisfy all constraints are selected to form a candidate thickness subset;

[0048] In the candidate thickness subset, the thicknesses are sorted in descending order of comprehensive quantitative evaluation values, and the thickness corresponding to the maximum comprehensive quantitative evaluation value is selected as the preliminary optimal thickness.

[0049] If multiple thickness values ​​have the same comprehensive quantitative evaluation value or the difference is less than the preset evaluation value tolerance threshold, then the fire resistance time of these thickness values ​​is further compared, and the one with the longest fire resistance time is selected as the final optimal thickness; if the fire resistance time is still the same, then the one with the smallest extreme temperature rise of the substrate is selected as the final optimal thickness.

[0050] The final determined optimal thickness value and its associated construction parameters are output as the optimization result.

[0051] A parameter simulation and optimization system for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels includes:

[0052] The simulation construction module is used to obtain a set of parameters related to the protection of the fire-exposed surface, build a thickness-insulation performance simulation model based on the parameter set, set the value range and iteration step size of the coating thickness optimization variable, and configure performance constraints and engineering constraints. The parameter set includes the critical temperature of the substrate, the temperature rise curve of the fire scenario, the thermal conductivity of the coating, the expansion ratio of the coating, the application rate, and the curing temperature threshold. The performance constraints are that the temperature rise of the fire-exposed substrate is ≤ the critical temperature of the substrate and the fire resistance time is ≥ the preset design threshold. The engineering constraints are that the coating loss coefficient is ≤ the preset loss value and the application temperature is not lower than the curing temperature threshold.

[0053] The simulation module is traversed, the associated parameter set is input into the thickness-thermal insulation performance simulation model, and all values ​​of the coating thickness optimization variable are traversed according to the iteration step size and the simulation is performed to obtain the real-time temperature rise time history data of the fire-exposed substrate and the thermal barrier efficiency of the coating expansion carbonization layer under each thickness value.

[0054] The index calculation module determines the thermal insulation performance index corresponding to each thickness based on the temperature rise time history data and thermal barrier efficiency, and determines the engineering adaptability index corresponding to each thickness based on the construction coating rate and curing temperature threshold.

[0055] The multi-objective optimization module constructs a multi-objective optimization judgment function, assigns preset weight coefficients to thermal insulation performance, construction cost and process adaptability respectively, substitutes the thermal insulation performance index and engineering adaptability index corresponding to each thickness value into the multi-objective optimization judgment function, and calculates the comprehensive quantitative evaluation value corresponding to each thickness value.

[0056] The verification output module verifies whether the comprehensive quantitative evaluation value corresponding to each thickness value simultaneously meets the performance constraints and engineering constraints. It then selects the coating thickness value that meets all constraints and has the optimal comprehensive quantitative evaluation value, and generates an optimization result that includes the optimal coating thickness and matching construction parameters.

[0057] Compared with the prior art, the beneficial effects of the present invention are:

[0058] This invention constructs a thickness-insulation performance simulation model that integrates key parameters such as expansion trigger temperature, stable carbonization temperature, carbonized layer thermal conductivity, and dynamic expansion ratio. Within each iteration time step, the expansion ratio, equivalent thermal conductivity, carbonized layer thickness, and thermal resistance are calculated in real-time based on the coating temperature. The carbonized layer thermal resistance is then substituted into the substrate heat transfer control equation to solve for the substrate temperature rise time history data. This accurately simulates the thermal barrier behavior of the coating throughout the entire process from triggered expansion to complete carbonization. This solves the problems of misjudgment of insulation efficiency and thickness optimization deviations caused by traditional static models that neglect the nonlinearity of the expansion process, the evolution of carbonized layer thermophysical properties, and the dynamic coupling relationship between thickness and thermal resistance. This significantly improves simulation accuracy and repeatability. Furthermore, by introducing an adaptive step-size traversal mechanism, the thickness value is dynamically refined based on the rate of change of the refractory time and the extreme value of the substrate temperature rise, effectively reducing the computational complexity while ensuring the accuracy of key performance indicators. By reducing the number of redundant thickness simulations, the drawbacks of long cycles, high costs, and discrete data in real fire tests are overcome, enabling rapid optimization of multiple thicknesses. Based on this, a multi-objective optimization judgment function is constructed that comprehensively considers thermal insulation performance, construction costs, and process adaptability. Indicators such as fire resistance time, extreme temperature rise of the substrate, coating dosage per unit area, and construction temperature margin are substituted into the function for comprehensive quantitative calculation. The optimal thickness and corresponding construction parameters are then selected to simultaneously meet constraints such as substrate temperature rise ≤ critical temperature, fire resistance time ≥ design threshold, coating loss coefficient ≤ preset value, and construction temperature not lower than the curing temperature threshold. This systematically solves the problem in existing technologies where thickness design cannot simultaneously consider the dynamic characteristics of fire scenarios, the evolution of coating thermal properties, and actual constraints of engineering construction. It achieves synergistic optimization of fireproof thickness design for bridge and tunnel fire-exposed surfaces in complex fire scenarios, balancing fire safety and construction economy. Attached Figure Description

[0059] Figure 1 This is a flowchart of the parameter simulation optimization method for the thickness of fireproof coatings on fire-exposed surfaces of bridges and tunnels according to the present invention;

[0060] Figure 2 This is a diagram of the cable test component of the present invention;

[0061] Figure 3 This is a schematic diagram of the longitudinal arrangement of the measuring points on the specimen of the present invention;

[0062] Figure 4 This is a schematic diagram of the cross-section of the specimen and the transverse arrangement of the thermocouples according to the present invention;

[0063] Figure 5 This is a module diagram of the parameter simulation optimization system for the thickness of fireproof coatings on fire-exposed surfaces of bridges and tunnels, as described in this invention. Detailed Implementation

[0064] Example 1

[0065] Please see Figure 1The present invention provides an embodiment of a parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels, comprising the following steps:

[0066] S1. Obtain the set of parameters related to the protection of the fire-exposed surface, build a thickness-insulation performance simulation model based on the parameter set, set the value range and iteration step size of the coating thickness optimization variable, and configure performance constraints and engineering constraints. The parameter set includes the critical temperature of the substrate, the temperature rise curve of the fire scenario, the thermal conductivity of the coating, the expansion ratio of the coating, the application rate, and the curing temperature threshold. The performance constraints are that the temperature rise of the fire-exposed substrate is ≤ the critical temperature of the substrate and the fire resistance time is ≥ the preset design threshold. The engineering constraints are that the coating loss coefficient is ≤ the preset loss value and the construction temperature is not lower than the curing temperature threshold.

[0067] S2. Input the associated parameter set into the thickness-thermal insulation performance simulation model, iterate through all values ​​of the coating thickness optimization variable according to the iteration step size and perform simulation to obtain the real-time temperature rise time history data of the substrate on the fire surface and the thermal barrier efficiency of the coating expansion carbonization layer under each thickness value.

[0068] S3. Determine the thermal insulation performance index corresponding to each thickness based on the temperature rise time history data and thermal barrier efficiency, and determine the engineering adaptability index corresponding to each thickness based on the construction coating rate and curing temperature threshold.

[0069] S4. Construct a multi-objective optimization judgment function, assign preset weight coefficients to thermal insulation performance, construction cost and process adaptability respectively, substitute the thermal insulation performance index and engineering adaptability index corresponding to each thickness value into the multi-objective optimization judgment function, and calculate the comprehensive quantitative evaluation value corresponding to each thickness value.

[0070] S5. Verify whether the comprehensive quantitative evaluation value corresponding to each thickness value simultaneously satisfies the performance constraints and engineering constraints. Select the coating thickness value that satisfies all constraints and has the optimal comprehensive quantitative evaluation value, and generate an optimization result that includes the optimal coating thickness and supporting construction parameters. Specifically, the optimal coating thickness and supporting construction parameters in this embodiment include: the optimal coating thickness value d_opt, and the supporting construction parameters corresponding to the optimal coating thickness. The supporting construction parameters include the coating amount per unit area M (d_opt), the construction temperature margin ΔT (d_opt), and the construction process control requirements determined based on the construction coating rate and curing temperature threshold.

[0071] Existing technologies for simulating and optimizing the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels generally employ static thermal parameters (such as fixed thermal conductivity and constant expansion ratio) for modeling. This results in the model failing to accurately reflect the dynamic physical characteristics of the coating during the actual temperature rise process in a fire. This application deeply analyzes four specific technical problems arising from this: First, by ignoring the gradual transition between the expansion trigger temperature and the stable charring temperature, using a fixed expansion ratio cannot accurately calculate the actual charred layer thickness at different fire development stages, leading to an overestimation or underestimation of the insulation efficiency. Second, the lack of an independent charred layer thermal conductivity parameter and its dynamic characteristics changing with temperature, along with the use of the original coating thermal conductivity, leads to distortion in the simulation of the heat transfer process, significantly reducing the prediction accuracy of the substrate temperature rise time history data. Third, the failure to establish a relationship between the charred layer thickness and the initial thickness... The nonlinear multiple relationship sub-model, coupled with the substrate temperature rise module, causes the complete causal chain of "initial thickness → thickness after expansion → thermal barrier efficiency → substrate temperature rise suppression" to break, resulting in thickness optimization results deviating from physical reality. Fourth, the failure to accurately model the dynamic characteristics in this embodiment directly leads to either redundant waste and increased costs in engineering applications of optimized thickness, or insufficient fire resistance time, threatening the safety of bridge and tunnel structures. In summary, this application aims to solve the technical problem that existing simulation models fail to consider the coating expansion trigger temperature, the dynamic evolution of the thermal conductivity of the carbonized layer, and the nonlinear growth relationship of the carbonized layer thickness, resulting in an inability to accurately simulate the dynamic thermal barrier behavior of intumescent fireproof coatings in real fire scenarios, thus causing a serious deviation between thickness optimization results and thermal insulation performance, and making it difficult to balance bridge and tunnel fire safety and construction economy.

[0072] This embodiment addresses the aforementioned technical problems by using the main cable of a suspension bridge as the protected object. A high-performance aerogel-reinforced fireproof and heat-insulating coating is employed. Based on the fire resistance design targets of ≤300℃ for the main cable steel wire temperature and ≥60min for a 100MW fire scale, as specified in the "Technical Specification for Comprehensive Fire-Resistant Sealing Protection of Bridge Load-Bearing Cables" (China Communications and Transportation Association, T / CCTAS61-2023, pp. 3-6, October 2023), parameter simulation optimization of the fireproof coating thickness is performed. The main cable steel wire is a 1960MPa grade high-strength steel wire with a diameter of 6mm and a material density ρ=7850kg·m³. -3 Specific heat capacity c = 460 J·(kg·K) -1 Thermal conductivity λ = 45 W·(m·K) -1The scaled-down model of the main cable used in this experiment was fabricated based on the design parameters of the main cable section of the suspension bridge. A total of 7 scaled-down cable models were designed, each test component being 2000mm long and composed of 1159 high-strength steel wires with a diameter of 6mm. The measured outer diameter of the cable body is approximately 225mm, and the weight of a single cable body is approximately 386kg. To accurately monitor the temperature distribution inside the main cable during a fire, 10 K-type armored thermocouples (temperature range -200℃~1300℃, accuracy ±1℃) were arranged at the middle section (1000mm from the end) of each test component, distributed in three 120° radius directions. Among them, 3 thermocouples were arranged on the outer side of the protective layer, 3 thermocouples on the first layer of steel wires, 1 thermocouple on the middle layer of steel wires, and 1 thermocouple on the steel wire at the center. The specific arrangement is as follows: Figure 2 As shown ( Figure 2 Photographs of cable test components. Figure 3 The test points are arranged longitudinally on the specimen. Figure 4 This is a schematic diagram of the transverse arrangement of thermocouples, where... 223mm is the measured outer diameter of the cable scale model (symbol). (Representing the outer diameter), 2000mm is the total length of the cable test component, A is the sectioning symbol, representing the sectioning position of the AA section view, used to indicate that the main cable test component is hypothetically sectioned at this position to clearly show the internal structure and cross-sectional dimensions of the component. It is a standard sectioning symbol used in engineering drawings to express the internal structure. ); The fireproof layer is coated on the surface of the cable body. The fire scenario uses the HC temperature rise curve simulating the combustion of non-hazardous chemicals in a truck: the rising phase is 10 minutes from 20℃ to 1100℃, the stable phase is 60 minutes maintaining 1100℃, and the decay phase is 20 minutes from 1100℃ to 20℃. Based on this, a thickness-insulation performance simulation model is built based on the parameter set, including:

[0073] The expansion trigger temperature, stable carbonization temperature, initial thermal conductivity of the coating, thermal conductivity of the carbonized layer, minimum expansion ratio, and maximum expansion ratio are obtained from the parameter set. In this embodiment, the initial thermal conductivity of the coating and the thermal conductivity of the carbonized layer correspond to the thermal conductivity values ​​of the coating in its unexpanded and fully carbonized states, respectively. The minimum and maximum expansion ratios correspond to the expansion ratio values ​​of the coating in its unexpanded and fully carbonized states, respectively. The expansion trigger temperature and stable carbonization temperature are used to define the temperature range from the start of expansion to the formation of a stable carbonized layer. For example, this embodiment uses a high-performance aerogel toughening method. The main technical parameters of the fire-retardant and heat-insulating coating are determined according to the "Fire-retardant Coatings for Steel Structures" (issued by the State Administration for Market Regulation and the Standardization Administration of China, GB14907-2018, pp. 3, 6-8, June 2019) and a third-party type test report: the expansion trigger temperature T_trigger is set to 350℃, meaning the coating begins to foam and expand at this temperature; the stable carbonization temperature T_stable is set to 600℃, meaning the coating completes expansion and forms a stable carbonized layer above this temperature; and the initial thermal conductivity λ_coat is set to 0.08 W·(m·K). -1 (Calculated based on water absorption rate and material composition according to JC / T 2663-2022); the thermal conductivity λ_char of the carbonized layer is taken as 0.15 W·(m·K). -1 (Based on the measured thermal conductivity of the carbonized layer after the heat resistance test in GB14907-2018); the minimum expansion ratio β_min is set to 1 (the coating thickness remains unchanged when it is not expanded); the maximum expansion ratio β_max is set to 30 (based on the test results of elongation at break and expansion ratio in ASTM D638-24 or GB / T 1040.2-2022, the thickness of the aerogel coating after expansion can reach 30 times the initial thickness).

[0074] Based on the expansion trigger temperature T_trigger and the stable charring temperature T_stable, the temperature range during the fire temperature rise process is divided into: the non-expansion zone (T < T_trigger) where the temperature T is below the expansion trigger temperature; the expansion transition zone (T_trigger ≤ T ≤ T_stable) where the temperature is between the expansion trigger temperature and the stable charring temperature; and the fully charred zone (T > T_stable) where the temperature is above the stable charring temperature. A piecewise function of the expansion ratio β(T) with respect to temperature T is established, wherein in the expansion transition zone, the expansion ratio decreases from the minimum expansion ratio β_min according to a preset... The interpolation model monotonically increases to the maximum expansion ratio β_max. In the unexpanded region and the fully carbonized region, the expansion ratios are constant at β_min and β_max, respectively. The interpolation model in this embodiment is determined by fitting the coating's thermogravimetric analysis or expansion ratio test data, using one of linear interpolation, S-curve interpolation, or exponential interpolation. For example, the specific division criteria are as follows: when the coating temperature T is below the expansion trigger temperature of 350℃, it belongs to the unexpanded region; when the coating temperature T is between 350℃ and 600℃, it belongs to the expansion transition region; when the coating temperature T is above 600℃, it belongs to the fully carbonized region. In the expansion transition region, the expansion ratio β(T) monotonically increases from the minimum expansion ratio 1 to the maximum expansion ratio 30 according to the preset interpolation model. In the unexpanded region and the fully carbonized region, the expansion ratio β(T) is constant at the minimum expansion ratio 1 and the maximum expansion ratio 30, respectively. In this embodiment, the preset interpolation model adopts linear interpolation, that is, within the temperature range of 350℃ to 600℃, the expansion ratio increases linearly with the increase of temperature: β(T)=1+(T-350). (600-350)×(30-1). This linear relationship is obtained by fitting the volume expansion test data of the coating during the heating process, which conforms to the approximate change law of the material in the expansion transition zone.

[0075] Based on the initial thermal conductivity of the coating and the thermal conductivity of the carbonized layer, a piecewise function of the equivalent thermal conductivity with respect to temperature is established. In the unexpanded region, the equivalent thermal conductivity equals the initial thermal conductivity of the coating; in the fully carbonized region, the equivalent thermal conductivity equals the thermal conductivity of the carbonized layer; and in the expansion transition region, the equivalent thermal conductivity transitions from the initial thermal conductivity of the coating to the thermal conductivity of the carbonized layer according to a carbonization degree function. It should be further explained that, in this embodiment, the transition of the equivalent thermal conductivity from the initial thermal conductivity of the coating to the thermal conductivity of the carbonized layer according to the carbonization degree function in the expansion transition region specifically involves: curve fitting based on measured data of the thermal conductivity of the carbonized layer of the coating changing with temperature to establish a transition function of the equivalent thermal conductivity with respect to temperature. This transition function changes continuously within the range from the expansion trigger temperature to the stable carbonization temperature, and is selected from linear transition, nonlinear transition, or piecewise constant approximation. In this embodiment, the equivalent thermal conductivity also adopts a linear transition. That is, in the unexpanded region (T<350℃), the equivalent thermal conductivity λ_eff(T)=λ_coat=0.08W·(m·K) -1 In the fully carbonized region (T>600℃), λ_eff(T)=λ_char=0.15W·(m·K) -1 In the expansion transition region (350℃≤T≤600℃), λ_eff(T) varies from 0.08 W·(m·K) depending on the degree of carbonization. -1 Linear transition to 0.15 W / (m·K) -1 That is, λ_eff(T) = 0.08 + (T - 350) (600-350)×(0.15-0.08). This linear relationship was verified by fitting measured data of the thermal conductivity of the carbonized layer with temperature, and it can accurately reflect the evolution trend of thermal conductivity within the allowable range of engineering accuracy.

[0076] Within each iteration time step of the simulation model, the current coating temperature is obtained, the current expansion ratio is determined according to the piecewise function of the expansion ratio with respect to temperature, and the current equivalent thermal conductivity is determined according to the piecewise function of the equivalent thermal conductivity with respect to temperature; in this embodiment, within each iteration time step of the simulation model... The current coating temperature is obtained within t, and the time step is further set. The steps of t are as follows: Determine a fixed time step based on the numerical stability condition, wherein the numerical stability condition is the Fourier number. Where λ is the thermal conductivity of the substrate, ρ is the density of the substrate, and c is the specific heat capacity of the substrate. x represents the spatial grid step size; alternatively, an adaptive time step size can be used, which adjusts the step size in real time based on the temperature change rate of the current iteration step. When the temperature change rate exceeds a preset threshold, the step size decreases; when it falls below the threshold, the step size increases, to meet the preset convergence accuracy requirements. The temperature change rate threshold should be determined by combining the heating rate of the fire temperature rise curve, the thermal response characteristics of the coating, the critical temperature control accuracy of the substrate, and the stability requirements of the simulation values. It should be determined through pre-experiment calibration or engineering experience, ensuring that the step size adjustment accurately captures the temperature abrupt change range while avoiding excessively fine step sizes that lead to low computational efficiency.

[0077] For example, in this embodiment, the simulation time step is uniformly set to a fixed value. t = 1 second. After verification, the spatial grid step size of the base material steel wire is taken as... When x=5mm, the Fourier number f0=45×1 (7850×460×0.005 2 The value ≈ 0.4985 < 0.5, which meets the stability requirements. The current coating temperature T_current is obtained from the heat transfer calculation results of the previous time step. For example, if the current coating temperature T_current is 450℃ in a certain time step, then the current expansion ratio β(450℃) = 1 + (450 - 350) is calculated according to the piecewise function of the expansion ratio. (600-350)×(30-1)=12.6; The current equivalent thermal conductivity λ_eff(450℃) is calculated as 0.08+(450-350) based on the piecewise function of equivalent thermal conductivity. (600-350)×(0.15-0.08)=0.108W·(m·K) -1 .

[0078] The current carbonized layer thickness is calculated based on the product of the initial coating thickness and the current expansion ratio. For example, in this embodiment, the initial coating thickness d_initial is the variable to be optimized, with a value range of 2.0 mm to 8.0 mm and an iteration step size of 0.1 mm. Taking an initial thickness of 6.0 mm as an example, when the current coating temperature is 450℃ and the current expansion ratio is 12.6, the current carbonized layer thickness d_char = d_initial × β(T_current) = 6.0 mm × 12.6 = 75.6 mm.

[0079] The thermal resistance of the current carbonized layer is calculated based on the ratio of the current carbonized layer thickness to the current equivalent thermal conductivity. In this embodiment, the calculation of the current carbonized layer thermal resistance further includes considering the non-uniformity of the carbonized layer along its thickness direction: when a temperature gradient exists within the carbonized layer causing uneven thermal conductivity distribution, the current carbonized layer thickness d_char is discretized along the thickness direction into N sub-layers, each with a thickness Δy_i. Based on the average temperature T_i of this sub-layer, the equivalent thermal conductivity λ_eff(T_i) of this sub-layer is determined according to the piecewise function of the equivalent thermal conductivity with respect to temperature. The total thermal resistance R of the current carbonized layer is calculated by summing the thermal resistances of each sub-layer. Where N is the number of sub-layers, x_i represents the thickness of the i-th sublayer, T_i represents the average temperature of the i-th sublayer, and λ_eff(T_i) represents the equivalent thermal conductivity of the i-th sublayer. For example, in this embodiment, to simplify calculations, the temperature gradient within the carbonized layer is not considered; that is, it is assumed that the carbonized layer temperature is uniform, and the overall thermal resistance is used for calculation. Taking an initial thickness of 6.0 mm and a current coating temperature of 450 °C as an example, the current carbonized layer thickness of 75.6 mm is converted to 0.0756 μm, and the current equivalent thermal conductivity is 0.108 W·(m·K). -1 The current thermal resistance of the carbonized layer is:

[0080] R=d_char λ_eff(T_current)=0.0756m (0.108W·m -1 ·K -1 = 0.7m²·K·W -1 To account for non-uniformity, the carbonized layer can be divided into 10 sub-layers along its thickness, each sub-layer having a thickness of... x_i = 7.56 mm, and based on the temperature distribution within the carbonized layer (assuming a linear distribution or calculated from the previous time step), the average temperature T_i of each sublayer is determined. Then, the thermal conductivity of each sublayer is calculated, and the total thermal resistance is obtained by summing these values. For example, assuming the inner wall temperature of the carbonized layer is 450℃ and the outer surface temperature is 1100℃, then the temperature distribution along the thickness direction is linear, and the average temperature of the i-th sublayer is T_i = 450 + (i - 0.5) × (1100 - 450). 10. Substituting into the λ_eff(T) formula, the thermal conductivity of each sublayer can be obtained, and the total thermal resistance R is finally calculated to be approximately 0.72 m. 2 ·K·W -1 The result is close to that of the uniform hypothesis, indicating that the uniform hypothesis has sufficient accuracy in this case.

[0081] Substituting the current thermal resistance of the carbonized layer into the substrate heat transfer control equation, the temperature value of the substrate on the fire-exposed surface at the current time step is obtained, and the temperature rise time history data of the substrate on the fire-exposed surface is updated. In this embodiment, the substrate heat transfer control equation is a one-dimensional transient heat conduction equation: Where x is the spatial coordinate variable along the radial direction of the main cable wire, in meters (m). These are partial differential operators used to characterize the partial derivative operations of multivariable functions. The first partial derivative of temperature with respect to time represents the rate of temperature change of the substrate per unit time. Let be the first partial derivative of temperature with respect to spatial coordinate x (temperature gradient), representing the temperature change per unit length along the radial direction. The heat flux divergence term represents the rate of change of heat flux per unit volume along the radial direction, used to describe the heat diffusion and accumulation law of heat conduction inside the substrate; the boundary conditions are set as follows: a fire scenario temperature rise curve T_fire(t) is applied to the outer surface of the carbonized layer, and the contact thermal resistance R at the interface between the substrate and the carbonized layer is considered. con The interfacial heat flow continuity condition is T char T represents the temperature of the inner wall of the carbonized layer. sub The substrate surface temperature is used; the initial condition is set to ambient temperature T0. Exemplarily, in this embodiment, the substrate is the main cable wire with a diameter of 6mm, and the computational domain is a radial one-dimensional domain (from the center of the wire to the surface). Spatial discretization uses the finite difference method, with 20 nodes and a time step Δt = 1s. The contact thermal resistance R_contact is empirically set to 0.01m. 2 ·K·W -1 (This value can be calibrated through preliminary testing). The outer surface temperature of the carbonized layer is directly taken from the temperature rise curve T_fire(t) in a fire scenario, i.e., during the rising stage, T_fire(t) = 20 + 108 × (t) (600) (Time t is in seconds, 10min=600s to reach 1100℃), steady stage T_fire(t)=1100℃, decay stage T_fire(t)=1100-108×((t-4200)) 1200) (It begins to decay after stabilizing for 60 minutes, and decays for 20 minutes = 1200 seconds). Within each time step, first, based on the current coating temperature (i.e., the inner wall temperature T of the carbonized layer)... char Update the thermal resistance R of the carbonized layer, then substitute it into the interfacial heat flow continuity condition, and implicitly solve for the substrate temperature distribution at the next moment using the substrate heat conduction equation, and update T. charThe new inner wall temperature of the carbonized layer (i.e., the substrate-side temperature at the interface between the carbonized layer and the substrate) is used. Through iterative calculations at each time step, the temperature rise time history data of the main cable steel wire is finally obtained throughout the entire process from the start of the fire (0 min) to the required fire resistance limit (60 min) and the subsequent decay stage. For example, for a coating with an initial thickness of 6.0 mm, the simulation results show that the surface temperature of the steel wire reaches 300℃ at 58 min, meeting the requirement of a fire resistance limit ≥ 60 min.

[0082] This embodiment introduces key parameters characterizing the true dynamic properties of coatings, such as expansion trigger temperature, stable carbonization temperature, carbonized layer thermal conductivity, and maximum expansion ratio. Within each iteration time step, the expansion ratio, equivalent thermal conductivity, carbonized layer thickness, and thermal resistance are calculated in real-time based on temperature. Furthermore, the time step is set in conjunction with numerical stability conditions, the non-uniform thermal resistance distribution along the carbonized layer thickness direction is considered, and the boundary conditions of the substrate heat transfer control equation and contact thermal resistance handling methods are clearly defined. This enables the simulation model to accurately simulate the thermal barrier behavior of the coating throughout the entire process from triggered expansion to complete carbonization. This solves the problems of misjudgment of insulation efficiency and thickness optimization deviations caused by traditional static models that neglect the nonlinearity of the expansion process, the evolution of carbonized layer thermal properties, and the dynamic coupling relationship between thickness and thermal resistance. It significantly improves simulation accuracy and repeatability, providing a reliable thickness-insulation performance mapping relationship for subsequent multi-objective optimization. This ensures that the fireproof thickness design of bridge and tunnel main cables in complex fire scenarios simultaneously meets the technical requirements of structural safety and construction economy.

[0083] In this embodiment, during the process of iterating through all values ​​of the coating thickness optimization variable according to the iteration step size and performing simulation to obtain the substrate temperature rise time history data and the thermal barrier efficiency of the carbonized layer for each thickness, firstly, since the temperature rise curve of a fire scenario includes three stages of dynamic change: heating, stabilization, and decay, and the thermal response characteristics of coatings of different thicknesses are different in each stage, if a single-stage or simplified isothermal loading method is used for the iterative simulation, it is impossible to accurately capture the coupling relationship between thickness and fire development process, resulting in distortion of the extracted substrate temperature rise extreme values. Secondly, when iterating through different thickness values, each thickness needs to be completely simulated for 90 minutes. The entire process of a fire involves a large amount of computation and low efficiency. If we simply rely on increasing the step size or refining the mesh to improve accuracy, it will significantly increase the simulation time and make it difficult to complete the rapid optimization of multiple thicknesses within the engineering cycle. Thirdly, existing simulations usually only focus on whether the final temperature rise extreme value meets the constraints during the traversal process, without conducting phased quantitative evaluation of the response speed of each thickness in the heating stage, the heat insulation maintenance capacity in the stable stage, and the temperature drop characteristics in the decay stage. This results in the optimization results meeting the extreme value requirements, but there may be a risk of local temperature rise exceeding the standard in the middle or later stages of the fire, which cannot fully guarantee fire safety throughout the entire life cycle.

[0084] It should be further explained that this embodiment obtains real-time temperature rise time history data of the substrate exposed to fire and the thermal barrier efficiency of the coating expansion and carbonization layer for various thickness values, including:

[0085] Set the initial iteration step size, step size adjustment threshold, and minimum iteration step size; starting from the lower limit of the thickness value range, select the first thickness value with the initial iteration step size. For this thickness value, based on the thickness-insulation performance simulation model, dynamically calculate the current expansion ratio, current equivalent thermal conductivity, current carbonized layer thickness, and current carbonized layer thermal resistance according to the current coating temperature within each iteration time step. Substitute the current carbonized layer thermal resistance into the substrate heat transfer control equation, and combine it with the current flame temperature as the boundary condition to solve for the substrate temperature value at the current time step. Iterate until the total time corresponding to the temperature rise curve of the fire scenario, and obtain the substrate temperature rise time history data and carbonized layer thermal barrier efficiency time history data corresponding to this thickness value. Extract the fire resistance time and substrate temperature rise extreme value corresponding to this thickness value from the temperature rise time history data.

[0086] Let the current thickness value be the first selected thickness value, and the current step size be the initial iteration step size. The current thickness sequence includes this first thickness value. Starting from the current thickness value, select the next candidate thickness value with the current step size. If the candidate thickness value exceeds the upper limit of the thickness value range, the traversal ends; otherwise, perform the above simulation process for the candidate thickness value to obtain its corresponding substrate temperature rise time history data, carbonized layer thermal barrier efficiency time history data, refractory time, and substrate temperature rise extreme value.

[0087] The candidate thickness value is compared with the previous thickness value, and the rate of change of fire resistance time is calculated, which is the absolute value of the difference in fire resistance time between the two thickness values ​​divided by the fire resistance time of the previous thickness value; at the same time, the rate of change of the extreme value of substrate temperature rise is calculated, which is the absolute value of the difference in extreme values ​​of substrate temperature rise between the two thickness values ​​divided by the extreme value of substrate temperature rise of the previous thickness value.

[0088] If the rate of change of refractory time and the rate of change of extreme temperature rise of substrate are both less than or equal to the step size adjustment threshold, then the candidate thickness value and its data are added to the thickness sequence, and the current thickness value is updated to the candidate thickness value. The next candidate thickness value is then selected at the current step size.

[0089] When the calculated rate of change of fire resistance time or the rate of change of extreme temperature rise of the substrate for the current adjacent thickness pair is greater than the step size adjustment threshold, perform the following operations:

[0090] Take the arithmetic mean of the current thickness value and the candidate thickness values ​​as the intermediate thickness value to be simulated;

[0091] Halve the current iteration step size, and use the halved step size to simulate the intermediate thickness value to obtain the substrate temperature rise time history data, carbonized layer thermal barrier efficiency time history data, and corresponding refractory time, substrate temperature rise extreme value and other data.

[0092] Insert the intermediate thickness value and its corresponding simulation data into the specified position between the current thickness value and the candidate thickness value in the thickness sequence;

[0093] Update the current iteration step size to the halved step size, and starting from the first adjacent thickness pair in the thickness sequence, recalculate the rate of change of refractory time and the rate of change of extreme temperature rise of the substrate in sequence, and repeat the comparison, insertion, and sequence update operations.

[0094] Before each comparison operation of adjacent thickness pairs, it is first determined whether the current iteration step size is less than the minimum iteration step size. If the condition is met, the iteration is terminated immediately. If the condition is not met, the comparison, insertion, and backtracking operations are continuously performed until the rate of change of refractory time and the rate of change of extreme temperature rise of the substrate for all adjacent thickness pairs in the thickness sequence are not greater than the step size adjustment threshold.

[0095] When the current step size is less than the minimum iteration step size, stop subdividing the interval and continue to select the next candidate thickness value with the current step size (i.e., the minimum iteration step size), and repeat the above process until the entire thickness value interval is covered.

[0096] The final thickness values, along with their corresponding substrate temperature rise time history data and carbonized layer thermal barrier efficiency time history data, are output as the traversal results.

[0097] For example, in this embodiment, the initial iteration step size Δd0 is set to 0.5mm (i.e., the interval for the first selection of thickness values), the step size adjustment threshold ε is 5% (used to determine whether the upper limit of the rate of change of the step size needs to be refined), and the minimum iteration step size Δd_min is 0.1mm (the minimum allowable thickness interval). Starting from the lower limit of the thickness value range of 2.0mm, thickness values ​​are selected sequentially with Δd0: First, simulation is performed for d1=2.0mm, obtaining the fire resistance time t_crit(d1)=30min (the time when the substrate temperature first reaches 300℃) and the substrate temperature rise extreme value T_max(d1)=320℃ (the highest temperature in the entire process); then simulation is performed for d2=2.5mm, obtaining t_crit(d2)=35min and T_max(d2)=290℃. In this embodiment, d1 is the first coating thickness value participating in the simulation calculation within the thickness traversal sequence, corresponding to the initial value of the lower limit of the thickness optimization range; d2 is the second coating thickness value participating in the simulation calculation obtained by increasing the initial iteration step size.

[0098] Calculate the rate of change of fire resistance time δ_t = |t_crit(d2) - t_crit(d1)| t_crit(d1)≈16.7%, substrate temperature rise extreme change rate δ_T=|T_max(d2)-T_max(d1)| Since T_max(d1)≈9.4%, and both are greater than ε, an intermediate thickness d_mid=(d1+d2) is inserted between d1 and d2. 2 = 2.25mm, and using half the current step size of 0.25mm for simulation, t_crit(d_mid) = 32.5min and T_max(d_mid) = 305℃ are obtained. After insertion, comparing d1 and d_mid: δ_t1 = 8.3% > ε, δ_T1 = 4.7% ≤ ε, so d_mid2 = (d1 + d_mid) needs to be inserted again. Simulate 2 = 2.125 mm with a step size of 0.125 mm; simultaneously compare d_mid2 and d2: δ_t2 = 7.7% > ε, δ_T2 = 4.9% ≤ ε, insert d_mid3 = 2.375 mm. Repeat the above process until δ_t and δ_T between all adjacent thickness values ​​are ≤ ε or the current step size is less than Δd_min, finally obtaining the thickness sequence that meets the accuracy requirements and its corresponding temperature rise time history data and thermal resistance efficiency time history data, which are output as the traversal result. In this embodiment, δ_t1 is the rate of change of fire resistance time corresponding to the first pair of adjacent thicknesses (i.e., d1 and the inserted intermediate thickness d_mid); δ_T1 is the rate of change of extreme temperature rise of the substrate corresponding to the first pair of adjacent thicknesses (i.e., d1 and the inserted intermediate thickness d_mid); δ_t2 is the rate of change of fire resistance time corresponding to the second pair of adjacent thicknesses (i.e., the inserted intermediate thicknesses d_mid and d2); δ_T2 is the rate of change of extreme temperature rise of the substrate corresponding to the second pair of adjacent thicknesses (i.e., the inserted intermediate thicknesses d_mid and d2).

[0099] This embodiment introduces key parameters characterizing the true dynamic properties of coatings, such as expansion trigger temperature, stable carbonization temperature, thermal conductivity of the carbonized layer, and maximum expansion ratio. Within each iteration time step, the expansion ratio, equivalent thermal conductivity, carbonized layer thickness, and thermal resistance are calculated in real-time based on temperature. Simultaneously, an adaptive step-size traversal mechanism dynamically refines the thickness value based on the rate of change of the fire resistance duration and the extreme temperature rise of the substrate. This enables the simulation model to accurately simulate the thermal barrier behavior of the coating throughout the entire process from triggered expansion to complete carbonization. This solves the problems of misjudgment of insulation efficiency and thickness optimization deviations caused by traditional static models that ignore the nonlinearity of the expansion process, the evolution of the thermal properties of the carbonized layer, and the dynamic coupling relationship between thickness and thermal resistance. This significantly improves simulation accuracy and repeatability. Furthermore, through adaptive step-size traversal, the number of simulations for redundant thicknesses is effectively reduced while ensuring the accuracy of key performance indicator calculations, improving optimization efficiency. This ensures that the fireproof thickness design of bridge and tunnel fire-exposed surfaces in complex fire scenarios can simultaneously meet the technical requirements of structural safety and construction economy.

[0100] It should be further explained that the process of obtaining the thermal performance indicators and engineering compatibility indicators in this embodiment includes:

[0101] For each thickness value d, the fire resistance time t_crit(d) and the extreme temperature rise value T_max(d) of the substrate are extracted from the substrate temperature rise time history data {T_sub(t)} corresponding to that thickness as thermal insulation performance indicators. The fire resistance time t_crit(d) is defined as the moment when the substrate temperature first reaches the substrate critical temperature of 300℃ (if it does not reach it throughout the entire process, the total fire duration of 90min is taken), and the extreme temperature rise value T_max(d) of the substrate is defined as the highest temperature value in the substrate temperature rise time history data. The coating amount per unit area M(d) = d × r_coat is calculated based on the product of the thickness value d and the application coverage rate r_coat, which serves as the first engineering adaptation indicator. The construction temperature margin ΔT = T_env - T_cure is calculated based on the difference between the construction ambient temperature T_env and the curing temperature threshold T_cure, which serves as the second engineering adaptation indicator. For example, in this embodiment, the application rate r_coat is taken as 1.5 kg·(m³) based on the "Fireproof Coatings for Steel Structures" (issued by the State Administration for Market Regulation and the Standardization Administration of China, GB14907-2018, pp. 3, 6-8, June 2019) and the coating product instructions. 2 ·mm) -1 This means that the coating consumption per square meter is 1.5 kg per millimeter of thickness; the curing temperature threshold T_cure is set to 5℃ (requiring the construction temperature to be no lower than 5℃), and the construction ambient temperature T_env is set to 20℃ (simulating normal temperature construction conditions). Taking the thickness value d1=2.0mm in the aforementioned traversal results as an example, its fire resistance time t_crit(2.0)=30min, the extreme temperature rise of the substrate T_max(2.0)=320℃, and the coating consumption per unit area M(2.0)=2.0mm×1.5kg·(m 2 ·mm) -1 =3.0 kg·m -2 The construction temperature margin ΔT = 20℃ - 5℃ = 15℃; for a thickness d2 = 2.5mm, the fire resistance time t_crit(2.5) = 35min, the maximum temperature rise of the substrate T_max(2.5) = 290℃, and the coating consumption per unit area M(2.5) = 2.5 × 1.5 = 3.75 kg·m -2 The construction temperature margin ΔT = 15℃ remains unchanged. These thermal insulation performance indicators and engineering adaptability indicators will serve as inputs to the subsequent multi-objective optimization decision function for comprehensive quantitative calculation.

[0102] It should be further explained that the comprehensive quantitative evaluation value calculated in this embodiment for each thickness value includes:

[0103] For each thickness value d, the comprehensive thermal insulation performance index I_th(d) is calculated based on its fire resistance time t_crit(d) and the extreme temperature rise of the substrate T_max(d). The calculation formula is I_th(d) = ω_t (t_crit(d) t_total)+ω_T (1-T_max(d) T_limit), where t_total is the total duration corresponding to the temperature rise curve of the fire scenario, T_limit is the critical temperature of the substrate, and ω_t and ω_T are preset sub-weighting coefficients for thermal insulation performance, with ω_t + ω_T = 1; it should be further explained that the preset basis for the thermal insulation performance sub-weighting coefficients ω_t and ω_T includes: assigning values ​​according to the relative importance of the fire resistance time requirement of the fire-protected surface and the critical temperature control of the substrate in the fire protection design objectives; increasing the value of ω_t when the fire resistance time is the main design constraint, and increasing the value of ω_t when the substrate temperature rise control is the main design constraint. Increase the value of ω_T; at the same time, based on the dimensional differences and numerical distribution range of the fire resistance time t_crit(d) and the extreme temperature rise of the substrate T_max(d), set ω_t and ω_T to balance their contributions to the comprehensive thermal insulation performance index after weighted summation, avoiding the dominance of a single index in the calculation results; in addition, the values ​​of ω_t and ω_T can be determined by pairwise comparison of the fire resistance time and the extreme temperature rise of the substrate using the analytic hierarchy process or expert experience scoring method, or calibrated by regression analysis of historical engineering data, and dynamically adjusted according to the actual application scenario in the subsequent multi-objective optimization process.

[0104] The construction cost index I_co(d) is calculated based on the amount of paint used per unit area M(d) for each thickness value d. The calculation formula is I_co(d) = 1 - M(d). M_max, where M_max is the preset maximum allowable amount of paint;

[0105] The process adaptability index I_pr(d) is calculated based on the construction temperature margin ΔT(d) corresponding to the thickness value d. The calculation formula is I_pr(d) = ΔT(d). ΔT_max, where ΔT_max is the preset maximum allowable temperature margin;

[0106] Construct a multi-objective optimization decision function F(d)=α I_th(d)+β I_co(d)+γ I_pr(d), where α, β, and γ are preset weight coefficients and α+β+γ=1; it should be further explained that the preset weight coefficients α, β, and γ in the multi-objective optimization judgment function described in this embodiment are assigned in layers according to the actual needs of the fire protection engineering of the bridge and tunnel fire-exposed surface: where α corresponds to the weight of thermal insulation performance. Based on the core defense objective of the main cable of the bridge being ≤300℃ for the steel wire temperature and ≥60min for the fire resistance limit ≥60min under a 100MW fire scale, combined with the requirements for structural safety redundancy in the "Technical Specification for Comprehensive Fire-Resistant Sealing Protection of Bridge Load-Bearing Cables" (issued by China Communications and Transportation Association, T / CCTAS61-2023, pp. 3, 13-14, October 2023), the value of α is set by those skilled in the art to be between 0.5 and 0.7. To ensure fire safety is the top priority; β corresponds to the weight of construction cost, determined by sensitivity analysis of coating usage per unit area and economic indicators based on the unit price of high-performance aerogel coatings, construction coverage rate, and project budget constraints; γ corresponds to the weight of process adaptability, determined by feasibility assessment based on the matching requirements of construction environment temperature and curing temperature threshold, combined with seasonal changes and time constraints in bridge and tunnel construction; the final values ​​of α, β, and γ are calculated by pairwise comparison of the relative importance of thermal insulation performance, construction cost, and process adaptability in bridge and tunnel fire protection projects using the analytic hierarchy process, or determined by regression fitting of historical project data through orthogonal experiments, and dynamically corrected according to actual application scenarios during multi-objective optimization.

[0107] Substitute I_th(d), I_co(d), and I_pr(d) corresponding to each thickness value into the multi-objective optimization judgment function to calculate the comprehensive quantitative evaluation value F(d) corresponding to each thickness value.

[0108] Furthermore, the following technical problems still exist in the construction and calculation process of the multi-objective optimization judgment function described in this embodiment: First, the comprehensive thermal insulation performance index I_th(d) simultaneously includes two sub-indices: fire resistance time t_crit(d) and substrate temperature rise extreme value T_max(d). However, the two have different dimensions and large differences in numerical range. Direct weighted summation may lead to a certain index dominating the calculation result, failing to truly reflect the comprehensive level of thermal insulation performance. Second, if the normalization benchmarks M_max and ΔT_max of the construction cost index I_co(d) and the process adaptability index I_pr(d) are not set properly, it may lead to an excessively wide distribution of index values ​​under different thicknesses. The concentration or dispersion of the target material affects the distinguishability of multi-objective optimization. Third, after the comprehensive quantitative evaluation value F(d) corresponding to each thickness value is calculated, it needs to be further verified with performance constraints and engineering constraints. However, F(d) itself is only a dimensionless evaluation value and cannot directly reflect whether the hard constraints such as substrate temperature rise ≤ critical temperature and fire resistance time ≥ design threshold are met. It is necessary to establish a correlation judgment mechanism between constraints and evaluation values. Fourth, when selecting the optimal thickness value, there may be multiple thicknesses that meet all constraints and have similar F(d) values. The existing judgment function does not consider the secondary selection strategy in this case, making it difficult to ensure the uniqueness of the output results and the engineering applicability.

[0109] It should be further explained that, after constructing the multi-objective optimization decision function and calculating the comprehensive quantitative evaluation value F(d) corresponding to each thickness value, this embodiment also includes the following steps:

[0110] The thickness values ​​d and their corresponding fire resistance time t_crit(d), substrate temperature rise extreme value T_max(d), coating consumption per unit area M(d), construction temperature margin ΔT(d), and comprehensive quantitative evaluation value F(d) are associated and stored to form a comprehensive evaluation dataset of thickness-performance-cost-process.

[0111] For each thickness value d in the comprehensive evaluation dataset, determine whether it simultaneously satisfies the performance constraints t_crit(d)≥t_design and T_max(d)≤T_limit, and the engineering constraints M(d)≤M_max_limit and ΔT(d)≥0, where t_design is a preset design threshold and M_max_limit is the maximum allowable amount of coating corresponding to the construction loss constraint;

[0112] The thickness values ​​that satisfy all constraints are selected to form a candidate thickness subset D_candidate={d|t_crit(d)≥t_design,T_max(d)≤T_limit,M(d)≤M_max_limit,ΔT(d)≥0};

[0113] In the candidate thickness subset D_candidate, the thicknesses are sorted in descending order of the comprehensive quantitative evaluation value F(d), and the thickness value corresponding to the maximum value of F(d) is selected as the preliminary optimal thickness d_opt;

[0114] If multiple thickness values ​​have the same F(d) value or the difference is less than the preset evaluation value tolerance threshold δ_F, then the fire resistance time t_crit(d) of these thickness values ​​is further compared, and the one with the longest fire resistance time is selected as the final optimal thickness; if the fire resistance time is still the same, then the one with the smallest extreme value of substrate temperature rise T_max(d) is selected as the final optimal thickness.

[0115] The final determined optimal thickness value and its associated construction parameters (including paint usage per unit area M(d_opt), construction temperature margin ΔT(d_opt), etc.) are output as the optimization results.

[0116] This embodiment addresses technical issues encountered in multi-objective optimization processes, such as dimensional differences and contribution imbalances among sub-indicators of thermal insulation performance, sensitivity to normalization benchmark settings, disconnect between comprehensive evaluation values ​​and hard constraints, and the dilemma of selecting the best from multiple candidate values. It constructs a comprehensive thermal insulation performance index that includes fire resistance time and extreme temperature rise of the substrate, and introduces sub-weighting coefficients ω_t and ω_T to achieve dimensional uniformity and contribution balance. Simultaneously, it constructs construction cost and process adaptability indices based on coating usage per unit area and construction temperature margin. Furthermore, it uses the analytic hierarchy process (AHP) or historical data regression to calibrate the multi-objective weighting coefficients α, β, and γ, enabling scientific weighting and collaborative optimization of thermal insulation performance, construction cost, and process adaptability under the actual needs of bridge and tunnel fire protection projects. Finally, it associates and stores each thickness value and its corresponding performance, cost, and process indices with the comprehensive evaluation value to form comprehensive evaluation data. The system performs joint verification of performance and engineering constraints on each thickness value in the dataset, filters out a subset of candidate thicknesses that meet all hard constraints, sorts the candidate subsets by comprehensive evaluation value and selects the optimal value, and introduces a secondary selection rule based on fire resistance time and substrate temperature rise extreme value when evaluation values ​​are similar. This ensures that the final output optimal thickness not only meets rigid requirements such as substrate temperature rise ≤ critical temperature, fire resistance time ≥ design threshold, coating dosage ≤ maximum allowable value, and construction temperature ≥ curing threshold, but also achieves optimality in multi-objective comprehensive trade-off. At the same time, it avoids the ambiguity of results caused by similar evaluation values, significantly improves the uniqueness, engineering applicability and decision reliability of the optimization results, and fundamentally solves the technical problem that the existing fireproof coating thickness design is difficult to take into account the dynamic characteristics of fire scenarios, the evolution of coating thermal performance and the actual constraints of engineering construction.

[0117] It should be further noted that this embodiment includes the following steps when determining the normalization benchmarks M_max and ΔT_max:

[0118] Based on the budget ceiling and material unit price of the bridge and tunnel fire protection project, the economic threshold of coating usage per unit area is calculated. Combined with the construction coating rate r_coat, the corresponding maximum allowable coating thickness is deduced. Considering a construction loss margin of 5% to 10%, the value of M_max is finally determined. At the same time, based on the historical data of extreme ambient temperature in the area where the bridge and tunnel are located and the requirements of the construction season, the acceptable lower limit of the construction ambient temperature is set. Using the curing temperature threshold as the benchmark, the maximum allowable temperature margin ΔT_max=T_env_max-T_cure is calculated, where T_env_max is the upper limit design value of the construction ambient temperature.

[0119] It should be further explained that, after constructing the multi-objective optimization decision function, this embodiment also includes a dynamic adjustment step for the weight coefficients:

[0120] After obtaining the candidate thickness subset D_candidate, the distribution dispersion of the comprehensive quantitative evaluation value F(d) corresponding to each thickness value is calculated. If the difference between the maximum and second largest F(d) values ​​is less than the preset evaluation value tolerance threshold δ_F, and there are multiple thickness values ​​in the candidate thickness subset, the values ​​of α, β, and γ are re-evaluated according to the actual needs of the current project: if the risk of construction cost overrun is high, β is appropriately increased and α and γ are appropriately decreased; if the construction environment temperature is close to the curing threshold, γ is appropriately increased and α and β are appropriately decreased; after adjustment, F(d) is recalculated and sorted until the weight coefficients are stable or the preset number of iterations is reached.

[0121] It should be further noted that this embodiment also includes a model calibration step after the simulation model is built:

[0122] Using the actual fire test data of the scaled-down model of the main cable, the measured temperature rise time history data of the substrate at a specific thickness was extracted and compared with the simulation results under the same working conditions to calculate the temperature deviation at each time point. Based on the deviation, the values ​​of contact thermal resistance R_contact and thermal conductivity λ_char of the carbonized layer were corrected by least squares inversion, so that the average absolute error between the simulation model and the test data was controlled within 5℃. The calibrated parameters were then re-substituted into the simulation model to update the thickness-insulation performance mapping relationship.

[0123] It should be further noted that this embodiment introduces a coating loss coefficient for correction when calculating the amount of coating used per unit area:

[0124] Based on the loss coefficient k_loss (valued between 1.05 and 1.15) corresponding to the construction process (such as troweling or spraying), the actual paint consumption per unit area is corrected to M_actual(d) = d × r_coat × k_loss. M_actual(d) is then used as the comparison object in the engineering constraints, i.e., M_actual(d) ≤ M_max_limit. Simultaneously, the calculation formula for the construction cost index I_co(d) is adjusted accordingly to I_co(d) = 1 - M_actual(d). M_max is used to more accurately reflect the economic efficiency of construction.

[0125] Example 2

[0126] Please see Figure 5 Another embodiment of the present invention provides a parameter simulation optimization system for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels, comprising:

[0127] The simulation construction module is used to obtain a set of parameters related to the protection of the fire-exposed surface, build a thickness-insulation performance simulation model based on the parameter set, set the value range and iteration step size of the coating thickness optimization variable, and configure performance constraints and engineering constraints. The parameter set includes the substrate critical temperature, the temperature rise curve of the fire scenario, the coating thermal conductivity, the coating expansion ratio, the application rate, and the curing temperature threshold. The performance constraints are that the temperature rise of the fire-exposed substrate is ≤ the substrate critical temperature and the fire resistance time is ≥ the preset design threshold. The engineering constraints are that the coating loss coefficient is ≤ the preset loss value and the application temperature is not lower than the curing temperature threshold.

[0128] The simulation module is traversed, the associated parameter set is input into the thickness-thermal insulation performance simulation model, and all values ​​of the coating thickness optimization variable are traversed according to the iteration step size and the simulation is performed to obtain the real-time temperature rise time history data of the fire-exposed substrate and the thermal barrier efficiency of the coating expansion carbonization layer under each thickness value.

[0129] The index calculation module determines the thermal insulation performance index corresponding to each thickness based on the temperature rise time history data and thermal barrier efficiency, and determines the engineering adaptability index corresponding to each thickness based on the construction coating rate and curing temperature threshold.

[0130] The multi-objective optimization module constructs a multi-objective optimization judgment function, assigns preset weight coefficients to thermal insulation performance, construction cost and process adaptability respectively, substitutes the thermal insulation performance index and engineering adaptability index corresponding to each thickness value into the multi-objective optimization judgment function, and calculates the comprehensive quantitative evaluation value corresponding to each thickness value.

[0131] The verification output module verifies whether the comprehensive quantitative evaluation value corresponding to each thickness value simultaneously meets the performance constraints and engineering constraints. It then selects the coating thickness value that meets all constraints and has the optimal comprehensive quantitative evaluation value, and generates an optimization result that includes the optimal coating thickness and matching construction parameters.

[0132] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments under the guidance of the present invention without departing from the spirit and scope of the claims. All of these variations are within the protection scope of the present invention.

Claims

1. A method for parameter simulation optimization of the thickness of a fireproof coating for a bridge tunnel fire surface, characterized by, include: Obtain the set of parameters related to the protection of the fire-exposed surface, build a thickness-thermal insulation performance simulation model based on the set of parameters, set the value range and iteration step size of the coating thickness optimization variable, and configure performance constraints and engineering constraints. The associated parameter set is input into the thickness-thermal insulation performance simulation model. All values ​​of the coating thickness optimization variable are traversed according to the iteration step size and simulation is performed to obtain the real-time temperature rise time history data of the substrate on the fire-exposed surface and the thermal barrier efficiency of the coating expansion carbonization layer under each thickness value. Based on the temperature rise time history data and thermal barrier efficiency, the thermal insulation performance index corresponding to each thickness is determined, and the engineering adaptability index corresponding to each thickness is determined based on the construction coating rate and curing temperature threshold. A multi-objective optimization judgment function is constructed, and preset weight coefficients are assigned to thermal insulation performance, construction cost and process adaptability respectively. The thermal insulation performance index and engineering adaptability index corresponding to each thickness value are substituted into the multi-objective optimization judgment function to calculate the comprehensive quantitative evaluation value corresponding to each thickness value. Verify whether the comprehensive quantitative evaluation value corresponding to each thickness value simultaneously satisfies the performance constraints and engineering constraints. Select the coating thickness value that satisfies all constraints and has the best comprehensive quantitative evaluation value, and generate an optimization result that includes the optimal coating thickness and matching construction parameters.

2. The method for parametric simulation optimization of the thickness of the fireproof coating for the bridge-tunnel fire surface as claimed in claim 1, characterized in that, A thickness-insulation performance simulation model is built based on the aforementioned parameter set, including: Obtain the expansion trigger temperature, stable carbonization temperature, initial thermal conductivity of the coating, thermal conductivity of the carbonized layer, minimum expansion ratio, and maximum expansion ratio from the parameter set. Based on the expansion trigger temperature and the stable carbonization temperature, the temperature range during the fire temperature rise process is divided into an unexpanded zone, an expansion transition zone, and a fully carbonized zone. A piecewise function of the expansion ratio with respect to temperature is established. In the expansion transition zone, the expansion ratio monotonically increases from the minimum expansion ratio to the maximum expansion ratio according to a preset interpolation model. In the unexpanded zone and the fully carbonized zone, the expansion ratio is always equal to the minimum expansion ratio and the maximum expansion ratio, respectively. Based on the initial thermal conductivity of the coating and the thermal conductivity of the carbonized layer, a piecewise function of the equivalent thermal conductivity with respect to temperature is established. In the unexpanded region, the equivalent thermal conductivity is equal to the initial thermal conductivity of the coating; in the fully carbonized region, the equivalent thermal conductivity is equal to the thermal conductivity of the carbonized layer; and in the expansion transition region, the equivalent thermal conductivity transitions from the initial thermal conductivity of the coating to the thermal conductivity of the carbonized layer according to the degree of carbonization function.

3. The method for parametric simulation optimization of the thickness of the fireproof coating for the bridge-tunnel portal according to claim 2, characterized in that, The thickness-insulation performance simulation model built based on the parameter set also includes: Within each iteration time step of the simulation model, the current coating temperature is obtained, the current expansion ratio is determined according to the piecewise function of the expansion ratio with respect to temperature, and the current equivalent thermal conductivity is determined according to the piecewise function of the equivalent thermal conductivity with respect to temperature. The current carbonized layer thickness is calculated by multiplying the initial coating thickness by the current expansion ratio. Calculate the thermal resistance of the current carbonized layer based on the ratio of the current carbonized layer thickness to the current equivalent thermal conductivity. Substitute the current thermal resistance of the carbonized layer into the heat transfer control equation of the substrate to obtain the temperature value of the substrate on the fire-exposed surface at the current time step, and update the temperature rise time history data of the substrate on the fire-exposed surface.

4. The parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels as described in claim 3, characterized in that, The acquisition of real-time temperature rise time history data of the substrate exposed to fire and the thermal barrier efficiency of the coating expansion and carbonization layer for various thickness values ​​includes: Set the initial iteration step size, set the step size adjustment threshold, and set the minimum iteration step size; Starting from the lower limit of the value range, the current thickness value is selected with the initial iteration step size. For the current thickness value, based on the thickness-thermal insulation performance simulation model, the current expansion ratio, current equivalent thermal conductivity, current carbonized layer thickness and current carbonized layer thermal resistance are dynamically calculated according to the current coating temperature within each iteration time step. Substitute the current thermal resistance of the carbonized layer into the heat transfer control equation of the substrate, and combine the flame temperature at the current moment as the boundary condition to solve for the temperature value of the substrate at the current time step. Iterate to the total time corresponding to the temperature rise curve of the fire scene to obtain the substrate temperature rise time history data and carbonized layer thermal barrier efficiency time history data corresponding to the thickness value. Extract the fire resistance time and extreme temperature rise value of the substrate corresponding to the current thickness value from the substrate temperature rise time history data. The fire resistance time refers to the moment when the substrate temperature first reaches the substrate critical temperature. If it does not reach the critical temperature throughout the entire process, the total fire duration is taken. The current thickness value is compared with the fire resistance time and the extreme temperature rise of the substrate corresponding to the previous thickness value. The change rate of fire resistance time and the change rate of extreme temperature rise of the substrate are calculated. The change rate refers to the absolute value of the difference between the current thickness value and the corresponding index of the previous thickness value divided by the corresponding index of the previous thickness value.

5. The parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels as described in claim 4, characterized in that, The acquisition of real-time temperature rise time history data of the substrate exposed to fire and the thermal barrier efficiency of the coating expansion and carbonization layer for various thickness values ​​also includes: Determine whether the rate of change of the fire resistance time or the rate of change of the extreme value of the substrate temperature rise is greater than the step size adjustment threshold. For the current adjacent thickness value pairs, compare the rate of change of the fire resistance time with the rate of change of the extreme temperature rise of the substrate; if either rate of change is greater than the step size adjustment threshold, insert an intermediate thickness value between the thickness pairs, complete the simulation of the intermediate thickness value with half of the current iteration step size and insert the sequence, and backtrack to the beginning position of the thickness pair to re-execute the comparison and insertion operation; if the rate of change of all adjacent thickness value pairs is not greater than the step size adjustment threshold, or the current iteration step size is less than the minimum iteration step size, then terminate the iteration. The final thickness values, along with their corresponding substrate temperature rise time history data and carbonized layer thermal barrier efficiency time history data, are output as the traversal results.

6. The parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels as described in claim 5, characterized in that, The process of obtaining the thermal insulation performance indicators and engineering compatibility indicators includes: For each thickness value, the fire resistance time and the extreme value of the substrate temperature rise are extracted from the substrate temperature rise time history data corresponding to that thickness as thermal insulation performance indicators. The fire resistance time refers to the moment when the substrate temperature first reaches the substrate critical temperature. If it does not reach the critical temperature throughout the process, the total time corresponding to the temperature rise curve of the fire scenario is taken. The extreme value of the substrate temperature rise refers to the highest temperature value in the substrate temperature rise time history data. The amount of paint used per unit area is calculated by multiplying the thickness value by the application rate, which serves as the first engineering compatibility index. The construction temperature margin is calculated based on the difference between the construction ambient temperature and the curing temperature threshold, which serves as the second engineering compatibility index.

7. The parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels as described in claim 6, characterized in that, The calculation yields a comprehensive quantitative evaluation value corresponding to each thickness value, including: For each thickness value d, the comprehensive thermal insulation performance index I_th(d) is calculated based on its fire resistance time t_crit(d) and the extreme temperature rise of the substrate T_max(d); The construction cost index I_co(d) is calculated based on the amount of paint used per unit area M(d) for each thickness value d; The process adaptability index I_pr(d) is calculated based on the construction temperature margin ΔT(d) corresponding to the thickness value d; Construct a multi-objective optimization decision function; Substitute I_th(d), I_co(d), and I_pr(d) corresponding to each thickness value into the multi-objective optimization judgment function to calculate the comprehensive quantitative evaluation value F(d) corresponding to each thickness value.

8. The parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels as described in claim 7, characterized in that, The calculation of the comprehensive quantitative evaluation value corresponding to each thickness value also includes: The thickness values ​​and their corresponding fire resistance time, substrate temperature rise extreme value, coating amount per unit area, construction temperature margin, and comprehensive quantitative evaluation value are associated and stored to form a comprehensive evaluation dataset of thickness-performance-cost-process. For each thickness value in the comprehensive evaluation dataset, determine whether it simultaneously meets the performance constraints of fire resistance time not less than the preset design threshold and substrate temperature rise extreme value not exceeding substrate critical temperature, and the engineering constraints of coating amount per unit area not exceeding the maximum allowable coating amount corresponding to construction loss constraint and construction temperature margin not less than zero. The thickness values ​​that satisfy all constraints are selected to form a candidate thickness subset; In the candidate thickness subset, the thicknesses are sorted in descending order of comprehensive quantitative evaluation values, and the thickness corresponding to the maximum comprehensive quantitative evaluation value is selected as the preliminary optimal thickness. If multiple thickness values ​​have the same comprehensive quantitative evaluation value or the difference is less than the preset evaluation value tolerance threshold, then the fire resistance time of these thickness values ​​is further compared, and the one with the longest fire resistance time is selected as the final optimal thickness; if the fire resistance time is still the same, then the one with the smallest extreme temperature rise of the substrate is selected as the final optimal thickness. The final determined optimal thickness value and its associated construction parameters are output as the optimization result.

9. The parameter simulation optimization method for the thickness of fire-resistant coatings on fire-exposed surfaces of bridges and tunnels as described in claim 1, characterized in that, The parameter set includes the substrate critical temperature, fire scenario temperature rise curve, coating thermal conductivity, coating expansion ratio, application coverage, and curing temperature threshold. The performance constraints are that the temperature rise of the fire-exposed substrate is ≤ the substrate critical temperature and the fire resistance time is ≥ the preset design threshold. The engineering constraints are that the coating loss coefficient is ≤ the preset loss value and the application temperature is not lower than the curing temperature threshold. The fire scenario temperature rise curve is a simulated hydrocarbon combustion HC temperature rise curve, which includes a sequentially connected heating stage, a stabilization stage, and a decay stage. The heating stage is when the temperature linearly rises from the initial temperature to 1100℃ within 10 minutes. The stabilization stage is when the temperature remains constant at 1100℃ for 60 minutes. The decay stage is when the temperature linearly drops from 1100℃ to the initial temperature for 20 minutes.

10. A parameter simulation optimization system for the thickness of fire-retardant coatings on fire-exposed surfaces of bridges and tunnels, implemented based on the parameter simulation optimization method for the thickness of fire-retardant coatings on fire-exposed surfaces of bridges and tunnels as described in any one of claims 1-9, characterized in that, include: The simulation construction module is used to obtain a set of parameters related to the protection of the fire-exposed surface, build a thickness-insulation performance simulation model based on the parameter set, set the value range and iteration step size of the coating thickness optimization variable, and configure performance constraints and engineering constraints. The parameter set includes the substrate critical temperature, the temperature rise curve of the fire scenario, the coating thermal conductivity, the coating expansion ratio, the application rate, and the curing temperature threshold. The performance constraints are that the temperature rise of the fire-exposed substrate is ≤ the substrate critical temperature and the fire resistance time is ≥ the preset design threshold. The engineering constraints are that the coating loss coefficient is ≤ the preset loss value and the application temperature is not lower than the curing temperature threshold. The simulation module is traversed, the associated parameter set is input into the thickness-thermal insulation performance simulation model, and all values ​​of the coating thickness optimization variable are traversed according to the iteration step size and the simulation is performed to obtain the real-time temperature rise time history data of the fire-exposed substrate and the thermal barrier efficiency of the coating expansion carbonization layer under each thickness value. The index calculation module determines the thermal insulation performance index corresponding to each thickness based on the temperature rise time history data and thermal barrier efficiency, and determines the engineering adaptability index corresponding to each thickness based on the construction coating rate and curing temperature threshold. The multi-objective optimization module constructs a multi-objective optimization judgment function, assigns preset weight coefficients to thermal insulation performance, construction cost and process adaptability respectively, substitutes the thermal insulation performance index and engineering adaptability index corresponding to each thickness value into the multi-objective optimization judgment function, and calculates the comprehensive quantitative evaluation value corresponding to each thickness value. The verification output module verifies whether the comprehensive quantitative evaluation value corresponding to each thickness value simultaneously meets the performance constraints and engineering constraints. It then selects the coating thickness value that meets all constraints and has the optimal comprehensive quantitative evaluation value, and generates an optimization result that includes the optimal coating thickness and matching construction parameters.

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