Concrete structure durability prediction and intelligent early warning method
By employing a multi-field coupling effect and adaptive deep learning optimization method, the problems of incomplete multi-field coupling and insufficient adaptability in the durability prediction and early warning of concrete structures are solved. This enables high-precision prediction and dynamic early warning in complex environments, thereby improving the life prediction and health monitoring capabilities of concrete structures.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- GUANGXI NEW DEV TRANSPORT GRP CO LTD
- Filing Date
- 2025-11-24
- Publication Date
- 2026-04-21
AI Technical Summary
Existing methods for predicting and warning the durability of concrete structures suffer from incomplete multi-field coupling, lack of consistent multi-scale mapping, reliance on experience for threshold setting, lack of uncertainty quantification mechanisms, lack of adaptive calibration capabilities, and insufficient generalization performance under extreme environments. These issues result in insufficient prediction accuracy and a lack of hierarchical early warning mechanisms.
By employing a multi-field coupling effect and adaptive deep learning optimization method, and using a multi-scale chloride ion diffusion-reaction-damage coupling model, combined with temporal deep learning and Monte Carlo Dropout to quantify uncertainty, and utilizing a joint threshold determination of reliability and maintenance cost, damage identification, remaining life prediction and three-level intelligent early warning are achieved.
It improves the prediction accuracy and interpretability of concrete structures in complex environments, realizes adaptive optimization of model parameters and dynamic adjustment of early warning thresholds, provides prediction output with confidence intervals, and ensures the stability and reliability of the prediction system during its service life.
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Figure CN121902240A_ABST
Abstract
Description
Technical Field
[0001] This invention belongs to the interdisciplinary field of civil engineering and materials science, specifically relating to a method for predicting the durability of concrete structures and providing intelligent early warning. This method is applicable to the life-cycle safety assessment and operation and maintenance decisions of infrastructure primarily composed of concrete, such as bridges, tunnels, hydraulic structures, port structures, and highway subgrades and pavements. Background Technology
[0002] With the rapid development of transportation, water conservancy, and urban infrastructure, a large number of concrete structures have entered the medium- and long-term service stage. These structures are subjected to the coupled effects of multiple fields such as temperature, humidity, chloride ion transport, and external loads for a long time, which makes them prone to deterioration processes such as pore penetration, chemical reactions, steel corrosion, and crack propagation, leading to stiffness reduction, load-bearing capacity reduction, and durability failure.
[0003] Existing methods for predicting and monitoring the durability of concrete structures mainly include the following technical approaches:
[0004] (1) Degradation model based on physicochemical mechanism
[0005] These models typically describe the chloride ion migration, carbonization reaction, and mechanical property degradation processes using diffusion equations, electrochemical corrosion models, or damage mechanics models. Their advantage lies in their good physical interpretability, but they are computationally complex, difficult to calibrate parameters, and lack adaptability to changes in the field environment.
[0006] (2) Model based on empirical statistics and lifespan regression
[0007] This method uses monitoring or experimental data to estimate lifetime indicators through multiple regression, Bayesian updates, or reliability analysis. While computationally simple, it is highly dependent on the representativeness and stability of the data and struggles to explain the nonlinear evolution patterns under complex environmental coupling.
[0008] (3) Predictive models based on machine learning or deep learning
[0009] In recent years, algorithms such as Convolutional Neural Networks (CNN), Recurrent Neural Networks (RNN), and Gated Recurrent Units (GRU) have been used for multi-source monitoring data analysis, and can capture time series features relatively well. However, these models are mostly "black box" algorithms, lacking physical constraints and interpretability; at the same time, their prediction accuracy and stability decrease significantly in data distribution drift or extreme environments.
[0010] (4) Monitoring and alarm methods based on fixed thresholds
[0011] These methods typically determine the state based on preset strain, temperature, or chloride ion thresholds, making them suitable for simple monitoring scenarios. However, their alarm thresholds often rely on empirical settings and lack dynamic adjustment mechanisms, making it difficult to balance the risks of false alarms and missed alarms, and also unable to achieve lifespan prediction and risk classification.
[0012] In summary, existing technologies have the following significant shortcomings in predicting and providing early warning of the durability of concrete structures:
[0013] (1) Incomplete multi-field coupling: Most models treat temperature, humidity, stress and chloride ion migration separately, failing to form a unified multi-field coupling expression, which leads to a decrease in prediction accuracy in complex environments.
[0014] (2) Lack of multi-scale consistent mapping: The degradation parameters of macroscopic components are difficult to correspond to the microscopic porosity and crack transmission characteristics, resulting in physical faults that limit the interpretability and engineering applicability of the model.
[0015] (3) Threshold setting depends on experience: Fixed threshold alarms lack dynamic optimization mechanism and cannot be adaptively adjusted according to changes in structural status or service environment, resulting in false alarms or missed alarms.
[0016] (4) No uncertainty quantification mechanism: Traditional prediction output is a single point value, without providing confidence intervals or reliability indicators, making it difficult to assess the credibility of the results.
[0017] (5) The model lacks adaptive calibration capability: the parameters of the existing algorithm are fixed after training, and it cannot respond to environmental changes, material aging or sensor drift during long-term service, resulting in the gradual accumulation of prediction errors.
[0018] (6) Incomplete parameter calibration and data closed loop: There is a lack of systematic test inversion and field verification process, and no engineering traceability system has been established for parameter range, resulting in poor reproducibility.
[0019] (7) Insufficient generalization performance under extreme conditions: In harsh environments such as high temperature, dryness, salt spray or freeze-thaw, the physical simplification of existing models and data drift are superimposed, resulting in poor stability of prediction results. Summary of the Invention
[0020] To address the shortcomings of existing technologies, this invention provides a method for predicting and intelligently warning the durability of concrete structures based on multi-field coupling effects and adaptive deep learning optimization. The method integrates multi-field coupling effects and adaptive deep learning: first, a multi-scale chloride ion diffusion-reaction-damage coupling model is established to characterize material performance degradation; then, time-series deep learning is used to predict damage evolution online, and Monte Carlo Dropout is employed to quantify uncertainty; finally, a joint threshold of reliability and maintenance cost is used to determine the lifespan limit, achieving damage identification, remaining life prediction, and a three-level intelligent warning system. This addresses the limitations of existing technologies in simultaneously considering multi-scale transmission, damage evolution, and uncertainty, resulting in insufficient accuracy in predicting the remaining life of concrete structures under complex service environments and a lack of a tiered warning mechanism.
[0021] To achieve the above objectives, the specific solution of the present invention is as follows:
[0022] A method for predicting and intelligently warning about the durability of concrete structures includes the following steps:
[0023] Step 1, Data Acquisition and Standardization: A multi-point sensor network with synchronous sampling is deployed at the service site of the concrete structure to continuously acquire raw time-series data of stress, temperature, relative humidity and chloride ion concentration under the same time reference. The raw time-series data of stress, temperature, relative humidity and chloride ion concentration are normalized according to the maximum and minimum values within their calibration intervals to obtain standardized stress, standardized temperature, standardized relative humidity and standardized chloride ion concentration, which are then arranged in chronological order to form a dimensionless standardized input vector sequence.
[0024] Step 2, Multi-scale Coupled Diffusion and Reaction Modeling: Based on the standardized temperature and standardized relative humidity obtained in Step 1, calculate the equivalent diffusion coefficient of temperature and humidity coupling. Then, substitute the equivalent diffusion coefficient of temperature and humidity coupling into the chloride ion diffusion reaction equation at the pore scale to obtain the chloride ion concentration distribution at the pore scale. Subsequently, introduce the measured crack width and crack density to correct the equivalent diffusion coefficient for crack amplification effect, and obtain the crack-scale corrected diffusion coefficient. Finally, push the crack-scale corrected diffusion coefficient up to the component scale through a multi-scale mapping operator to obtain the macroscopic equivalent diffusion coefficient.
[0025] Step 3, Multi-field Coupled Damage Evolution and Stiffness Degradation Description: Using the standardized stress, standardized temperature, standardized relative humidity and standardized chloride ion concentration from Step 1, calculate the growth rate of macroscopic damage variables according to the preset coupling coefficient, obtain the current macroscopic damage variables through time integration, and then calculate the current equivalent elastic modulus based on the current macroscopic damage variables and the initial elastic modulus to complete the stiffness degradation description.
[0026] Step 4, Adaptive Deep Learning Prediction and Uncertainty Quantization: Extract a continuous time window of length T from the standardized input vector sequence in Step 1 to form a standardized input vector subsequence of length T. Input the standardized input vector subsequence of length T into a gated recurrent unit network to obtain the damage prediction mean and prediction variance at future time points. Then, obtain the damage prediction distribution composed of the prediction mean and prediction variance through multiple Monte Carlo forward calculations, and further provide the damage prediction value and prediction confidence interval.
[0027] Step 5, Determining the optimal early warning threshold based on the trade-off between reliability and cost: Based on the damage prediction distribution consisting of the prediction mean and prediction variance obtained in Step 4, calculate the structural reliability, and construct a joint objective function by weighting the reliability and maintenance cost. Determine the optimal damage early warning threshold by minimizing this joint objective function.
[0028] Step 6, Sliding window retraining and adaptive calibration of the model: The damage prediction value in step 4 is continuously compared with the reference damage value obtained by actual measurement or high confidence inversion at the same time using a sliding window. When the mean absolute error within the window exceeds the preset error threshold, the parameters of the gated recurrent unit network are updated by gradient descent to complete the model retraining and adaptive calibration.
[0029] Step 7, Intelligent Early Warning and Remaining Life Output: When the upper bound of the prediction confidence interval given in Step 4 reaches the optimal damage early warning threshold determined in Step 5, an early warning is immediately triggered, and the remaining life is estimated based on the current average damage prediction, damage growth rate and failure threshold damage, thus completing the closed-loop feedback of prediction, optimization, calibration and early warning.
[0030] Furthermore, the formula for extreme value normalization described in step 1 is as follows:
[0031] (2),
[0032] In the formula: Indicates the first Each monitoring quantity at time The measured value, when =1, 2, 3, 4 represent stress, temperature, relative humidity, and chloride ion concentration, respectively; , This indicates the minimum and maximum values of the monitored quantity within the calibration range; This represents the dimensionless value after normalization. Indicates the sampling time; Indicates the monitoring quantity index;
[0033] The formula for the dimensionless standardized input vector sequence is as follows:
[0034] (3),
[0035] In the formula: This represents the standardized input vector used in subsequent mechanistic models and deep learning models. Represents the normalized stress; This represents the normalized temperature. Represents normalized relative humidity; This represents the normalized chloride ion concentration.
[0036] Furthermore, the formula for calculating the equivalent diffusion coefficient of the temperature and humidity coupling mentioned in step 2 is as follows:
[0037] (4),
[0038] (5),
[0039] In the formula: D eq (T,H) represents the equivalent diffusion coefficient of temperature and humidity coupling; Indicates the reference diffusion coefficient; The function representing the coupled effects of temperature and humidity; , This represents the temperature sensitivity coefficient and the humidity sensitivity coefficient;
[0040] The chloride ion diffusion reaction equation at the pore size is as follows:
[0041] (6),
[0042] In the formula: The partial derivative sign is used to describe chloride ion concentration. Relative to time variables The instantaneous rate of change reflects the rate at which chloride ion concentration changes over time; This refers to the chloride ion concentration in the pore solution. Indicates time; Represents the spatial gradient operator; This represents the equivalent diffusion coefficient of temperature and humidity coupling, which varies with temperature and humidity. Indicates temperature; Indicates relative humidity; k b This represents the chloride ion binding rate constant;
[0043] The formula for correcting the crack amplification effect is as follows:
[0044] (7),
[0045] (8),
[0046] In the formula: Indicates the crack transmission amplification factor; , Represents the empirical coefficient; Indicates the crack width; Indicates crack density; This represents the corrected equivalent diffusion coefficient after considering the crack amplification effect; Represents the equivalent diffusion coefficient;
[0047] The macroscopic equivalent diffusion coefficient is obtained through a multi-scale mapping function, which is as follows:
[0048] (9),
[0049] In the formula: The macroscopic equivalent diffusion coefficient representing the component size; The multi-scale mapping operator is derived based on weighted harmonic mean and geometric factor calibration. This represents the corrected equivalent diffusion coefficient after considering the crack amplification effect; This indicates the crack density.
[0050] Furthermore, the formula for calculating the growth rate of the macroscopic damage variable mentioned in step 3 is as follows:
[0051] (10)
[0052] In the formula: Indicates the growth rate of macroscopic damage variables; This represents a macroscopic damage variable, which is dimensionless and ranges from 0 to 1. ~ The coupling coefficients, whose dimensions are given by calibration after balancing with each product term; Indicates temperature; Indicates relative humidity; Indicates stress; Indicates the chloride ion concentration in the pore solution;
[0053] The formula for the current equivalent elastic modulus is as follows:
[0054] (11),
[0055] In the formula: Indicates the current equivalent elastic modulus; Indicates the initial elastic modulus; This represents a macroscopic damage variable, which is dimensionless and ranges from 0 to 1.
[0056] Furthermore, the formulas for the predicted mean and variance of damage at future time points mentioned in step 4 are as follows:
[0057] (12),
[0058] In the formula: Indicates time Damage prediction value; Indicates length is The input sequence window is the normalized multi-field vector sequence obtained from S1; Indicates the length of the time window, in units of sample points; Represents the set of GRU network parameters; Represents the nonlinear mapping of the GRU neural network;
[0059] The formulas for the predicted damage value and the prediction confidence interval are as follows:
[0060] (15)
[0061] In the formula: This represents the prediction confidence interval, with the lower and upper bounds being respectively... ; This represents the predicted mean; Indicates the prediction variance; This represents the confidence quantile coefficient.
[0062] Furthermore, the formula for calculating the structural reliability described in step 5 is as follows:
[0063] (17)
[0064] In the formula: Indicates time Structural reliability; Represents a probability operator; Indicates time Damage random variables; The damage threshold used to determine failure;
[0065] The joint objective function is as follows:
[0066] (18)
[0067] In the formula: Indicates the overall optimization objective; , Indicates the weighting coefficient; This represents the cost function, expressed in monetary terms or normalized cost.
[0068] Furthermore, the formula for the continuous comparison of the sliding window in step 6 is as follows:
[0069] (19)
[0070] In the formula: Indicates the first The average absolute error within each sliding window; This indicates the number of sample points contained in the sliding window; Indicates time Predicted damage; Indicates time Measured or high-confidence inversion reference damage value;
[0071] when When incremental retraining is triggered, the update formula is:
[0072] (20)
[0073] In the formula: , This indicates the parameters after the update compared to the parameters before the update; Indicates the learning rate; This represents the gradient of the loss function with respect to the parameters.
[0074] Furthermore, the formula for estimating the remaining lifetime described in step 7 is as follows:
[0075] (twenty two),
[0076] In the formula: Indicates remaining lifespan, and The time units are consistent; Indicates failure threshold damage; This represents the mean damage prediction at the current moment; This indicates the rate of damage growth at the current moment.
[0077] An application of the method as described above, wherein the method is used for life-cycle safety assessment and operation and maintenance decision-making of concrete-based infrastructure in bridges, tunnels, hydraulic structures, port structures or roadbeds and pavements.
[0078] Furthermore, the concrete structure is subjected to a complex service environment characterized by high temperature and dryness, large diurnal temperature differences, salt spray erosion, or freeze-thaw salt corrosion, and is used to predict the durability of the concrete structure and conduct long-term safety assessments.
[0079] Advantages of the present invention
[0080] (1) The method for predicting and intelligently warning about the durability of concrete structures in this invention makes the micro-diffusion-reaction-damage mechanism explicit by constructing a multi-field coupling of temperature-humidity-stress-chloride ions and a three-scale mapping of “pore-crack-component”. The prediction results no longer rely on a pure black box, thus improving the credibility.
[0081] (2) This invention introduces an adaptive control logic module into the GRU temporal network to dynamically adjust the network structure parameters and learning rate according to the distribution characteristics of the input data, so as to realize the automatic optimization of model parameters as the environment and data change. Combined with sliding window error-triggered retraining, the model parameters are automatically updated as the environment and data distribution change, avoiding performance drift during service life and maintaining accuracy stability and robustness.
[0082] (3) This invention embeds the Monte Carlo Dropout method in the deep learning prediction stage, performs probability sampling and variance analysis on each prediction result, and generates prediction output with confidence intervals. This effectively distinguishes uncertainties caused by data noise, sensor anomalies, or model drift, enabling the system to have the ability to self-assess the reliability of predictions. Compared with traditional single-point prediction models, this invention can provide output results with confidence information, which helps maintenance personnel assess the risk confidence level in decision-making.
[0083] (4) This invention adopts a joint objective function of reliability and maintenance cost, and uses probabilistic reliability and cost functions to construct a dynamic threshold criterion, so that the early warning threshold can be automatically adjusted according to structural status, environmental changes and maintenance strategies. It achieves the optimal balance between safety risk control and operation and maintenance economy, avoids the superposition of false alarms and false alarms, and significantly improves the scientificity and feasibility of the early warning strategy.
[0084] (5) This invention innovatively embeds a physical constraint term into the deep learning loss function, forming a two-way feedback between the mechanistic model parameters and the network training process. The mechanistic equation constrains the learning boundary of the network, ensuring that the model training does not deviate from the physically reasonable domain; the network prediction results can also correct the mechanistic parameters in reverse, forming a dynamic correction closed loop. Moreover, this fusion mechanism maintains physical consistency and enhances the model's adaptability to complex nonlinear environments, enabling the prediction results to have high generalization stability in multi-condition and multi-regional environments.
[0085] (6) By introducing sliding window error detection and adaptive retraining logic, this invention can automatically initiate the calibration process and correct model parameters in real time when model performance deteriorates or the monitoring environment drifts. It also avoids mismatch and accumulated errors caused by long-term use of static models, ensuring that the prediction system operates stably for a long time during its service life.
[0086] (7) This invention clearly defines, sources, and applicable scopes of each key parameter in both the modeling and algorithm stages, including diffusion coefficient, damage variable, coupling coefficient, and reliability function. This disclosure method facilitates reproduction and verification by researchers and engineers, improves the reproducibility and engineering portability of the method, and meets the standardization requirements in the field of structural health monitoring.
[0087] (8) This invention combines predictive output with reliability analysis to construct a multi-level early warning and maintenance priority mechanism, which can automatically generate maintenance suggestions and resource allocation schemes based on the degree of damage and confidence interval. This design forms a closed loop of "monitoring-prediction-early warning-decision", providing systematic decision support for the intelligent operation and maintenance of infrastructure such as bridges, tunnels, hydraulic structures and ports.
[0088] In summary, this invention proposes a unified physical modeling framework for multi-field coupling and multi-scale mapping at the theoretical level; establishes a deep learning prediction system based on mechanism-data fusion at the methodological level to achieve adaptive model optimization; and constructs an interpretable, updatable, and reproducible intelligent early warning method system for concrete structures at the application level. This technical system provides a novel methodology and a highly reliable technical foundation for long-term health monitoring of concrete structures under extreme environments, and has significant engineering application prospects and promotional value. Attached Figure Description
[0089] Figure 1 This is a flowchart of the concrete structure durability prediction and intelligent early warning method of the present invention. Detailed Implementation
[0090] The present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. It should be noted that the specific embodiments are not intended to limit the scope of the present invention.
[0091] like Figure 1 As shown in the illustration, this specific embodiment provides a method for predicting the durability and providing intelligent early warning of concrete structures, enabling damage identification, life prediction, and early warning in complex service environments. This method employs a five-dimensional fusion approach—mechanism modeling, data-driven approach, uncertainty quantification, dynamic threshold optimization, and online retraining—as its core technical route, maintaining both physical interpretability and intelligent adaptability. Specifically, it includes the following steps:
[0092] Step 1, Data Acquisition and Standardization:
[0093] To achieve synchronization and comparability among multiple variables, it is essential to ensure the spatiotemporal consistency and dimensional uniformity of the collected data.
[0094] Therefore, a multi-point sensor network with synchronous sampling is deployed at the service site of the concrete structure to continuously acquire raw time-series data of stress, temperature, relative humidity, and chloride ion concentration under the same time reference. The raw time-series data of stress, temperature, relative humidity, and chloride ion concentration are normalized according to their maximum and minimum values within their calibration intervals, resulting in standardized stress, standardized temperature, standardized relative humidity, and standardized chloride ion concentration. These are then arranged in chronological order to form a dimensionless standardized input vector sequence; as detailed below:
[0095] 1. The original time series data is defined as follows: (1).
[0096] In the formula: Sampling time The stress; Sampling time Temperature; Sampling time relative humidity; Sampling time Chloride ion concentration; The sampling time.
[0097] 2. To eliminate the influence of dimensions and ensure the uniformity of multiple field inputs, each physical quantity is normalized according to its maximum and minimum values within its calibration interval, as shown in the following formula:
[0098] (2),
[0099] In the formula: Indicates the first Each monitoring quantity at time The measured value, when =1, 2, 3, 4 represent stress, temperature, relative humidity, and chloride ion concentration, respectively; , This indicates the minimum and maximum values of the monitored quantity within the calibration range; This represents the dimensionless value after normalization. Indicates the sampling time; Indicates the monitoring quantity index;
[0100] 3. The formula for the dimensionless standardized input vector sequence is as follows:
[0101] (3),
[0102] In the formula: This represents the standardized input vector used in subsequent mechanistic models and deep learning models. Represents the normalized stress; This represents the normalized temperature. Represents normalized relative humidity; This represents the normalized chloride ion concentration.
[0103] This step ensures the comparability of different physical quantities in the numerical space, laying a unified data foundation for subsequent multi-scale modeling and neural network training.
[0104] Step 2, Multi-scale Coupled Diffusion and Reaction Modeling: Based on the standardized temperature and standardized relative humidity obtained in Step 1, calculate the equivalent diffusion coefficient of temperature and humidity coupling. Then, substitute the equivalent diffusion coefficient of temperature and humidity coupling into the chloride ion diffusion reaction equation at the pore scale to obtain the chloride ion concentration distribution at the pore scale. Subsequently, introduce the measured crack width and crack density to correct the equivalent diffusion coefficient for crack amplification effect, and obtain the crack-scale corrected diffusion coefficient. Finally, push the crack-scale corrected diffusion coefficient up to the component scale through a multi-scale mapping operator to obtain the macroscopic equivalent diffusion coefficient.
[0105] 1. The formula for calculating the equivalent diffusion coefficient of the temperature and humidity coupling is as follows:
[0106] (4),
[0107] (5),
[0108] In the formula: D eq (T,H) represents the equivalent diffusion coefficient of temperature and humidity coupling; Indicates the reference diffusion coefficient; The function representing the coupled effects of temperature and humidity; , This represents the temperature sensitivity coefficient and the humidity sensitivity coefficient;
[0109] 2. The chloride ion diffusion reaction equation at the pore size is as follows:
[0110] (6),
[0111] In the formula: The partial derivative sign is used to describe chloride ion concentration. Relative to time variables The instantaneous rate of change reflects the rate at which chloride ion concentration changes over time; This refers to the chloride ion concentration in the pore solution. Indicates time; Represents the spatial gradient operator; This represents the equivalent diffusion coefficient of temperature and humidity coupling, which varies with temperature and humidity. Indicates temperature; Indicates relative humidity; k b This represents the chloride ion binding rate constant.
[0112] 3. At the crack scale, the crack amplification effect is introduced to correct the diffusion process:
[0113] (7),
[0114] (8),
[0115] In the formula: Indicates the crack transmission amplification factor; , Represents the empirical coefficient; Indicates the crack width; Indicates crack density; This represents the corrected equivalent diffusion coefficient after considering the crack amplification effect; Represents the equivalent diffusion coefficient;
[0116] 4. The macroscopic equivalent diffusion coefficient is obtained through a multi-scale mapping function, which is as follows:
[0117] (9),
[0118] In the formula: The macroscopic equivalent diffusion coefficient representing the component size; The multi-scale mapping operator is derived based on weighted harmonic mean and geometric factor calibration. This represents the corrected equivalent diffusion coefficient after considering the crack amplification effect; This indicates the crack density.
[0119] This step realizes the transmission relationship between the three scales of pores, cracks and components, and establishes the physical coupling basis of multi-field temperature and humidity stress and diffusion reaction behavior.
[0120] Step 3, Description of Multi-Field Coupled Damage Evolution and Stiffness Degradation: Using the standardized stress, standardized temperature, standardized relative humidity, and standardized chloride ion concentration from Step 1, the growth rate of macroscopic damage variables is calculated according to the preset coupling coefficient, as shown in the following formula:
[0121] (10)
[0122] In the formula: Indicates the growth rate of macroscopic damage variables; This represents a macroscopic damage variable, which is dimensionless and ranges from 0 to 1. ~ The coupling coefficients, whose dimensions are given by calibration after balancing with each product term; Indicates temperature; Indicates relative humidity; Indicates stress; This indicates the chloride ion concentration in the pore solution.
[0123] The current macroscopic damage variable is obtained by time integration, and the current equivalent elastic modulus is calculated based on the current macroscopic damage variable and the initial elastic modulus to complete the stiffness degradation description.
[0124] The formula for the current equivalent elastic modulus is as follows:
[0125] (11),
[0126] In the formula: Indicates the current equivalent elastic modulus; Indicates the initial elastic modulus; This represents the damage variable. Should it be changed to: This represents a macroscopic damage variable, which is dimensionless and ranges from 0 to 1.
[0127] This process establishes a macroscopic damage dynamics equation for the evolution of material properties under multiple field effects, providing target variables and trend priors for deep learning models.
[0128] Step 4, Adaptive Deep Learning Prediction and Uncertainty Quantization: Extract a continuous time window of length T from the standardized input vector sequence in Step 1 to form a standardized input vector subsequence of length T. Input the standardized input vector subsequence of length T into a gated recurrent unit (GRU) network. The mean and variance of the damage prediction at future time steps are obtained by mapping using formula (12) in one step.
[0129] (12),
[0130] In the formula: Indicates time Damage prediction value; Indicates length is The input sequence window is the normalized multi-field vector sequence obtained from S1; Indicates the length of the time window, in units of sample points; Represents the set of GRU network parameters; Represents the nonlinear mapping of the GRU neural network;
[0131] To quantify the prediction confidence, a Monte Carlo Dropout mechanism is introduced. The damage prediction distribution, consisting of the prediction mean and prediction variance, is obtained through multiple forward calculations in Monte Carlo. The final damage prediction value and prediction confidence interval are then calculated according to formulas (13) to (15).
[0132] (13)
[0133] (14)
[0134] (15)
[0135] In the formula: This represents the predicted value obtained from the m-th random Dropout forward computation. Indicates the number of times to move forward randomly; This represents the predicted mean; Indicates the prediction variance; Indicates the confidence quantile coefficient; This represents the prediction confidence interval, with the lower and upper bounds being respectively... .
[0136] The network parameters are updated iteratively using the Adam optimization algorithm:
[0137] (16)
[0138] In the formula: This represents the parameters for the (k+1)th iteration; This represents the parameters for the k-th iteration; Indicates the learning rate; , The exponential moving average estimates of the first and second moments of the gradient of the loss function; This represents the numerical stability constant to prevent the denominator from being zero.
[0139] The entire parameter optimization process is dynamically adjusted by adaptive control logic based on the distribution characteristics of the input data, ensuring stable convergence of prediction error and variance.
[0140] Step 5, Determining the optimal early warning threshold based on the trade-off between reliability and cost: Based on the damage prediction distribution obtained in Step 4, which consists of the prediction mean and prediction variance, the structural reliability is calculated. The formula for calculating the structural reliability is as follows:
[0141] (17)
[0142] In the formula: Indicates time Structural reliability; Represents a probability operator; Indicates time Damage random variables; This represents the damage threshold used to determine failure.
[0143] A joint objective function is constructed using a weighted sum of reliability and maintenance cost, as follows:
[0144] (18)
[0145] In the formula: Indicates the overall optimization objective; , Indicates the weighting coefficient; This represents the cost function, expressed in monetary terms or normalized cost.
[0146] The optimal damage warning threshold is determined by minimizing this joint objective function. This achieves a balance between reliability and maintenance costs. The threshold serves as an intelligent early warning criterion, connecting prediction and risk management.
[0147] Step 6, Sliding Window Retraining and Adaptive Model Calibration: A sliding window is used to continuously compare the damage prediction value from Step 4 with the reference damage value obtained at the same time through actual measurement or high-confidence inversion. When the mean absolute error within the window exceeds a preset error threshold, incremental retraining is triggered. The parameters of the gated recurrent unit network are updated using gradient descent, completing model retraining and adaptive calibration. The formula for the continuous comparison within the sliding window is as follows:
[0148] (19)
[0149] In the formula: Indicates the first The average absolute error within each sliding window; This indicates the number of sample points contained in the sliding window; Indicates time Predicted damage; Indicates time The measured or high-confidence inversion reference damage value.
[0150] Indicates the preset error threshold, when When incremental retraining is triggered, the update formula is:
[0151] (20)
[0152] In the formula: , This indicates the parameters after the update compared to the parameters before the update; Indicates the learning rate; This represents the gradient of the loss function with respect to the parameters.
[0153] The adaptive control logic dynamically adjusts the retraining frequency and learning rate based on data distribution drift and error, maintaining the long-term stability and generalization ability of the model.
[0154] Step 7, Intelligent Early Warning and Remaining Life Output: When the upper bound of the prediction confidence interval given in Step 4 reaches the optimal damage early warning threshold determined in Step 5. When this happens, an early warning will be triggered immediately;
[0155] (twenty one),
[0156] In the formula: Indicates time The upper bound of the prediction confidence interval; This represents the optimal early warning threshold obtained through the joint optimization of reliability and cost in step 5.
[0157] Based on the current damage prediction mean, damage growth rate, and failure threshold damage, the remaining lifetime is estimated using the following formula:
[0158] (twenty two),
[0159] In the formula: Indicates remaining lifespan, and The time units are consistent; Indicates failure threshold damage; This represents the mean damage prediction at the current moment; This indicates the rate of damage growth at the current moment.
[0160] This enables a closed-loop feedback mechanism for prediction, optimization, calibration, and early warning.
[0161] The above method is used for the life-cycle safety assessment and operation and maintenance decision-making of infrastructure mainly composed of concrete, such as bridges, tunnels, hydraulic structures, port structures, or highway subgrades and pavements. The concrete structure is subjected to complex service environments such as high temperature and dryness, large diurnal temperature differences, salt spray erosion, or freeze-thaw salt corrosion, and is used to predict the durability and long-term safety of the concrete structure.
Claims
1. A method for predicting and intelligently warning the durability of concrete structures, characterized in that, Includes the following steps: Step 1, Data Acquisition and Standardization: A multi-point sensor network with synchronous sampling is deployed at the service site of the concrete structure to continuously acquire raw time-series data of stress, temperature, relative humidity and chloride ion concentration under the same time reference. The data are then normalized according to the maximum and minimum values within their respective calibration intervals to obtain standardized stress, standardized temperature, standardized relative humidity and standardized chloride ion concentration. These are then arranged in chronological order to form a dimensionless standardized input vector sequence. Step 2, Multi-scale coupled diffusion and reaction modeling: Calculate the equivalent diffusion coefficient of temperature and humidity coupling based on the normalized temperature and normalized relative humidity obtained in Step 1, and then substitute the equivalent diffusion coefficient of temperature and humidity coupling into the chloride ion diffusion reaction equation at the pore scale to obtain the chloride ion concentration distribution at the pore scale. Subsequently, the measured crack width and crack density are introduced to correct the crack amplification effect on the equivalent diffusion coefficient, resulting in a crack scale-corrected diffusion coefficient. Finally, the crack scale-corrected diffusion coefficient is pushed up to the component scale using a multi-scale mapping operator to obtain the macroscopic equivalent diffusion coefficient. Step 3, Multi-field Coupled Damage Evolution and Stiffness Degradation Description: Using the standardized stress, standardized temperature, standardized relative humidity and standardized chloride ion concentration from Step 1, calculate the growth rate of macroscopic damage variables according to the preset coupling coefficient, obtain the current macroscopic damage variables through time integration, and then calculate the current equivalent elastic modulus based on the current macroscopic damage variables and the initial elastic modulus to complete the stiffness degradation description. Step 4, Adaptive Deep Learning Prediction and Uncertainty Quantization: Extract a continuous time window of length T from the standardized input vector sequence in Step 1 to form a standardized input vector subsequence of length T. Input the standardized input vector subsequence of length T into a gated recurrent unit network to obtain the damage prediction mean and prediction variance at future time points. Then, obtain the damage prediction distribution composed of the prediction mean and prediction variance through multiple Monte Carlo forward calculations, and further provide the damage prediction value and prediction confidence interval. Step 5, Determining the optimal early warning threshold based on the trade-off between reliability and cost: Based on the damage prediction distribution consisting of the prediction mean and prediction variance obtained in Step 4, calculate the structural reliability, and construct a joint objective function by weighting the reliability and maintenance cost. Determine the optimal damage early warning threshold by minimizing this joint objective function. Step 6, Sliding window retraining and adaptive calibration of the model: The damage prediction value in step 4 is continuously compared with the reference damage value obtained by actual measurement or high confidence inversion at the same time using a sliding window. When the mean absolute error within the window exceeds the preset error threshold, the parameters of the gated recurrent unit network are updated by gradient descent to complete the model retraining and adaptive calibration. Step 7, Intelligent Early Warning and Remaining Life Output: When the upper bound of the prediction confidence interval given in Step 4 reaches the optimal damage early warning threshold determined in Step 5, an early warning is immediately triggered, and the remaining life is estimated based on the current average damage prediction, damage growth rate and failure threshold damage, thus completing the closed-loop feedback of prediction, optimization, calibration and early warning.
2. The method according to claim 1, characterized in that, The formula for extreme value normalization mentioned in step 1 is as follows: （2）， In the formula: Indicates the first Each monitoring quantity at time The measured value, when =1, 2, 3, 4 represent stress, temperature, relative humidity, and chloride ion concentration, respectively; , This indicates the minimum and maximum values of the monitored quantity within the calibration range; This represents the dimensionless value after normalization. Indicates the sampling time; Indicates the monitoring quantity index; The formula for the dimensionless standardized input vector sequence is as follows: （3）， In the formula: This represents the standardized input vector used in subsequent mechanistic models and deep learning models. Represents the normalized stress; This represents the normalized temperature. Represents normalized relative humidity; This represents the normalized chloride ion concentration.
3. The method according to claim 1, characterized in that, The formula for calculating the equivalent diffusion coefficient of the temperature and humidity coupling mentioned in step 2 is as follows: （4）， （5）， In the formula: D eq (T,H) represents the equivalent diffusion coefficient of temperature and humidity coupling; Indicates the reference diffusion coefficient; The function representing the coupled effects of temperature and humidity; , This represents the temperature sensitivity coefficient and the humidity sensitivity coefficient; The chloride ion diffusion reaction equation at the pore size is as follows: （6）， In the formula: The partial derivative sign is used to describe chloride ion concentration. Relative to time variables The instantaneous rate of change reflects the rate at which chloride ion concentration changes over time; This refers to the chloride ion concentration in the pore solution. Indicates time; Represents the spatial gradient operator; This represents the equivalent diffusion coefficient of temperature and humidity coupling, which varies with temperature and humidity. Indicates temperature; Indicates relative humidity; k b This represents the chloride ion binding rate constant; The formula for correcting the crack amplification effect is as follows: （7）， （8）， In the formula: Indicates the crack transmission amplification factor; , Represents the empirical coefficient; Indicates the crack width; Indicates crack density; This represents the corrected equivalent diffusion coefficient after considering the crack amplification effect; Represents the equivalent diffusion coefficient; The macroscopic equivalent diffusion coefficient is obtained through a multi-scale mapping function, which is as follows: （9）， In the formula: The macroscopic equivalent diffusion coefficient representing the component size; The multi-scale mapping operator is derived based on weighted harmonic mean and geometric factor calibration. This represents the corrected equivalent diffusion coefficient after considering the crack amplification effect; This indicates the crack density.
4. The method according to claim 1, characterized in that, The formula for calculating the growth rate of the macroscopic damage variable mentioned in step 3 is as follows: （10）， In the formula: Indicates the growth rate of macroscopic damage variables; ~ The coupling coefficients, whose dimensions are given by calibration after balancing with each product term; Indicates temperature; Indicates relative humidity; Indicates stress; Indicates the chloride ion concentration in the pore solution; The formula for the current equivalent elastic modulus is as follows: （11）， In the formula: Indicates the current equivalent elastic modulus; Indicates the initial elastic modulus; This represents a macroscopic damage variable, which is dimensionless and ranges from 0 to 1.
5. The method according to claim 1, characterized in that, The formulas for the predicted mean and variance of damage at future time points mentioned in step 4 are as follows: （12）， In the formula: Indicates time Damage prediction value; Indicates length is The input sequence window is the normalized multi-field vector sequence obtained from S1; Indicates the length of the time window, in units of sample points; Represents the set of GRU network parameters; Represents the nonlinear mapping of the GRU neural network; The formulas for the predicted damage value and the prediction confidence interval are as follows: （15）， In the formula: This represents the prediction confidence interval, with the lower and upper bounds being respectively... ; This represents the predicted mean; Indicates the prediction variance; This represents the confidence quantile coefficient.
6. The method according to claim 1, characterized in that, The formula for calculating the structural reliability mentioned in step 5 is as follows: （17）， In the formula: Indicates time Structural reliability; Represents a probability operator; Indicates time Damage random variables; The damage threshold used to determine failure; The joint objective function is as follows: （18）， In the formula: Indicates the overall optimization objective; , Indicates the weighting coefficient; This represents the cost function, expressed in monetary terms or normalized cost.
7. The method according to claim 1, characterized in that, The formula for the continuous comparison of the sliding window mentioned in step 6 is as follows: （19）， In the formula: Indicates the first The average absolute error within each sliding window; This indicates the number of sample points contained in the sliding window; Indicates time Predicted damage; Indicates time Measured or high-confidence inversion reference damage value; when When incremental retraining is triggered, the update formula is: （20）， In the formula: , This indicates the parameters after the update compared to the parameters before the update; Indicates the learning rate; This represents the gradient of the loss function with respect to the parameters.
8. The method according to claim 1, characterized in that, The formula for estimating the remaining lifetime described in step 7 is as follows: （22）， In the formula: Indicates remaining lifespan, and The time units are consistent; Indicates failure threshold damage; This represents the mean damage prediction at the current moment; This indicates the rate of damage growth at the current moment.
9. An application of the method as described in any one of claims 1 to 8, characterized in that, The method is used for the life-cycle safety assessment and operation and maintenance decision-making of infrastructure with concrete as the main component, such as bridges, tunnels, hydraulic structures, port structures, or highway subgrades and pavements.
10. The application as described in claim 9, characterized in that, The concrete structure is subjected to complex service environments including high temperature and dryness, large diurnal temperature differences, salt spray erosion, or freeze-thaw salt corrosion. It is used to predict the durability of the concrete structure and conduct long-term safety assessments.