A reinforced concrete component life prediction method based on chlorine ion concentration monitoring

Abstract

The application discloses a reinforced concrete component life prediction method based on chlorine ion concentration monitoring and belongs to the technical field of civil engineering structure health monitoring and durability evaluation. The method comprises the following steps: step S1, embedding an electrochemical type concrete chlorine ion penetration depth sensor in a target reinforced concrete component; based on a full solid three-electrode system and an array type sensing matrix of the sensor, continuously and in-situ collecting chlorine ion concentration data at different depths and different times to form a time-space concentration field data set; through extended Kalman filter recursion inversion, an exponential decay type time-varying diffusion coefficient model conforming to cement hydration physical laws is constructed, and a dynamic surface chlorine ion concentration under environmental periodic fluctuation is fitted by using a Fourier series, so that the fundamental defect of constant parameters of a traditional Fick model is completely abandoned.

Description

Technical Field

[0001] This invention relates to the field of civil engineering structural health monitoring and durability assessment technology, and in particular to a method for predicting the life of reinforced concrete components based on chloride ion concentration monitoring. Background Technology

[0002] Chloride ion corrosion is a core cause of steel reinforcement corrosion, reduced durability, and even service failure in concrete structures under chloride environments, seriously affecting the safety and service life of concrete structures such as cross-sea bridges, port terminals, and coastal buildings. Accurately predicting the time required for chloride ions to diffuse to the steel reinforcement surface and reach a critical concentration (i.e., the structural service life or remaining life) is a key basis for structural durability design, maintenance strategy development, and life cycle cost assessment.

[0003] Currently, methods for predicting the chloride ion corrosion life of reinforced concrete components are mainly divided into three categories, but all of them have significant technical shortcomings:

[0004] Traditional methods for predicting chloride ion attack lifetime are based on Fick's second law. They obtain the chloride ion concentration distribution in concrete through chemical titration of borehole samples, then fit the apparent diffusion coefficient and surface chloride ion concentration to the analytical solution using constant parameters to calculate the lifetime. However, this method has fundamental flaws: First, borehole sampling is a destructive test, cumbersome to operate, unable to provide continuous monitoring, and the results are delayed, with poor representativeness of single-point measurements. Second, it assumes a constant diffusion coefficient and a constant surface concentration, which deviates significantly from reality—concrete hydration is continuous, density increases over time, and the diffusion coefficient decreases; environmental factors such as wet-dry cycles, tides, and temperature changes cause periodic fluctuations in surface chloride ion concentration. The prediction error under the constant parameter assumption can be several times higher, failing to meet the needs of accurate engineering assessments. Third, the prediction result is a single deterministic value, unable to provide the uncertainty range of the lifetime, leading to overly risky or conservative decisions.

[0005] In recent years, researchers have attempted to embed electrochemical chloride ion sensors in concrete to achieve in-situ continuous monitoring. However, existing sensor technologies have several shortcomings: First, the reference electrodes are mostly liquid structures, prone to leakage, and have poor resistance to the high-alkali environment of concrete, resulting in insufficient long-term monitoring stability. Second, the sensing structures are mostly single-depth or have a few measuring points, resulting in low depth resolution and an inability to accurately capture the position of the chloride ion penetration front and concentration profile distribution. Third, the encapsulation process is imperfect, and the electrodes and leads are easily corroded by concrete hydration products, leading to a short sensor lifespan. Fourth, the power supply method is limited, mostly using disposable lithium batteries, with limited battery life (usually less than three to five years), which cannot meet the ultra-long-term monitoring needs of concrete structures, and battery replacement requires structural damage. More importantly, even after obtaining monitoring data, existing methods remain at the level of "data acquisition + simple fitting"—still substituting the monitoring data into a Fick model with constant parameters, failing to address core scientific issues such as the time-varying nature of the diffusion coefficient, the dynamic nature of boundary conditions, and the quantification of parameter uncertainties. The value of the monitoring data is not fully explored, and the improvement in prediction accuracy is limited.

[0006] Some studies have attempted to use black-box models such as neural networks and support vector machines to directly predict lifespan based on historical monitoring data. While these methods can fit complex nonlinear relationships, they have fundamental drawbacks: First, pure black-box models lack physical constraints, and extrapolating from outside the training data range can easily produce absurd results that violate physical laws, making reliability unreliable. Second, they require a large amount of high-quality, long-term training data, which is extremely scarce in practical engineering. Third, the model parameters are fixed and cannot be dynamically updated with new monitoring data, lacking self-evolution capabilities.

[0007] To address this, we provide a method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring. Summary of the Invention

[0008] The purpose of this invention is to solve the problems in the prior art by proposing a method for predicting the life of reinforced concrete components based on chloride ion concentration monitoring.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A method for predicting the life of reinforced concrete members based on chloride ion concentration monitoring includes the following steps:

[0011] Step S1: An electrochemical concrete chloride ion penetration depth sensor is pre-embedded in the target reinforced concrete component. Based on the sensor's all-solid-state three-electrode system and array-type sensing substrate, chloride ion concentration data at different depths and times are continuously and in situ collected to form a spatiotemporal concentration field dataset.

[0012] Step S2: Based on the initial concentration data collected in Step S1, the apparent chloride ion diffusion coefficient in the reinforced concrete cover as a function of time is calculated by using extended Kalman filtering or particle swarm optimization algorithm, and its decay function model is constructed.

[0013] Step S3: Based on the chloride ion concentration data at the concrete surface collected in Step S1, the time-varying surface chloride ion concentration function under environmental influence is fitted using Fourier series or piecewise Gaussian process.

[0014] Step S4: Substitute the time-varying diffusion coefficient from step S2 and the dynamic surface chloride ion concentration function from step S3 into the modified Fick's second law, and use the finite difference method combined with a long short-term memory neural network to perform a hybrid numerical-intelligent solution to construct a chloride ion concentration spatiotemporal distribution predictor.

[0015] Step S5: Based on the predictor in step S4, and combined with the critical chloride ion concentration threshold for depassivation of the steel bar, solve the probability density function of the chloride ion concentration at the depth of the steel bar reaching the threshold for the first time, and then calculate the probability distribution of the remaining life of the component; and use subsequent real-time monitoring data to dynamically correct the model parameters through a Bayesian recursive update algorithm to achieve real-time calibration and uncertainty quantification of the prediction results.

[0016] Step S6: Output the predicted remaining life probability range of reinforced concrete components. When the predicted life is lower than the design service life or the real-time monitoring concentration exceeds the warning threshold, automatically issue a multi-level durability warning signal.

[0017] Preferably, the decay function model in step S2 is in the form of exponential decay, the state equation of the extended Kalman filter takes the current parameter vector to be inverted as the state variable, the observation equation takes the measured concentration as the observation, and the initial diffusion coefficient and decay factor are estimated in real time through recursive iteration.

[0018] Preferably, the input features of the long short-term memory neural network in step S4 include time step, depth location, historical concentration gradient, current diffusion coefficient estimate, and surface chloride ion concentration; the neural network is used to correct systematic errors caused by model simplification in the finite difference method.

[0019] Preferably, the probability density function in step S5 is obtained by Monte Carlo simulation, specifically: a large number of random samples are taken based on the posterior probability distribution of the initial diffusion coefficient, attenuation factor and surface chloride ion concentration parameters, the prediction model of step S4 is executed for each sample, the time distribution of the concentration at the location of the steel bar reaching the critical threshold for the first time is statistically analyzed, and the probability density function is obtained by fitting the kernel density estimation.

[0020] Preferably, the all-solid-state three-electrode system in the electrochemical concrete chloride ion penetration depth sensor is arranged in multiple groups at equal intervals along the axial direction of the sensing substrate to provide high depth resolution, and its in-situ monitoring data is directly used as the input of the spatiotemporal concentration field dataset in step S1.

[0021] Preferably, the electrochemical concrete chloride ion penetration depth sensor has a built-in temperature compensation module, and the collected data synchronously includes temperature information; the apparent diffusion coefficient retrieved in step S2 is further normalized to the reference temperature using the Arrhenius equation to eliminate the influence of temperature fluctuations on the identification of diffusion parameters.

[0022] Preferably, the method further includes step S7: mapping the monitoring data and prediction results from steps S1 to S5 to a component-level or structural-level digital twin model in real time, dynamically displaying the chloride ion concentration field, permeation front, and lifetime probability cloud map using color cloud maps, and supporting scenario simulation and lifetime gain effect evaluation of different maintenance strategies.

[0023] Preferably, the electrochemical concrete chloride ion penetration depth sensor includes a solar complementary power supply unit, which provides the method with a power supply capability of more than ten years, ensuring that the Bayesian recursive update strategy based on long-term monitoring data in step S5 can be continuously executed, and realizing the self-evolution of the prediction model throughout its entire life cycle.

[0024] Preferably, the multi-level durability warning signals in step S6 include: a yellow warning, used to indicate a set percentage of predicted remaining service life that is less than the design life; an orange warning, used to indicate a set percentage of measured chloride ion concentration at the depth of the reinforcing steel that reaches a critical threshold; and a red warning, used to indicate that measured chloride ion concentration at the depth of the reinforcing steel reaches or exceeds the critical threshold.

[0025] Preferably, the all-solid-state three-electrode system of the electrochemical concrete chloride ion penetration depth sensor in step S1 consists of a silver / silver chloride working electrode, a manganese dioxide / silver oxide all-solid-state reference electrode, and a titanium alloy counter electrode, with no liquid components; the sensing substrate is a polyetheretherketone engineering plastic rod, and six to ten sets of the all-solid-state three-electrode system are arranged at equal intervals along the axial direction, corresponding to a monitoring depth covering the conventional protective layer thickness of the main concrete reinforcement.

[0026] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0027] 1. This invention constructs an exponentially decaying time-varying diffusion coefficient model that conforms to the physical laws of cement hydration through extended Kalman filter recursive inversion. It then uses Fourier series to fit the dynamic surface chloride ion concentration under periodic environmental fluctuations, completely eliminating the fundamental defect of the constant parameters in the traditional Fick model. Based on this, it integrates Monte Carlo simulation and kernel density estimation to output the complete probability density function and remaining lifetime quantile interval for the first arrival of chloride ions. This represents a leap from deterministic single-value prediction to probabilistic uncertainty quantification, providing a scientific basis for reliability-based durability design, and significantly improving prediction accuracy compared to traditional methods.

[0028] 2. This invention creatively combines an implicit finite difference physical solver with a long short-term memory neural network to construct a hybrid-driven predictor. The physical part ensures mass conservation and extrapolation reliability, while the neural network part learns and compensates for system errors caused by discretization, achieving an optimal balance between computational efficiency and accuracy. Furthermore, utilizing the ultra-long-term endurance provided by the solar complementary power supply unit, a Bayesian recursive dynamic update strategy is implemented, enabling the model parameters and lifetime predictions to continuously self-calibrate and gradually refine with new monitoring data. This achieves self-evolution of the prediction model throughout its entire lifecycle, completely overcoming the technical defect of traditional methods that require "one-time calibration and remain unchanged throughout life."

[0029] 3. This invention uses an all-solid-state array electrochemical sensor as the data source, and arranges multiple sets of three-electrode systems at equal intervals along the protective layer thickness to simultaneously acquire chloride ion concentration profiles with high depth resolution, providing rich spatial information constraints for inversion and prediction. Based on this, the monitoring data and prediction results are mapped in real time to a digital twin model, dynamically displaying concentration field cloud maps, penetration front migration, and lifetime probability cloud maps. It also supports "what-if" scenario simulations and lifetime gain quantification assessments for various maintenance strategies such as applying rust inhibitors, adding protective layers, and electrochemical dechlorination. Combined with multi-level early warning signals, a closed-loop intelligent operation and maintenance system is formed, encompassing "data acquisition → parameter inversion → prediction update → visual decision-making → graded response," significantly improving the intelligence level and engineering practicality of durability management of reinforced concrete structures under chloride environments. Attached Figure Description

[0030] Figure 1 This is a flowchart illustrating a method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring, as proposed in this invention. Detailed Implementation

[0031] The technical solutions of the present invention will be clearly and completely described below with reference to the accompanying drawings of the embodiments of the present invention. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without creative effort are within the scope of protection of the present invention.

[0032] Example, refer to Figure 1 A method for predicting the life of reinforced concrete members based on chloride ion concentration monitoring, comprising:

[0033] Step S1: High-resolution spatiotemporal concentration field data acquisition

[0034] Before concrete pouring, an electrochemical concrete chloride ion penetration depth sensor is pre-embedded in the target component. This sensor employs an all-solid-state three-electrode system and a PEEK engineering plastic sensing substrate, with multiple sets of electrodes arranged at equal intervals along the axial direction to form an array-type sensing structure. The sensor incorporates a temperature compensation module and is equipped with a solar-powered complementary power supply unit.

[0035] After the concrete curing is completed, sensors continuously collect chloride ion concentration data and synchronous temperature data at different depths at set sampling intervals. The measuring points at each depth are equidistantly distributed along the thickness of the protective layer, completely covering the location of the main reinforcement bars. All raw data is uploaded to the cloud platform in real time via a wireless communication module, forming a dataset including depth dimensions. Time dimension With concentration dimension A three-dimensional spatiotemporal concentration field dataset.

[0036] Step S2: Time-varying diffusion coefficient inversion based on extended Kalman filter

[0037] Concentration data from the initial monitoring phase are used for inversion. The parameter vector to be inverted is defined as the initial diffusion coefficient. With decay factor ,remember Establish the state equation and observation equation for the extended Kalman filter.

[0038] Formula 1 (State Equation - Random Walk Model):

[0039]

[0040] In the formula: This represents the state vector at time k. This represents the state vector from the previous time step. Let Q represent the process noise introduced during the propagation of the state vector from the (k-1)th sampling time to the kth sampling time. Let Q represent the process noise covariance matrix, k represent the sampling time number, and the value of k ranges from (1 to the total number of sampling times). Let η represent the process noise random vector, and N(0,Q) represent a multivariate normal distribution with a mean of 0 and a covariance matrix of Q.

[0041] Formula 2 (Observation Equation – Concentration Calculation Based on Error Function):

[0042]

[0043] In the formula: This represents the chloride ion concentration inside the concrete calculated according to Fick's second law. The calculated observations, represented by the observation equations, characterize the theoretical chloride ion concentration calculated based on the current state parameters. This indicates the initial chloride ion concentration in the concrete. This indicates the chloride ion concentration on the concrete surface. The depth from the concrete surface is represented by t, and the service time is represented by t. Indicates the effective chloride ion diffusion coefficient. ( ) represents the complementary error function.

[0044] in Take the estimated diffusion coefficient value at the current moment. The observation equation is: .

[0045] In the formula: Let R represent the observation noise random vector, and let R represent the observation noise covariance matrix.

[0046] The recursive iterative process of the Extended Kalman Filter (EKF) includes prediction and update. The prediction step calculates the state prior estimate and its covariance prior matrix. The update step first calculates the Jacobian matrix (partial derivatives of the calculated concentration values ​​with respect to the state vector), then calculates the Kalman gain matrix, and finally corrects the state prior estimate using actual concentration observations to obtain the state posterior estimate and its covariance posterior matrix. After recursive processing at all time points in the initial stage, the result is... and The optimal estimate.

[0047] Formula 3 (Exponential decay model of time-varying apparent chloride ion diffusion coefficient):

[0048]

[0049] In the formula: This represents the apparent chloride ion diffusion coefficient at time t. This represents the initial apparent chloride ion diffusion coefficient. The diffusion coefficient and attenuation coefficient are represented by t, which represents the service time. ( ) represents the natural exponential function.

[0050] Step S3: Fitting dynamic boundary conditions based on Fourier series

[0051] Time series of surface chloride ion concentration measured by the electrode closest to the concrete surface of the sensor Considering the periodic fluctuations in the environment, Fourier series fitting is used.

[0052] Formula 4 (Fourier series expansion of surface chloride ion concentration):

[0053]

[0054] In the formula: This represents the chloride ion concentration on the concrete surface at time t. Represents the constant term of the Fourier series. Denotes the Fourier coefficients of the nth cosine term. Denotes the Fourier coefficients of the nth-order sine term. The index represents the order of the Fourier expansion, N represents the total order of the Fourier expansion, T represents the period, and t represents the service time.

[0055] The dominant cycle Take the environmental characteristic cycle (such as annual or tidal cycle), order Select based on goodness of fit. Solve for coefficients using the least squares method. , , This yields a smooth periodic function. .

[0056] Step S4: Data-Physical Fusion Drives Predictive Model Construction

[0057] Substitute the time-varying diffusion coefficient from step S2 and the dynamic boundary conditions from step S3 into the modified one-dimensional unsteady diffusion control equation.

[0058] Formula 5 (Modified Fick's Second Law governing equation):

[0059]

[0060] In the formula: C represents the chloride ion concentration inside the concrete. Let represent the apparent chloride ion diffusion coefficient at time t, x represent the depth coordinate from the concrete surface, L represent the maximum depth of the concrete calculation area, and t represent the service time. This represents the partial derivative.

[0061] Boundary conditions: , (Pick Large enough); initial conditions: ,in This represents the chloride ion concentration at the concrete surface (x=0) at time t.

[0062] Discretization is performed using the implicit finite difference method. The spatial domain is divided into... equidistant grids, step size Time step .remember ,in, Let represent the chloride ion concentration at the nth time step and the ith spatial node, where iΔx represents the position coordinates of the ith spatial node, Δx represents the spatial offset step length, nΔt represents the time corresponding to the nth time step, Δt represents the time offset step length, i represents the spatial node number, and n represents the time step number.

[0063] Formula 6 (Implicit Finite Difference Discrete Scheme):

[0064]

[0065] In the formula: This represents the apparent chloride ion diffusion coefficient at the interface between the i-th and i+1-th spatial nodes at the (n+1)-th time step. This represents the interface position between two adjacent spatial nodes, and n+1 represents the next time step.

[0066] The interfacial diffusion coefficient was calculated using harmonic averaging. The equations were rearranged into a tridiagonal system, which was solved using the Thomas algorithm to obtain the predicted concentration for the physical component. .

[0067] To correct for the systematic errors of the finite difference method, a long short-term memory neural network is constructed. The input feature vector includes: the normalized value at the current time step, the normalized value at the current depth, the historical concentration gradient sequence, the current diffusion coefficient estimate, the current surface chloride ion concentration, and the current temperature. The network output is the concentration increment. The training objective is to minimize the mean squared error between the predicted increment and its actual value. The final output of the hybrid predictor is:

[0068]

[0069] In the formula: This represents the predicted chloride ion concentration at depth x and time t. The depth from the exposed concrete surface is represented by t, and the service time is represented by t.

[0070] Step S5: Probabilistic lifetime prediction and Bayesian dynamic update

[0071] Setting the depth of reinforcing bars and critical chloride ion concentration threshold Based on the posterior distribution of the parameters obtained in steps S2 and S3 (including...) , (And each Fourier coefficient), and perform a large number of random samplings to generate a parameter sample set. For each sample, call the hybrid predictor to simulate the time history of chloride ion concentration at the depth of the rebar, and record the first time when the concentration first reaches the critical threshold. Obtain the sample set .

[0072] Formula 7 (Kernel density estimation of the fitted probability density function):

[0073]

[0074] In the formula: This represents the length of the m-th temperature change cycle, where m represents the measurement sequence number. The function represents the change of temperature over time, where t represents the service time.

[0075] in The Gaussian kernel function has a bandwidth of [missing information]. Determined by the Silverman criterion.

[0076] Step S6: Output and Multi-level Early Warning

[0077] The system outputs the remaining lifetime probability distribution (probability density curve, cumulative distribution curve, box plot) and real-time concentration profile in real time. Early warning logic:

[0078] A yellow alert is triggered when the median predicted remaining lifespan is lower than a set percentage of the designed service life.

[0079] An orange alert is triggered when the measured concentration at the depth of the reinforcing steel reaches a set proportion of the critical threshold.

[0080] A red alert is triggered when the measured concentration at the depth of the reinforcing steel reaches or exceeds the critical threshold.

[0081] Early warning information is pushed to the operation and maintenance platform to assist in tiered decision-making.

[0082] Furthermore, the decay function model is in the form of exponential decay. The state equation of the extended Kalman filter uses the current parameter vector to be inverted as the state variable, and the observation equation uses the measured concentration as the observation. The initial diffusion coefficient and decay factor are estimated in real time through recursive iteration.

[0083] During the initial monitoring phase of the sensor, chloride ion concentration data at multiple depths and time points are collected. The state vector is defined to include two components: the initial diffusion coefficient and the attenuation factor. The state equation is set as a random walk model, meaning that the current state vector equals the previous state vector plus process noise, where the process noise reflects the natural random fluctuations of the parameters.

[0084] The observation equation establishes a mapping relationship between measured concentration and state vector: for any depth and time, based on the time-varying diffusion coefficient determined by the current state vector, the concentration prediction value is calculated using the error function solution of Fick's second law. Since the interval between adjacent observation times is short, the diffusion coefficient can be approximated as constant in single-step prediction.

[0085] The Extended Kalman Filter (EKF) recursively performs prediction and update. In the prediction phase, the state prior estimate and its covariance prior matrix are calculated based on the state equation. In the update phase, the partial derivatives of the observation function with respect to the state vector (Jacobi matrix) are first calculated, then the Kalman gain matrix is ​​calculated, and finally, the state prior estimate is corrected using actual concentration observations to obtain the state posterior estimate and the covariance posterior matrix.

[0086] After processing the data from all time points in the initial monitoring phase, the filtering converges to the optimal estimate. Based on this, the time-varying diffusion coefficient model exhibits an exponential decay form: the diffusion coefficient equals the initial diffusion coefficient multiplied by an exponential function with a decay factor as a parameter. This form conforms to the physical law that the density of concrete gradually increases and the resistance to chloride ion diffusion gradually strengthens during cement hydration.

[0087] Furthermore, the input features of the long short-term memory neural network include time step, depth location, historical concentration gradient, current diffusion coefficient estimate, and surface chloride ion concentration; the neural network is used to correct systematic errors caused by model simplification in the finite difference method.

[0088] In hybrid-driven predictors, although the finite difference method satisfies physical conservation, its calculation results exhibit systematic deviations from actual concentrations due to limitations in discrete mesh size and the non-homogeneity of concrete. These deviations follow a pattern related to spatiotemporal location, concentration gradient, diffusion coefficient, and boundary conditions.

[0089] To learn and compensate for this bias, a Long Short-Term Memory (LSTM) neural network is constructed. The network's input feature vector consists of five components: the first is the time step, representing the temporal position of the current moment relative to the starting point; the second is the depth position, representing the spatial coordinates; the third is the historical concentration gradient, i.e., the sequence of concentration changes with depth over several time steps prior to the current moment, used to capture the trend of concentration front movement; the fourth is the current diffusion coefficient estimate, derived from a time-varying diffusion coefficient model; and the fifth is the current surface chloride ion concentration, derived from a dynamic boundary condition fitting function.

[0090] Feature vectors are input into the LSTM layer in chronological order. Each LSTM unit contains a forget gate, input gate, output gate, and cell state, enabling it to selectively remember long-term dependent information and forget irrelevant noise. The network output is a single scalar, representing the concentration prediction increment—the deviation of the actual concentration in that spatiotemporal state from the value calculated using the finite difference method.

[0091] During the training phase, high-precision benchmark data (such as ultra-fine mesh finite element simulation results) is used to generate training samples, and the difference between the finite difference method predicted value and the benchmark true value is calculated as the label. The mean squared error loss is minimized through backpropagation. After training, a neural network is embedded into a hybrid predictor: the finite difference method quickly calculates the physical benchmark value, and the neural network outputs an incremental estimate based on the current features. The two are added together to obtain the final predicted concentration.

[0092] Furthermore, the probability density function was obtained through Monte Carlo simulation. Specifically, a large number of random samples were taken based on the posterior probability distribution of the initial diffusion coefficient, attenuation factor, and surface chloride ion concentration parameters. A prediction model was executed for each sample, the time distribution of the concentration at the location of the steel bar reaching the critical threshold for the first time was statistically analyzed, and the probability density function was obtained by fitting the kernel density estimation.

[0093] After parameter inversion and boundary fitting are completed, the posterior probability distributions of each uncertainty parameter are obtained, including the initial diffusion coefficient, attenuation factor, and coefficients of each order in the Fourier series of surface concentration. Each parameter is described by its mean and variance (or covariance).

[0094] The Monte Carlo simulation process is as follows: Based on the aforementioned posterior distribution, a large number of random samples are generated to produce a parameter sample set. Each sample contains a complete set of parameter values. For each sample, the hybrid predictor is invoked to simulate the evolution curve of chloride ion concentration at the depth of the reinforcing steel bar over a sufficiently long period from the current time to the future. Hourly checks are performed to determine whether the concentration first reaches or exceeds the critical threshold, and the time of this first reach is recorded. If the threshold is not reached throughout the entire simulation period, it is recorded as infinity.

[0095] After all samples have been processed, the first-arrival time sample set is obtained. Kernel density estimation is used to transform the discrete samples into a continuous probability density function: a Gaussian kernel function is placed at each sample point, all kernels are superimposed and normalized, and the bandwidth is determined through cross-validation or empirical rules. Finally, a smooth probability density function is obtained, with an integral value of one. Integrating this function yields the cumulative distribution function, and the inverse function gives the first-arrival time corresponding to any quantile.

[0096] Furthermore, the all-solid-state three-electrode system in the electrochemical concrete chloride ion penetration depth sensor is arranged in multiple groups at equal intervals along the axial direction of the sensing substrate, providing high depth resolution. Its in-situ monitoring data is directly used as the input to the spatiotemporal concentration field dataset.

[0097] The sensor's sensing substrate is a slender rod-shaped structure with multiple mounting slots precisely machined along the axial direction, with equal center-to-center distance between adjacent slots. Each mounting slot contains a set of all-solid-state three-electrode systems, including a working electrode, a reference electrode, and a counter electrode. Each electrode set operates independently, synchronously measuring the chloride ion concentration at its corresponding depth.

[0098] After the sensor is pre-embedded, concentration data at each depth measuring point (determined by the axial coordinate of the mounting groove) is collected in real time. Due to the small and uniform electrode spacing, the sensor provides a fine distribution of chloride ion concentration along the thickness of the protective layer with high depth resolution (the distance between adjacent measuring points is the resolution).

[0099] This array structure can simultaneously acquire concentration data from multiple depths, from the concrete surface to near the reinforcing bars, forming a high-resolution concentration profile. This data serves directly as the raw input to the spatiotemporal concentration field dataset, requiring no interpolation or smoothing preprocessing. In step S1, the system records the concentration values ​​at each depth and time step according to a set sampling frequency, forming a three-dimensional array. The high depth resolution allows for clear differentiation of the location and shape of the chloride ion permeation front, providing rich spatial information constraints for subsequent inversion of the time-varying diffusion coefficient.

[0100] Furthermore, the sensor's built-in temperature compensation module synchronously collects temperature information, and the apparent diffusion coefficient retrieved in step S2 is further normalized to the reference temperature using the Arrhenius equation.

[0101] The sensor integrates a high-precision temperature-sensitive element and works synchronously with the three-electrode system to record the temperature value at the corresponding depth inside the concrete at each sampling time. Temperature data is collected and transmitted along with concentration data.

[0102] In step S2, during the time-varying diffusion coefficient inversion, the estimated diffusion coefficient at the original temperature is first obtained. Since temperature significantly affects ion mobility, these estimates need to be normalized to the same reference temperature to eliminate interference from ambient temperature fluctuations. Normalization is performed using the Arrhenius equation: the ratio of the diffusion coefficient at any temperature to the diffusion coefficient at the reference temperature is equal to an exponential function with the ratio of excitation energy to the gas constant as the exponent, where the denominator of the exponent term is the absolute temperature, and the numerator is a quantity related to the reference temperature and excitation energy.

[0103] In the specific processing, for each diffusion coefficient value obtained from the inversion, the synchronously recorded temperature value is used to convert it into an equivalent diffusion coefficient at the reference temperature using the Arrhenius relation. A normalized diffusion coefficient sequence is used when constructing the exponential decay model. In subsequent prediction steps, the temperature data monitored in real time by the temperature compensation module is used to convert the diffusion coefficient at the reference temperature back to the actual ambient temperature using the Arrhenius relation, in order to accurately predict chloride ion transport under actual service conditions.

[0104] Furthermore, the monitoring data and prediction results from steps S1 to S5 are mapped in real time into a digital twin model to dynamically display the chloride ion concentration field, the permeation front, and the lifetime probability cloud map using color cloud maps, and to support scenario simulation and lifetime gain assessment for different maintenance strategies.

[0105] Based on the completed predictions, a digital twin system is constructed that interacts with the physical components in real time. This system is based on a 3D visualization platform and maps information such as real-time sensor data, inverted material parameters, and predicted remaining lifetime probability distribution into the virtual model.

[0106] The core display functions include: chloride ion concentration field cloud map - displaying the current concentration at any location within the protective layer in a color gradient manner; dynamic curve of the permeation front - drawing isoconcentration lines in the component profile view and displaying the animation of the front corresponding to the critical threshold migrating inward over time; lifetime probability cloud map - different regions represent the remaining lifetime quantile intervals with hue and transparency, and high-risk areas are highlighted.

[0107] The scenario simulation function allows users to set different maintenance strategies, and the system automatically evaluates the lifetime gain. Supported scenarios include: coating the surface with a rust inhibitor (reducing surface chloride ion flux), increasing the protective layer thickness (extending the diffusion path), and electrochemical dechlorination (changing the internal concentration distribution). After the user selects a strategy, the system recalculates the remaining lifetime probability distribution using the prediction model, compares it with the baseline scenario, and outputs the lifetime extension increment and confidence interval.

[0108] Furthermore, the electrochemical concrete chloride ion penetration depth sensor includes a solar-powered complementary power supply unit, which provides the method with more than ten years of endurance, ensuring the continuous execution of the Bayesian recursive update strategy and enabling the prediction model to self-evolve throughout its entire lifecycle.

[0109] The sensor's power supply unit adopts a three-source complementary architecture: the main energy source is a flexible solar panel, which is attached to the surface of the concrete structure in a location with sufficient sunlight; the auxiliary energy source is a rechargeable lithium battery, which is charged by the solar panel when there is sufficient sunlight; and the backup energy source is a spare disposable lithium battery, which is only activated when both the main and auxiliary energy sources are insufficient.

[0110] The solar power generation module features overcharge, over-discharge, and reverse connection protection. The energy storage module's capacity is matched to ensure that the sensor can continue to operate normally for an extended period even under continuous cloudy or rainy conditions. The power management module monitors the status of each energy source in real time, automatically switching the power supply mode according to sunlight conditions and energy storage capacity, and providing regulated output for the signal acquisition and transmission module.

[0111] The ultra-long-term autonomous power supply enables the sensor to operate continuously throughout the entire lifespan of the structure without the need to replace batteries or external power sources. This provides the necessary data continuity guarantee for the Bayesian recursive update strategy: recursive updates require the continuous absorption of new observation data to correct model parameters. Within the sensor's operational lifespan, the system continuously collects new data at a preset frequency. Each time new data is acquired, the Bayesian recursive update module is automatically triggered to recalculate the posterior distribution of parameters and update the remaining lifetime probability prediction. This process repeats continuously, allowing the prediction model to gradually refine over time, achieving self-evolution of prediction performance.

[0112] Furthermore, the multi-level durability warning signals include yellow, orange, and red warnings, with each level of warning corresponding to specific triggering conditions.

[0113] A yellow alert is triggered when the median predicted remaining lifespan is lower than a set percentage of the design service life. This percentage can be configured according to the owner's safety management requirements. A yellow alert indicates a decline in structural durability reserves; although corrosion has not yet occurred, there is a risk of medium- to long-term failure. Recommended response measures: Increase monitoring frequency, conduct visual inspections, and develop a preventative maintenance plan.

[0114] An orange alert is triggered when the real-time chloride ion concentration at the depth of the reinforcing steel reaches a set percentage of the critical chloride ion concentration threshold. This percentage is typically set in the warning zone below the critical value, indicating that the chloride ion front has approached the steel surface and the depassivation process may be about to begin. An orange alert can also be triggered by a lower quantile (e.g., a decimal place) of the predicted remaining service life being below a more stringent percentage of the design service life. Recommended response measures: Immediately conduct detailed electrochemical testing, prepare a repair plan, and implement surface treatment or rust-inhibiting measures as appropriate.

[0115] A red alert is triggered when the real-time chloride ion concentration at the depth of the reinforcing steel reaches or exceeds the critical chloride ion concentration threshold. This means that the accumulated chloride ion concentration around the reinforcing steel has met the thermodynamic conditions for depassivation, and corrosion may have already begun. Recommended response measures: Immediately initiate emergency repair procedures, including electrochemical dechlorination, sacrificial anode protection, or localized repairs, while also increasing the load-bearing capacity assessment.

[0116] All warning signals are pushed to the cloud monitoring center via wireless network and displayed prominently in the digital twin model. The warning information includes the current predicted lifetime probability range and measured concentration data, allowing engineers to assess the risk level and select response plans.

[0117] Furthermore, the all-solid-state three-electrode system consists of a silver / silver chloride working electrode, a manganese dioxide / silver oxide all-solid-state reference electrode, and a titanium alloy counter electrode, with no liquid components; the sensing substrate is a polyetheretherketone engineering plastic rod, with six to ten sets of all-solid-state three-electrode systems arranged at equal intervals along the axial direction, corresponding to a monitoring depth covering the conventional protective layer thickness of the main concrete reinforcement.

[0118] The working electrode is a silver / silver chloride ion selective electrode, prepared from high-purity silver wire via electrolytic chlorination. The diameter of the silver wire is selected to suit the processing requirements. The surface of the sensing end is coated with two functional films in sequence: the inner layer is a PVC-based chloride ion selective film with extremely high chloride / hydroxyl ion selectivity, effectively shielding against hydroxide interference in the highly alkaline environment of concrete; the outer layer is a cement-based alkali-resistant protective layer, ensuring compatibility between the electrode and the concrete substrate and resisting erosion by hydration products.

[0119] The reference electrode is a manganese dioxide / silver oxide all-solid-state reference electrode, with no liquid internal reference solution. The potential is stable over a long period with minimal drift, and it can be adapted to the high-alkalinity and humid environment of concrete without maintenance.

[0120] The counter electrode is made of titanium alloy wire, which has excellent corrosion resistance, high conductivity and chemical inertness. It does not participate in the reaction in electrochemical measurement, but only assists in the acquisition of potential signals.

[0121] The sensing substrate is made of polyetheretherketone (PEEK) engineering plastic, integrally molded into a slender rod-like structure. This material possesses comprehensive properties such as high strength, high insulation, resistance to strong alkalis, resistance to concrete hydration erosion, and resistance to vibration and impact.

[0122] Multiple mounting slots are machined along the axial direction of the sensing substrate, with equal spacing between adjacent slots. A complete three-electrode system is fixed within each mounting slot. The number of electrode groups is selected based on the required protective layer thickness, typically six to ten groups, corresponding to a monitoring depth range that fully covers the conventional protective layer thickness of the main concrete reinforcement. The leads of each electrode group are sealed and encapsulated before converging to a shielded signal line at the tail.

[0123] The above description is only a preferred embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any equivalent substitutions or modifications made by those skilled in the art within the scope of the technology disclosed in the present invention, based on the technical solution and inventive concept of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring, characterized in that, Includes the following steps: Step S1: An electrochemical concrete chloride ion penetration depth sensor is pre-embedded in the target reinforced concrete component. Based on the sensor's all-solid-state three-electrode system and array-type sensing substrate, chloride ion concentration data at different depths and times are continuously and in situ collected to form a spatiotemporal concentration field dataset. Step S2: Based on the initial concentration data collected in Step S1, the apparent chloride ion diffusion coefficient in the reinforced concrete cover as a function of time is calculated by using extended Kalman filtering or particle swarm optimization algorithm, and its decay function model is constructed. Step S3: Based on the chloride ion concentration data at the concrete surface collected in Step S1, the time-varying surface chloride ion concentration function under environmental influence is fitted using Fourier series or piecewise Gaussian process. Step S4: Substitute the time-varying diffusion coefficient from step S2 and the dynamic surface chloride ion concentration function from step S3 into the modified Fick's second law, and use the finite difference method combined with a long short-term memory neural network to perform a hybrid numerical-intelligent solution to construct a chloride ion concentration spatiotemporal distribution predictor. Step S5: Based on the predictor in step S4, and combined with the critical chloride ion concentration threshold for depassivation of the steel bar, solve the probability density function of the chloride ion concentration at the depth of the steel bar reaching the threshold for the first time, and then calculate the probability distribution of the remaining life of the component; and use subsequent real-time monitoring data to dynamically correct the model parameters through a Bayesian recursive update algorithm to achieve real-time calibration and uncertainty quantification of the prediction results. Step S6: Output the predicted remaining life probability range of reinforced concrete components. When the predicted life is lower than the design service life or the real-time monitoring concentration exceeds the warning threshold, automatically issue a multi-level durability warning signal.

2. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The decay function model described in step S2 is in the form of exponential decay. The state equation of the extended Kalman filter uses the current parameter vector to be inverted as the state variable, and the observation equation uses the measured concentration as the observation. The initial diffusion coefficient and decay factor are estimated in real time through recursive iteration.

3. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The input features of the long short-term memory neural network in step S4 include time step, depth location, historical concentration gradient, current diffusion coefficient estimate, and surface chloride ion concentration; the neural network is used to correct systematic errors caused by model simplification in the finite difference method.

4. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The probability density function mentioned in step S5 is obtained by Monte Carlo simulation method. Specifically, a large number of random samples are taken based on the posterior probability distribution of the initial diffusion coefficient, attenuation factor and surface chloride ion concentration parameters. The prediction model of step S4 is executed for each sample. The time distribution of the concentration at the location of the steel bar reaching the critical threshold for the first time is statistically analyzed, and the probability density function is obtained by fitting with kernel density estimation.

5. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The all-solid-state three-electrode system in the electrochemical concrete chloride ion penetration depth sensor is arranged in multiple groups at equal intervals along the axial direction of the sensing substrate, providing high depth resolution. Its in-situ monitoring data is directly used as the input of the spatiotemporal concentration field dataset in step S1.

6. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The electrochemical concrete chloride ion penetration depth sensor has a built-in temperature compensation module, and the collected data synchronously includes temperature information. The apparent diffusion coefficient retrieved in step S2 is further normalized to the reference temperature using the Arrhenius equation to eliminate the influence of temperature fluctuations on the identification of diffusion parameters.

7. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, It also includes step S7: mapping the monitoring data and prediction results from steps S1 to S5 to a component-level or structural-level digital twin model in real time, dynamically displaying the chloride ion concentration field, permeation front, and lifetime probability cloud map with color cloud maps, and supporting scenario simulation and lifetime gain effect evaluation of different maintenance strategies.

8. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The electrochemical concrete chloride ion penetration depth sensor includes a solar complementary power supply unit, which provides the method with a power supply capability of more than ten years, ensuring that the Bayesian recursive update strategy based on long-term monitoring data in step S5 can be continuously executed, and realizing the self-evolution of the prediction model throughout its entire life cycle.

9. The method for predicting the lifespan of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The multi-level durability warning signals mentioned in step S6 include: a yellow warning, used to indicate the percentage of predicted remaining service life that is less than the design life; an orange warning, used to indicate the percentage of measured chloride ion concentration at the depth of the reinforcing steel that reaches a critical threshold; and a red warning, used to indicate that the measured chloride ion concentration at the depth of the reinforcing steel reaches or exceeds the critical threshold.

10. The method for predicting the life of reinforced concrete components based on chloride ion concentration monitoring according to claim 1, characterized in that, The all-solid-state three-electrode system of the electrochemical concrete chloride ion penetration depth sensor described in step S1 consists of a silver / silver chloride working electrode, a manganese dioxide / silver oxide all-solid-state reference electrode, and a titanium alloy counter electrode, with no liquid components; the sensing substrate is a polyetheretherketone engineering plastic rod, and six to ten sets of the all-solid-state three-electrode system are arranged at equal intervals along the axial direction, corresponding to a monitoring depth covering the conventional protective layer thickness of the main concrete reinforcement.

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