Humidity optimization control method for foamed concrete member curing process

Abstract

The invention discloses a curing and curing humidity control method for foamed concrete, and the method comprises the following steps: S1, data collection, data preprocessing and model initialization; step S2: a, based on the statistical characteristics of the humidity prediction residual error, carrying out preliminary adjustment on the process noise covariance matrix Q in the step S1; b, further adjusting the process noise covariance matrix Q in the step S1 based on the space gradient of the humidity prediction residual; and S3, carrying out humidity estimation and maintenance humidity control based on adaptive Kalman filtering. The invention relates to the technical field of data processing, and has the beneficial effects that a humidity control method can be combined with control strategies such as model prediction control and the like, and optimal control on a spraying area, spraying quantity and spraying time is realized by utilizing a humidity prediction model and an optimization algorithm, so that the curing quality of foamed concrete is improved, the cracking risk is reduced, and the quality of the foamed concrete is improved. The performance and the durability are ensured.

Description

Technical Field

[0001] The present invention relates to the field of concrete humidity control, and particularly to a humidity control method for the curing and maintenance of foamed concrete. Background Art

[0002] The performance of concrete is closely related to its curing process. Sufficient moisture during the hardening process of concrete is a necessary condition for the hydration reaction of cement and is crucial for the development of concrete strength and durability. Foamed concrete is more sensitive to humidity changes due to its porous structure. Too low humidity during the curing process will cause the concrete to lose water too quickly, resulting in problems such as plastic shrinkage cracking, reduced strength, and poor durability; too high humidity will lead to the accumulation of surface hydration products, affecting the appearance quality and even delaying the hardening process. Precise control of the humidity during the curing of foamed concrete is of great significance for ensuring its engineering quality.

[0003] Traditional concrete curing methods, such as sprinkler curing and covering curing, mainly rely on experience and manual operation, making it difficult to achieve precise control of humidity and prone to local over-wetting or drying. In recent years, with the development of sensor technology and automatic control technology, some automatic spraying curing systems based on sensor feedback have emerged. These systems can improve the accuracy and efficiency of humidity control to a certain extent by monitoring the humidity on the concrete surface in real time and automatically controlling the start and stop of the spraying device.

[0004] To more accurately describe the spatio-temporal evolution of the humidity field inside concrete, some studies have applied Fick's second law to model the humidity diffusion process in concrete. The humidity diffusion model established based on Fick's second law can reflect the variation law of humidity with time and space. At the same time, in order to estimate the humidity distribution inside concrete using limited sensor measurement information, state estimation algorithms such as Kalman Filter have also been introduced into concrete humidity estimation. The Kalman Filter is a recursive estimation algorithm that can fuse the model prediction value and the sensor measurement value to give the optimal estimate of the system state. Summary of the Invention

[0005] The purpose of the present invention is to solve the above problems and design a humidity control method for the curing and maintenance of foamed concrete.

[0006] The technical solution of the present invention to achieve the above purpose is a humidity control method for the curing and maintenance of foamed concrete, including the following steps:

[0007] Step S1: Data collection, data preprocessing, and model initialization;

[0008] Step S2:

[0009] a. Based on the statistical characteristics of the humidity prediction residuals, preliminarily adjust the process noise covariance matrix in the model initialization in step S1 ;

[0010] b. Based on the spatial gradient of the humidity prediction residuals, further adjust the process noise covariance matrix in the model initialization in step S1 ;

[0011] Step : Humidity estimation and curing humidity control based on adaptive Kalman filtering

[0012] Furthermore, in step S1, humidity data is obtained, the ambient temperature and humidity are measured through humidity sensors arranged inside and on the surface of the foamed concrete component, and they are recorded simultaneously at the same time to form time series data

[0013] Data preprocessing

[0014] The collected data is processed as follows: Detect outliers to eliminate obvious incorrect data, and correct suspicious data; Use the moving average filtering method to smooth the data and reduce the influence of random noise

[0015] The following operations are performed in model initialization

[0016] Define the state vector : Divide the foamed concrete component into three-dimensional grids, and the state vector contains the humidity values of each grid node

[0017] ;

[0018] where is the humidity value of the grid node in the th row, th column, and th layer, , , are respectively the number of grid nodes in the directions

[0019] Construct the state transition matrix : Based on the three-dimensional humidity diffusion equation, discretize it using the finite difference method to obtain the state transition matrix , considering the humidity-dependent diffusion coefficient , optionally considering the influence of heat of hydration, according to the boundary conditions, correct . In the central difference format, the discretized form of the three-dimensional humidity diffusion equation is as follows

[0020] ;

[0021] wherein, : the humidity value of the th grid node at a moment; : the time step; : are respectively the grid spacings in the directions;

[0022] Combining the discretized equations of all grid nodes can obtain the state transition matrix which is a sparse matrix, and its non-zero elements are determined by the above difference scheme and boundary conditions;

[0023] Construct the observation matrix : mapping the state vector to the sensor measurement value, the number of rows of

[0024] Initialize the state estimate : Use the humidity sensor to measure the humidity distribution of the component at the initial moment as the initial state estimate;

[0025] Initialize the state estimate covariance matrix : Set it as a relatively large diagonal matrix, indicating a high uncertainty in the initial estimate. The diagonal elements can be set as the variances of the initial humidity measurements;

[0026] Initialize the process noise covariance matrix : Set it as a diagonal matrix, and the diagonal elements represent the initial variances of each state variable, and the diagonal elements of

[0027] Initialize the measurement noise covariance matrix : Set it according to the accuracy index of the humidity sensor, which is also a diagonal matrix, and the diagonal elements represent the measurement noise variances of each sensor.

[0028] Furthermore, for a in step S2, based on the statistical characteristics of the humidity prediction residual, the specific steps for preliminary adjustment of the process noise covariance matrix in step S1 are as follows:

[0029] Based on the statistical characteristics of the humidity prediction residual for The matrix is initially adjusted, and the humidity prediction residual is the difference between the sensor measurement value and the model prediction value. The non-Gaussian degree is quantified by calculating the kurtosis and skewness of the residual sequence. The kurtosis reflects the peakedness of the distribution, and the skewness reflects the asymmetry of the distribution. Based on the kurtosis and skewness, a non-Gaussianity index is constructed, abbreviated as: and dynamically adjust according to the magnitude of the matrix, calculate the humidity prediction residual, that is, the difference between the sensor measurement value and the model prediction value:

[0030] ;

[0031] where is the humidity prediction residual vector at time is the humidity sensor measurement value vector at time is the observation matrix; is the predicted state vector at time based on the state at time

[0032] For each sensor , calculate the kurtosis and skewness of its residual sequence within a sliding window. The size of the sliding window is , that is, considering the residuals of the past time steps. The sliding window: The sliding window is used to calculate the local statistical characteristics of the residual sequence, that is, kurtosis and skewness. The calculation formulas for kurtosis and skewness are as follows:

[0033] ;

[0034] ;

[0035] where is the kurtosis of the residual sequence of sensor at time ; is the skewness of the residual sequence of sensor at time ; is the humidity prediction residual of sensor at time ; is the mean value of the residuals within the sliding window;

[0036] Based on the kurtosis and skewness, construct a non-Gaussianity index :

[0037] ;

[0038] Among them, is the non-Gaussianity index at the moment; is the number of sensors; and are respectively the kurtosis and skewness weights of the

[0039] Construct the optimization factor:

[0040] ;

[0041] Among them, is the optimization factor at the is the adaptive forgetting factor;

[0042] The update formula of

[0043] ;

[0044] Among them, is the forgetting factor coefficient ; is the initial value of, which can be set to or ;

[0045] Update the process noise covariance matrix :

[0046] ;

[0047] Among them, is the updated process noise covariance matrix at the is the reference value of the process noise covariance matrix.

[0048] Furthermore, in step S2, based on the spatial gradient of the humidity prediction residual, the process noise covariance matrix in step S1 is further adjusted. The specific steps are as follows:

[0049] In step , based on the statistical characteristics of the humidity prediction residual, namely kurtosis and skewness, the process noise covariance matrix was initially adjusted to adapt to the non-Gaussianity of the process noise. On the basis of step , considering the spatial gradient information of the humidity prediction residual, the process noise covariance matrix is adjusted. Based on the spatial gradient of the humidity prediction residual, a local anomaly index is constructed, abbreviated as: ; Calculate the spatial gradient of the humidity prediction residual. For the three-dimensional case, the sensors are distributed in a three-dimensional grid inside the foamed concrete component. For the sensors , where are the number of sensors in the three directions respectively), and its residual gradient at can be expressed as:

[0050] ;

[0051] ;

[0052] ;

[0053] ;

[0054] Among them, is the gradient of the residual of sensor in the direction at ; is the gradient of the residual of sensor in the direction at ; is the gradient of the residual of sensor in the direction at ; is the magnitude of the residual gradient of sensor at ; is the humidity prediction residual of sensor at ; and are the spacings of the sensor in the and directions respectively;

[0055] Calculate the expected residual gradient. The following formula is used to calculate the expected residual gradient:

[0056] ;

[0057] Among them, is the magnitude of the expected residual gradient of sensor at , represents the expected residual; is the humidity diffusion coefficient calculated according to the time prediction state ; is calculated according to the prediction state to obtain The magnitude of the humidity gradient at a moment, whose calculation method is similar to that of the residual gradient, except that the residual is replaced by the predicted humidity value :

[0058] ;

[0059] ;

[0060] ;

[0061] ;

[0062] Based on the actual residual gradient and the expected residual gradient, construct a local anomaly index, abbreviated as :

[0063] ;

[0064] where is the local anomaly index of the sensor at moment; is a very small positive number;

[0065] Construct an optimization factor :

[0066] ;

[0067] where is the optimization factor at moment; is the number of effective sensors participating in the calculation; is an adjustable parameter;

[0068] Update the process noise covariance matrix :

[0069] ;

[0070] where is the process noise covariance matrix adjusted at moment through step ; is the process noise covariance matrix adjusted at moment through step ;

[0071] Further, based on the humidity estimation result obtained in the foregoing steps, humidity control is performed during the curing process of the foamed concrete. At each time step, the optimal estimation of the internal humidity field of the concrete at the current moment is obtained by using the optimized adaptive Kalman filtering algorithm to form a humidity estimation value. According to this humidity estimation value and in combination with the preset humidity control target, it is judged whether spraying is required. The surface humidity estimation value determines whether to start the spraying system. When the surface humidity is lower than the set lower limit, spraying is triggered.

[0072] Further, the internal humidity estimation value and the calculated humidity gradient information are used to assist in decision-making. When the internal humidity is generally low or there are areas with excessively large local humidity gradients, even if the surface humidity meets the requirements, the spraying strategy can be appropriately adjusted to achieve more refined and forward-looking humidity control.

[0073] A humidity optimization control method for the curing process of foamed concrete components fabricated by using the technical solution of the present invention. The humidity control method can be combined with control strategies such as model predictive control ( ), etc. By using the humidity prediction model and the optimization algorithm, the optimized control of the spraying area, spraying amount, and spraying time is realized. In this way, the present invention can effectively solve the problems of insufficient humidity control accuracy, difficulty in taking into account the surface and internal humidity requirements, and inability to effectively handle local anomalies in the prior art, thereby improving the curing quality of foamed concrete, reducing the cracking risk, and ensuring its performance and durability. Description of the Drawings

[0074] Figure 1 is a structural schematic diagram of a humidity optimization control method for the curing process of foamed concrete components described in the present invention. Detailed Embodiments

[0075] The present invention will be specifically described below with reference to the drawings. As Figure 1 shown, a humidity control method for the curing of foamed concrete, steps : Data acquisition, preprocessing, and model initialization.

[0076] First, data acquisition, data preprocessing, and model initialization are performed.

[0077] In terms of data acquisition, humidity data is obtained by humidity sensors arranged inside and on the surface of the foamed concrete components. The sensor types can be selected as resistive, capacitive, fiber optic, etc. For the internal sensors, their arrangement method is a regular grid (three-dimensional) arrangement; for the surface sensors, a uniform distribution arrangement is adopted. The number and spacing of the sensors need to be determined according to the size and shape of the components. In addition, the ambient temperature and humidity also need to be measured simultaneously for subsequent model calculation and boundary condition determination. The sensor measurement data (humidity, temperature) and the time stamp are recorded together to form time series data.

[0078] In terms of data preprocessing, the collected data is processed as follows: Detect outliers to eliminate obviously incorrect data, and correct suspicious data; Use the moving average filtering method to smooth the data and reduce the influence of random noise; If the sampling times of different sensors or data acquisition systems are not synchronized, time synchronization processing is required to align the data to a unified time reference.

[0079] In terms of model initialization, the present invention performs the following operations:

[0080] Define the state vector : Divide the foamed concrete component into three-dimensional grids, and the state vector contains the humidity values of each grid node:

[0081] ;

[0082] Among them, is the humidity value of the grid node in the row, column, and layer, , , are respectively the number of grid nodes in the

[0083] Construct the state transition matrix : Based on the three-dimensional humidity diffusion equation, use the finite difference method ( ) for discretization to obtain the state transition matrix . Considering the diffusion coefficient dependent on humidity, optionally consider the influence of hydration heat release, and correct according to the boundary conditions (perfectly dry, given humidity, convection).

[0084] Taking the central difference format as an example, the discretized form of the three-dimensional humidity diffusion equation is as follows:

[0085] ;

[0086] Among them:

[0087] : the humidity value of the th grid node at time

[0088] : The time step.

[0089] : Are respectively the grid spacings in the

[0090] , and the same applies to other directions.

[0091] Combining the discretized equations of all grid nodes can obtain the state transition matrix . is a sparse matrix, and its non-zero elements are determined by the above difference scheme and boundary conditions.

[0092] Construct the observation matrix : Map the state vector to the sensor measurement value. The number of rows of is equal to the number of sensors, and the number of columns is equal to the number of state variables (total number of grid nodes). Each row corresponds to a sensor, and the element corresponding to the grid node where the sensor is located in this row is .

[0093] Initialize the state estimate : Use the humidity sensor to measure the humidity distribution of the component at the initial moment as the initial state estimate.

[0094] Initialize the state estimate covariance matrix : Set it as a large diagonal matrix, indicating a high uncertainty in the initial estimate. The diagonal elements can be set as the variance of the initial humidity measurement or set according to experience.

[0095] Initialize the process noise covariance matrix : Set it as a diagonal matrix, and the diagonal elements represent the initial variances of each state variable. Due to the lack of prior knowledge, the diagonal elements of

[0096] Initialize the measurement noise covariance matrix : Set it according to the accuracy index of the humidity sensor. is also a diagonal matrix, and the diagonal elements represent the measurement noise variances of each sensor.

[0097] It should be noted that: The adopted model and initialization method are based on existing technologies, including the three-dimensional humidity diffusion equation described by the second law, the finite difference method ( ), the numerical discretization method, and the Kalman filter state estimation algorithm. Specifically, the present invention is based on the second law to establish a humidity diffusion model, uses the central difference scheme to discretize the diffusion equation, and obtains the state transition matrix The Kalman filter algorithm is used for humidity state estimation, and the state estimation is updated according to the sensor measurement values. The initial parameters of the Kalman filter algorithm, including the initial state estimate value, state estimation covariance matrix, process noise covariance matrix, and measurement noise covariance matrix, are all set according to the conventional method.

[0098] Step :

[0099] a. Based on the statistical characteristics of the humidity prediction residuals, the process noise covariance matrix is preliminarily adjusted.

[0100] During the curing process of foamed concrete, the spatio-temporal evolution of the humidity field is affected by various factors. In addition to the main humidity diffusion process, there are many complex factors that are difficult to accurately model. These complex factors cause the actual process noise to deviate from the Gaussian white noise distribution assumed by the traditional Kalman filter algorithm, resulting in a decrease in the filtering estimation accuracy.

[0101] First of all, the inhomogeneity of the foamed concrete material is an important factor leading to the complication of the process noise. The internal pore structure of foamed concrete (such as pore size, porosity, connectivity, etc.) is not completely uniform, but shows a certain random distribution. This inhomogeneity of the microscopic structure leads to differences in the humidity diffusion ability at different positions, making it difficult for the macroscopic model to accurately describe the humidity changes in each tiny area, thus generating prediction deviations, which are attributed to the process noise in the Kalman filter.

[0102] Secondly, the complexity of the cement hydration reaction also has a significant impact on the characteristics of the process noise. Cement hydration is a complex physico-chemical process involving multiple mineral components and multiple reaction stages, and its rate is non-linearly affected by various factors such as temperature, humidity, cement mineral composition, and admixtures. The hydration reaction not only consumes water and changes the humidity field, but also causes changes in the pore structure, further affecting the humidity diffusion. Existing models usually adopt simplified hydration models, which are difficult to accurately describe the dynamic impact of the hydration process on the humidity field, thus leading to the complication of the process noise.

[0103] In addition, the complexity and uncertainty of the boundary conditions are also important sources of the process noise. The moisture exchange between the concrete surface and the surrounding environment is affected by various factors such as wind speed, ambient temperature and humidity, and surface covering conditions. These factors are often difficult to accurately measure or predict, and may change over time, resulting in the boundary conditions being difficult to accurately determine. This uncertainty will affect the humidity field inside the concrete through the boundary, thereby increasing the process noise.

[0104] Due to the combined effect of the above complex factors, the actual process noise often does not satisfy the assumptions of traditional Kalman filtering. Specifically, the process noise no longer follows a Gaussian distribution but exhibits non-Gaussianity, that is, the probability distribution shows skewness (skewness is not zero) or has longer tails (kurtosis deviates from 3); the statistical characteristics (such as variance) of the process noise change over time, showing time-variation; due to material inhomogeneity and spatial differences in the hydration reaction, there is a correlation in the humidity changes in adjacent regions, resulting in the process noise not being spatially independent and showing spatial correlation.

[0105] In traditional Kalman filtering, the process noise covariance matrix is usually set as a fixed diagonal matrix, which cannot reflect the non-Gaussianity, time-variation, and spatial correlation of the process noise. This will lead to a decrease in the estimation accuracy of Kalman filtering and even cause the filter to diverge. To solve this problem, a preliminary adjustment of the matrix is proposed based on the statistical characteristics of the humidity prediction residuals. The humidity prediction residuals, that is, the difference between the sensor measurement value and the model prediction value, contain information not captured by the model and can reflect the characteristics of the process noise.

[0106] Specifically, the non-Gaussian degree is quantified by calculating the kurtosis and skewness of the residual sequence. Kurtosis and skewness are common indicators in statistics to measure the degree of deviation of data distribution from the normal distribution. Kurtosis reflects the peakedness of the distribution, and skewness reflects the asymmetry of the distribution. Based on kurtosis and skewness, a non-Gaussianity index ( is constructed, and the matrix is dynamically adjusted according to the magnitude of : when is large, it indicates that the non-Gaussianity of the process noise is strong, and the matrix is increased to reduce the dependence on the sensor measurement value; when is small, it indicates that the process noise is close to the Gaussian distribution, and the matrix is decreased to trust the sensor measurement value more. In this way, the matrix can adaptively reflect the non-Gaussian characteristics of the process noise, thereby improving the estimation accuracy of Kalman filtering.

[0107] First, calculate the humidity prediction residuals, that is, the difference between the sensor measurement value and the model prediction value:

[0108] ;

[0109] where:

[0110] is the humidity prediction residual vector at time (the dimension is , (where is the number of sensors). It represents the difference between the model predicted value and the actual measured value of the sensor. The larger the residual, the less accurate the model prediction.

[0111] is the vector of humidity sensor measurement values at time (with dimension ). It is the humidity value directly measured by the humidity sensors arranged in the foamed concrete component.

[0112] is the observation matrix (with dimension , being the number of state variables). It describes the relationship between the state variables (i.e., the humidity at each point inside the concrete) and the sensor measurement values. Each row of corresponds to a sensor, and the element of the state variable corresponding to the position of this sensor in this row is , and the other elements are .

[0113] is the predicted state vector at time based on the state at time (with dimension ). It is the humidity value at each point inside the concrete predicted according to the humidity diffusion model (state transition equation) at time . at time.

[0114] Subsequently, for each sensor , calculate the kurtosis of its residual sequence within the sliding window and skewness . The size of the sliding window is (i.e., considering the residuals of the past time steps).

[0115] Sliding window: The sliding window is used to calculate the local statistical characteristics (kurtosis and skewness) of the residual sequence, and the selection of its size needs to be balanced: If it is too small, the statistical results are easily affected by random noise; If it is too large, it is difficult to reflect the time-varying characteristics of the noise. It is determined based on experience or experiments.

[0116] The calculation formulas for kurtosis and skewness are as follows:

[0117] ;

[0118] ;

[0119] Where:

[0120] is the sensor at the kurtosis of the residual sequence at time. Kurtosis is an index to measure the sharpness of data distribution. For a normal distribution (Gaussian distribution), the kurtosis is . If the kurtosis is greater than , it means the distribution is sharper than the normal distribution; if the kurtosis is less than , it means the distribution is flatter than the normal distribution.

[0121] is the sensor at the skewness of the residual sequence at time. Skewness is an index to measure the symmetry of data distribution. For a normal distribution, the skewness is . If the skewness is greater than , it means the distribution is right-skewed (the long tail is on the right); if the skewness is less than , it means the distribution is left-skewed.

[0122] is the sensor at the humidity prediction residual at time.

[0123] is the mean residual within the sliding window. It represents the average residual of the sensor in the past time steps.

[0124] Based on kurtosis and skewness, construct a non-Gaussianity index :

[0125] ;

[0126] where:

[0127] is the non-Gaussianity index (scalar) at time; it comprehensively reflects the non-Gaussian degree of all sensor residual sequences; the larger it is, the stronger the overall non-Gaussianity; is the number of sensors; and are respectively the kurtosis and skewness weights of the th sensor. They are set according to the importance or reliability of different sensors. If a certain sensor is more vulnerable to interference, or its measured value has less impact on the overall humidity estimation, its weight can be set to a smaller value. Usually, if there is no special reason, the weights of all sensors are set to .

[0128] Further, construct the optimization factor

[0129] ;

[0130] in:

[0131] for The optimization factor (scalar) at the moment. It is based on the non-Gaussian index The size of the process noise covariance matrix is ​​adjusted .

[0132] is the adaptive forgetting factor. It is used to smooth changes and make the algorithm focus more on recent data, thereby reducing the impact of historical data. The update formula is:

[0133] ;

[0134] in, is the forgetting factor coefficient . The closer , indicating that the greater the impact of historical data, The more gradual the change; The closer , which means the smaller the impact of historical data, More sensitive to changes in current data. Typically, Can be taken close The value of wait.

[0135] for The initial value can be set to or .

[0136] Finally, the process noise covariance matrix is ​​updated :

[0137] ;

[0138] in:

[0139] for The updated process noise covariance matrix is ​​an important parameter in the Kalman filter algorithm, reflecting the uncertainty of the model prediction. The larger it is, the less reliable the model prediction is, and the Kalman filter will rely more on sensor measurements; The smaller it is, the more reliable the model prediction is, and the Kalman filter will rely more on the model prediction.

[0140] is the reference value (initial value) of the process noise covariance matrix. It is usually set according to prior knowledge of model uncertainty. In the absence of prior knowledge, is set to a diagonal matrix, and the diagonal elements represent the initial variances of each state variable.

[0141] Explanation of the functions of each part of the formula:

[0142] By dynamically adjusting the process noise covariance matrix , the accuracy of the Kalman filter in the humidity estimation of foamed concrete is improved. The design of the above formula is precisely to achieve this goal. First, the calculation of the humidity prediction residual is the basis of the entire optimization strategy. The residual reflects the difference between the model prediction and the actual observation, and these differences mainly come from the process noise and various complex factors not considered in the model. Therefore, the analysis of the residual can reveal the characteristics of the process noise and provide a basis for adjusting the matrix.

[0143] Secondly, the introduction of kurtosis and skewness is to quantify the non-Gaussian degree of the residual sequence. The traditional Kalman filter assumes that the process noise follows a Gaussian distribution, but in practical applications, due to factors such as material inhomogeneity and hydration reaction, the process noise often shows non-Gaussian characteristics. Kurtosis and skewness are commonly used indicators in statistics to measure the degree of deviation of data distribution from the Gaussian distribution. By calculating the kurtosis and skewness of the residual sequence, it is judged whether the process noise has non-Gaussianity and the strength of non-Gaussianity.

[0144] Furthermore, a non-Gaussianity index is constructed to integrate the kurtosis and skewness information of all sensors and obtain an overall non-Gaussianity measure. The advantage of doing this is to avoid the influence of outliers of individual sensors on the overall judgment and improve the stability of the evaluation. The larger the value of

[0145] is, the stronger the non-Gaussianity of the process noise and the lower the reliability of the model prediction. Based on the non-Gaussianity index , an optimization factor is designed. The role of is to dynamically adjust the matrix according to the size of . When , making the Kalman filter rely more on model predictions and reducing trust in sensor measurements that may contain outliers. When is small, it indicates that the process noise is close to a Gaussian distribution. At this time, is close to , is close to its reference value , and the Kalman filter works in a conventional manner.

[0146] To make the change of smoother and avoid drastic fluctuations in the matrix caused by abnormal data at individual moments, an adaptive forgetting factor is introduced. can perform a weighted average on the historical values of , so that the at the current moment is not only affected by the at the current moment, but also affected by the at past moments, and the weights of data closer to the current moment are larger. This can improve the stability of the algorithm and make it pay more attention to recent data, thus better adapting to the time-varying characteristics of the process noise.

[0147] Finally, by to adjust the matrix, the optimization of the Kalman filter algorithm is achieved. The adjusted matrix can adaptively reflect the non-Gaussian characteristics of the process noise, enabling the Kalman filter to maintain a high estimation accuracy when facing complex and non-Gaussian process noise.

[0148] b. Based on the spatial gradient of the humidity prediction residuals, further adjustment is made to the process noise covariance matrix .

[0149] In step , the process noise covariance matrix was initially adjusted based on the statistical characteristics (kurtosis and skewness) of the humidity prediction residuals to adapt to the non-Gaussian nature of the process noise. However, the adjustment in step mainly focuses on the characteristics of the residual sequence in the time dimension and ignores the information of the residuals in the spatial dimension. During the curing process of foamed concrete, due to the inhomogeneity of the material and the spatial differences in hydration reactions, boundary conditions, etc., the humidity field often exhibits complex spatial distribution characteristics, and there are significant humidity gradients between adjacent regions. This spatial gradient information is crucial for accurately estimating the humidity field.

[0150] Traditional Kalman filtering assumes that the process noise is spatially independent, that is, the process noises at different positions are uncorrelated with each other. This assumption often does not hold when there are significant spatial gradients in the humidity field. For example, if the humidity changes abnormally in a certain area due to material defects or local drying, this abnormality will not only affect the humidity estimation in that area, but also affect the humidity estimation in its surrounding areas. If this spatial correlation is ignored, the estimation accuracy of the Kalman filter will be affected.

[0151] To solve this problem, the present invention further considers the spatial gradient information of the humidity prediction residuals on the basis of step to adjust the process noise covariance matrix . Specifically, if the humidity prediction residual gradient in a certain area is significantly greater than the expected gradient calculated according to the humidity diffusion model, it indicates that there are local anomalies (such as material defects, local drying, abnormal hydration reactions, etc.) that are not captured by the model in this area. These local anomalies will cause the process noise to show spatial correlation, and its intensity is related to the magnitude of the residual gradient.

[0152] Therefore, based on the spatial gradient of the humidity prediction residuals, a local anomaly index ( ) is constructed. The larger it is, the more the humidity change in this area deviates from the model's expectation, and the more significant the local anomaly is. Then, according to the magnitude of , the matrix is further adjusted. When is large, it indicates that there are strong local anomalies, and further increase the matrix to make the Kalman filter more dependent on the spatial smoothing effect of the model prediction results, reduce the trust in the sensor measurement values in this area, so as to reduce the impact of local anomalies on the overall humidity estimation. When is small, it indicates that the humidity change in this area conforms to the model expectation, keep the matrix unchanged, or slightly reduce the matrix.

[0153] In this way, the matrix can not only reflect the non-Gaussianity of the process noise (step ), but also reflect the spatial correlation of the process noise, so as to more comprehensively adapt to the complex characteristics of the humidity field of foamed concrete and further improve the estimation accuracy and robustness of the Kalman filter.

[0154] First, calculate the spatial gradient of the humidity prediction residuals. For the three-dimensional case, the sensors are distributed in a three-dimensional grid inside the foamed concrete component. Then, for the sensor , where are the number of sensors in the three directions respectively), its residual gradient at time can be expressed as:

[0155] ;

[0156] ;

[0157] ;

[0158] ;

[0159] wherein:

[0160] is the sensor at the gradient of the residual at time in the direction of.

[0161] is the sensor at the gradient of the residual at time in the direction of.

[0162] is the sensor at the gradient of the residual at time in the direction of.

[0163] is the sensor at the magnitude (scalar) of the residual gradient at time.

[0164] is the sensor at the humidity prediction residual at time.

[0165] and are respectively the spacings of the sensor in and directions.

[0166] Subsequently, the expected residual gradient is calculated. The expected residual gradient is calculated according to the humidity diffusion model, which reflects the expected value of the residual gradient in the absence of local anomalies. The present invention calculates the expected residual gradient using the following formula:

[0167] ;

[0168] wherein:

[0169] is the magnitude (scalar) of the expected residual gradient of the sensor at time, Denotes the expected residual.

[0170] Is based on The predicted state at the moment The humidity diffusion coefficient calculated.

[0171] Is the Magnitude of the humidity gradient at the moment calculated according to the predicted state. Its calculation method is similar to the residual gradient, except that the residual Is replaced with the predicted humidity value :

[0172] ;

[0173] ;

[0174] ;

[0175] ;

[0176] Based on the actual residual gradient and the expected residual gradient, construct the local anomaly index (LAI):

[0177] ;

[0178] Where:

[0179] Is the sensor At The local anomaly index (scalar) at the moment. It reflects the deviation degree between the actual residual gradient and the expected residual gradient. The larger it is, the more the humidity change in this area deviates from the model's expectation, and the more significant the local anomaly is.

[0180] Is a very small positive number, used to prevent the denominator from being zero. In the embodiment of the present invention, it is set to .

[0181] Furthermore, construct the optimization factor :

[0182] ;

[0183] Where:

[0184] Is The optimization factor at the moment. It adjusts the process noise covariance matrix According to the size of the local anomaly index .

[0185] is the number of effective sensors participating in the calculation.

[0186] is an adjustable parameter used to control the influence degree. The larger the

[0187] Finally, update the process noise covariance matrix :

[0188] ;

[0189] where:

[0190] is the process noise covariance matrix adjusted at time after step

[0191] is the process noise covariance matrix adjusted at time after step

[0192] Functions and design intents of each part of the formula:

[0193] Based on the spatial gradient information of the humidity prediction residual, further adjust the process noise covariance matrix to adapt to possible local anomalies in the humidity field of foamed concrete and improve the estimation accuracy of the Kalman filter. First, by calculating the gradients of the humidity prediction residual in three spatial directions and their modulus length the local anomaly regions in the humidity field are identified. These local anomalies are caused by factors such as material defects, local drying, and uneven hydration reactions, which will cause the actual humidity change to deviate from the model's expectation. To distinguish normal humidity changes from humidity changes caused by local anomalies, the expected residual gradient

[0194] is introduced, which is calculated based on the humidity diffusion model and reflects the expected value of the residual gradient in the absence of local anomalies. Furthermore, a local anomaly index is constructed to quantify the deviation degree between the actual residual gradient and the expected residual gradient. The larger the value, the greater the deviation and the more significant the local anomaly. Based on the local anomaly index, the present invention designs an optimization factor whose function is to dynamically adjust the matrix according to the magnitude of , thereby increasing , making the Kalman filter rely more on the spatial smoothing effect of the model prediction result, reducing the trust in the sensor measurement values in this area, so as to reduce the impact of local anomalies on the overall humidity estimation; when is small, it indicates that the humidity change in this area conforms to the model expectation. At this time is close to , the matrix remains basically unchanged, and the Kalman filter is carried out in the conventional way. The parameter controls the influence degree of . The larger it is, the more sensitive it is to local anomalies. In this way, the optimization factor can effectively identify and process local anomalies in the humidity field, and further improve the adaptability of the Kalman filter to complex humidity fields.

[0195] Step : Humidity estimation and curing humidity control based on adaptive Kalman filter.

[0196] Based on the humidity estimation result obtained in the foregoing steps, the humidity control in the foamed concrete curing process is carried out. At each time step, the optimal estimation of the internal humidity field of the concrete at the current moment is obtained by using the optimized adaptive Kalman filter algorithm (as described in step S2). According to this humidity estimation value, combined with the preset humidity control target (such as surface humidity range, maximum allowable humidity gradient, etc.), it is judged whether spraying is required. Specifically, it is mainly determined whether to start the spraying system according to the surface humidity estimation value. When the surface humidity is lower than the set lower limit, spraying is triggered. At the same time, the present invention also refers to the internal humidity estimation value and the calculated humidity gradient information to assist in decision-making. For example, when the internal humidity is generally low or there is a region with too large a local humidity gradient, even if the surface humidity meets the requirements, the spraying strategy can be appropriately adjusted to achieve more refined and forward-looking humidity control.

[0197] Further, the proposed humidity control method can be combined with control strategies such as model predictive control ( ), and by using the humidity prediction model and optimization algorithm, the optimized control of the spraying area, spraying amount and spraying time is realized. In this way, it can effectively solve the problems of insufficient humidity control accuracy, difficulty in taking into account the surface and internal humidity requirements, and inability to effectively handle local anomalies in the prior art, thereby improving the curing quality of foamed concrete, reducing the cracking risk, and ensuring its performance and durability.

[0198] It should be noted that: The present invention is based on step The obtained optimized Kalman filtering algorithm is used to estimate the internal humidity field of the foamed concrete component in real time, and the curing humidity is controlled according to the estimation result. The specific process is as follows: First, set the initial time step , and obtain the initial state estimate value , the initial state estimate covariance matrix , the reference value of the process noise covariance matrix , and the measurement noise covariance matrix according to step . Then, for each time step , loop to perform the following operations:

[0199] 1. Data acquisition: Obtain the sensor measurement values (humidity measurement values) and environmental temperature data at the current moment .

[0200] 2. Kalman filter prediction step: Predict the state at the current moment according to the state estimate value at the previous moment and the state transition equation: , , where is the state transition matrix calculated according to the humidity and temperature data at moment.

[0201] 3. Calculate the humidity-dependent diffusion coefficient : Calculate the humidity diffusion coefficient according to the predicted humidity at the current moment and the temperature data collected in step .

[0202] 4. Execute step of and , calculate the optimization factors and , and update the matrix: Calculate the humidity prediction residual , calculate the kurtosis and skewness of the residual sequence, construct the non-Gaussianity index , calculate the optimization factor , calculate the residual space gradient ∇ and its modulus , calculate the expected residual gradient , construct the local anomaly index , calculate the optimization factor , and update the process noise covariance matrix: .

[0203] 5. Perform the Kalman filter update step: Calculate the Kalman gain , update the state estimate: , update the state estimate covariance: .

[0204] The above technical solutions only reflect the preferred technical solutions of the technical solutions of the present invention. Some changes that those skilled in the art may make to some parts thereof all reflect the principles of the present invention and fall within the protection scope of the present invention.

Claims

1. A humidity control method for curing foamed concrete, characterized in that, It includes the following steps: Step : Data collection, data preprocessing, and model initialization; Step : a. Based on the statistical characteristics of the humidity prediction residuals, the process noise covariance matrix in the model initialization in step S1 is preliminarily adjusted; b. Further adjust the process noise covariance matrix for the model initialization in step S1 based on the spatial gradient of the humidity prediction residual ; Step : Humidity estimation based on adaptive Kalman filtering and curing humidity control.

2. The curing humidity control method for foamed concrete according to claim 1, characterized in that In step S1, humidity data is obtained, the ambient temperature and humidity are measured by humidity sensors arranged inside and on the surface of the foamed concrete component, and they are recorded simultaneously at the same time to form time series data; Data preprocessing: The collected data is processed as follows: Detect outliers to eliminate obviously incorrect data, and correct suspicious data; Use the moving average filtering method to smooth the data and reduce the influence of random noise; The following operations are carried out in terms of model initialization: Define the state vector : Divide the foamed concrete component into three-dimensional grids, and the state vector contains the humidity values of each grid node: ； Among them, is the humidity value of the grid node at the -th row, the -th column, and the -th layer. , , are respectively the number of grid nodes in the directions; Construct the state transition matrix : Based on the three-dimensional moisture diffusion equation, discretize it using the finite difference method to obtain the state transition matrix , considering the moisture-dependent diffusion coefficient , optionally considering the influence of hydration heat release, according to the boundary conditions, correct . In the central difference format, the discretized form of the three-dimensional moisture diffusion equation is as follows: ； Among them, : humidity value of the th grid node at the moment; : time step; : are respectively grid spacings in the directions; Combining the discretized equations of all grid nodes yields the state transition matrix is a sparse matrix, and its non-zero elements are determined by the above-mentioned difference scheme and boundary conditions; Construct the observation matrix : Map the state vector to the sensor measurements, The number of rows is equal to the number of sensors, and the number of columns is equal to the number of state variables. Each row corresponds to a sensor; Initial state estimation value : Measure the humidity distribution of the component at the initial moment using a humidity sensor as the initial state estimation value; Initialize the state estimation covariance matrix : Set it as a relatively large diagonal matrix, indicating a higher uncertainty in the initial estimate. The diagonal elements can be set as the variances of the initial humidity measurements; Initialize the process noise covariance matrix : Set it as a diagonal matrix, and the diagonal elements represent the initial variances of each state variable. The diagonal elements of Initialize the measurement noise covariance matrix : Set according to the accuracy index of the humidity sensor, which is also a diagonal matrix, and the diagonal elements represent the measurement noise variances of each sensor.

3. The curing and maintenance humidity control method for foamed concrete according to claim 1, wherein a in the step S2, based on the statistical characteristics of the humidity prediction residual, the process noise covariance matrix in the step S1 The specific steps for preliminary adjustment are as follows: Based on the statistical characteristics of the humidity prediction residual, preliminary adjustment of the matrix is performed. The humidity prediction residual is the difference between the sensor measurement value and the model prediction value. The non-Gaussian degree is quantified by calculating the kurtosis and skewness of the residual sequence. The kurtosis reflects the peak degree of the distribution, and the skewness reflects the asymmetry of the distribution. Based on the kurtosis and skewness, a non-Gaussianity index is constructed, abbreviated as: and dynamically adjust the matrix according to the magnitude of Calculate the humidity prediction residual, which is the difference between the sensor measurement value and the model prediction value: ； wherein, is the humidity prediction residual vector at a moment; is the humidity sensor measurement value vector at a moment; is the observation matrix; is the predicted state vector at a moment based on the state at a moment; For each sensor , calculate its residual sequence The kurtosis and skewness within the sliding window , that is, considering the residuals of the past time steps, sliding window: The sliding window is used to calculate the local statistical characteristics of the residual sequence, that is, kurtosis and skewness. The calculation formulas for kurtosis and skewness are as follows: ； ； Among them, is the kurtosis of the residual sequence of the sensor at moment; is the skewness of the residual sequence of the sensor at moment; is the humidity prediction residual of the sensor at moment; is the mean value of the residuals within the sliding window Construct a non-Gaussianity index based on kurtosis and skewness : ； Among them, is the non-Gaussianity index at a moment; is the number of sensors; and are the kurtosis and skewness weights of the th sensor, respectively; Construct an optimization factor: ； Among them, is the optimization factor at a certain moment; is the adaptive forgetting factor; The update formula is as follows: ； Among them, is the forgetting factor coefficient ; is the initial value of, which can be set to or ; Update the process noise covariance matrix : ； Among them, is the process noise covariance matrix updated at each moment; is the reference value of the process noise covariance matrix.

4. The curing and maintenance humidity control method for foamed concrete according to claim 1, wherein b) in step S2, based on the spatial gradient of the humidity prediction residual, further adjust the process noise covariance matrix in step S1 The specific steps are as follows: In step , based on the statistical characteristics of the humidity prediction residuals, namely kurtosis and skewness, the process noise covariance matrix was preliminarily adjusted to adapt to the non-Gaussianity of the process noise. On the basis of step , considering the spatial gradient information of the humidity prediction residuals, the process noise covariance matrix was adjusted. Based on the spatial gradient of the humidity prediction residuals, a local anomaly index was constructed, abbreviated as: ; the spatial gradient of the humidity prediction residuals was calculated. For the three-dimensional case, the sensors are distributed in a three-dimensional grid inside the foamed concrete component. Then, for the sensor , where are the number of sensors in the three directions respectively), its residual gradient at the moment can be expressed as: ； ； ； ； Among them, is the sensor at the gradient of the residual at time in the direction; is the sensor at the gradient of the residual at time in the direction; is the sensor at the gradient of the residual at time in the direction; is the sensor at the magnitude of the residual gradient at time; is the sensor at the humidity prediction residual at time; and are respectively the spacings of the sensor in and directions; Calculate the expected residual gradient, and the expected residual gradient is calculated by the following formula: ； Among them, is the sensor at the magnitude of the expected residual gradient at time, indicating the expected residual; is based on the predicted state at time to calculate the humidity diffusion coefficient; is the magnitude of the humidity gradient at time calculated according to the predicted state, and its calculation method is similar to that of the residual gradient, except that the residual is replaced by the predicted humidity value : : ； ； ； ； Based on the actual residual gradient and the expected residual gradient, construct a local anomaly index, abbreviated as : ； Among them, is the sensor at the local anomaly index at the moment; is a very small positive number; Build optimization factor : ； Among them, is the optimization factor at a certain moment; is the number of effective sensors participating in the calculation; is an adjustable parameter; Update the process noise covariance matrix : ； Among them, is the process noise covariance matrix adjusted after the step at time ; is the process noise covariance matrix adjusted after the step at time .

5. The curing and maintenance humidity control method for foamed concrete according to claim 1, characterized in that, In step S3, based on the humidity estimation result obtained from the previous steps, humidity control during the curing process of foamed concrete is carried out. At each time step, the optimal estimation of the internal humidity field of the concrete at the current moment is obtained by using the optimized adaptive Kalman filtering algorithm to form a humidity estimation value. According to this humidity estimation value, combined with the preset humidity control target, it is judged whether spraying is required. The surface humidity estimation value determines whether to start the spraying system. When the surface humidity is lower than the set lower limit, spraying is triggered.

6. The curing humidity control method for foamed concrete according to claim 1, characterized in that The internal humidity estimation value and the calculated humidity gradient information are used to assist in decision-making. When the internal humidity is generally low or there are areas with excessive local humidity gradients, even if the surface humidity meets the requirements, the spraying strategy can be appropriately adjusted to achieve more refined and forward-looking humidity control.

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