Cement microstructure evolution method and system based on fully convolutional mixed density network

Abstract

The present invention relates to the field of image generation technology, specifically to a cement microstructure evolution method and system based on a fully convolutional mixed density network, the method comprising: obtaining a scanned image of a cement sample and preprocessing it, extracting multi-level features using an encoder, restoring the features to the original resolution of the input image using a decoder, obtaining predicted probability distribution parameters, and performing effective sampling on the probability distribution based on a sampling rule designed based on a priori assumptions to obtain an evolution result; the encoder performs image downsampling using the convolution layer and pooling layer of a set deep convolutional neural model, the upsampling module in the decoder corresponds to the downsampling stage of the encoder, and the output of the last group of upsampling modules uses a distribution output module to obtain the probability size of all states that may change in the cement microstructure at the next moment during the hydration evolution process, and form probability distribution parameters. The complex distribution of the complete hydration process that evolves multiple different possible results under uncertain conditions can be fitted.

Description

Technical Field

[0001] The present invention relates to the technical field of image generation, and in particular to a cement microstructure evolution method and system based on a fully convolutional mixed density network. Background Art

[0002] The statements in this section merely provide background information related to the present invention and do not necessarily constitute prior art.

[0003] The cement hydration process refers to a series of complex physical and chemical reactions that occur when cement particles are exposed to water, forming hydration products and microstructures that affect the final mechanical properties of cement. Understanding and controlling the cement hydration process is of great significance for the development of high-performance cement materials and improving the durability of engineering structures.

[0004] The hydration reaction of cement involves complex physical and chemical reaction rules and is affected by many factors, including temperature, humidity, chemical composition and particle distribution, which makes its hydration process highly nonlinear and complex. Therefore, experimental methods are time-consuming and labor-intensive to study cement hydration reactions, and it is difficult to meet the rapid feedback requirements of material research and development and engineering applications.

[0005] Some hydration process modeling methods use deep learning technology to learn the evolution law of cement material microstructure from experimental data, and realize rapid cement evolution modeling by simulating the complex reaction process of materials. Most of these models rely only on microstructure images with time sequence as training data, and the output of the model is the predicted image result of the next age. However, the hydration reaction of cement is a complex physical and chemical change process involving multiple components and multiple conditions. The cement microstructure image information cannot cover all factors affecting hydration, such as physical environment, missing information between discrete pixels, etc. These incomplete information conditions make it difficult for existing deep learning models to effectively model the real randomness of the hydration process. The lack of uncertainty modeling of randomness makes the model output tend to be deterministic, which cannot fully reflect the multiple possible evolution results with different corresponding probabilities that may occur in the cement hydration process, limiting the applicability and credibility of evolution modeling. Summary of the invention

[0006] In order to solve the technical problems existing in the above-mentioned background technology, the present invention provides a cement microstructure evolution method and system based on a fully convolutional mixed density network, which captures all possibilities of the cement evolution process and its probability distribution by constructing a probability distribution model, thereby realizing uncertainty estimation and prediction of the probability distribution of various possibilities of the cement microevolution process under incomplete information.

[0007] In order to achieve the above object, the present invention adopts the following technical solution:

[0008] The first aspect of the present invention provides a cement microstructure evolution method based on a fully convolutional mixed density network, comprising the following steps:

[0009] Obtaining scanned images of cement samples and preprocessing them;

[0010] The encoder is used to extract multi-level features from the preprocessed image, and the decoder is used to restore the features to the original resolution of the input image to obtain the predicted probability distribution parameters. The sampling rules designed based on the prior assumptions are then used to effectively sample the probability distribution constructed by the distribution parameters to obtain the evolution results.

[0011] Among them, the encoder uses the convolution layer and pooling layer of the set deep convolutional neural model to downsample the image. The upsampling module in the decoder corresponds to the downsampling stage of the encoder. The output of the last group of upsampling modules uses the distribution output module to obtain the probability distribution parameters of all state probabilities that may change in the cement microstructure at the next moment during the hydration evolution process.

[0012] Furthermore, the scanned images of cement samples were obtained and preprocessed, specifically: cement samples with different formulations were prepared, and image data of each sample was obtained by scanning at different ages and performing spatiotemporal registration, and a paired data set was formed by cropping the image and combining the corresponding hydration days as age label records.

[0013] Furthermore, the encoder uses the convolutional layers and pooling layers of the set deep convolutional neural model to downsample the image. Specifically, the pre-trained VGG16 model is used as the backbone network, the initialization parameters are derived from the convolutional weights of VGG16, and only the convolutional layers and pooling layers are used for image downsampling.

[0014] Furthermore, in the encoder, the age information of the input image is encoded in the form of one-hot encoding, and is embedded in the form of channels at the end of the output channel of the first-layer convolutional module as age conditional input.

[0015] Furthermore, the distribution output module receives the output of the last group of upsampling modules of the decoder and sends them to the output parameter module , output parameter module and output parameter modules , and obtain the distribution weight coefficient , mean and standard deviation .

[0016] Furthermore, the output parameter module In the above example, the output of the last group of upsampling modules passes through the convolution layer conv_pi_in, the activation layer relu_pi_in, the BatchNormal layer bn_pi_in, the convolution layer conv_pi_h, the activation layer relu_pi_h, the BatchNormal layer bn_pi_h, the convolution layer conv_pi_out and the normalized exponential function layer softmax in turn to obtain the predicted distribution weight coefficient .

[0017] Furthermore, the output parameter module In the above example, the output of the last group of upsampling modules passes through the convolution layer conv_mu_in, the activation layer relu_mu_in, the BatchNormal layer bn_mu_in, the convolution layer conv_mu_h, the activation layer relu_mu_h, the BatchNormal layer bn_mu_h, the convolution layer conv_mu_out, the activation layer conv_mu_out_act and the value range mapping layer in turn, and the activated value range [0.1] is mapped to the grayscale image value range [0,255] to obtain the predicted mean. .

[0018] Furthermore, the output parameter module In the above example, the output of the last group of upsampling modules passes through the convolution layer conv_sigma_in, the activation layer relu_sigma_in, the BatchNormal layer bn_sigma_in, the convolution layer conv_sigma_h, the activation layer relu_sigma_h, the BatchNormal layer bn_sigma_h, the convolution layer conv_sigma_out and the activation layer conv_sigma_out_act. The output result is then passed through the weighted exponential function exp to obtain the predicted standard deviation. . Multiplying a coefficient before the exponential function constrains the value range of sigma, indirectly constraining the degree of "opening width, narrowness, thickness" of the complex distribution, and indirectly constraining the shape of the distribution.

[0019] Furthermore, effective sampling is performed on the probability distribution constructed by the distribution parameters according to the sampling rule designed based on the prior hypothesis, including the following steps:

[0020] Through random sampling, the predicted probability distribution parameters are obtained to determine whether the sampling point is within the set threshold range;

[0021] If the sampling point is within the threshold range, the sampling value is accepted and used as the prediction result for the next moment, and the sampling ends;

[0022] If the sampling point is not within the threshold range, further determine whether the sampling point has reached the maximum sampling number. If it is still not, re-sample;

[0023] If the sampling point reaches the maximum number of sampling times, all sampling will be rejected, the original state will be maintained unchanged, and the sampling will end.

[0024] A second aspect of the present invention provides a cement microstructure evolution system based on a fully convolutional mixed density network, comprising:

[0025] The data acquisition unit is configured to: obtain a scanned image of the cement sample and pre-process it;

[0026] The encoder is configured to: downsample the preprocessed image and extract multi-level features in the image;

[0027] The decoder is configured to: map the feature map size to the original resolution of the input image and obtain a set of predicted probability distribution parameters;

[0028] The sampling output unit is configured to perform effective sampling on the probability distribution constructed by the distribution parameters based on the sampling rules designed based on the priori assumptions to obtain the evolution results.

[0029] Compared with the prior art, one or more of the above technical solutions have the following beneficial effects:

[0030] 1. Each pixel in the image or different materials composed of many pixels represent the corresponding actual material structure information and spatial structure meaning. Stretching, scaling, cropping and other operations on the image will destroy the spatial information represented by the image. Therefore, the network model is designed in the form of full convolution to perform lossless input processing and output of images of any size to avoid unnecessary information loss and noise introduction.

[0031] 2. Under the condition of incomplete information, the current state may correspond to multiple evolutionary results with different probabilities of hydration in the next state, which will lead to multiple uncertainties in the cement hydration evolution results. The existing network model can only predict a single result (the most likely result), ignoring the possibility of other results. It is difficult to model the randomness under this state and it is impossible to fully express the hydration prediction process for all possible evolutionary states. This scheme embeds the mixed density network at the tail of the fully convolutional network backbone network to obtain the probability distribution parameters of all state probabilities that may change in the cement microstructure at the next moment, thereby more accurately characterizing the randomness of the hydration process and the multiple possibilities of hydration evolution results under the condition of incomplete information. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] The accompanying drawings in the specification, which constitute a part of the present invention, are used to provide a further understanding of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute improper limitations on the present invention.

[0033] Figure 1 is a schematic diagram of cement microstructure evolution process based on a fully convolutional mixed density network provided by one or more embodiments of the present invention;

[0034] Figure 2 is a schematic diagram of a fully convolutional mixed density network model provided by one or more embodiments of the present invention;

[0035] Figure 3 It is a schematic diagram of the principle of the mixed density model concept provided by one or more embodiments of the present invention;

[0036] Figure 4 is a schematic diagram of randomly selecting different samples for evolution experiments provided by one or more embodiments of the present invention;

[0037] Figure 5 It is a schematic diagram of multiple independent repetitions of prediction evolution experiments on the same sample provided by one or more embodiments of the present invention.

[0038] Figure 6 It is a schematic diagram of a sampling process for sampling a predicted distribution provided by one or more embodiments of the present invention. DETAILED DESCRIPTION

[0039] The present invention will be further described below in conjunction with the accompanying drawings and embodiments.

[0040] It should be noted that the following detailed descriptions are exemplary and are intended to provide further explanation of the present invention. Unless otherwise specified, all technical and scientific terms used herein have the same meanings as those commonly understood by those skilled in the art to which the present invention belongs.

[0041] The following embodiment provides a cement microstructure evolution method and system based on a fully convolutional mixed density network, which combines the fully convolutional network FCN and the mixed density network MDN to perform uncertainty estimation and prediction on the probability distribution of various possibilities of the cement microevolution process under incomplete information.

[0042] Embodiment 1:

[0043] The cement microstructure evolution method based on the fully convolutional mixed density network includes the following steps:

[0044] Obtaining scanned images of cement samples and preprocessing them;

[0045] The encoder is used to extract multi-level features from the preprocessed image, and the decoder is used to restore the features to the original resolution of the input image to obtain the predicted probability distribution parameters. The sampling rules designed based on the prior assumptions are then used to effectively sample the probability distribution constructed by the distribution parameters to obtain the evolution results.

[0046] Among them, the encoder uses the convolution layer and pooling layer of the set deep convolutional neural model to downsample the image. The upsampling module in the decoder corresponds to the downsampling stage of the encoder. The output of the last group of upsampling modules uses the distribution output module to obtain the probability distribution parameters of all state probabilities that may change in the cement microstructure at the next moment during the hydration evolution process.

[0047] This embodiment achieves evolution through three parts: data preparation, model construction, and sampling output. The specific process is as follows: Figure 1 shown.

[0048] Data preparation includes making Portland cement samples with different formulations, scanning and imaging each sample with a micro-CT device at different ages, registering and preprocessing the image data, and then cropping the image and combining the corresponding hydration days as age label records to form a paired data set.

[0049] Model construction: Establish a probability distribution model (conditional fully convolutional mixed density deep neural network model) and use the data obtained in the previous step to train the model. This enables the model to directly output the distribution parameters that can represent the probability distribution of the microstructure image under the specified conditional age.

[0050] Sampling output: The model established above outputs the probability distribution parameters of the predicted image. The distribution needs to be sampled to obtain the final evolution result. Based on the prior assumption, sampling is performed from the complex hydration distribution according to the designed sampling rules. Samples that meet the predetermined fluctuation threshold are accepted, and samples that do not meet the threshold are removed and resampled. If a suitable sample cannot be found after multiple attempts, the original value is used as the result of this sampling.

[0051] The meaning of the prior assumption is: it is believed that the hydration process of cement is very slow 24 hours after the start of hydration, so it is unlikely to have a violent reaction within the continuous time change. Corresponding to the image pixels, the pixel grayscale change is smooth and slow, so the jitter mutation value outside the threshold is rejected and resampled.

[0052] Data preparation.

[0053] Step 1.1: Evolution sample preparation and curing. Each "pixel" in the cement microstructure image represents the material state or material properties (e.g., chemical composition, density, porosity, etc.) and local environment (e.g., temperature, pH, ion concentration, etc.) at that location. In order to more comprehensively study the evolution process of different types of silicate cement, this embodiment constructs and selects three different formulations of Portland cement, which are marked as A, B, and C respectively. At the same time, in order to explore the influence of water-cement ratio on the evolution of cement microstructure, the experiment configures four types of cement samples with different combinations according to the above considerations: A35, A45, B35 and C45, corresponding to different formulations and water-cement ratio combinations. After the cement sample is prepared, it is placed in an environment of 20°C and 95% humidity for curing for 24 hours to ensure that the sample undergoes initial hydration reaction under standard conditions.

[0054] After curing, all samples were demoulded to obtain four cement cylinder samples of the same specifications. These samples were placed in narrow-necked bottles and continued to be water-cured at a constant temperature of 25°C. Sampling was performed at the specified curing days (2, 3, 4, 5, 6, 7, 14, 21 and 28 days). At each sampling, a high-resolution desktop micro-computed tomography scanner (such as SkyScan1172) was used to perform micro-CT scanning imaging of different cement samples of different ages to record the internal structural changes of each sample in detail. After scanning, the samples were returned to the narrow-necked bottles for continued curing to ensure complete observation of the cement hydration process during the entire curing period.

[0055] The image data obtained by the above method form a data set. This data set contains microscopic CT data of cement samples with four different formulas and water-cement ratio combinations at nine different ages, forming sequential tomographic image data, which provides basic data for in-depth analysis of the hydration reaction and structural evolution of cement materials.

[0056] Step 1.2 Registration and preprocessing of original image data. In order to construct the in-situ time series data set required for the model, since the spatial position of the original cement data set in the time series is not completely corresponding, it is necessary to perform image enhancement and data registration processing on the acquired four-dimensional data (three-dimensional image of the time series, three-dimensional image data + time series dimension): In the four-dimensional time series registration process, firstly, the downsampling process and local phase matching technology are used to determine the approximate range of transformation parameters in the coarse positioning stage, and then high-precision parameter optimization is performed in the fine tracking stage. This method can complete the fast spatiotemporal series registration operation of the acquired data under the specified accuracy requirements while reducing the amount of calculation.

[0057] However, as the cement hydration process is ongoing, the internal structure of the sample will change slightly, and the sample is not static in the time dimension, which makes it almost impossible to achieve complete matching at the pixel level of the entire image. Therefore, additional preprocessing is performed on the time series 4D data set obtained after registration: by intercepting the core area (size 720×720×720), removing the edge part with large registration deviation, and mapping the grayscale value to between 0 and 255, finally obtaining time series data that can be used for model training.

[0058] Step 1.3 Construction of training dataset. The four cement sample datasets after temporal registration were sorted according to the predetermined time points. Each sample collected 720×720×720 cube data blocks at 2, 3, 4, 5, 6, 7, 14, 21 and 28 days. Subsequently, each cube was cut into 720 720×720 cement image slices along the longitudinal axis and stored in their respective directories for subsequent processing and analysis.

[0059] In order to construct the training dataset required for the model, random sampling was performed from four sample datasets: during the random sampling process, the corresponding position slice data at time points t and t+1 in the folder named by the day were selected. Then, a 256×256 image area was randomly cropped from each 720×720 full-size slice, and its corresponding hydration days were combined as age label records to form paired data for training. Finally, a dataset containing 30,000 paired images was constructed to provide sufficient training samples for the model. This process ensures the diversity and temporal consistency of the training data to support the model's effective learning of the diversity of microstructural evolution during cement hydration under incomplete information conditions.

[0060] Model building and training.

[0061] Step 2.1 Age-conditional fully convolutional mixed density network construction. In-depth analysis of the data set mainly faces the following challenges: high dimensionality of the data, complex nonlinear system mapping, non-single mapping, and time series continuity requirements. In order to effectively capture the deep features in the data and construct the probability distribution of the evolution process, this embodiment uses a fully convolutional mixed density network model, which adopts an end-to-end input and output design.

[0062] The model structure diagram is as follows Figure 2As shown, it includes two parts, an encoder and a decoder. The encoder includes five stacked convolution blocks, and the decoder includes five stacked deconvolution blocks, and a distribution output module arranged at the end of the last convolution block. Five convolution blocks form a convolution module, and five deconvolution blocks form a deconvolution module. Among them, features 1-features 4 extracted by convolution blocks 1-convolution blocks 4 are respectively input into the corresponding deconvolution blocks 4-deconvolution blocks 1, and feature 5 extracted by convolution block 5 is input into deconvolution block 1. The convolution block is used to downsample the input image, also known as a downsampling module, so that the spatial resolution of the image is gradually reduced, and the features are transitioned from shallow local information to deep global information; the deconvolution block upsamples the feature information from the convolution module, also known as an upsampling module, which gradually improves the resolution of the feature map, and is combined with the feature information of the corresponding stage of the encoder to be input into the distribution output module. The distribution output module has output parameter modules arranged in parallel. , output parameter module and output parameter modules , used to fit the output parameters of the network representing the mixture density , and , by fitting and predicting numerous parameter groups, a variety of possible cement microstructure states are expressed.

[0063] Encoder part: The encoder part aims to extract multi-level features from the input image data. The structure is composed of a stack of network blocks consisting of multiple convolutional layers, activation functions and pooling layers. As the network depth increases, the spatial resolution of the image gradually decreases and the number of channels gradually increases, so that the features transition from shallow local information to deep global information. Specifically, to optimize feature extraction, the encoder uses a pre-trained VGG16 model as the backbone network, and the initialization parameters are derived from the convolution weights of VGG16. The original VGG16 model contains 5 modules, a total of 13 convolutional layers and 3 fully connected layers, as well as a pooling layer after each module. In the encoder, only convolutional layers and pooling layers are used for image downsampling, and the fully connected layers are omitted. In addition, the age information of the input image is encoded in the form of one-hot encoding and embedded in the tail of the output channel of the first convolutional block in the form of channels as age condition input. At the same time, the output of each convolutional block is retained to help the decoder recover image details and make up for the information that may be lost during upsampling. The pooling layers in the encoder are all 3×3 maximum pooling layers, which can effectively reduce the number of model parameters and improve training efficiency and generalization ability.

[0064] In the encoder, the first convolution block contains the sequentially connected convolution layer conv1_1, activation layer relu1_1, age condition information onehot encoding layer, input information and age condition encoding information channel concatenation layer, convolution layer conv1_2, activation layer relu1_2, and pooling layer pool1;

[0065] The second convolution block contains the sequentially connected convolution layer conv2_1, activation layer relu2_1, convolution layer conv2_2, activation layer relu2_2, and pooling layer pool2;

[0066] The third convolution block contains the sequentially connected convolution layer conv3_1, activation layer relu3_1, convolution layer conv3_2, activation layer relu3_2, convolution layer conv3_3, activation layer relu3_3, and pooling layer pool3;

[0067] The fourth convolution block contains the sequentially connected convolution layer conv4_1, activation layer relu4_1, convolution layer conv4_2, activation layer relu4_2, convolution layer conv4_3, activation layer relu4_3, and pooling layer pool4;

[0068] The fifth convolution block contains the sequentially connected convolution layer conv5_1, activation layer relu5_1, convolution layer conv5_2, activation layer relu5_2, convolution layer conv5_3, activation layer relu5_3, and pooling layer pool5.

[0069] By retaining the output features[1], features[2], features[3], features[4], features[5] of each convolution block, it helps the decoder recover image details.

[0070] Decoder: The main task of the decoder is to restore the high-level features extracted by the encoder to the original resolution of the input image and realize the prediction of the probability distribution parameters of the micro-evolution of cement at the pixel level. The decoder includes five deconvolution blocks connected in sequence and a distribution output module connected to the end of the deconvolution block. The distribution output module includes output parameter modules arranged in parallel. , output parameter module and output parameter modules .

[0071] The output of the distribution output module is used to fit the output parameters of the network representing the mixture density. , and , can represent complex mixed distributions, for example, the simplest Gaussian distribution, in addition to being represented by images, can also be represented by and The distribution characteristics can be accurately described, and the same is true for the complex distribution composed of the weighted superposition of multiple Gaussian distributions predicted above. By fitting and predicting numerous parameter groups, a variety of possible cement microstructure states can be expressed.

[0072] Among them, the five groups of convolution blocks in the encoder correspond to the deconvolution blocks in the encoder, which are used for downsampling and upsampling respectively. The feature map channel group output at the tail of the last group of deconvolution blocks is used as the input of the distribution output module. The Gaussian kernel of the distribution output module is represented in the form of channels. The network takes 3 groups of Gaussian kernel mixed distributions to fit the hydration distribution, which is used to fit the output parameters of the mixed density network. , and , and use this as the decoder output to construct and represent all possible probability distributions in the hydration evolution process. The resolution of the feature map is gradually improved by upsampling through deconvolution, and combined with the feature information of the corresponding stage of the encoder to achieve more accurate image reconstruction. Finally, the decoder outputs three sets of distribution parameter maps with the same resolution size as the input image, namely , and A parameter diagram is used to represent the complex probability distribution of all the state probabilities that may change at the next moment.

[0073] In the decoder part, the 5 deconvolution block structures are:

[0074] The first deconvolution block outputs features[5] from the encoding layer through deconvolution deconv1, then passes through the activation layer LeakyReLU1, and is added to features[4]. The result is passed through the BatchNormal layer bn1 to obtain the result y1;

[0075] The second deconvolution block passes y1 through the deconvolution layer deconv2, then through the activation layer LeakyReLU2, and is added to features[3]. The result is passed through the BatchNormal layer bn2 to obtain the result y2.

[0076] The third deconvolution block passes y2 through the deconvolution layer deconv3, then through the activation layer LeakyReLU3, and is added to features[2]. The result is passed through the BatchNormal layer bn3 to obtain the result y3;

[0077] The fourth deconvolution block passes y3 through the deconvolution layer deconv4, then through the activation layer LeakyReLU4, and is added to features[1]. The result is passed through the BatchNormal layer bn4 to obtain the result y5;

[0078] The fifth deconvolution block passes y4 through the deconvolution layer deconv5, then through the activation layer LeakyReLU5, and then the result directly passes through the BatchNormal layer bn5 to obtain the output result y5.

[0079] The distributed output modules are output parameter modules arranged in parallel , output parameter module and output parameter modules ,in:

[0080] Output parameter module , used to output distribution weight coefficients , containing a convolutional layer conv_pi_in with y5 as input and connected sequentially, an activation layer relu_pi_in with LeakyReLU activation function, a BatchNormal layer bn_pi_in, a convolutional layer conv_pi_h, another activation layer relu_pi_h with LeakyReLU activation function, a BatchNormal layer bn_pi_h, a convolutional layer conv_pi_out and a normalized exponential function layer softmax;

[0081] Output parameter module , used to output the mean , including the convolution layer conv_mu_in with y5 as input and connected sequentially, the activation layer relu_mu_in of the LeakyReLU activation function, the BatchNormal layer bn_mu_in, the convolution layer conv_mu_h, the activation layer relu_mu_h of the LeakyReLU activation function, the BatchNormal layer bn_mu_h, the convolution layer conv_mu_out and the activation layer conv_mu_out_act of the Sigmoid activation function. The activation function outputs the result in the range of 0-1 and multiplies it by 255 to expand the data value range to 0-255;

[0082] Output parameter module , used to output the standard deviation , including the convolution layer conv_sigma_in with y5 as input and connected sequentially, the activation layer relu_sigma_in of the LeakyReLU activation function, the BatchNormal layer bn_sigma_in, the convolution layer conv_sigma_h, the activation layer relu_sigma_h of the LeakyReLU activation function, the BatchNormal layer bn_sigma_h, the convolution layer conv_sigma_out and the activation layer conv_sigma_out_act of the LeakyReLU activation function. The output result is then passed through the exponential function exp, and the final result is multiplied by 5 to expand the standard deviation range.

[0083] The three output parameter modules predict the parameters of multiple simple distributions (this model uses a mixture of Gaussian distributions): weights , mean and standard deviation ; Through these simple distributions, multiple groups of Gaussian distributions can be constructed, and then they are weighted and combined according to the weight size to form a complex distribution. By training these three parameter groups, the complex distribution of the cement hydration evolution process to be learned can be fitted as closely as possible. The idea of ​​the mixed density model is that any complex distribution can be represented by a weighted combination of multiple simple distributions. For example Figure 3 As shown, three simple Gaussian distributions Gaussian 1: N (4, 0.5), Gaussian 2: N (7, 1) and Gaussian 3: N (10, 1.5) are mixed to obtain a complex distribution X (Mixed Gaussian Distribution), where the horizontal axis is the value of the random variable and the vertical axis is the probability density of these values. Similarly, in this embodiment, the deconvolution block of the decoder and the three parallel output parameter modules constitute a mixed density module to fit the probability distribution of complex hydration evolution.

[0084] By mixing basic distributions to represent the way to construct complex distributions, the distribution fitting problem expected by this solution can be fitted. Some problems that traditional networks cannot solve or are difficult to solve directly can be solved, such as multi-value mapping problems and randomness capture and expression problems.

[0085] Therefore, this embodiment adopts a combination of a fully convolutional network FCN and a mixed density network MDN to obtain a fully convolutional mixed density network, wherein, in order to prevent the spatial information represented by the image from being destroyed due to operations such as stretching, scaling, and cropping of the image, the use of a fully convolutional network FCN can be used to losslessly process any image, and can process any image size input and output the same size. Under incomplete information conditions, the current state may correspond to multiple possible evolutionary results with different probabilities of hydration of the next state, while the existing network model can only predict a single result (the most likely result), ignoring the possibility of other results, and it is difficult or impossible to model the randomness under this state, and it is difficult to fully express the hydration prediction process for all possible evolutionary states. Therefore, the MDN module is used to model the probability distribution of all probability changes to achieve this purpose.

[0086] In order to verify whether the model is consistent with the design expectations, we randomly select Figure 4 The samples shown in the figure were used for multiple independent repeated prediction experiments, and the experimental results were as follows Figure 5As shown. It can be found that the macroscopic hydration trends of the three groups of images are the same and remain consistent; the microscopic local details, as the age continues to go backward, it can be found that the local differences in the details are getting bigger and bigger, indicating that the model of this embodiment is consistent with the expected assumptions and meets the design requirements. In the case of incomplete information, it can solve the problem of predicting the general trend at the macro level and capturing the possible results and expressing the randomness of evolution at the micro level.

[0087] Step 2.2 Loss design and iterative optimization training. The loss function of the model consists of two weighted losses, one of which is , which is used to quantify the uncertainty of each pixel predicted by the model and incorporate this uncertainty into the optimization process of the model; the other part is Weighted , which is used to ensure the consistency of the overall features between the model's predictions at the macro level and the actual image; namely:

[0088] ；

[0089] in, and It is a weight coefficient used to balance the importance of the two loss components. By adjusting these two coefficients, macro stability and micro uncertainty can be controlled.

[0090] in, To express and quantify the degree of random uncertainty. That is, by measuring the difference between the probability distribution learned by the model and the probability distribution of the real data, the model prediction distribution is made as close to the real distribution as possible, thereby directly quantifying the prediction uncertainty. That is:

[0091] ;

[0092] in represents the weight parameter of the model, Representative View Detailed image data points at a given moment, represents the probability density function of the high score distribution, Representative The mixing coefficients of the components, and the total probability sum of the mixing coefficients is 1.

[0093] at the same time, The error introduced by the extra data space jitter brought by constrained registration ensures the stability of the evolution process at the macro level, that is, constrains the hydration image at the current moment and the image corresponding to the next moment to be similar, and the output will not cause mutations due to excessive differences. Therefore, the weighted mean square error (Weighted MSE) loss is designed to constrain the difference between the two, that is, to constrain the mean of each Gaussian kernel. are all near the original position values ​​and are weighted Dynamically adjust the constraint strength to achieve overall constraint and optimization.

[0094] Weighted Mean Squared Error (MSE) is shown below:

[0095] ;

[0096] Therefore, this loss function is further described as:

[0097] ;

[0098] in, and is the weight coefficient used to balance the importance of the two loss components, Representative View Detailed image data points at a given moment, Probability density function representing the Gaussian distribution.

[0099] This loss allows this embodiment to reasonably apply the MSE loss to the model whose output is a distribution parameter while maintaining its original meaning. By minimizing the weighted MSE loss between the true value and the expected value of the distribution, the prediction of the macroscopic hydration evolution trend can be met while capturing the uncertainty of the prediction through the mixed density network. At this point, a complete hydration micro-local modeling process has been constructed.

[0100] Step 2.3 Iterative optimization training. In the network training part, the Adam optimizer is selected for optimization in the two-dimensional image training process, and the learning rate is set to , the batch size (BatchSize) is set to 32, and the training iteration round is set to 1600. At the same time, the balance weight coefficient of the two losses in the experiment and Set to 0.5:0.5 (the actual two balance coefficients can be flexibly adjusted according to demand and prediction results, and it is recommended that the difference between the two should not exceed one order of magnitude).

[0101] Step 3.1 Design and implementation of probability distribution sampling. The output of this model is the probability distribution parameters of the microstructure image at a given age. For a model whose output is a distribution to represent the uncertainty part, it is necessary to solve the problem of how to sample from the distribution to obtain the hydration microstructure image at a certain age. In addition, since the output parameters , and The resulting mixed complex distribution is infinite in both the positive and negative directions on the coordinate axis, while the actual grayscale result range of the hydrated microstructure image is from 0 to 255. Although the probability of the sampled value exceeding the grayscale range is very small, with the increase in the number of sampling times, it is difficult to avoid obtaining abnormal values ​​that do not meet the requirements.

[0102] In response to these problems, this embodiment proposes a sampling method, the specific contents of which are as follows: Based on a series of prior assumptions, the core assumption is that cement hydration follows a stable evolutionary trajectory because the probability of pixel mutation of material properties in a short period of time is small. This assumption is specifically reflected in the micro-CT image as continuous moments and The grayscale changes of pixels are small, and there is rarely or basically no sudden sharp increase or decrease in pixel values.

[0103] Based on the given assumptions, the sampling process is as follows Figure 4 As shown, the following steps are included:

[0104] Set the sampling reception threshold and maximum sampling times;

[0105] According to the predicted distribution parameter group , and Build distribution;

[0106] Perform distributed random sampling, and determine whether the sampling point is within the threshold range in turn. If not, further determine whether the sampling point reaches the maximum number of sampling times. If still not, resample;

[0107] If the sampling point is within the threshold range, the current distribution sampling value is accepted as the prediction result for the next moment, and the sampling ends;

[0108] If the sampling point is not within the threshold range, further determine whether the sampling point has reached the maximum sampling number. If it is still not, re-sample;

[0109] If the sampling point reaches the maximum number of sampling times, all sampling will be rejected, the original state will be maintained unchanged, and the sampling will end.

[0110] In this embodiment, based on the given assumptions, the parameters , and The complex hydration distribution constructed by the output is sampled. Samples that meet the predetermined fluctuation threshold range will be accepted, and samples that do not meet this standard will be eliminated and resampled. If the ideal sample cannot be found after multiple sampling attempts, the original value is used as the sample for this sampling iteration. At the same time, since the image is an 8-bit grayscale image with a grayscale range of 0-255 and a range of 32 for each bit, the upper and lower limits of the acceptance threshold of the sampling algorithm are set to 16.

[0111] The age-conditional fully convolutional mixed density deep neural network model proposed in this embodiment solves the randomness problem of cement microevolution in traditional models under the scenario of incomplete modeling information. That is, under the condition of incomplete information, the evolution result may not be unique, but may correspond to a variety of possible results with different probabilities.

[0112] The reasons are as follows: First, considering that the images that may be processed in the cement hydration process may have different sizes due to different sources, different equipment parameters, different configurations, etc., and the traditional model generally has a fixed image input size. At this time, in order to feed information into the network model, the input image size needs to be consistent, and the image is stretched, scaled, or cropped to make the image size consistent. For conventional image processing, information loss is acceptable.

[0113] For real physical and chemical experiments such as cement hydration process, each pixel in the image or different substances composed of many pixels represent the corresponding actual material structure information and spatial structure meaning. Image stretching, scaling or cropping will destroy the spatial information represented by the image, resulting in a certain degree of image data distortion. This distortion may destroy some important features in the image to some extent, making it more difficult for the model to learn effective feature representation or learn wrong image features.

[0114] On the other hand, scaling images may cause changes in resolution, which in turn affects image quality. Shrinking a high-resolution image to a lower resolution may result in loss of details, while scaling a low-resolution image to a higher resolution may introduce blur and noise, which may have a certain degree of uncontrollable negative impact on model learning.

[0115] At the same time, although cropping the image will not affect the image quality or destroy the image structure information, it will lose some of the spatial feature information of the original image. Although the commonly used generative models often pre-process the input to unify the input size for computational efficiency and quality balance, for real cement evolution images, the above operation will destroy the image structure information or lose some spatial detail information, and the impact is unacceptable.

[0116] Since Fully Convolutional Networks (FCNs) can process any image end-to-end and losslessly process image data of any size, it can solve the above problems well. Therefore, this embodiment selects Fully Convolutional Neural Networks (FCNs) as the main network architecture, and on this basis, further designs are made for the randomness requirements of cement microevolution in scenarios with incomplete information.

[0117] Fully convolutional neural networks (FCNs) are usually used for pixel-level image segmentation tasks. Compared with traditional neural networks, they have stronger feature extraction capabilities and higher spatial resolution, and can output segmentation results of the same size as the input image. However, for the various uncertainties in the results of the cement hydration process caused by incomplete modeling information, fully convolutional neural networks (FCNs) alone cannot meet the above requirements.

[0118] Secondly, the model designed in this embodiment must be able to capture all possible evolutionary results from the current state to the next state under incomplete information conditions. Therefore, this embodiment further improves the basic model FCNs to capture all possible evolutionary results and their probability of occurrence, so as to construct a complete probability distribution of the evolutionary process, and finally achieve the fitting of the evolutionary distribution representing all possible cement hydration processes.

[0119] In response to the above problems and discussions, this embodiment designs and introduces a mixture density network (MDN) module with the ability to fit complex distributions at the tail of the decoder part of the basic model fully convolutional neural network FCNs. Compared with the traditional mixture density model constructed in a fully connected form, this embodiment designs it as a sub-module, and designs it to be fully convolutional instead of fully connected, and embeds it into the tail part of the decoder in the form of channels, so that the designed model can not only be able to losslessly process input images of any size, but also have the ability to fit any complex distribution, thereby ensuring that the complete hydration process with multiple different possible results evolving under uncertain conditions can be fitted.

[0120] In addition, the cement hydration rate becomes slower and slower with the increase of hydration age (days), that is, the hydration rate is gradually decreasing, which is not the same. The age needs to be introduced into the design model as an additional condition.

[0121] Therefore, a new model, Fully Convolutional Mixture Density Networks (FCMDNs), was designed and constructed.

[0122] This embodiment designs an age-conditional fully convolutional mixed density (c-FCMDN) architecture, which is based on a fully convolutional neural network and uses an autoregressive method to predict cement microstructure in a time series. The input of the model is a cement microstructure image at a certain moment, and the output is a microstructure image at the next moment. The front end of the model uses a VGG network as a feature extractor to perform deep feature extraction on the input image. The extracted feature map is restored to the original resolution through multi-layer deconvolution, and a parameter group representing a complex distribution is obtained through a distribution parameter module to construct a complex cement evolution distribution. Finally, according to the design rules under the prior assumptions, sampling is performed to obtain the microstructure prediction result at the next moment.

[0123] The c-FCMDN model allows the evolution output at each moment to be used as the input of the next moment through time autoregression, thereby building a dynamic relationship in the time series. The uncertainty description of cement hydration reaction is achieved through probabilistic modeling, making the evolution results more in line with the actual situation.

[0124] The loss function of the c-FCMDN model consists of the weighted mean square error (Weighted MSE) and the weighted MDNLoss. The Weighted MSE is used for macro constraints, and the MDNLoss is used to quantify the uncertainty of the model at the micro level, so that the evolutionary modeling results have both stability and authenticity.

[0125] Compared with traditional evolutionary methods, this model uses a mixed density network to estimate the probability density of the evolution results under the uncertainty of cement hydration process, and generates possible output distributions, so as to more accurately describe the randomness of the hydration process and the multiple possibilities of hydration evolution results under the condition of incomplete information. In addition, the model abandons the traditional evolutionary mechanism based on empirical rules and directly learns the evolution law from the real time series cement microstructure image data, so that the output cement hydration microstructure is closer to the real state.

[0126] Embodiment 2:

[0127] Cement microstructure evolution system based on fully convolutional mixed density network, including:

[0128] The data acquisition unit is configured to: obtain a scanned image of the cement sample and pre-process it;

[0129] The encoder is configured to: downsample the preprocessed image and extract multi-level features in the image;

[0130] The decoder is configured to: map the feature map size to the original resolution of the input image and obtain a set of predicted probability distribution parameters;

[0131] The sampling output unit is configured to perform effective sampling on the probability distribution constructed by the distribution parameters based on the sampling rules designed based on the priori assumptions to obtain the evolution results.

[0132] Compared with traditional evolutionary methods, under the uncertainty of cement hydration process, the probability density of the evolution process is estimated through the fully convolutional mixed density network, and the probability distribution of the possible evolution result set is generated, so as to more accurately characterize the randomness of the hydration process and the multiple possibilities of hydration evolution results under the condition of incomplete information. In addition, the model abandons the traditional evolutionary mechanism based on empirical rules and directly learns the evolution law from the real time series cement microstructure image data, so that the output cement hydration microstructure is closer to the real state.

[0133] The above are only preferred embodiments of the present invention and are not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A cement microstructure evolution method based on a fully convolutional mixed density network, characterized in that: The following steps are involved: Obtaining scanned images of cement samples and preprocessing them; The encoder is used to extract multi-level features from the preprocessed image, and the decoder is used to restore the features to the original resolution of the input image to obtain the predicted probability distribution parameters. The sampling rules designed based on the prior assumptions are then used to effectively sample the probability distribution constructed by the distribution parameters to obtain the evolution results. The encoder uses the convolution layer and pooling layer of the set deep convolutional neural model to downsample the image. The upsampling module in the decoder corresponds to the downsampling stage of the encoder. The output of the last group of upsampling modules uses the distribution output module to obtain the probability distribution parameters of all the state probabilities that may change in the cement microstructure at the next moment during the hydration evolution process. The encoder uses the convolutional layer and pooling layer of the set deep convolutional neural model to downsample the image. Specifically, the pre-trained VGG16 model is used as the backbone network, the initialization parameters are derived from the convolutional weights of VGG16, and only the convolutional layer and pooling layer are used for image downsampling; The decoder's deconvolution block and the three parallel output parameter modules constitute a mixed density module.

2. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: The scanned images of cement samples were obtained and preprocessed, specifically: cement samples with different formulations were prepared, and image data of each sample was obtained by scanning at different ages. The images were cropped and combined with the corresponding hydration days as age label records to form a paired data set.

3. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: In the encoder, the age information of the input image is encoded in the form of one-hot encoding and embedded in the form of channels at the end of the output channel of the first-layer convolutional module as age conditional input.

4. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: The distributed output module receives the output of the last group of upsampling modules of the decoder and sends them to the output parameter module , output parameter module and output parameter modules , and obtain the distribution weight coefficient , mean and standard deviation .

5. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: Output parameter module In the above example, the output of the last group of upsampling modules passes through the convolution layer conv_pi_in, the activation layer relu_pi_in, the BatchNormal layer bn_pi_in, the convolution layer conv_pi_h, the activation layer relu_pi_h, the BatchNormal layer bn_pi_h, the convolution layer conv_pi_out and the normalized exponential function layer softmax in turn to obtain the predicted distribution weight coefficient .

6. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: Output parameter module In the above example, the output of the last group of upsampling modules passes through the convolution layer conv_mu_in, the activation layer relu_mu_in, the BatchNormal layer bn_mu_in, the convolution layer conv_mu_h, the activation layer relu_mu_h, the BatchNormal layer bn_mu_h, the convolution layer conv_mu_out, the activation layer conv_mu_out_act and the range mapping layer to obtain the predicted mean. .

7. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: Output parameter module In the above example, the output of the last group of upsampling modules passes through the convolution layer conv_sigma_in, the activation layer relu_sigma_in, the BatchNormal layer bn_sigma_in, the convolution layer conv_sigma_h, the activation layer relu_sigma_h, the BatchNormal layer bn_sigma_h, the convolution layer conv_sigma_out and the activation layer conv_sigma_out_act. The output result is then passed through the weighted exponential function exp to obtain the predicted standard deviation. .

8. The cement microstructure evolution method based on a fully convolutional mixed density network as claimed in claim 1, characterized in that: The sampling rules designed based on the prior assumptions are used to effectively sample the probability distribution constructed by the distribution parameters, including the following steps: Through random sampling, the predicted probability distribution parameters are obtained to determine whether the sampling point is within the threshold range; If the sampling point is within the threshold range, the sampling value is accepted and used as the prediction result for the next moment, and the sampling ends; If the sampling point is not within the threshold range, further determine whether the sampling point has reached the maximum sampling number. If it is still not, re-sample; If the sampling point reaches the maximum number of sampling times, all sampling will be rejected, the original state will be maintained unchanged, and the sampling will end.

9. A cement microstructure evolution system for implementing the cement microstructure evolution method based on a fully convolutional mixed density network as described in any one of claims 1 to 8, characterized in that: include: The data acquisition unit is configured to: obtain a scanned image of the cement sample and pre-process it; The encoder is configured to: downsample the preprocessed image and extract multi-level features in the image; The decoder is configured to: map the feature map size to the original resolution of the input image and obtain a set of predicted probability distribution parameters; The sampling output unit is configured to perform effective sampling on the probability distribution constructed by the distribution parameters based on the sampling rules designed based on the priori assumptions to obtain the evolution results.

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