Product quality prediction method based on dual-channel information complementary fusion stacked autoencoder
By introducing a dual-channel information complementary fusion stack structure into the autoencoder, extracting and fusing hidden layer information, the problem of low information utilization in the prior art is solved, and the accuracy and efficiency of industrial process product quality prediction is significantly improved.
Patent Information
- Application Number
- CN202211139360.0
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- Filing Date
- 2022-09-19
- Publication Date
- 2024-12-24
- Estimated Expiration
- 2042-09-19
AI Technical Summary
The existing data-driven industrial process product quality prediction methods are low in information processing and utilization, resulting in low prediction accuracy and efficiency.
Using the method of stacked autoencoder based on dual-channel information complementary fusion, through stacked autoencoder design, the top-down and bottom-up information transmission and fusion channels are added, as well as the gated structure, extract and fuse hidden layer information, and perform Weighted fusion to improve prediction accuracy.
It effectively improves information utilization, suppresses noise, and improves the accuracy and efficiency of product quality prediction.
Smart Images
Figure CN115688870B_ABST
Abstract
Description
Technical Field
[0001] The present invention belongs to the field of industrial process control, and in particular relates to a product quality prediction method based on a dual-channel information complementary fusion stacked autoencoder. Background Art
[0002] With the continuous development and progress of modern industrial technology, how to ensure the product quality in the industrial production process has become one of the key issues that need to be addressed in the field of industrial process control. In the industrial production process, real-time measurement and accurate prediction of product quality variables are very important to practitioners. Through the changes in quality variables, the production process status can be monitored in real time, and the process control strategy can be adjusted in a timely manner. At the same time, it can also reduce production costs, improve production efficiency, and optimize product quality. With the continuous development and progress of modern measurement methods, more data can be obtained from process measurements, and a large amount of data has been accumulated in the industrial production process. The data describes the real situation of each production stage of manufacturing, provides valuable data resources for understanding, analyzing and optimizing the manufacturing process, and is the source of intelligence for realizing intelligent manufacturing. Therefore, how to reasonably use the data information accumulated in the manufacturing process and establish an intelligent analysis model suitable for the industrial process to better serve the intelligent decision-making and quality control of the manufacturing process is a hot issue that the industry pays more attention to. At present, the models suitable for industrial process product quality prediction can be mainly divided into mechanism-based modeling, expert experience-based modeling and data-driven modeling. Since industrial process systems are often complex black box states, data-driven models have become the main research direction in recent years, and they also have better prediction effects. Data-driven quality prediction methods use intelligent analysis technologies such as machine learning and deep learning to deeply mine, model and analyze industrial data, and provide users and industries with real-time and accurate product quality prediction results. As a black box model, the data-driven model can solve the problem of unclear mechanism of the research object. The data-driven model can be established using only one algorithm or integrated with multiple algorithms. At the same time, the algorithm used in the data-driven model can flexibly adjust the internal hyperparameters or improve it using optimization algorithms according to actual problems. Data-driven models are usually established using historical data, aiming to describe the internal operating laws and related mode differences of the research object, and can be combined with the parameter input of online data to realize the online output of the model. However, some existing data-driven modeling methods are not perfect in the processing and utilization of industrial process data information, and the utilization rate of effective information is low. Therefore, there is an urgent need to provide a product quality prediction method with better data information utilization, so that the model can more effectively extract effective information, suppress noise, and improve the accuracy and efficiency of product quality prediction. Summary of the invention
[0003] The purpose of the present invention is to provide a product quality prediction method based on dual-channel information complementary fusion stacked autoencoder to address the deficiencies of the prior art. The method comprises the following steps:
[0004] A product quality prediction method based on dual-channel information complementary fusion stacked autoencoder, the method comprising the following steps:
[0005] Step 1: Collect sensor data and product quality data of industrial processes to obtain training data sets Among them, x represents the input sample, y represents the sample label, and M represents the number of labeled samples;
[0006] Step 2: constructing a dual-channel information complementary fusion stacked autoencoder model for product quality prediction, and using the training set to train the dual-channel information complementary fusion stacked autoencoder model;
[0007] The dual-channel information complementary fusion stacked autoencoder model includes a stacked autoencoder, a top-down information transmission and fusion channel, a bottom-up information transmission and fusion channel, and a gating structure;
[0008] The top-down information transmission and fusion channel includes a plurality of information complementary fusion modules; the information complementary fusion module extracts the hidden layer information of the stacked autoencoder, performs information fusion, and regresses the fused information to obtain the output value of the corresponding information complementary fusion module; and at the same time, transmits the fused information from the upper layer to the lower layer;
[0009] The bottom-up information transmission and fusion channel includes a plurality of information complementary fusion modules; the information complementary fusion module extracts the hidden layer information of the stacked autoencoder, performs information fusion, and regresses the fused information to obtain the output value of the corresponding information complementary fusion module; and at the same time, transmits the fused information from the lower layer to the upper layer;
[0010] The gate control structure is used to collect the fusion information and output values of multiple information complementary fusion modules in two information transmission and fusion channels, and then use the fusion information to calculate the weight of the output value, and finally use the weight and output value to perform weighted fusion calculation to obtain the overall prediction result of the model;
[0011] Step 3: Collect industrial field work data and input it into the trained dual-channel information complementary fusion stacked autoencoder model to output the corresponding product quality prediction results.
[0012] Furthermore, in step 2, the stacked autoencoder structure includes a multi-layer encoder and a multi-layer decoder, and the output of each layer of the stacked autoencoder is a reconstruction of the input;
[0013] For a single-layer autoencoder, the calculation formula is as follows:
[0014]
[0015]
[0016] in, is the encoder function, is the decoder function, x represents the input data set, h represents the output of the encoder and the input of the decoder, is the output of the decoder; W (e) ,W (d) is the weight coefficient matrix of the encoder and decoder, b (e) ,b (d) is the bias coefficient matrix of the encoder and decoder;
[0017] For stacked autoencoders, the output of the previous encoder is used as the input of the next encoder, and the calculation formula is as follows:
[0018]
[0019] Where L represents the number of hidden layers. and is the weight coefficient matrix and bias coefficient matrix corresponding to the hidden layer.
[0020] Furthermore, the information complementary fusion module includes a dimensionality reduction fusion channel, a dimensionality increase fusion channel and a regressor, the high-dimensional information passes through the dimensionality reduction fusion channel, and the low-dimensional information passes through the dimensionality increase fusion channel;
[0021] Among them, the calculation formula of dimensionality reduction fusion is:
[0022]
[0023]
[0024] Among them, f DR is the function of the dimension reduction fusion channel, h i is high-dimensional information, h j is low-dimensional information, h i Information after dimensionality reduction, The information after fusion; and They are weight coefficient matrix and bias coefficient matrix respectively;
[0025] The calculation formula of dimensional fusion is:
[0026]
[0027]
[0028] Among them, f DA is the dimension-upgrading fusion channel function, h j Information after dimensionality upgrade, and They are weight coefficient matrix and bias coefficient matrix respectively; The information after fusion;
[0029] The fused information is passed through the regressor to obtain the corresponding module output value and The calculation formula is as follows:
[0030]
[0031]
[0032] Among them, f R is the regressor function, and They are the weight coefficient matrix and bias coefficient matrix of the regressor function respectively.
[0033] Furthermore, the expression for the bottom-up information transmission and the information transmission by the fusion channel is:
[0034]
[0035]
[0036] Among them, f ICFB Represents the functional expression of the information complementary fusion module;
[0037] The expression of the top-down information transmission and the information transmission by the fusion channel is:
[0038]
[0039]
[0040] Furthermore, the calculation expression of the weight of the output value calculated by the gating structure using the fusion information is as follows:
[0041]
[0042] Among them, g k is the gating function, W g,k and b g,k The weight coefficient matrix and deviation coefficient matrix output by the corresponding module;
[0043] The gating structure uses weights and output values to perform weighted fusion calculation to obtain the calculation expression of the overall prediction result of the model as follows:
[0044]
[0045] Furthermore, in the step 2, the dual-channel information complementary fusion stacked autoencoder is trained using a stochastic gradient descent algorithm, and the model training loss function is a mean square error function (MSE), which is expressed as follows:
[0046]
[0047] Among them, x i represents the i-th data, Represents the reconstruction of the data by the stacked autoencoder.
[0048] The beneficial effects of the present invention are as follows:
[0049] In view of the problem that the existing product quality prediction model has low utilization rate of industrial process data information, the present invention proposes a product quality prediction method based on a dual-channel information complementary fusion stacked autoencoder. In this method, a top-down information transmission and fusion channel, a bottom-up information transmission and fusion channel and a gating structure are designed outside the stacked autoencoder. Both information transmission and fusion channels include multiple information complementary fusion modules, which can extract the hidden layer information inside the stacked autoencoder and perform fusion transmission in two directions, thereby enhancing the utilization rate of effective information and suppressing noise. Furthermore, the output value of the information complementary fusion module and the output information are calculated and weightedly fused through the gating structure, thereby improving the adaptability and prediction accuracy of the model. BRIEF DESCRIPTION OF THE DRAWINGS
[0050] Figure 1 Schematic diagram of the autoencoder;
[0051] Figure 2 Schematic diagram of stacked autoencoders;
[0052] Figure 3 It is a schematic diagram of information complementary fusion module;
[0053] Figure 4 Schematic diagram of stacked autoencoders with complementary fusion of dual-channel information;
[0054] Figure 5 Schematic diagram of the gate control module structure;
[0055] Figure 6 This is a curve chart of product quality prediction results for different models. DETAILED DESCRIPTION
[0056] The present invention will be described in detail below based on the accompanying drawings and preferred embodiments, and the purpose and effects of the present invention will become more clear. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not used to limit the present invention.
[0057] The present invention aims at the problem that the existing product quality prediction model has a low utilization rate of industrial process data information, and proposes a product quality prediction method based on a dual-channel information complementary fusion stacked autoencoder. The method first adopts the design of a stacked autoencoder, receives and trains the input data information, and obtains the information of the hidden layer of the stacked autoencoder. Afterwards, outside the stacked autoencoder, a top-down information transmission and fusion channel, a bottom-up information transmission and fusion channel, and a gating structure are designed. This structural design can extract the hidden layer information inside the stacked autoencoder and perform fusion transmission in two directions. Furthermore, the module output value and output information are calculated and weighted fused through the gating structure to obtain the final product quality prediction result. The design of the model enables the model to extract and utilize information more effectively, enhance the utilization rate of effective information, suppress noise, and improve the effect of product quality prediction.
[0058] The method of the present invention comprises the following specific steps:
[0059] Step 1: Collect sensor data and product quality data of industrial processes to obtain training data sets Among them, x represents the input sample, y represents the sample label, and M represents the number of labeled samples;
[0060] Step 2: Construct a dual-channel information complementary fusion stacked autoencoder model for product quality prediction, and use the industrial process data sample set to train the dual-channel information complementary fusion stacked autoencoder model;
[0061] (2.1) Construct a stacked autoencoder model, which includes multiple layers of encoders and decoders. The model output is a reconstruction of the input. For a single-layer autoencoder, such as Figure 1 As shown, the calculation formula is as follows:
[0062]
[0063]
[0064]
[0065] in, is the encoder function, is the decoder function, x represents the input data set, h represents the output of the encoder and the input of the decoder, is the output of the decoder. (e) ,W(d) is the weight coefficient matrix of the encoder and decoder, b (e) ,b (d) is the bias coefficient matrix of the encoder and decoder. AE (θ) is the mean square error formula used in the training process of the single-layer autoencoder. The training requires J AE The closer the result of (θ) is to 0, the better. For stacked autoencoders, the output of the previous encoder can be used as the output of the next encoder, such as Figure 2 As shown, the calculation formula is as follows:
[0066] Where L represents the number of hidden layers. and is the weight coefficient matrix and bias coefficient matrix corresponding to the hidden layer.
[0067] (2.2) Establish an information complementary fusion module to extract and fuse the hidden layer information in the stacked autoencoder, and further transmit the fused information. The information complementary fusion module includes a dimensionality reduction fusion channel, a dimensionality increase fusion channel and a regressor, such as Figure 3 As shown, the information complementary fusion module extracts and collects two different information, where h i is high-dimensional information, h j The high-dimensional information is reduced to the dimension equivalent to the low-dimensional information through the dimensionality reduction fusion channel, and the low-dimensional information is upgraded to the dimension of the high-dimensional information through the dimensionality increase fusion channel. The two channels are used to achieve dimensional unification, and then the information of the same dimension is fused to obtain the fused information. The fused information will include both the high-dimensional information and the low-dimensional information.
[0068] Among them, the calculation formula of the dimension reduction fusion channel is:
[0069]
[0070]
[0071] Among them, f DR is the function of dimensionality reduction fusion channel, h i Information after dimensionality reduction, The information after fusion; and They are the weight coefficient matrix and the bias coefficient matrix in the dimension reduction fusion channel formula respectively;
[0072] In addition, the calculation formula of the dimensional fusion channel is:
[0073]
[0074]
[0075] Among them, f DA is the function of the dimension-upgrading fusion channel, h j Information after dimensionality upgrade, For the information after fusion, and They are the weight coefficient matrix and the deviation coefficient matrix in the dimension-upgrading fusion channel formula respectively;
[0076] The fused information is passed through the regressor to obtain the corresponding module output value and The calculation formula is as follows:
[0077]
[0078]
[0079] Among them, f R is the regressor function, and They are the weight coefficient matrix and bias coefficient matrix in the regressor function respectively.
[0080] (2.3) For the fusion information extracted and fused by the information complementary fusion module, the present invention completes the information extraction, fusion and directional transmission of the entire stacked autoencoder by designing a top-down information transmission and fusion channel and a bottom-up information transmission and fusion channel. The specific structures of these two channels are as follows: Figure 4 As shown, the expression of the bottom-up information transmission and the fusion channel for information transmission is:
[0081]
[0082]
[0083] Among them, f ICFB It represents the functional expression of the information complementary fusion module. In the bottom-up information fusion and transmission channel, the bottom-level information complementary fusion module first extracts the information of the two adjacent hidden layers h1 and h2 at the bottom, and then obtains the fused information Then the bottom layer information fusion module passes the fusion information to the second information complementary fusion module from bottom to top. At the same time, the second information complementary fusion module extracts the third hidden layer information h3 and After information fusion with h3, it is passed to the third information complementary fusion module from bottom to top. Similarly, the hidden layer information in the stacked autoencoder is extracted, fused and transmitted from the bottom layer to the top layer.
[0084] The expression of the top-down information transmission and the information transmission by the fusion channel is:
[0085]
[0086]
[0087] Among them, f ICFB It represents the functional expression of the information complementary fusion module. In the top-down information fusion and transmission channel, the top-level information complementary fusion module first extracts the top two adjacent hidden layers h L and h L-1 The information is fused to obtain fused information Then the top information fusion module passes the fusion information to the second information complementary fusion module from top to bottom. At the same time, the second information complementary fusion module extracts the L-2 hidden layer information h L-2 ,Will and h L-2 After information fusion, it is passed to the third information complementary fusion module from top to bottom. Similarly, the hidden layer information in the stacked autoencoder is extracted, fused and transmitted from the upper layer to the lower layer.
[0088] (2.4) The calculation expression of the weight of the output value calculated by the gate control structure using the fusion information is as follows:
[0089]
[0090] Among them, g k is the gating function, W g,k and b g,k The weight coefficient matrix and deviation coefficient matrix output by the corresponding module;
[0091] The specific structure of the gate control structure is shown in the attached Figure 5 As shown, when calculating the overall prediction result of the model, the overall prediction structure includes two parts, one part is the weighted fusion of the output value of each information complementary fusion module in the top-down information fusion and transmission channel and the weight calculated by it, and the other part is the weighted fusion of the output value of each information complementary fusion module in the bottom-up information fusion and transmission channel and the weight calculated by it. The gate control structure uses the weight and output value to perform weighted fusion calculation to obtain the calculation expression of the overall prediction result of the model as follows:
[0092]
[0093] in, It is the weighted fusion of the output value of each information complementary fusion module in the bottom-up information fusion and transmission channel and its calculated weight; It is a weighted fusion of the output value of each information complementary fusion module in the top-down information fusion and transmission channel and its calculated weight.
[0094] (2.5) Using the industrial process sample dataset constructed in step 1, the dual-channel gated multi-expert hybrid stacked autoencoder model is trained using a stochastic gradient descent algorithm. The model training loss function is the mean square error function (MSE), which is expressed as follows:
[0095]
[0096] Among them, x i represents the i-th data, Represents the reconstruction of the data by the stacked autoencoder.
[0097] Step three: Collect industrial field work data and input it into the dual-channel information complementary fusion stacked autoencoder model for product quality prediction, and output the corresponding product quality prediction results.
[0098] The effectiveness of the method of the present invention is verified by a specific industrial process example. In the experiment, sensor data in blast furnace ironmaking in the actual production process was collected and data collection was performed. The data set has a total of 110 process variables, and the quality variable to be predicted is silicon content. Silicon content is one of the important molten iron quality indicators in the blast furnace ironmaking process, which can well reflect the operating status and product quality of the blast furnace ironmaking industrial system.
[0099] The collected data includes a total of 20,000 data, of which 12,000 data are used as training sets, 4,000 data are used as validation sets, and 4,000 data are used as test sets. The training data set is used for model training, the validation data set is used for model parameter selection, and the test data set is used for model testing. In order to evaluate the prediction performance of the designed product quality prediction model, there are two main evaluation criteria used in the experiment. One of the evaluation criteria is the root mean square error, which is defined as follows:
[0100]
[0101] Among them, N represents the total amount of data in the test set, y i and are the true value and predicted value of the output quality variable respectively. Another evaluation criterion is the coefficient of determination, referred to as R 2 , which is defined as follows:
[0102]
[0103] in, Represents the average value of the quality variable. For the above evaluation criteria, the smaller the RMSE value and the higher the R 2The larger the value, the higher the prediction performance of the model.
[0104] The test results of the comparative experiment are shown in Table 1, where SAE represents the stacked autoencoder model, GSAE represents the gated multi-expert hybrid stacked autoencoder model, and DC-ICF-SAE represents the dual-channel information complementary fusion stacked autoencoder model of the present invention. As can be seen from Table 1, compared with the SAE and GSAE models, the DC-ICF-SAE model proposed in the present invention achieves the smallest RMSE and the largest R 2 , indicating that the method of the present invention has better prediction performance.
[0105] Table 1
[0106] Model RMSE <![CDATA[R 2 ]]> SAE 0.0401 0.9041 GSAE 0.0389 0.9185 DC-ICF-SAE 0.0286 0.9504
[0107] also, Figure 6 The product quality prediction results of SAE, GSAE and DC-ICF-SAE models are given. Figure 6 It can be seen that there is a relatively obvious deviation between the predicted values output by the SAE and GSAE models and the actual measured values, and the prediction effect has a more obvious decline in places where the quality variable values change rapidly. In contrast, the predicted values output by the DC-ICF-SAE model proposed in the present invention have a high degree of consistency with the actual measured values, and have better prediction effects and smaller prediction deviations in parts where the quality variable values change rapidly. The experimental results show that the product quality prediction method based on dual-channel information complementary fusion stacked autoencoders proposed in the present invention better processes data information, extracts more effective information, and has a better prediction effect on product quality.
[0108] Those skilled in the art can understand that the above are only preferred examples of the invention and are not intended to limit the invention. Although the invention is described in detail with reference to the above examples, those skilled in the art can still modify the technical solutions recorded in the above examples or replace some of the technical features therein with equivalents. Any modification, equivalent replacement, etc. made within the spirit and principle of the invention shall be included in the protection scope of the invention.
Claims
1. A product quality prediction method based on dual-channel information complementary fusion stacked autoencoder, characterized in that: The method comprises the following steps: Step 1: Collect sensor data and product quality data of industrial processes to obtain training data sets Among them, x represents the input sample, y represents the sample label, and M represents the number of labeled samples; Step 2: constructing a dual-channel information complementary fusion stacked autoencoder model for product quality prediction, and using the training set to train the dual-channel information complementary fusion stacked autoencoder model; The dual-channel information complementary fusion stacked autoencoder model includes a stacked autoencoder, a top-down information transmission and fusion channel, a bottom-up information transmission and fusion channel, and a gating structure; The top-down information transmission and fusion channel includes multiple information complementary fusion modules; the information complementary fusion module extracts the hidden layer information of the stacked autoencoder, performs information fusion, and regresses the fused information to obtain the output value of the corresponding information complementary fusion module; at the same time, the fused information is transmitted from the upper layer to the lower layer; the expression for information transmission by the top-down information transmission and fusion channel is: in, It means that the top two adjacent hidden layers h are extracted by the top information complementary fusion module L and h L-1 The information obtained by fusion is the fusion information; f ICFB-tb Represents the functional expression of the top-down information complementary fusion module; The bottom-up information transmission and fusion channel includes multiple information complementary fusion modules; the information complementary fusion module extracts the hidden layer information of the stacked autoencoder, performs information fusion, and regresses the fused information to obtain the output value of the corresponding information complementary fusion module; at the same time, the fused information is transmitted from the lower layer to the upper layer; the expression for information transmission by the bottom-up information transmission and fusion channel is: Among them, f ICFB Represents the functional expression of the information complementary fusion module; represents the fusion information obtained by fusing the information of the two adjacent hidden layers h1 and h2 extracted by the bottom layer information complementary fusion module; f ICFB-bt The functional expression of the bottom-up information complementary fusion module; The gate control structure is used to collect the fusion information and output values of multiple information complementary fusion modules in two information transmission and fusion channels, and then use the fusion information to calculate the weight of the output value, and finally use the weight and output value to perform weighted fusion calculation to obtain the overall prediction result of the model; Step 3: Collect industrial field work data and input it into the trained dual-channel information complementary fusion stacked autoencoder model to output the corresponding product quality prediction results.
2. The product quality prediction method based on dual-channel information complementary fusion stacked autoencoder according to claim 1 is characterized in that: In the step 2, the stacked autoencoder structure includes a multi-layer encoder and a multi-layer decoder, and the output of each layer of the stacked autoencoder is a reconstruction of the input; For a single-layer autoencoder, the calculation formula is as follows: in, is the encoder function, is the decoder function, x represents the input data set, h represents the output of the encoder and the input of the decoder, is the output of the decoder; W (e) ,W (d) is the weight coefficient matrix of the encoder and decoder, b (e) ,b (d) is the bias coefficient matrix of the encoder and decoder; For stacked autoencoders, the output of the previous encoder is used as the input of the next encoder, and the calculation formula is as follows: Where L represents the number of hidden layers. and is the weight coefficient matrix and bias coefficient matrix corresponding to the hidden layer.
3. The product quality prediction method based on dual-channel information complementary fusion stacked autoencoder according to claim 2 is characterized in that: The information complementary fusion module includes a dimensionality reduction fusion channel, a dimensionality increase fusion channel and a regressor, high-dimensional information passes through the dimensionality reduction fusion channel, and low-dimensional information passes through the dimensionality increase fusion channel; Among them, the calculation formula of dimensionality reduction fusion is: Among them, f DR is the function of the dimension reduction fusion channel, h i is high-dimensional information, h j is low-dimensional information, h i Information after dimensionality reduction, is the information after fusion; W i DR and They are weight coefficient matrix and bias coefficient matrix respectively; The calculation formula for dimensional fusion is: Among them, f DA is the dimension-upgrading fusion channel function, h j Information after dimensionality upgrade, and They are weight coefficient matrix and bias coefficient matrix respectively; The information after fusion; The fused information is passed through the regressor to obtain the corresponding module output value and The calculation formula is as follows: Among them, f R is the regressor function, W i R , and They are the weight coefficient matrix and bias coefficient matrix of the regressor function respectively.
4. The product quality prediction method based on dual-channel information complementary fusion stacked autoencoder according to claim 1 is characterized in that: The calculation expression of the weight of the output value calculated by the gating structure using the fusion information is as follows: Among them, g k is the gating function, W g,k and b g,k The weight coefficient matrix and deviation coefficient matrix output by the corresponding module; The gating structure uses weights and output values to perform weighted fusion calculation to obtain the calculation expression of the overall prediction result of the model as follows: in, It is the weighted fusion of the output value of each information complementary fusion module in the bottom-up information fusion and transmission channel and its calculated weight; It is a weighted fusion of the output value of each information complementary fusion module in the top-down information fusion and transmission channel and its calculated weight.
5. The product quality prediction method based on dual-channel information complementary fusion stacked autoencoder according to claim 4 is characterized in that: In the step 2, the stochastic gradient descent algorithm is used to train the dual-channel information complementary fusion stacked autoencoder, and the model training loss function is the mean square error function, which is expressed as follows: Among them, x i represents the i-th data, Represents the reconstruction of the data by the stacked autoencoder.