CN110189800B - Furnace oxygen content soft measurement modeling method based on multi-granularity cascade cyclic neural network - Google Patents

Furnace oxygen content soft measurement modeling method based on multi-granularity cascade cyclic neural network Download PDF

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CN110189800B
CN110189800B CN201910371758.9A CN201910371758A CN110189800B CN 110189800 B CN110189800 B CN 110189800B CN 201910371758 A CN201910371758 A CN 201910371758A CN 110189800 B CN110189800 B CN 110189800B
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宋执环
伊金静
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Abstract

The invention discloses a furnace oxygen content soft measurement modeling method based on a multi-granularity cascade cyclic neural network. The invention mainly comprises a multi-granularity sliding window scanning part and a cascade cyclic neural network part. Firstly, scanning an original input data set by using a plurality of sliding windows with different sizes, and respectively training an obtained feature vector with different scales by a long-time memory unit and a gated cycle unit to generate a corresponding conversion feature vector; and the conversion characteristic vectors corresponding to different window sizes are respectively trained by a cascade cyclic neural network to obtain corresponding predicted values, and finally, the predicted value of the oxygen content corresponding to the input sample is generated. The method can not only process the nonlinearity and the time-varying property of the process, but also fully extract the process data characteristics through the multi-granularity cascade framework, better process the multi-modal characteristics of the process data and further improve the prediction precision.

Description

Furnace oxygen content soft measurement modeling method based on multi-granularity cascade cyclic neural network
Technical Field
The invention belongs to the field of industrial process soft measurement, and relates to a furnace oxygen content soft measurement modeling method based on a multi-granularity cascade cyclic neural network.
Background
In order to reduce production cost, monitor production process, adjust control strategy, improve production efficiency and optimize product quality, real-time measurement and accurate prediction of process key quality variables are very important. In the face of the problem that a measuring instrument cannot measure the quality variable value in real time under a complex production environment, the soft measurement method indirectly estimates and predicts the key quality variable by constructing a mathematical model taking an auxiliary variable as an input main variable as an output. Due to the advantages of easy development, flexible configuration, timely tracking and quick response, the method is rapidly developed and effectively practiced in academia and industry. Different soft measurement methods are proposed and applied one after the other, depending on the different data characteristics of the process. Due to the fact that complex characteristics such as nonlinearity, dynamics and multimodality often exist in an industrial process, a soft measurement modeling method aiming at the multimodality nonlinear time-varying process needs to be researched, and therefore the value of the key quality variable can be estimated in a self-adaptive mode.
Disclosure of Invention
The invention aims to provide a furnace oxygen content soft measurement modeling method based on a multi-granularity cascade circulation neural network aiming at the complex characteristics of nonlinearity, dynamics, multi-modal and the like in the actual industrial process.
The invention is realized by the following technical scheme:
the method comprises the following steps: acquiring historical measurement data of a section of furnace as a training data set, wherein the historical measurement data comprises a plurality of groups of data samples, each group of data samples comprises a furnace oxygen content measurement value at the same moment and a plurality of auxiliary variable measurement values related to the furnace oxygen content, and the auxiliary variable measurement values comprise temperature, pressure and flow measurement values;
step two: carrying out standardization processing on the training data set to obtain a standardized training data set with a mean value of 0 and a variance of 1;
step three: obtaining a multi-granularity cascading cyclic neural network by adopting a deep forest model and improving the model, wherein the multi-granularity cascading cyclic neural network comprises a multi-granularity scanning part and a cascading output part, the multi-granularity scanning part comprises a plurality of sliding windows with different sizes, all the sliding windows are independent and not connected with each other, and each sliding window is connected with the respective cascading output part;
inputting the auxiliary variable measured values of each group of standardized data samples into each sliding window, outputting the auxiliary variable measured values through a cascade output part to obtain furnace oxygen content predicted values corresponding to each sliding window under each group of data samples, calculating the error between the furnace oxygen content predicted values output by each sliding window and the furnace oxygen content measured values by adopting a Root Mean Square Error (RMSE) method, and taking the furnace oxygen content predicted values with the minimum error values as the furnace oxygen content output values finally output under each group of data samples;
step four: obtaining the serial number i of the optimal sliding window, the serial number N of the cascade structure and the serial number k of the optimal output cyclic neural network unit in the output structure according to the finally output furnace oxygen content output value under each group of data samples, thereby obtaining the optimized multi-granularity cascade cyclic neural network and realizing the modeling of soft measurement;
step five: and (4) acquiring a new auxiliary variable measured value, inputting the new auxiliary variable measured value into the multi-granularity cascade circulation neural network obtained in the step four to obtain a furnace oxygen content output value, and realizing real-time online soft measurement of the furnace oxygen content.
In the third step, each sliding window has the same connection structure with the respective cascade output part, specifically: the sliding window comprises a long-time memory cyclic neural network unit LSTM and a gate control cyclic neural network unit GRU, the sliding window is connected with a common cascade output part through the long-time memory cyclic neural network unit LSTM and the gate control cyclic neural network unit GRU respectively, the cascade output part comprises a cascade structure and an output structure, the cascade structure is mainly formed by cascade connection of multi-stage combined cyclic neural networks, and each stage of combined cyclic neural network of the cascade structure is a parallel cyclic neural network structure formed by the two long-time memory cyclic neural network units LSTM and the two gate control cyclic neural network units GRU; the last stage of the cascade structure is connected with an output structure, and the output structure is a parallel cyclic neural network structure formed by two long-time memory cyclic neural network units LSTM and two gate control cyclic neural network units GRU.
In the third step, the method for outputting the furnace oxygen content predicted value through each sliding window is the same, and the method specifically comprises the following steps:
3.1) taking the standardized training data set as the input of a multi-granularity scanning part, and performing sliding scanning on the standardized training data set through a sliding window to generate a feature vector;
3.2) inputting the feature vector into a long-time and short-time memory unit LSTM to obtain a first local feature vector, inputting the feature vector into a gating circulation unit GRU to obtain a second local feature vector, and connecting the first local feature vector and the second local feature vector to obtain a conversion feature vector as the output of the multi-granularity scanning part; concatenation refers to the merging of feature vectors.
3.3) inputting the conversion characteristic vector to the first stage of the cascade structure of the cascade output part, outputting four augmentation characteristic vectors in parallel through two long-term memory units LSTM and two gating circulation units GRU of the first stage, correspondingly outputting one augmentation characteristic vector by one unit (LSTM or GRU), connecting the four augmentation characteristic vectors and the conversion characteristic vector to obtain a first stage characteristic vector, taking the first stage characteristic vector as the input of the second stage, and analogizing in sequence, wherein in each subsequent stage, the output of the previous stage and the conversion characteristic vector are connected to be taken as the input of the current stage.
And 3.4) inputting the output of the last stage of combined cycle neural network into an output structure to obtain four preliminary predicted values, calculating the error value of each preliminary predicted value and the furnace oxygen content measured value by adopting a Root Mean Square Error (RMSE) method, and outputting the preliminary predicted value with the minimum error value as the furnace oxygen content predicted value output by each sliding window. The recurrent neural network unit (LSTM or GRU) with the smallest output error value is the corresponding recurrent neural network unit with the optimal output in the output structure.
Step three, the calculation method of the root mean square error RMSE of each sliding window is the same, and specifically comprises the following steps:
Figure BDA0002050218240000031
wherein, RMSEiAn error value representing the ith sliding window, j represents the group number of the data samples (i.e., the jth group of data samples), m represents the total group number of the data samples, y represents the total group number of the data samplesjRepresents the furnace oxygen content measurement for the jth data sample,
Figure BDA0002050218240000032
and (4) representing the furnace oxygen content predicted value of the ith sliding window, wherein I is the serial number of the sliding window, and I is the total number of the sliding windows.
According to the method, all individual learners in the deep forest model are set as the recurrent neural network RNN to obtain the multi-granularity cascade recurrent neural network, the error of furnace oxygen content prediction is reduced through an improved network structure, and the prediction precision of the furnace oxygen content prediction is improved.
The invention has the beneficial effects that: the method can effectively solve the problems of nonlinearity, multimodality, time-varying property and the like in the industrial process, adaptively estimate the value of the key quality variable in the actual industrial process, and obtain better prediction effect than the traditional method. The method can not only process the nonlinearity and the time-varying property of the process, but also fully extract the process data characteristics through the multi-granularity cascade framework, better process the multi-modal characteristics of the process data and further improve the prediction precision.
Drawings
FIG. 1 is a block diagram of a multi-granular cascaded recurrent neural network process;
FIG. 2 is a process flow diagram of a one stage furnace process;
FIG. 3 is a graph of a prediction of furnace oxygen content for a segment based on deep forest regression;
FIG. 4 is a graph of a one-stage furnace oxygen content prediction based on a multi-particle size cascade cyclic neural network.
Detailed Description
The present invention will be described in further detail with reference to specific embodiments.
As shown in fig. 1 and 2, the multi-granularity cascaded recurrent neural network includes a multi-granularity scanning portion and a cascaded output portion, the multi-granularity scanning portion includes a plurality of sliding windows of different sizes, and the sliding windows are independent of each other and are not connected to each other. Each sliding window is connected with the respective cascade output part, and the connection of one sliding window is taken as an example for specific description: the sliding window is connected with a cascade output part through a long and short time memory unit LSTM and a gate control circulation unit GRU respectively, the cascade output part comprises a cascade structure and an output structure, the cascade structure is mainly formed by cascade connection of multistage circulating neural networks RNN, and each stage of circulating neural networks RNN of the cascade structure is a parallel network structure formed by two long and short time memory units LSTM and two gate control circulation units GRU; the last stage of the recurrent neural network RNN of the cascade structure is connected with an output structure, and the output structure is a parallel network structure formed by two long-time memory units LSTM and two gate control recurrent units GRU.
The method comprises the following steps: constructing a training data set X, wherein X belongs to Rm×dWherein R represents a set of real numbers, m represents a total number of data samples, and d represents a total number of measurements in a set of data samples; the measurements include a furnace oxygen content measurement at the same time and a plurality of auxiliary variable measurements associated with the furnace oxygen content.
Step two: unifying the dimension of the training data set X by adopting a standardized method for later soft measurement modeling to obtain a standardized training data set X with the mean value of 0 and the variance of 1std，Xstd∈Rm×d。
Step three: obtaining a multi-granularity cascade cyclic neural network by adopting a deep forest model and improving the model, and standardizing a training data set XstdInputting the data into a multi-granularity cascade cyclic neural network to train a deep forest classification model. The method comprises the following specific steps:
3.1) establishing I sliding windows of different sizes, standardizing a training data set XstdThrough the ith window diGenerating a feature vector fvi，
Figure BDA0002050218240000041
Wherein d isiD-1 is not more than d, I is the serial number of the sliding window, I belongs to 1, 2.
3.2) ith sliding Window diGenerated feature vector fviThe first local feature vectors generated by a long-short time memory unit and a gated loop unit are respectively input into the first local feature vectors
Figure BDA0002050218240000042
And a second local feature vector
Figure BDA0002050218240000043
First local feature vector lf1iAnd a second local feature vector lf2iConcatenating to obtain transformed feature vectors
Figure BDA0002050218240000044
3.3) transformation feature vector of the ith sliding window
Figure BDA0002050218240000045
Input to the respective cascade output parts, and convert the feature vectors tfiN th through cascaded recurrent neural networksi(ni∈1,2,...,Ni) Stage generation with an augmented feature
Figure BDA0002050218240000046
Wherein N isiIs the total number of cascaded output sections of the ith sliding window, will augment the feature
Figure BDA0002050218240000047
And the transformed feature vector tfiIs connected as the n-thiLevel feature vector
Figure BDA0002050218240000048
Inputting the data into the next stage cascade structure, and repeating the steps until the last stage feature vector is output
Figure BDA0002050218240000049
3.4) the last stage feature vector
Figure BDA00020502182400000410
Inputting the four preliminary predicted values into a combined cycle neural network to output the four preliminary predicted values of the ith window, wherein the four preliminary predicted values are respectively expressed as
Figure BDA00020502182400000411
Figure BDA00020502182400000412
Taking the four primary predicted values with the minimum error value with the furnace oxygen content measured value as the furnace oxygen content predicted value of the ith window
Figure BDA00020502182400000413
The four preliminary prediction values are calculated in the same way, specifically as follows:
Figure BDA00020502182400000414
in the formula, RMSE represents error values, i.e. error values calculated by four preliminary predicted values respectively,
Figure BDA0002050218240000051
when k is 1,2,3, and 4, the preliminary prediction values are expressed respectively
Figure BDA0002050218240000052
Preliminary prediction value
Figure BDA0002050218240000053
Preliminary prediction value
Figure BDA0002050218240000054
Preliminary prediction value
Figure BDA0002050218240000055
Then, outputting the furnace oxygen content predicted value of the sliding window with the minimum error value as a final furnace oxygen content output value;
k*＝argmin(RMSE1,RMSE2,RMSE3,RMSE4) (2)
in the formula, k*Indicating the serial number of the recurrent neural network element corresponding to the preliminary predicted value of the output, argmin indicating the minimization operation, RMSE1,RMSE2,RMSE3,RMSE4Respectively represent the preliminary predicted values
Figure BDA0002050218240000056
Preliminary prediction value
Figure BDA0002050218240000057
Preliminary prediction value
Figure BDA0002050218240000058
And preliminary predicted values
Figure BDA0002050218240000059
The resulting error value is calculated.
Obtaining the predicted values of all sliding windows according to the method of the third step
Figure BDA00020502182400000510
And selecting the furnace oxygen content predicted value with the minimum error RMSE value with the furnace oxygen content measured value of the corresponding data sample as the final furnace oxygen content output value
Figure BDA00020502182400000511
Figure BDA00020502182400000512
Wherein, RMSEiAn error value representing the ith sliding window, j represents the group number of the data samples (i.e., the jth group of data samples), m represents the total group number of the data samples, y represents the total group number of the data samplesjRepresents the furnace oxygen content measurement for the jth data sample,
Figure BDA00020502182400000513
and (4) representing the furnace oxygen content predicted value of the jth data sample in the ith window, wherein I is the serial number of the sliding window, and I is the total number of the sliding windows.
i*＝argmin(RMSE1,RMSE2,...,RMSES) (4)
i*Representing sliding windows with minimum error valueSequence number, argmin denotes minimization operation, RMSE1,RMSE2,...,RMSESRespectively, the error values of the 1 st and 2 nd … … th windows I.
Step four: according to the structure of the optimized multi-granularity cascade cyclic neural network obtained in the third step, the structure comprises the sequence number of the optimal sliding window, the stage number of the cascade output part and the sequence number of the optimal combined cyclic neural network, and modeling of soft measurement is completed;
step five: and acquiring a new auxiliary variable measured value and inputting the new auxiliary variable measured value into the multi-granularity cascade circulation neural network to obtain a furnace oxygen content output value, thereby realizing soft measurement of the furnace oxygen content.
The implementation method of the long-time memory unit and the gate control circulation unit comprises the following steps:
the long-time memory unit introduces an input gate, a forgetting gate and an output gate to calculate a hidden state and then obtain an output value; the gate control cycle unit introduces a reset gate and an update gate to calculate a hidden state and then obtain an output value; the two types of cyclic neural networks adopt Euclidean distance (Euclidean distance) as a loss function between actual output and target output to evaluate the network performance, adopt an Adam optimization algorithm to minimize the target loss function, deal with the problem of gradient explosion by cutting gradients (clip gradient), and adopt a dropout regularization method to relieve the overfitting phenomenon.
The specific embodiment of the invention is as follows:
this case is extracted from a hydrogen production unit in an ammonia synthesis process, as shown in figure 2. After the desulfurization unit, the natural gas mixed steam stream was transferred to a pre-reformer where hydrocarbons and a portion of methane were converted to CO2, CO and H2O, with a reaction temperature of about 510 ℃. Then the heat treatment is carried out by a preheater, the output of the pre-reformer is transferred to a primary furnace, and the following chemical reactions are carried out in the primary furnace:
Figure BDA0002050218240000061
Figure BDA0002050218240000062
Figure BDA0002050218240000063
depending on the reaction mechanism, the temperature in the column is increased to 580 degrees Celsius. For this purpose, fuel gas (fuel gas) is introduced to be uniformly combusted in the dense burner to provide a reaction temperature. The fuel gas consists of two parts, raw natural gas and process exhaust gas. Furthermore, the gas temperature is raised to 300 ℃ by a number of heat exchangers or preheaters before it is transferred to the tower, making it easier to burn.
It can be seen that the reaction temperature is an important factor in ensuring hydrogen production in the first stage furnace. In order to maintain the temperature at a certain level, the combustion conditions in the furnace, which are related to the oxygen content in the furnace, need to be monitored in real time. If a mass spectrometer is used to detect the oxygen content, it is too costly. And the oxygen content in the furnace varies frequently due to the multi-modal operating conditions of the process. In order to reduce the overhead and to make an effective real-time prediction of the oxygen content, a soft measurement method suitable for multi-modal processes is needed. Table 1 lists the main input output variables and the corresponding descriptions. The first 13 variables in the table are inputs for soft measurement modeling including temperature, pressure and flow, and the last variable is the furnace oxygen content of the output variable.
The specific implementation process of the method comprises the following steps: 26860 pieces of process data are collected at continuous equal time intervals, and in the process of selecting the training set and the test set, a sampling mode of interval sampling for respectively classifying two adjacent sample points into the training set and the test set is adopted. 13430 data are used as training samples for modeling, and 13430 data are additionally collected as testing samples for verifying the effectiveness of the multi-granularity cascade cyclic neural network method. As shown in Table 1, there were 13 additional variable measurements associated with furnace oxygen content selected in the implementation, the sampling locations for the 13 measurements are shown in FIG. 2, and the 13 additional variable measurements and the oxygen content at the top of the furnace (furnace oxygen content measurement) numbered Y form a set of data samples.
TABLE 1 variables and corresponding description in the first stage of the furnace
Figure BDA0002050218240000064
Figure BDA0002050218240000071
And inputting the data sample set into the measurement model of the invention to obtain the output value of the oxygen content of the furnace. The furnace oxygen content output value of the invention is compared with the local prediction result of the deep forest model, and the result is shown in table 2.
TABLE 2 comparison of local prediction results for the method of the present invention and other methods
Modeling method Root mean square error Correlation coefficient
Deep forest regression 0.576696 0.911535
Multi-granularity cascade cyclic neural network 0.412565 0.954725
As can be seen from Table 2, the root mean square error of the prediction result of the multi-granularity cascade cyclic neural network-based method is smaller than that of the prediction result of the deep forest regression model, which shows that the improved model network structure of the invention is greatly improved compared with the soft measurement modeling prediction capability of the traditional deep forest; the correlation coefficient of the present invention refers to the degree of linear correlation between the predicted value and the measured value. The correlation coefficient of the method is larger than that of a deep forest regression model, and the method shows that the linear correlation between the predicted value and the measured value obtained by the method is stronger and can better reflect the change process of the oxygen content of the actual furnace.
As shown in the figures 3 and 4, the fitting effect based on the multi-granularity cascade cyclic neural network is better, the self-adaptive tracking effect on the change of the oxygen content of the furnace is better, and the prediction precision is higher compared with a deep forest regression method.
The method improves the deep forest regression model, generates different conversion characteristic vectors through different windows, obtains corresponding predicted values through training of a cascade cyclic neural network, and finally generates the predicted value of the oxygen content corresponding to the input sample. The method can not only process the nonlinearity and the time-varying property of the process, but also fully extract the process data characteristics through the multi-granularity cascade framework, better process the multi-modal characteristics of the process data and further improve the prediction precision. The method can also effectively process time sequence data, solve the problem of nonlinearity in the industrial process, and can also adaptively estimate the value of the key variable for the multi-modal process.
The above-described embodiments are intended to illustrate rather than to limit the invention, and any modifications and variations of the present invention are within the spirit of the invention and the scope of the claims.

Claims (4)

1. A furnace oxygen content soft measurement modeling method based on a multi-granularity cascade cyclic neural network is characterized by comprising the following specific steps:
the method comprises the following steps: acquiring historical measurement data of a section of furnace as a training data set, wherein the historical measurement data comprises a plurality of groups of data samples, each group of data samples comprises a furnace oxygen content measurement value at the same moment and a plurality of auxiliary variable measurement values related to the furnace oxygen content, and the auxiliary variable measurement values comprise temperature, pressure and flow measurement values;
step two: carrying out standardization processing on the training data set to obtain a standardized training data set with a mean value of 0 and a variance of 1;
step three: obtaining a multi-granularity cascading cyclic neural network by adopting a deep forest model and improving the model, wherein the multi-granularity cascading cyclic neural network comprises a multi-granularity scanning part and a cascading output part, the multi-granularity scanning part comprises a plurality of sliding windows with different sizes, all the sliding windows are independent and not connected with each other, and each sliding window is connected with the respective cascading output part;
inputting the auxiliary variable measured values of each group of standardized data samples into each sliding window, outputting the auxiliary variable measured values through a cascade output part to obtain furnace oxygen content predicted values corresponding to each sliding window under each group of data samples, calculating the error between the furnace oxygen content predicted values output by each sliding window and the furnace oxygen content measured values by adopting a Root Mean Square Error (RMSE) method, and taking the furnace oxygen content predicted values with the minimum error values as the furnace oxygen content output values finally output under each group of data samples;
step four: obtaining the optimal serial number of a sliding window, the cascade structure series and the optimal output serial number of a cyclic neural network unit in an output structure according to the furnace oxygen content output value finally output under each group of data samples, thereby obtaining an optimized multi-granularity cascade cyclic neural network and realizing the modeling of soft measurement;
step five: and (4) acquiring a new auxiliary variable measured value, inputting the new auxiliary variable measured value into the multi-granularity cascade circulation neural network obtained in the step four to obtain a furnace oxygen content output value, and realizing soft measurement of the furnace oxygen content.
2. The furnace oxygen content soft measurement modeling method based on the multi-granularity cascade circulation neural network as claimed in claim 1, characterized in that:
in the third step, each sliding window has the same connection structure with the respective cascade output part, specifically: the sliding window comprises a long-time memory cyclic neural network unit LSTM and a gate control cyclic neural network unit GRU, the sliding window is connected with a common cascade output part through the long-time memory cyclic neural network unit LSTM and the gate control cyclic neural network unit GRU respectively, the cascade output part comprises a cascade structure and an output structure, the cascade structure is mainly formed by cascade connection of multi-stage combined cyclic neural networks, and each stage of combined cyclic neural network of the cascade structure is a parallel cyclic neural network structure formed by the two long-time memory cyclic neural network units LSTM and the two gate control cyclic neural network units GRU; the last stage of the cascade structure is connected with an output structure, and the output structure is a parallel cyclic neural network structure formed by two long-time memory cyclic neural network units LSTM and two gate control cyclic neural network units GRU.
3. The furnace oxygen content soft measurement modeling method based on the multi-granularity cascade circulation neural network as claimed in claim 1, characterized in that: in the third step, the method for outputting the furnace oxygen content predicted value through each sliding window is the same, and the method specifically comprises the following steps:
3.1) taking the standardized training data set as the input of a multi-granularity scanning part, and performing sliding scanning on the standardized training data set through a sliding window to generate a feature vector;
3.2) inputting the feature vector into a long-time and short-time memory unit LSTM to obtain a first local feature vector, inputting the feature vector into a gating circulation unit GRU to obtain a second local feature vector, and connecting the first local feature vector and the second local feature vector to obtain a conversion feature vector as the output of the multi-granularity scanning part;
3.3) inputting the conversion characteristic vector to the first stage of the cascade structure of the cascade output part, outputting four augmentation characteristic vectors in parallel through two long-term memory units LSTM and two gating circulation units GRU of the first stage, connecting the four augmentation characteristic vectors and the conversion characteristic vector to obtain a first stage characteristic vector, taking the first stage characteristic vector as the input of the second stage, and so on, and connecting the output of the previous stage and the conversion characteristic vector as the input of the current stage in each subsequent stage;
and 3.4) inputting the output of the last stage of combined cycle neural network into an output structure to obtain four preliminary predicted values, calculating the error value of each preliminary predicted value and the furnace oxygen content measured value by adopting a Root Mean Square Error (RMSE) method, and outputting the preliminary predicted value with the minimum error value as the furnace oxygen content predicted value output by each sliding window.
4. The furnace oxygen content soft measurement modeling method based on the multi-granularity cascade circulation neural network as claimed in claim 1, characterized in that:
step three, the calculation method of the root mean square error RMSE of each sliding window is the same, and specifically comprises the following steps:
Figure FDA0002783996990000021
wherein, RMSEiError value representing the ith sliding window, j representing the group number of data samples, m representing the total group number of data samples, yjRepresents the furnace oxygen content measurement for the jth data sample,
Figure FDA0002783996990000022
and (4) representing the furnace oxygen content predicted value of the ith sliding window, wherein I is the serial number of the sliding window, and I is the total number of the sliding windows.
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