A rock fracture state identification method and related equipment

Abstract

The present invention discloses a method for identifying and monitoring rock fracture states and related equipment. The method comprises: obtaining an acoustic emission signal of the rock fracture process; converting the acoustic emission waveform of the rock acoustic emission signal into a time-frequency graph of the acoustic emission signal; inputting the time-frequency graph of the rock acoustic emission signal into a neural network model, and classifying and identifying the time-frequency graph of the rock acoustic emission signal using the neural network model to determine whether the rock is in a fracture stage. Based on rock fracture acoustic emission data under different stress environments, the present invention converts the waveform of the acoustic emission data into a time-frequency graph, retaining all the waveform features while completing dimensionality upgrade of the acoustic emission data, and then using a convolutional neural network to classify the features of the time-frequency graph. Thus, the convolutional neural network model is used to determine the stage of rock fracture, enabling simple and convenient identification and monitoring of rock fracture stages, which can be used for disaster prevention and early warning in rock engineering and provide a basis for dynamic adjustment of operating parameters.

Description

Technical Field

[0001] The present invention relates to the technical field of geological monitoring, and in particular to a rock fracture state identification method and related equipment. Background Art

[0002] The fracture state of reservoir rock is a crucial indicator in oil and gas development projects. Hydraulic fracturing is the most common method for oil and gas extraction. This involves continuously drilling a well, delivering a fracturing pipe into the reservoir, and then injecting high-pressure fluid to fracture the reservoir rock, creating gas flow channels and enabling efficient extraction. However, high-yield oil and gas reservoirs are often buried at great depths and associated with complex three-dimensional in-situ stress fields. These in-situ stresses are highly susceptible to disturbances caused by hydraulic fracturing operations, exhibiting irregular dynamic variations in magnitude and direction. This often leads to uncontrolled failure of the wellbore and the rock mass in the fractured reservoir area, resulting in significant economic losses. Researchers have used rock mechanics models based on linear derivation (e.g., the Mohr-Coulomb and Hoeke-Brown strength criteria) to predict rock failure and attempt to control injection processes based on the fracture state of the reservoir rock mass. However, the deep three-dimensional stress field undergoes dynamic and nonlinear changes under hydraulic fracturing operations, making it difficult for assessment methods based on specific parameters to adapt to real-time stress field changes.

[0003] Therefore, there is an urgent need to find a method that can dynamically monitor and identify the fracture state of deep rock. However, due to the lack of effective tools and methods, monitoring the fracture state / stage of deep engineering rock masses has always been a challenging task, and there is currently no comprehensive and targeted response plan. Summary of the Invention

[0004] The purpose of the present invention is to provide a rock fracture state identification and monitoring method and related equipment, aiming to solve the problem of difficulty in identifying and monitoring the rock fracture stage in the prior art.

[0005] The technical solutions adopted by the present invention to solve the technical problems are as follows:

[0006] The present invention provides a rock fracture state identification and monitoring method, comprising:

[0007] Obtaining acoustic emission signals from rocks;

[0008] Converting the acoustic emission waveform of the rock's acoustic emission signal into a time-frequency diagram of the acoustic emission signal;

[0009] The time-frequency diagram of the rock's acoustic emission signal is input into the neural network model, and the time-frequency diagram of the rock's acoustic emission signal is classified and identified by the neural network model to obtain a judgment result on whether the rock is in the fracture stage.

[0010] According to the above technical means, the embodiment of the present application converts the waveform of the acoustic emission data into a time-frequency diagram based on the acoustic emission data of rock fracture under different stress environments, retains all the characteristics of the waveform while completing the dimensionality upgrade of the acoustic emission data, and then uses a convolutional neural network to classify and identify the characteristics of the time-frequency diagram, so as to judge the stage of rock fracture through the convolutional neural network model. It can simply and conveniently realize the identification and monitoring of the rock fracture stage, which is used for rock engineering disaster prevention and early warning and provides a basis for dynamic adjustment of operation parameters.

[0011] Furthermore, the transforming of the acoustic emission waveform of the acoustic emission signal of the rock into the time-frequency diagram of the acoustic emission signal is specifically transforming the acoustic emission waveform of the acoustic emission signal of the rock into the time-frequency diagram of the acoustic emission signal by wavelet transform.

[0012] According to the above technical means, the embodiment of the present application transforms the acoustic emission waveform of the acoustic emission signal into a time-frequency diagram of the acoustic emission signal through wavelet transformation. The wavelet transform retains almost all the characteristics of the waveform, and the wavelet transform can focus on any detail of the signal. It is very suitable for the feature extraction of the rock fracture stage, which requires focusing on the regional details of the acoustic emission signal.

[0013] Furthermore, the neural network model is specifically obtained by pre-training image recognition capabilities and then performing classification recognition training.

[0014] According to the above technical means, the embodiment of the present application uses a transfer learning method to directly use the data of the existing database to train the neural network model to have basic image recognition capabilities, so that the neural network model has the ability to extract and recognize features such as edges, regions and colors of the image, and on this basis further classification and recognition training is obtained to obtain the final verified neural network model.

[0015] Furthermore, the classification and recognition training includes:

[0016] Lock some or all parameters related to image recognition capabilities and train the remaining parameters;

[0017] Enable locked parameters related to image recognition capabilities and train the neural network model.

[0018] According to the above technical means, in order to prevent the use of time-frequency graphs for high-precision training from destroying the ability of the pre-trained convolutional layer to extract image features, the embodiment of the present application first locks the convolutional layer, opens the fully connected layer, and only trains the fully connected layer, thereby avoiding the initial loss function Loss being too large to destroy the pre-trained weights of the convolutional layer.

[0019] Furthermore, the neural network model includes a VGG19 model;

[0020] The method of locking some or all parameters related to image recognition capability and training the remaining parameters is as follows:

[0021] Lock the convolutional layer, open the fully connected layer, and only train the fully connected layer;

[0022] The parameters related to the image recognition capability that are unlocked and locked are specifically:

[0023] Turn on the convolutional layer and train the neural network model.

[0024] According to the above technical means, the VGG19 network model used in the embodiment of the present application has excellent reliability and stability, and can better realize the identification and monitoring of rock fractures.

[0025] Furthermore, the convolutional layers are opened to train the neural network model, specifically, some convolutional layers at the head are opened for training a set number of times, and then the convolutional layers are opened step by step for training.

[0026] According to the above technical means, in order to further protect the underlying function of extracting basic features of the image, the embodiment of the present application adopts a method of opening the convolution layer step by step to prevent the destruction of the pre-trained weights of the convolution layer during classification and recognition training to the greatest extent.

[0027] Furthermore, when the convolution layer is opened and the neural network model is trained, fine-tuning training is performed based on the time-frequency diagrams of the acoustic emission signals with different window widths to obtain the optimal window width and the corresponding neural network model.

[0028] According to the above technical means, the embodiment of the present application quickly obtains the optimal window width and the neural network with the best effect corresponding to the optimal window width through fine-tuning.

[0029] Furthermore, the optimal window width is specifically a window width that can completely include a identifiable feature of a fracture but does not include other broken waveform features.

[0030] According to the above technical means, the embodiment of the present application sets a suitable wavelet transform window width, so as to relatively completely include a recognizable feature of a rupture, while avoiding the incorporation of more other rupture waveform features, which affects the accuracy of model training and thus leads to a reduction in recognition accuracy.

[0031] In addition, to achieve the above-mentioned purpose, the present invention also provides a terminal, which includes: a memory, a processor, and a rock fracture state identification and monitoring program stored in the memory and runnable on the processor. When the rock fracture state identification and monitoring program is executed by the processor, the terminal is controlled to implement the steps of the rock fracture state identification and monitoring method described above.

[0032] In addition, to achieve the above-mentioned purpose, the present invention also provides a computer-readable storage medium, which stores a rock fracture state identification and monitoring program, and when the rock fracture state identification and monitoring program is executed by a processor, it implements the steps of the rock fracture state identification and monitoring method as described above.

[0033] The present invention adopts the above technical solution to achieve the following effects:

[0034] Based on the acoustic emission data of rock fracture under different stress environments, the present invention converts the waveform of the acoustic emission data into a time-frequency diagram, retains all the characteristics of the waveform while completing the dimensionality upgrade of the acoustic emission data, and then uses a convolutional neural network to classify the characteristics of the time-frequency diagram. The convolutional neural network model is used to judge the stage of rock fracture, which can simply and conveniently realize the identification and monitoring of rock fracture stages, and provide a basis for disaster prevention and early warning of rock engineering and dynamic adjustment of operation parameters. BRIEF DESCRIPTION OF THE DRAWINGS

[0035] Figure 1 This is a flowchart of the steps of the rock fracture state identification and monitoring method in a preferred embodiment of the present invention;

[0036] Figure 2 It is a comparison diagram of the acoustic emission waveform converted into a time-frequency diagram by wavelet transformation in a preferred embodiment of the present invention;

[0037] Figure 3 The wavelet transform data patterns of different window widths in the preferred embodiment of the present invention are;

[0038] Figure 4 is the recognition accuracy of the rupture stage under different window widths in the preferred embodiment of the present invention;

[0039] Figure 5 Schematic diagram of the network results of the VGG19 neural network model used in the preferred embodiment of the present invention;

[0040] Figure 6 This is a flowchart of the steps of performing recognition training using the VGG19 neural network model used in the preferred embodiment of this aspect;

[0041] Figure 7 Schematic diagram of the operating environment of a preferred embodiment of the terminal of the present invention. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of the present invention more clear and distinct, the present invention is further described in detail below with reference to the accompanying drawings and examples. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0043] Example 1

[0044] See Figure 1 , Embodiment 1 of the present application is a method for identifying and monitoring rock fracture states, comprising the steps of:

[0045] S1. Obtaining the acoustic emission signal of rock;

[0046] Acoustic emission (AE) (frequency ≥ 10,000 Hz) refers to the transient elastic wave phenomenon generated by the energy released by the generation, expansion, and penetration of microcracks during the process of deformation, instability, and failure of a rock mass under load. The macroscopic deformation and failure of a rock mass is the overall manifestation of microscopic damage within the rock mass. AE signals can intuitively reflect the internal damage of the rock mass throughout the deformation and failure stages, as well as the evolution of the generation, expansion, and penetration of microcracks (small scale).

[0047] S2. converting the acoustic emission waveform of the rock acoustic emission signal into a time-frequency diagram of the acoustic emission signal;

[0048] For details, please refer to Figure 2 In this step, the acoustic emission signal waveform is transformed into a time-frequency diagram using wavelet transforms. This diagram retains almost all of the waveform's characteristics, including the main frequency distribution, frequency variation characteristics, and the variation pattern of the minimum power spectrum. At the same time, the data is dimensionalized to facilitate subsequent recognition of the acoustic emission signal using a neural network.

[0049] Wavelet transform (WT) is a new transform analysis method. It inherits and develops the idea of localization of short-time Fourier transform, while overcoming the shortcomings of window size not changing with frequency. It can provide a "time-frequency" window that changes with frequency. It is an ideal tool for signal time-frequency analysis and processing. Just as Fourier transform decomposes the signal into a superposition of a series of sine and cosine functions of different frequencies, wavelet transform decomposes the signal into a superposition of a series of wavelet functions (or wavelet function fitting of different time scales), and these wavelet functions are all obtained by translation and scaling of a basic wavelet function.

[0050] Its main features are that it can fully highlight the characteristics of certain aspects of the problem through transformation, can perform localized analysis of time (space) frequency, and gradually perform multi-scale refinement of signals (functions) through telescoping and translation operations, ultimately achieving time subdivision at high frequencies and frequency subdivision at low frequencies. It can automatically adapt to the requirements of time-frequency signal analysis, thereby focusing on any details of the signal. It is extremely suitable for use in situations such as feature extraction in the rock fracture stage, which requires focusing on regional details of acoustic emission signals.

[0051] Please refer to Figure 3The present invention tests the accuracy of the neural network in identifying the rock fracture stage under wavelet transform conditions with window widths of 1, 2, 3, 5, 10, and 15. Considering that the three-dimensional stress path can reflect a more realistic stress environment, the neural network will not be disturbed by the changes in the stress path when the stress path is specified, and the judgment will be more accurate. That is, the neural network's ability to identify and judge the rock fracture stage is different under the two conditions of specified stress path and unspecified stress path. Therefore, the present invention tests the accuracy of the neural network in identifying the time-frequency diagram after wavelet transform with different window widths in the two conditions.

[0052] Please refer to Figure 4 In tests conducted without specifying a stress path, the results show that window width significantly impacts the training accuracy and identification accuracy of the convolutional neural network model. As the window width increases, the accuracy of the neural network model for identifying sandstone fracture stages increases from a low of 80.2% to a high of 87.3%, without specifying a specific three-dimensional stress path (Rhodes angle). The accuracy rates for window widths ranging from 1 to 15 are 80.2%, 83.3%, 85.2%, 87.3%, and 86.3%, respectively. Notably, the accuracy decreases slightly when the window width increases from 10 to 15. Therefore, under the experimental conditions of the present invention, a window width of 10 is the optimal window width for identifying the fracture stage of sandstone specimens. In principle, this also means that 10 consecutive acoustic emission waveforms can relatively completely capture the identifiable characteristics of a fracture. However, if the window width is too large (e.g., a window width of 15), it will incorporate more waveform features of other fractures, affecting the accuracy of model training and resulting in a decrease in identification accuracy.

[0053] It is worth noting that the optimal window width of this embodiment is specifically tested on sandstone. The identifiable features of rock fractures of different materials vary in size, so the optimal window widths corresponding to rocks of different materials are also different.

[0054] In the present invention's test of a specified stress path, the inclusion of the specified stress path as prior information increases the accuracy compared to the test without specifying a stress path, without increasing computing power requirements. Specifically, the accuracy ranges from 88% to 94.6%, with the best effect achieved when the window width is 15.

[0055] S3. Inputting the time-frequency diagram of the acoustic emission signal of the rock into the neural network, classifying and identifying the time-frequency diagram of the acoustic emission signal of the rock to obtain the fracture stage of the rock.

[0056] Using a convolutional neural network model to identify the fracture stage of tight sandstone is essentially a classification problem. In this embodiment, the VGG19 network model within the CNN neural network is used to identify and determine the fracture stage of the rock. In other embodiments, other neural network models can also be used to identify and determine the fracture stage, and the present invention is not limited to this.

[0057] See Figure 5 The reliability and stability of the VGG19 network model have been verified in the process of widespread adoption. The VGG19 network model consists of 13 convolutional layers and 3 fully connected layers from front to back.

[0058] In this embodiment, in order to obtain the acoustic emission evolution process of rock fracture under different stress paths, the present invention carried out rock destruction experiments under seven different stress paths, and simultaneously performed acoustic emission monitoring throughout the fracture process. The acoustic emission signals were converted into time-frequency diagrams of the acoustic emission signals through wavelet transform, thereby providing a large amount of training data for neural network training.

[0059] The acoustic emission dataset of sandstone failure under each stress path (Rhodes angle) is a subset dataset. To prevent the impact of the number of training samples on the training effect of the convolutional neural network during training, 80% of the data is randomly sampled from each subset database to form the training dataset; the remaining 20% of the data is mixed to form the test dataset.

[0060] However, since the VGG19 network model has many network parameters, a large amount of data is required to train it. If all the time-frequency graphs are used directly for training, a large amount of manpower and material resources are needed to annotate the time-frequency graphs to obtain label data. Therefore, in this embodiment, a transfer learning method is used to pre-train the model to obtain basic image recognition capabilities, that is, the VGG19 network model is pre-trained with training data annotated by an existing database so that the VGG19 network model can obtain basic image recognition capabilities such as edge recognition, region recognition, and color recognition. On this basis, the VGG19 network model can extract the detailed features of the time-frequency graph from the time-frequency graph, and obtain the brightness features, distance features, and strip features of the time-frequency graph, which correspond to the acoustic emission energy size, energy range, and frequency range of the acoustic emission signal, respectively.

[0061] In this embodiment, the ImageNet dataset containing a large amount of general image data is used as a pre-training dataset to pre-train the VGG19 network model.

[0062] Please refer to Figure 6 After completing the pre-training of the model, the training dataset prepared above is used for subsequent classification and recognition training, wherein the classification and recognition training includes:

[0063] A1. Lock the convolutional layer, enable the fully connected layer, and train only the fully connected layer;

[0064] The purpose of this step is to prevent the use of time-frequency graphs for high-precision training from destroying the ability of the pre-trained convolutional layer to extract image features. Therefore, the convolutional layer is locked first, the fully connected layer is enabled, and only the fully connected layer is trained to avoid the initial loss function Loss being too large to destroy the pre-trained weights of the convolutional layer.

[0065] In this embodiment, the fully connected layer is first trained for 5 epochs to allow the network to obtain an initial accuracy. After obtaining the initial accuracy, the loss function LOSS will drop to an acceptable range, thereby avoiding excessive initial loss that damages the pre-trained weights of the convolutional layer.

[0066] Among them, epoch means the process of training all samples of the training data set once, that is, the training data set passes through the neural network once and returns once, that is, a process of forward propagation and back propagation is performed.

[0067] A2. Enable the convolutional layer and train the neural network model.

[0068] In this embodiment, after the initial training of the fully connected layer is completed, the convolutional layer is turned on to train the entire neural network model for 40 epochs, so as to retain more convolutional layers that have the function of extracting basic texture changes at the bottom layer, thereby obtaining better recognition accuracy.

[0069] In an optional embodiment, in order to better protect the underlying function of extracting basic features of the image, the first five convolutional layers of the neural network model can be enabled first, and the remaining convolutional layers can be locked for training for 40 epochs, and then the convolutional layers can be enabled step by step for training.

[0070] In addition, in this embodiment, in the process of gradually opening the convolutional layers for training, fine-tuning training is performed based on the time-frequency diagrams of acoustic emission signals with different window widths to obtain the optimal window width and the corresponding optimal neural network model.

[0071] In this embodiment, the Adam (Adaptive Moment Estimation) optimization algorithm is used. The Adam optimization algorithm combines the Momentum optimization algorithm and the RMSprop optimization algorithm. Unlike traditional gradient descent algorithms, which use a single step size for all input variables, the Adam optimization algorithm automatically adjusts the learning rate for each input variable of the objective function and updates the variables by using a moving average that exponentially decreases the gradient.

[0072] In this embodiment, the batch size of training is 16. Batch size refers to the number of samples in a single training. A batch size of 16 means that 16 samples in the training data set are used for training in one training.

[0073] After overall training, the neural network model has a high accuracy in identifying the fracture stage of rock. As mentioned above, in the test of the present invention on unspecified stress paths, the accuracy rates for window widths from 1 to 15 are: 80.2%, 83.3%, 85.2%, 87.3% and 86.3%, respectively.

[0074] In the present invention's test of a specified stress path, the inclusion of the specified stress path as prior information increases the accuracy compared to the test without specifying a stress path, without increasing computing power requirements. Specifically, the accuracy ranges from 88% to 94.6%, with the best effect achieved when the window width is 15.

[0075] Example 2

[0076] See Figure 7 Based on the above method, the present invention also provides a terminal, which includes: a memory 10, a processor 20, and a rock fracture state identification and monitoring program stored in the memory 10 and executable on the processor 20. When the rock fracture state identification and monitoring program is executed by the processor 20, the terminal is controlled to implement the steps of the rock fracture state identification and monitoring method described above.

[0077] In some embodiments, the memory 10 may be an internal storage unit of the terminal, such as a hard disk or memory of the terminal. In other embodiments, the memory 10 may also be an external storage device of the terminal, such as a plug-in hard disk, a smart memory card (Smart Media Card, SMC), a secure digital (Secure Digital, SD) card, a flash card (Flash Card), etc. equipped on the terminal. Furthermore, the memory 10 may also include both an internal storage unit of the terminal and an external storage device. The memory 10 is used to store application software and various types of data installed on the terminal, such as the program code of the installation terminal. The memory 10 may also be used to temporarily store data that has been output or is to be output. In one embodiment, a rock fracture state identification and monitoring program 40 is stored on the memory 10, and the rock fracture state identification and monitoring program 40 can be executed by the processor 20, thereby realizing the rock fracture state identification and monitoring method in the present application.

[0078] In some embodiments, the processor 20 may be a central processing unit (CPU), a microprocessor, or other data processing chip, configured to execute program codes or process data stored in the memory 10, such as executing the rock fracture state identification and monitoring method.

[0079] Example 3

[0080] This embodiment provides a storage medium, characterized in that the computer-readable storage medium stores a rock fracture state identification and monitoring program, and when the rock fracture state identification and monitoring program is executed by a processor, the steps of the rock fracture state identification and monitoring method described above are implemented.

[0081] In summary, based on the acoustic emission data of rock fracture under different stress environments, the present invention converts the waveform of the acoustic emission data into a time-frequency diagram, retains all the characteristics of the waveform while completing the dimensionality increase of the acoustic emission data, and then uses a convolutional neural network to classify the characteristics of the time-frequency diagram. The convolutional neural network model is used to judge the stage of rock fracture, which can simply and conveniently realize the identification and monitoring of the rock fracture stage, and provide a basis for disaster prevention and early warning of rock engineering and dynamic adjustment of operation parameters.

[0082] It should be noted that, in this document, the terms "comprises," "includes," or any other variations thereof are intended to encompass non-exclusive inclusion, such that a process, method, article, or terminal comprising a series of elements includes not only those elements but also other elements not explicitly listed, or elements inherent to such process, method, article, or terminal. In the absence of further limitations, an element defined by the phrase "comprising a ..." does not exclude the presence of other identical elements in the process, method, article, or terminal comprising the element.

[0083] Of course, those skilled in the art will appreciate that all or part of the processes in the above-described method embodiments can be implemented by instructing related hardware (such as a processor, controller, etc.) through a computer program. The program can be stored in a computer-readable storage medium, and when executed, the program can include the processes in the above-described method embodiments. The storage medium can be a memory, a magnetic disk, an optical disk, etc.

[0084] It should be understood that the application of the present invention is not limited to the above examples. For those skilled in the art, improvements or changes can be made based on the above description. All these improvements and changes should fall within the scope of protection of the claims attached to the present invention.

Claims

1. A method for identifying and monitoring rock fracture conditions, characterized in that: include Obtaining acoustic emission signals from rocks; Converting the acoustic emission waveform of the rock's acoustic emission signal into a time-frequency diagram of the acoustic emission signal; The time-frequency graph of the acoustic emission signal is input into the neural network model, and the time-frequency graph of the acoustic emission signal of the rock is classified and identified by the neural network model to obtain the judgment result of whether the rock is in the fracture stage; The neural network model is specifically obtained by pre-training image recognition capabilities and then performing classification recognition training; The classification and recognition training includes: Lock some or all parameters related to image recognition capabilities and train the remaining parameters; Enable locked parameters related to image recognition capabilities and train the neural network model.

2. A rock fracture state identification and monitoring method according to claim 1, characterized in that: The transforming of the acoustic emission waveform of the acoustic emission signal of the rock into the time-frequency diagram of the acoustic emission signal is specifically transforming the acoustic emission waveform of the acoustic emission signal of the rock into the time-frequency diagram of the acoustic emission signal by wavelet transform.

3. A rock fracture state identification and monitoring method according to claim 1, characterized in that: The neural network model includes a VGG19 model; The method of locking some or all parameters related to image recognition capability and training the remaining parameters is as follows: Lock the convolutional layer, open the fully connected layer, and only train the fully connected layer; The parameters related to the image recognition capability that are unlocked and locked are specifically: Turn on the convolutional layer and train the neural network model.

4. A rock fracture state identification and monitoring method according to claim 3, characterized in that: The convolutional layers are opened to train the neural network model, specifically, some convolutional layers at the head are opened first for training a set number of times, and then the convolutional layers are opened step by step for training.

5. A rock fracture state identification and monitoring method according to claim 3, characterized in that: The convolution layer is opened and the neural network model is trained. Fine-tuning training is performed based on the time-frequency diagram of the acoustic emission signal with different window widths to obtain the optimal window width and the corresponding neural network model.

6. A rock fracture state identification and monitoring method according to claim 5, characterized in that: The optimal window width is specifically a window width that can completely include a identifiable feature of a fracture but does not include other broken waveform features.

7. A terminal, characterized in that: The terminal includes: a memory, a processor, and a rock fracture state identification and monitoring program stored in the memory and executable on the processor. When the rock fracture state identification and monitoring program is executed by the processor, the terminal is controlled to implement the steps of the rock fracture state identification and monitoring method according to any one of claims 1 to 6.

8. A computer-readable storage medium, characterized in that The computer-readable storage medium stores a rock fracture state identification and monitoring program, which, when executed by a processor, implements the steps of the rock fracture state identification and monitoring method according to any one of claims 1 to 6.

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