A method, system, and equipment for constructing a knowledge graph of continuous casting process and predicting process parameters.

Abstract

This invention provides a method, system, and equipment for constructing a knowledge graph of continuous casting process and predicting process parameters, comprising the following steps: Step 1, obtaining a natural language description corresponding to the continuous casting process to obtain structured and unstructured data; Step 2, extracting corresponding triples from the obtained structured and unstructured data respectively; Step 3, aligning the triples corresponding to the structured data and the triples corresponding to the unstructured data to construct a knowledge graph of the continuous casting process. This invention can accurately identify entities and relationships in the continuous casting field, establish a relatively complete process knowledge graph, and predict the process parameters required for new steel grades through parameter prediction methods. Furthermore, this invention improves the automation level of the production process, thereby enhancing production efficiency and product quality.

Description

Technical Field

[0001] This invention belongs to the field of knowledge graph construction and process parameter prediction, specifically involving a method, system and equipment for constructing a knowledge graph of continuous casting process and predicting process parameters. Background Technology

[0002] Continuous casting involves the coordinated operation of multiple pieces of equipment and processes, requiring precise control of various parameters. This necessitates extensive production knowledge from the workers to address potential problems. However, due to the large number of equipment and processes involved in continuous casting, and the vast amount of related production knowledge, workers often struggle to grasp all the details and technical aspects. Furthermore, the knowledge base for continuous casting is extremely limited; a complete knowledge system is lacking in the field, often leading to excessively long pre-research phases when encountering new steel grade production needs. Therefore, improving the production knowledge level of workers and utilizing modern information technology to analyze and process production data have become crucial issues facing steel enterprises in continuous casting production.

[0003] The challenges in constructing knowledge graphs in the continuous casting field lie in how to fully utilize various types of production data to enrich the knowledge graph, and how to effectively extract entities and relationships within the domain from existing texts. The continuous casting domain lacks effective knowledge representation, with a large amount of knowledge hidden within textual materials; therefore, effectively combining existing extraction methods with the characteristics of the domain is undoubtedly a technical challenge. The technical difficulty in predicting continuous casting process parameters lies in the fact that current parameter prediction methods rely too heavily on expert knowledge, and some existing parameter prediction methods are not very applicable to the continuous casting field. Furthermore, incorporating knowledge graph assistance into continuous casting process parameter prediction and fully utilizing the structural information of the knowledge graph also presents technical challenges. Summary of the Invention

[0004] The purpose of this invention is to provide a method, system, and equipment for constructing a knowledge graph of continuous casting process and predicting process parameters, which solves the problems in the prior art of how to effectively extract entities and relationships in the continuous casting field from existing text and how to use knowledge graphs to complete process parameter prediction.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] This invention provides a method for constructing a knowledge graph of continuous casting processes, comprising the following steps:

[0007] Step 1: Obtain the natural language description corresponding to the continuous casting process to obtain structured and unstructured data;

[0008] Step 2: Extract the corresponding triples from the obtained structured and unstructured data respectively;

[0009] Step 3: Align the triples corresponding to the structured data with the triples corresponding to the unstructured data to construct a knowledge graph of the continuous casting process.

[0010] Preferably, in step 2, the corresponding triples are manually extracted from the structured data.

[0011] Preferably, in step 2, the corresponding triples are extracted from the unstructured data using a joint entity relationship extraction algorithm based on span entity labels and self-attention mechanism.

[0012] Preferably, in step 3, the triples corresponding to the structured data and the triples corresponding to the unstructured data are aligned to construct a continuous casting process knowledge graph. The specific method is as follows:

[0013] By using a multi-knowledge graph entity alignment model, triples corresponding to structured data and triples corresponding to unstructured data are aligned to construct a knowledge graph of continuous casting process.

[0014] A knowledge graph construction system for continuous casting processes, comprising:

[0015] The data acquisition unit is used to acquire the natural language description corresponding to the continuous casting process, and obtain structured data and unstructured data.

[0016] The triplet extraction unit is used to extract the corresponding triples from the obtained structured data and unstructured data respectively;

[0017] The graph construction unit is used to align the triples corresponding to structured data and the triples corresponding to unstructured data to construct a knowledge graph of continuous casting process.

[0018] A computer device, comprising:

[0019] A processor is used to execute computer programs;

[0020] A computer-readable storage medium storing a computer program that, when executed by the processor, performs the method.

[0021] A method for predicting continuous casting process parameters includes the following steps:

[0022] Step 1: Based on the continuous casting process knowledge graph described in claim 1, obtain the feature representations of key process nodes;

[0023] Step 2: Cluster the obtained continuous casting production data to obtain the clustering features corresponding to the continuous casting production data;

[0024] Step 3: Fuse the feature representations and clustering features of the key process nodes to obtain the fused features;

[0025] Step 4: Use the obtained fused features to train the set scoring function to obtain the trained scoring function.

[0026] Step 5: Use the trained scoring function to predict the parameters of the continuous casting process.

[0027] Preferably, in step 1, the feature representation of key process nodes is obtained from the continuous casting process knowledge graph using a graph attention algorithm.

[0028] A continuous casting process parameter prediction system, comprising:

[0029] The feature acquisition unit is used to obtain feature representations of key process nodes based on the continuous casting process knowledge graph.

[0030] Clustering units are used to cluster the acquired continuous casting production data to obtain the clustering features corresponding to the continuous casting production data.

[0031] The fusion unit is used to fuse the feature representations and clustering features of the obtained key process nodes to obtain the fused features;

[0032] The function training unit is used to train the set scoring function using the obtained fused features to obtain the trained scoring function.

[0033] The parameter prediction unit is used to predict the parameters of the continuous casting process using the trained scoring function.

[0034] A computer device, comprising:

[0035] A processor is used to execute computer programs;

[0036] A computer-readable storage medium storing a computer program that, when executed by the processor, performs the method.

[0037] Compared with the prior art, the present invention has the following beneficial effects:

[0038] This invention provides a method for constructing a knowledge graph of continuous casting processes and a method for predicting process parameters. It extracts entities and relationships within a domain from unstructured text using a joint entity relationship extraction algorithm based on span entity labels and a self-attention mechanism. A graph fusion algorithm based on graph convolutional networks aligns the manually constructed knowledge graph with the triples obtained from the entity relationship extraction algorithm to achieve knowledge graph fusion. To utilize the knowledge graph and historical production data to predict process parameters for new steel grades, historical data is first clustered according to key processes to obtain data features for parameter prediction. Then, the continuous casting process knowledge graph is segmented into subgraphs according to key processes. A graph attention network is used to extract features from the knowledge graphs segmented into key process subgraphs as structural features for parameter prediction. Finally, a feature fusion module fuses the two types of features as features for the process parameter prediction method, thus completing the process parameter prediction. This invention can accurately identify entities and relationships within the continuous casting domain, establish a relatively complete process knowledge graph, and predict the process parameters required for new steel grades. Furthermore, this invention improves the automation level of the production process, thereby enhancing production efficiency and product quality. Attached Figure Description

[0039] Figure 1 This is a diagram illustrating the construction process of the knowledge graph in the continuous casting field described in this invention.

[0040] Figure 2 This is a schematic diagram illustrating the construction process of the knowledge graph in the continuous casting field described in this invention;

[0041] Figure 3 This is a structural diagram of the entity relation joint extraction algorithm based on span entity labeling and attention mechanism described in this invention;

[0042] Figure 4 This is a structural diagram of the multi-knowledge graph entity alignment model described in this invention;

[0043] Figure 5 This is a network structure diagram of the knowledge graph-based continuous casting process parameter prediction method described in this invention.

[0044] Figure 6 This is a flowchart of the clustering algorithm for the continuous casting process described in this invention. Detailed Implementation

[0045] In the following description, specific details such as particular system architectures and techniques are set forth for illustrative purposes and not for limitation, in order to provide a thorough understanding of the embodiments of this application. However, those skilled in the art will understand that this application may also be implemented in other embodiments without these specific details. In other instances, detailed descriptions of well-known systems, apparatuses, circuits, and methods have been omitted so as not to obscure the description of this application with unnecessary detail.

[0046] It should be understood that, when used in this application specification and the appended claims, the term "comprising" indicates the presence of the described features, integrals, steps, operations, elements and / or components, but does not exclude the presence or addition of one or more other features, integrals, steps, operations, elements, components and / or a collection thereof.

[0047] It should also be understood that the term “and / or” as used in this application specification and the appended claims means any combination of one or more of the associated listed items and all possible combinations, and includes such combinations.

[0048] As used in this application specification and the appended claims, the term "if" may be interpreted, depending on the context, as "when," "once," "in response to determination," or "in response to detection." Similarly, the phrase "if determined" or "if detected [the described condition or event]" may be interpreted, depending on the context, as meaning "once determined," "in response to determination," "once detected [the described condition or event]," or "in response to detection [the described condition or event]."

[0049] Furthermore, in the description of this application and the appended claims, the terms "first," "second," "third," etc., are used only to distinguish descriptions and should not be construed as indicating or implying relative importance.

[0050] References to "one embodiment" or "some embodiments" as described in this specification mean that one or more embodiments of this application include a specific feature, structure, or characteristic described in connection with that embodiment. Therefore, the phrases "in one embodiment," "in some embodiments," "in other embodiments," "in still other embodiments," etc., appearing in different parts of this specification do not necessarily refer to the same embodiment, but rather mean "one or more, but not all, embodiments," unless otherwise specifically emphasized. The terms "comprising," "including," "having," and variations thereof mean "including but not limited to," unless otherwise specifically emphasized.

[0051] Example 1

[0052] See Figures 1 to 6This embodiment discloses a method for constructing a knowledge graph and predicting process parameters in continuous casting. It applies knowledge graphs to the continuous casting field and utilizes a joint entity relationship extraction algorithm based on span entity labels and a self-attention mechanism to extract domain entities and relationships from unstructured text. A graph fusion algorithm based on graph convolutional networks is used to align and fuse the manually generated knowledge graph with the extracted entity relationship results. To predict process parameters for new steel grades, historical production data is used to extract data features by clustering key processes. Features are then extracted from the key process subgraphs using a graph attention network. Finally, a feature fusion module is used to predict process parameters. The method includes the following steps:

[0053] Step 1. Based on the continuous casting production records and data, obtain the relevant natural language descriptions of the continuous casting process, organize and preprocess them to obtain structured text and unstructured text;

[0054] The preprocessing of continuous casting production records and data specifically includes the following aspects:

[0055] All data is classified into structured text and unstructured text, and the unstructured text is preprocessed in accordance with the algorithm training.

[0056] Step 2. Manually obtain triples for structured text, and extract triples for unstructured text using an entity relation joint extraction algorithm based on span entity labels and self-attention mechanism.

[0057] A joint entity relation extraction algorithm based on span entity labeling and self-attention mechanism is used to extract triples from unstructured text. The specific method is as follows:

[0058] First, the unstructured text is input into the pre-trained BERT model to obtain the feature map of the input text;

[0059] Then, the obtained feature maps are input into two classifiers in the BERT model. The two classifiers are used to predict the start and end positions of entities in the unstructured text, respectively, and these are used as possible head and tail entities in the knowledge graph triples. A multi-label classification strategy is then used to project the CLS tokens of the BERT model into the relation detection space to complete the encoding of entities and relations. Finally, the detected head entity set and relation set are used to predict the start position of the tail entity to ensure accurate identification of the head and tail entities and their relations in the knowledge graph triples.

[0060] The BERT model is based on a transformer model, which uses an encoder-decoder architecture. Within this architecture, it leverages attention mechanisms and fully connected layers to process text. This attention approach can be viewed as searching for hidden relationships within the input information sequence. To effectively capture entities and their locations, a span-based labeling model is used, employing four binary classifiers to predict the start and end positions of entities.

[0061] X = BERT(T)

[0062]

[0063] In the formula: X is the semantic feature map, BERT is the BERT model, and T is the text sentence. Let W represent the probabilities that the i-th marker in the input is the start and end position of the head and tail entities, respectively. head_start 、W head_end 、W tail_start 、W tail_end These are the weight matrices for the corresponding classifiers, and σ is the sigmoid activation function.

[0064] To better accomplish the entity extraction task, a loss function is set to train the classifier, and the obtained head and tail entities are placed into sets E respectively. h and E t middle.

[0065] Loss entity =Loss head +Loss tail

[0066]

[0067] In the formula: Loss entity Loss is the loss function for entity recognition. head Loss tail The loss functions for head entity prediction and tail entity prediction are p, respectively. θ (s|X) is the binary classification loss function.

[0068] In the BERT model, the CLS tag is added to the beginning of each input sequence. Specifically, when a series of texts is input into the BERT model for processing, the first input tag is this special CLS tag. After multiple transformations by BERT, the CLS tag captures the global information of the entire input sequence, and its hidden state encodes the information of the entire input sequence, which can be used for prediction of downstream tasks. To identify correlations in the text, a multi-label classification strategy is adopted, applying the CLS tag to the multi-label classification relation detection space. CLS is the loss function as shown in the following formula, and the detected relations are placed into the set R.

[0069] relation=σ(W relation X CLS )

[0070]

[0071] In the formula: relation is the relation detection function, W relation Let X be the weight matrix of the relation detection classifier. CLS For the CLS label representation of the BERT model, Loss relation This is the loss function for relation detection.

[0072] The relations are encoded using a fully connected layer, as follows:

[0073]

[0074] In the formula: To represent the relationship span, FullyConnect is a fully connected layer function. This is the relation embedding vector.

[0075] Finally, a binary classifier is used to identify the starting position of the tail entity corresponding to the current head entity and the relation, as shown in the following formula:

[0076]

[0077] In the formula: W represents the probability of the starting position of the tail entity. select Select the feature matrix A for the tail entity i This represents the attention representation results.

[0078] The loss function for this stage is:

[0079]

[0080] In the formula: Loss translate The loss function is used for the tail entity translation stage.

[0081] Its joint loss function is defined as follows:

[0082] Loss = aLoss entity +bLoss relation +cLoss translate

[0083] In the formula: Loss is the loss function of the joint entity relation extraction algorithm, and a, b, and c are constants.

[0084] Step 3. Use the multi-knowledge graph entity alignment model to align the triples obtained in the previous step, thereby completing the construction of the continuous casting process knowledge graph;

[0085] The update rules for entity and relation embeddings are as follows:

[0086]

[0087] Where: N r The set of relationships connected to entity i. Let r be the set of tail entities connected to entity i by relation r. The set of head entities connected to entity i by relation r. Let represent the l-th layer embeddings of the head entity, relation entity, and tail entity in the neural network, respectively, where σ is the activation function and W is the value of W. l Let L be the weight matrix of the l-th layer of the neural network; These are the parameters for the next layer of the graph neural network.

[0088] Using known aligned entities and relations, train the objective function of the following formula, such that in the shared embedding space, the distance between aligned entities and relations should be minimized, and the distance between unaligned entities and relations should be maximized.

[0089]

[0090] In the formula: F is the objective function, (e x ,e y (e′) represents a pair of aligned entities. x ,e′ y Let be a pair of unaligned entities, d(…,…) be the distance between the two entities in space, η be the hyperplane separating whether they are aligned, and (r x ,r y (r′) represents a pair of aligned relations. x ,r′ y ) represents a pair of unaligned relations; α represents hyperparameters, E a Given a set of known aligned entities.

[0091] Step 4. Based on the knowledge graph obtained in the previous step, use the graph attention algorithm to obtain the feature representations of key process nodes;

[0092] The update formula for graph attention networks:

[0093]

[0094] In the formula: e ij Let α represent the importance of the features of node j to node i. ij The weight coefficients are calculated for the attention mechanism, and W is the shared weight matrix. Let be the feature vectors of node i and node j.

[0095] Step 5. Use clustering algorithms to cluster the production data to obtain its clustering characteristics;

[0096] The objective function and constraints of the clustering algorithm for continuous casting process are as follows:

[0097]

[0098] In the formula: u ij For sample point x i With cluster center v j The membership degree, where m is the fuzzy index, m>1, d ij For sample point x i With cluster center v j The distance.

[0099] To minimize the objective function J(U,V), the Lagrange multiplier method is applied to the objective function while satisfying the constraints, yielding the membership matrix U and cluster centers v. j As shown in the following formula:

[0100]

[0101] In the formula: u ij For sample point x i With cluster center v j membership degree, d ij For sample point x i With cluster center v j The distance, v j It serves as the cluster center for a certain type.

[0102] Step 6. Use a feature fusion algorithm to fuse the feature representations and clustering features of the key process nodes obtained in Step 4, and use them as the classification basis for process parameter prediction. Train the scoring function to complete the process parameter prediction.

[0103] The fusion formula is as follows:

[0104]

[0105] In the formula: Z represents the fused feature representation. For the initial feature integration, M is the attention weight function. This is matrix multiplication.

[0106] The scoring function for the predicted results is selected as follows:

[0107] z(h,r,t)=‖h°rt‖

[0108] In the formula: z is the scoring function, h is the head entity, r is the relation, t is the tail entity, and ° is the Hadamard product.

[0109] Example 2

[0110] This embodiment also discloses a continuous casting process knowledge graph construction and process parameter prediction system, including:

[0111] A knowledge graph construction system for continuous casting processes, characterized in that it includes:

[0112] The data acquisition unit is used to acquire the natural language description corresponding to the continuous casting process, and obtain structured data and unstructured data.

[0113] The triplet extraction unit is used to extract the corresponding triples from the obtained structured data and unstructured data respectively;

[0114] The graph construction unit is used to align the triples corresponding to structured data and the triples corresponding to unstructured data to construct a knowledge graph of continuous casting process.

[0115] The feature acquisition unit is used to obtain feature representations of key process nodes based on the continuous casting process knowledge graph.

[0116] Clustering units are used to cluster the acquired continuous casting production data to obtain the clustering features corresponding to the continuous casting production data.

[0117] The fusion unit is used to fuse the feature representations and clustering features of the obtained key process nodes to obtain the fused features;

[0118] The function training unit is used to train the set scoring function using the obtained fused features to obtain the trained scoring function.

[0119] The parameter prediction unit is used to predict the parameters of the continuous casting process using the trained scoring function.

[0120] Example 3

[0121] This embodiment 3 provides a computer device, including: a memory for storing a computer program; and a processor for executing the computer program to implement the steps of a computer method.

[0122] When the processor executes the computer program, it implements the steps of the computer method described above, or, when the processor executes the computer program, it implements the functions of each module in the system described above.

[0123] For example, the computer program may be divided into one or more modules / units, which are stored in the memory and executed by the processor to complete the present invention. The one or more modules / units may be a series of computer program instruction segments capable of performing a preset function, the instruction segments describing the execution process of the computer program in the computer device.

[0124] The computer device may be a desktop computer, laptop, handheld computer, or cloud server, etc. The computer device may include, but is not limited to, a processor and memory. Those skilled in the art will understand that the above are examples of computer devices and do not constitute a limitation on the computer device; it may include more components than described above, or combine certain components, or different components. For example, the computer device may also include input / output devices, network access devices, buses, etc.

[0125] The processor can be a Central Processing Unit (CPU), or other general-purpose processors, digital signal processors (DSPs), application-specific integrated circuits (ASICs), field-programmable gate arrays (FPGAs), or other programmable logic devices, discrete gate or transistor logic devices, discrete hardware components, etc. A general-purpose processor can be a microprocessor, or any conventional processor. The processor is the control center of the computer device, connecting various parts of the computer device via various interfaces and lines.

[0126] The memory can be used to store the computer program and / or module, and the processor implements various functions of the computer device by running or executing the computer program and / or module stored in the memory, and by calling the data stored in the memory.

[0127] The memory may primarily include a program storage area and a data storage area. The program storage area may store the operating system and at least one application program required for a given function (such as sound playback or image playback). The data storage area may store data created based on the use of the phone (such as audio data or a phonebook). Furthermore, the memory may include high-speed random access memory (RAM) and non-volatile memory, such as hard disks, RAM, plug-in hard disks, SmartMediaCards (SMC), Secure Digital (SD) cards, flash cards, at least one disk storage device, flash memory device, or other volatile solid-state storage devices.

[0128] The above-described embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application, and should all be included within the protection scope of this application.

Claims

1. A method for constructing a knowledge graph of continuous casting process, characterized in that, Includes the following steps: Step 1: Based on the continuous casting production records and data, obtain the relevant natural language descriptions of the continuous casting process, organize and preprocess them to obtain structured text and unstructured text. Step 2: For structured text, triples are manually obtained; for unstructured text, triples are extracted using an entity relation joint extraction algorithm based on span entity labels and self-attention mechanism. A joint entity relation extraction algorithm based on span entity labeling and self-attention mechanism is used to extract triples from unstructured text. The specific method is as follows: First, the unstructured text is input into the pre-trained BERT model to obtain the feature map of the input text; Then, the obtained feature maps are input into two classifiers in the BERT model. The two classifiers are used to predict the start position and end position of entities in the unstructured text, respectively, and these are used as possible head and tail entities in the knowledge graph triples. Then, the CLS tokens of the BERT model are projected into the relation detection space using a multi-label classification strategy to complete the encoding of entities and relations. Finally, the detected head entity set and relation set are used to predict the starting position of the tail entity to ensure accurate identification of the head entity and tail entity and their relations in the knowledge graph triple. Step 3: Use the multi-knowledge graph entity alignment model to align the triples obtained in the previous step, thereby completing the construction of the continuous casting process knowledge graph; The update rules for entity and relation embeddings are as follows: In the formula: To be with the entity A set of connected relationships. To be with the entity Based on relationships The collection of connected tail entities. To be with the entity Based on relationships The collection of connected header entities. , , Let represent the first, second, and third entities of the head entity, relation entity, and tail entity in the neural network, respectively. Layer embedding, For activation function, For the neural network The weight matrix of the layer; These are the parameters for the next layer of the graph neural network; Using known aligned entities and relations, train the objective function of the following formula, such that in the shared embedding space, the distance between aligned entities and relations should be minimized, and the distance between unaligned entities and relations should be maximized; In the formula: Let be the objective function. For a pair of aligned entities, For a pair of entities that will not align, The distance between the two entities in space. To divide the hyperplanes that are not aligned, For a pair of aligned relationships, This is a pair of unaligned relationships; For super parameters, Given a set of known aligned entities.

2. A knowledge graph construction system for continuous casting process, characterized in that, Based on the method of claim 1, the system comprises: The data acquisition unit is used to acquire relevant natural language descriptions of the continuous casting process based on continuous casting production records and production data, organize and preprocess them to obtain structured text and unstructured text. The triple extraction unit is used to manually obtain triples for structured text and to extract triples for unstructured text using a joint entity relation extraction algorithm based on span entity labels and self-attention mechanism. The graph construction unit is used to align the triples obtained in the previous step using a multi-knowledge graph entity alignment model, thereby completing the construction of the continuous casting process knowledge graph.

3. A computer device, characterized in that, include: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program that, when executed by the processor, performs the method as described in claim 1.

4. A method for predicting continuous casting process parameters, characterized in that, Includes the following steps: Step 1: Based on the continuous casting process knowledge graph described in claim 1, obtain the feature representations of key process nodes; Step 2: Cluster the obtained continuous casting production data to obtain the clustering features corresponding to the continuous casting production data; Step 3: Fuse the feature representations and clustering features of the key process nodes to obtain the fused features; Step 4: Use the obtained fused features to train the set scoring function to obtain the trained scoring function. Step 5: Use the trained scoring function to predict the parameters of the continuous casting process.

5. The method for predicting continuous casting process parameters according to claim 4, characterized in that, In step 1, the graph attention algorithm is used to obtain the feature representations of key process nodes from the continuous casting process knowledge graph.

6. A continuous casting process parameter prediction system, characterized in that, Based on the prediction method of claim 4, the system includes: The feature acquisition unit is used to obtain feature representations of key process nodes based on the continuous casting process knowledge graph. Clustering units are used to cluster the acquired continuous casting production data to obtain the clustering features corresponding to the continuous casting production data. The fusion unit is used to fuse the feature representations and clustering features of the obtained key process nodes to obtain the fused features; The function training unit is used to train the set scoring function using the obtained fused features to obtain the trained scoring function. The parameter prediction unit is used to predict the parameters of the continuous casting process using the trained scoring function.

7. A computer device, characterized in that, include: A processor is used to execute computer programs; A computer-readable storage medium storing a computer program that, when executed by the processor, performs the method as described in claim 4.

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