Network technology service consultation intelligent matching system based on artificial intelligence

Abstract

The invention discloses a network technology service consultation intelligent matching system based on artificial intelligence, and relates to the technical field of artificial intelligence, and the system comprises the steps: collecting historical network technical problems and corresponding solutions through a data collection module, and extracting main and auxiliary keywords; the search popularity calculation module calculates the search popularity of a keyword combination and introduces parameters such as search times, user feedback scores and time attenuation factors to construct a formula, the database storage module stores questions and schemes after sorting the questions and the schemes according to the popularity, and when a user inputs the questions, the user question matching module extracts keywords and sends the keywords to the user question matching module; the method comprises the following steps: determining a combination with relatively high search popularity according to a main keyword, taking the combination as alternative data, converting the keyword into a digital vector to calculate similarity, and displaying a solution with the similarity higher than a threshold value to a user according to the size of the similarity, so that the system can efficiently and accurately provide a solution for a network technical problem for the user; and the network technology service consultation quality and efficiency are improved.

Description

Technical Field

[0001] The present invention relates to the field of artificial intelligence technology, and particularly to an intelligent matching system for network technology service consultation based on artificial intelligence. Background Art

[0002] In today's digital age, network technology is widely used in various fields, and users will encounter various problems in the process of using network technology. The traditional network technology service consultation method often relies on manual customer service to answer, with low efficiency and difficulty in meeting the needs of a large number of users. With the development of artificial intelligence technology, although some intelligent customer services are applied to network technology service consultation, there are still deficiencies in the accuracy of problem matching and solution provision. The existing systems cannot make full use of historical data and search popularity information, resulting in a low matching degree between the solutions obtained by users and the actual problems, and being unable to effectively solve users' network technology problems. Therefore, a new intelligent matching system is needed to improve service quality and efficiency. Summary of the Invention

[0003] Aiming at the deficiencies of the prior art, the present invention provides an intelligent matching system for network technology service consultation based on artificial intelligence, which solves the problem of low matching degree between the solutions obtained by users and the actual situation in actual network technology service consultation.

[0004] To achieve the above objectives, the present invention is realized through the following technical solutions: An intelligent matching system for network technology service consultation based on artificial intelligence, comprising:

[0005] A search popularity calculation module, which calculates the search popularity according to the search frequency of the combination of the main keyword and the secondary keyword, the user feedback score, the search depth adjustment coefficient, and the semantic similarity matrix;

[0006] A database storage module, which sorts the network technology problems and their corresponding solutions according to the search popularity and stores them in the search popularity database. The database structure includes a main keyword plus a secondary keyword field and a corresponding solution field;

[0007] User question matching module, which extracts the main keywords and secondary keywords of the user input question, counts the total number of characters Total of the two, locates the combination related to the main keyword in the search popularity database according to the main keyword, extracts the combinations with a search popularity greater than Sth, calculates the total number of characters Totali of the main keyword and secondary keyword in this combination. If Totali <= Total, add this combination to the alternative comparison combinations, and obtain the corresponding digital vector according to the Unicode table for the combination of the main keyword and secondary keyword. If Totali < Total, add 0 after the obtained digital vector, and the number of added 0s is Total - Totali, and the transformed digital vector is Vcompi. Also obtain the corresponding digital vector Vuser for the combination of the user's main keyword and secondary keyword according to the Unicode table, calculate the matching degree Gi between the vector Vcompi and Vuser. If Gi > Gth, add the solution to the corresponding network technology problem in the search popularity database to the database to be displayed, and take out the solution from the database to be displayed according to the size of the matching degree Gi and display it to the user, where Gth is the set matching degree threshold, i ∈ [1, e], and e is the number of combinations with a search popularity greater than Sth.

[0008] As a further solution of the present invention, before the search popularity calculation module, there are also a data collection module and a main and secondary keyword extraction module. The data collection module is used to collect historical data, and the historical data includes network technology problems and corresponding solutions; the main and secondary keyword extraction module is used to perform word segmentation processing on the network technology problems, construct a co-occurrence graph between the word segments, and extract the main keyword and secondary keyword from the co-occurrence graph. The co-occurrence graph can reveal the relationship and weight between the keywords.

[0009] As a further solution of the present invention, the specific steps for extracting the main keyword and secondary keyword are as follows:

[0010] Use a word segmentation tool to split the problem description text into individual words or phrases;

[0011] Link adjacent word segments in the same sentence and set the initial weight of these links to 1;

[0012] Perform the above processing on multiple network technology problem sentences, count the number of times each pair of linked word segments co-occur in all sentences, use it as the weight of the edge, and construct a co-occurrence graph between the word segments;

[0013] According to the co-occurrence graph, count the number of edges connected to each node, that is, the degree of the node, and the node represents the word segment;

[0014] Select the word segment corresponding to the node with the highest degree as the main keyword. If there are multiple nodes with the same and highest degree, select one of them as the main keyword by yourself;

[0015] Starting from the node corresponding to the main keyword, traverse the co-occurrence graph in hierarchical order. First, visit the direct neighbor nodes of the main keyword, record their weights, and then visit the neighbor nodes of these neighbor nodes, and so on. During the traversal, for each newly visited node, calculate the product of the weights of all edges on the path from the main keyword to this node as the comprehensive weight of this node;

[0016] Introduce an attenuation factor ɑ to adjust the comprehensive weight, and obtain the comprehensive weights Wi of all nodes directly and indirectly connected to the main keyword, where i ∈ [1, n], and n represents the number of all other nodes except the main keyword node;

[0017] Set a threshold Wth. If Wi > Wth, then take the word segment corresponding to the i-th node as the secondary keyword.

[0018] As a further solution of the present invention, after obtaining the code point corresponding to each character according to the Unicode table by combining the main keyword and the secondary keyword, it is also necessary to convert this code point into a decimal number.

[0019] As a further solution of the present invention, the search heat of the main keyword and a single secondary keyword is calculated through the following formula, and the specific formula is:

[0020]

[0021] In the formula, F is the search frequency, R is the user feedback score, and its value range is [-100, 100], d is the search depth adjustment coefficient, and its value range is [0, 1].

[0022] As a further solution of the present invention, the specific steps for calculating the search heat of the main keyword and multiple secondary keywords are as follows:

[0023] Use the word vector model to calculate the semantic similarity between every two secondary keywords. Suppose there are m secondary keywords K1, K2,..., Km, and the calculated semantic similarity matrix M is an m×m matrix, where Mij represents the semantic similarity between the secondary keywords Ki and Kj;

[0024] Calculate the average value of all non-diagonal elements in the matrix, where i ≠ j, and the specific formula is: S total The value range of is [0, 1];

[0025] According to the formula S’ = S × (1 + β × (S total - γ)) to obtain the search heat of the combination of the main keyword and multiple secondary keywords, where β is the weight adjustment coefficient and γ is the baseline value of the semantic association degree.

[0026] As a further solution of the present invention, when the data sparsity problem occurs, the specific method of using the semantic similarity between secondary keywords to adjust the search frequency is as follows:

[0027] Collect the combinations Ct where F < λ. Ct contains the main keyword and multiple secondary keywords. Screen out the combinations Cr, r ∈ [1, p], where p is the total number of combinations, that are the same as or similar to the main keyword of Ct. Here, λ ∈ [0, 1].

[0028] Calculate the semantic similarity Sr between Ct and Cr according to the word vector model, and find the combination Cr corresponding to max(Sr).

[0029] Count the search frequency Fr of Cr to obtain the estimated search frequency Festimate of Ct = max(Sr) × Fr.

[0030] The present invention provides an intelligent matching system for network technology service consulting based on artificial intelligence. Compared with the prior art, it has the following beneficial effects:

[0031] (1) The present invention constructs a co-occurrence graph through multiple network technology problems. This co-occurrence graph can clearly represent the relationship between words, not only simple co-occurrence problems, but also reflect the semantic association degree. In addition, observing the structure of the co-occurrence graph can quickly understand the core content of the text, which is helpful for the overall grasp and understanding of the text content.

[0032] (2) The present invention constructs a search popularity database based on the combination of the main keyword and secondary keywords, which can quickly locate the approximate range of the problem input by the user, reduce the redundant calculation amount, realize efficient resource allocation, and then accurately display the solution to the user by calculating the matching degree, enabling the user to first see the most relevant information and improving the user's satisfaction. Description of the Drawings

[0033] Figure 1 It is the system principle block diagram of the present invention. Detailed Embodiments

[0034] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0035] As Figure 1 , the present invention provides an intelligent matching system for network technology service consulting based on artificial intelligence, including:

[0036] Data collection module. The core task of this module is to comprehensively and accurately collect historical network technology problems and their corresponding solutions, and extract keywords from these problems through natural language processing technology to provide data support for subsequent search popularity calculation and intelligent matching;

[0037] The collection channels are mainly divided into three aspects: open-source data scraping, user feedback recording, and data sharing among cooperative enterprises and institutions;

[0038] For open-source data scraping, use data scraping tools to scrape relevant data from various public network technology forums, Q&A communities, technology blogs, and official support forums of manufacturers. For example, on GitHub, relevant programming problems and solutions can be scraped, such as the usage difficulties of different programming languages, framework construction problems, as well as project deployment, code optimization, etc. This tool can regularly and automatically access these platforms to extract network technology-related questions and answers;

[0039] For user feedback recording, the system automatically collects the problems and feedback submitted by users during the usage process. When users encounter network technology problems, they can submit problem descriptions through feedback channels within the system, such as online forms, customer service chat windows, etc. At the same time, the system can also record the actual solution situation of the problems raised by users. For example, a user of a network service provider encounters a slow network speed problem when using the network service and feedbacks the problem through the customer service chat window. The customer service staff records the problem and gives a solution;

[0040] For data sharing among cooperative enterprises and institutions, establish cooperative relationships with other relevant enterprises and institutions to obtain the problems and solutions they encounter in the process of network technology services. For example, cooperate with network equipment manufacturers to obtain the common problems encountered in their equipment after-sales support process and the corresponding repair and configuration solutions;

[0041] Clean and preprocess the data collected from the above three aspects: (1) Remove noise data: In the original data collected, there may be a large amount of noise information, such as advertisements, irrelevant replies, duplicate content, etc. Therefore, it is necessary to filter out these noise data. For example, for the data scraped from network forums, if it is just simple replies such as likes and thanks without substantial content, it can be removed through keyword filtering or text length judgment; (2) Unify the data format: Unify the data from different sources into a standard format that the system can process. For example, for problem descriptions and solutions, uniformly adopt the text format and perform encoding conversion on the text to ensure data consistency and compatibility; (3) Data classification processing: To facilitate subsequent keyword extraction, it is necessary to classify the data collected. For example, classify network technology problems according to different fields, such as network security, network architecture, wireless network, etc.

[0042] The main and secondary keyword extraction module uses appropriate word segmentation tools, such as the Chinese word segmentation tool Jieba or the English word segmentation tool NLTK, to segment the problem description text into individual words or phrases. For example, for the Chinese question "What should I do if my wireless network is always disconnected?", after using Jieba word segmentation, we can get {"I","of","wireless network","always","disconnected","what should I do"};

[0043] Link adjacent segmented words in the same sentence and set the initial weights of these links to 1. For example, after Jieba segmentation, the initial weights of the words “我-的”, “的-无线”, “无线-总是”, “总是-断网”, and “断网-什么” are all 1.

[0044] Perform the above processing on multiple sentences about network technology issues, count the number of times each pair of linked words co-appear in all sentences, use it as the edge weight, and build a co-occurrence graph between the words. For example, if the link "network-delay" appears in 10 sentences, its weight is updated to 10.

[0045] According to the co-occurrence graph, count the number of edges connected by each word, that is, the degree of the node. The words here can also be called nodes in the graph. For example, the node "network" is connected to 5 edges such as "how-network" and "network-delay", so its degree is 5;

[0046] Select the word corresponding to the node with the highest degree as the main keyword. If there are multiple nodes with the same and highest degree, select one of them as the main keyword according to specific business needs, or further screen by considering other factors, such as the importance of the word.

[0047] Starting from the node corresponding to the main keyword, traverse the graph structure in hierarchical order, first visit the direct neighbor nodes of the main keyword, record their weights, and then visit the neighbor nodes of these neighbor nodes, and so on. During the traversal process, for each newly visited node, calculate the product of the weights of all edges on the path from the main keyword to the node as the comprehensive weight of the node. For example, if the edge weight from "network server" to "operating system" is 5, and the edge weight from "operating system" to "kernel parameters" is 3, then the comprehensive weight of "kernel parameters" is 5×3=15;

[0048] As the path length increases, the relevance between the node and the main keyword may gradually weaken. Therefore, a decay factor ɑ is introduced to adjust the comprehensive weight. For example, for each edge traversed, the weight is multiplied by a decay factor. If ɑ = 0.9, the comprehensive weight of nodes farther from the main keyword will be relatively reduced, which is more in line with the characteristic that semantic relevance weakens with distance. For example, for the above-mentioned comprehensive weight from "network server" to "operating system" and then to "kernel parameters" is 5×3×0.9 = 13.5;

[0049] Calculate the comprehensive weights Wi of all nodes directly and indirectly connected to the main keyword, where i ∈ [1, n], and n represents the number of all other nodes except the main keyword node. Set a suitable threshold Wth. If Wi > Wth, then the word segmentation corresponding to the i-th node is used as a secondary keyword. The setting of the threshold Wth needs to be adjusted according to the actual data and application scenarios. An overly high threshold may result in missing important secondary keywords, while an overly low threshold may introduce too many irrelevant words.

[0050] The search popularity calculation module calculates the search popularity of the main keyword and a single secondary keyword according to the formula where F is the search frequency, that is, the number of times the combination of the main keyword and the secondary keyword is searched within a specific time period. The more times it is searched, the higher the degree of attention to this problem combination; R is the user feedback score, with a value range of [-100, 100]. It comprehensively considers the user's feedback on the search results, such as the user's satisfaction with the solution, the matching degree between the search results and the user's needs, etc. If the user is very satisfied with the search results and the feedback is positive, then R is a positive value. If the user is not satisfied with the search results and the feedback is negative, then R is a negative value. The setting of R enables the search popularity to be dynamically adjusted according to the actual user experience; d is the search depth adjustment coefficient, with a value range of [0, 1]. It is used to adjust the degree to which the search popularity is affected by time decay. If d is close to 1, it means that the time decay has a greater impact on the search popularity. If d is close to 0, it means that the impact of time decay is smaller. The value of d can be dynamically adjusted according to the data characteristics and business requirements. For example, for fields with rapid technological updates, d can be appropriately set to a larger value to highlight the popularity of new problems. For relatively stable fields, d can be set to a smaller value;

[0051] In addition to the search popularity of the combination of the main keyword and a single secondary keyword, the search popularity of the combination of the main keyword and multiple secondary keywords also needs to be considered. Since there may be semantic associations between multiple secondary keywords, and this kind of association will affect their weights in the calculation of search popularity, the specific operation steps are as follows: (1) Calculate the semantic similarity matrix: Use the word vector model to calculate the semantic similarity between every two secondary keywords. Suppose there are m secondary keywords K1, K2,..., Km, and the calculated semantic similarity matrix M is an m×m matrix, where Mij represents the semantic similarity between secondary keywords Ki and Kj; (2) Calculate the overall semantic association degree: To obtain the overall semantic association degree of multiple secondary keywords, calculate the average value of all non-diagonal elements in the matrix, i≠j, and the specific formula is: S total The value range of is [0, 1]. The closer the value is to 1, the stronger the semantic association between secondary keywords; (3) Search popularity adjustment: According to the formula S’=S×(1+β×(S total -γ)), obtain the search popularity of the combination of the main keyword and multiple secondary keywords, where β is the weight adjustment coefficient used to control the influence degree of semantic association on search popularity, which can be adjusted according to actual data and business requirements. Generally, β>0, and γ is the baseline value of semantic association degree. If S total >γ, increase the search popularity score. If S total <γ, reduce the search popularity score. The value of γ is usually around 0.5 and can be fine-tuned according to the actual situation;

[0052] When there are many secondary keywords, the problem of data sparsity may occur, that is, the search frequency of some combinations of secondary keywords is extremely low or even zero, that is, F<λ, where λ is a very small number, and the value range is usually [0, 1]. The semantic similarity between secondary keywords can be used to estimate the search frequency: Collect the combinations Ct where F<λ, which contain the main keyword and multiple secondary keywords, screen out the combinations Cr that are the same or similar to the main keyword in Ct, r∈[1, p], where p is the total number of combinations. Calculate the semantic similarity Sr between Ct and Cr according to the word vector model, and find the combination Cr corresponding to max(Sr). The search frequency of Cr is Fr, then the estimated search frequency Festimate of Ct = max(Sr)×Fr.

[0053] The database storage module sorts the network technology problems and their corresponding solutions according to the search popularity and stores them in the search popularity database. The database structure includes the main keyword plus secondary keyword field and the corresponding solution field.

[0054] User question matching module. When a user enters a network technology question, it extracts the main keywords and secondary keywords in the question, and counts the total number of characters Total of the extracted main keywords and secondary keywords. It locates a series of combinations related to the main keyword in the search popularity database according to the main keyword, and extracts the combinations with a search popularity greater than Sth from them. It obtains the total number of characters Totali of the main keyword and secondary keyword in each combination, where i ∈ [1, e], and e is the number of combinations with a search popularity greater than Sth. If Totali <= Total, it adds the corresponding ith combination to the alternative comparison combinations. By comparing the character counts, it can preferentially exclude those combinations with significantly different character counts and less likely to match, narrowing the search scope and improving the matching efficiency. For example, if the user enters "network fault repair method" with a total of 8 characters, and there is "network fault" in the database with a total of 4 characters, combinations with a character count less than or equal to 8 will be included in the alternatives, while combinations with a character count greater than 8, such as "detailed settings steps of network security protection system" with 14 characters, will be initially excluded.

[0055] For the main keywords and secondary keywords in the alternative comparison combinations, obtain the code points corresponding to each character according to the Unicode table, convert them into decimal numbers, and obtain the digital vector corresponding to each group of data. If Totali < Total, add 0 after the corresponding digital vector, and the number of added 0s is Total - Totali, obtaining the transformed digital vector as Vcompi. For the main keywords and secondary keywords extracted from the user, also convert each character into the corresponding decimal number according to the Unicode table, obtaining the corresponding digital vector as Vuser. Utilizing the uniqueness of Unicode encoding, the character information is converted into digital form for subsequent matching degree calculation.

[0056] Calculate the matching degree Gi between the vector Vcompi and Vuser. If Gi > Gth, where Gth is the set matching degree threshold, add the solution to the corresponding network technology question in the search popularity database to the database to be displayed. Retrieve the solutions from the database to be displayed according to the size of the matching degree Gi and display them to the user one by one, enabling the user to first see the most relevant information.

[0057] Some data in the above formula are numerically calculated after removing their dimensions, and the content not described in detail in this specification belongs to the prior art well-known to those skilled in the art.

[0058] The above embodiments are only used to illustrate the technical method of the present invention and not to limit it. Although the present invention has been described in detail with reference to the preferred embodiments, those of ordinary skill in the art should understand that the technical method of the present invention can be modified or equivalently replaced without departing from the spirit and scope of the technical method of the present invention.

Claims

1. An intelligent matching system for network technology service consultation based on artificial intelligence, characterized in that: Including: A search popularity calculation module, which calculates the search popularity based on the search frequency of the combination of the main keyword and the secondary keyword, the user feedback score, the search depth adjustment coefficient, and the semantic similarity matrix; A database storage module, which sorts the network technology problems and their corresponding solutions according to the search popularity and stores them in the search popularity database. The database structure includes a main keyword plus a secondary keyword field and a corresponding solution field; A user problem matching module, which extracts the main keyword and the secondary keyword of the user input problem, counts the total number of characters Total of the two, locates the combination about the main keyword in the search popularity database according to the main keyword, extracts the combination with the search popularity greater than Sth, calculates the total number of characters Totali of the main keyword and the secondary keyword of this combination. If Total i <= Total, add this combination to the alternative comparison combinations, and obtain the corresponding digital vector according to the Unicode table for the combination of the main keyword and the secondary keyword. If Totali < Total, add 0 after the obtained digital vector, and the number of added 0s is Total - Total i. The obtained transformed digital vector is Vcompi. The combination of the user's main keyword and the secondary keyword is also obtained as the corresponding digital vector Vuser according to the Unicode table, and the matching degree Gi between the vector Vcompi and Vuser is calculated. If Gi > Gth, add the solution of the corresponding network technology problem in the search popularity database to the database to be displayed, and take out the solution from the database to be displayed according to the size of the matching degree Gi and display it to the user. Among them, Gth is the set matching degree threshold, i ∈ [1, e], and e is the number of combinations with the search popularity greater than Sth.

2. The network technology service consultation intelligent matching system based on artificial intelligence according to claim 1 is characterized in that: Before the search popularity calculation module, there are also a data collection module and a main and secondary keyword extraction module. The data collection module is used to collect historical data, and the historical data includes network technology problems and corresponding solutions; the main and secondary keyword extraction module is used to perform word segmentation processing on the network technology problems, construct a co-occurrence graph between the word segments, and extract the main keyword and the secondary keyword from the co-occurrence graph. The co-occurrence graph can reveal the relationship and weight between the keywords.

3. The network technology service consultation intelligent matching system based on artificial intelligence according to claim 2 is characterized in that: The specific steps for extracting the main keyword and the secondary keyword are as follows: Use a word segmentation tool to split the problem description text into individual words or phrases; Link the adjacent word segments in the same sentence and set the initial weight of these links to 1; Perform the above processing on multiple network technology problem sentences, count the number of times each pair of linked word segments co-occur in all sentences, and use it as the weight of the edge to construct a co-occurrence graph between the word segments; According to the co-occurrence graph, count the number of edges connected to each node, that is, the degree of the node, and the node represents the word segment; Select the word segment corresponding to the node with the highest degree as the main keyword. If there are multiple nodes with the same and highest degree, select one of them as the main keyword by yourself; Starting from the node corresponding to the main keyword, traverse the co-occurrence graph in hierarchical order, first visit the direct neighbor nodes of the main keyword, record their weights, then visit the neighbor nodes of these neighbor nodes, and so on. During the traversal process, for each newly visited node, calculate the product of the weights of all edges on the path from the main keyword to the node as the comprehensive weight of the node; The attenuation factor ɑ is introduced to adjust the comprehensive weight, and the comprehensive weight Wi of all nodes directly and indirectly connected to the main keyword is calculated, i∈[1,n], n represents the number of all nodes except the main keyword node; Set a threshold Wth. If Wi>Wth, the word corresponding to the i-th node is used as the secondary keyword.

4. The network technology service consultation intelligent matching system based on artificial intelligence according to claim 1 is characterized in that: After combining the primary keyword and the secondary keyword to obtain the code point corresponding to each character according to the Unicode table, the code point needs to be converted into a decimal number.

5. The network technology service consultation intelligent matching system based on artificial intelligence according to claim 1 is characterized in that: The search popularity of the main keyword and a single sub-keyword is calculated using the following formula: Where F is the search frequency, R is the user feedback score, ranging from [-100, 100], and d is the search depth adjustment coefficient, ranging from [0, 1].

6. The network technology service consultation intelligent matching system based on artificial intelligence according to claim 1 is characterized in that: The specific steps to calculate the search popularity of the main keyword and multiple sub-keywords are: The word vector model is used to calculate the semantic similarity between every two sub-keywords. Assuming there are m sub-keywords K1, K2, ..., Km, the calculated semantic similarity matrix M is an m×m matrix, where Mij represents the semantic similarity between sub-keywords Ki and Kj; Calculate the average value of all off-diagonal elements in the matrix (i≠j). The specific formula is: S total The value range of is [0,1]; According to the formula S'=S×(1+β×(S total -γ)) to obtain the search popularity of the combination of the main keyword and multiple sub-keywords, where β is the weight adjustment coefficient and γ is the baseline value of the semantic association degree.

7. The network technology service consultation intelligent matching system based on artificial intelligence according to claim 6 is characterized in that: When data sparsity occurs, the specific method of using the semantic similarity between sub-keywords to adjust the search frequency is: Collect the combination Ct with F < λ, Ct contains the main keyword and multiple sub-keywords, and filter out the combination Cr that is the same or similar to the main keyword of Ct, r∈[1,p], p is the total number of combinations, where λ∈[0,1]; Calculate the semantic similarity Sr between Ct and Cr according to the word vector model, and find the combination Cr corresponding to max(Sr); The search frequency Fr of Cr is calculated, and the estimated search frequency Festimate of Ct is obtained: max(Sr)×Fr.

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