A prediction method and system for support forms based on multi-scale density peak clustering

Abstract

The present invention discloses a prediction method and system for supporting forms based on multi-scale density peak clustering, belonging to the field of information science. It includes: First, using the coal mine support parameter data collected on-site, calculate the similarity of multi-scale support forms of different coal mines and the semantic similarity of various attributes affecting the decision of support forms; Then, construct a hypergraph based on the multi-scale support form similarity and the semantic similarity of roadway attributes to represent the roadway attributes; Again, apply the attribute density peak mechanism and community detection method on the roadway attribute hypergraph to identify the overlapping communities of attribute hotspots; Finally, analyze the distribution of given attributes in the community to complete the prediction of support forms.

Description

Technical Field

[0001] The present invention belongs to the field of information science, and particularly relates to a prediction method and system for support forms based on multi-scale density peak clustering. Background Art

[0002] Coal mine support is to support and reinforce geological structures such as coal mine working faces and roadways to ensure the stability and safety of the working environment. In the past, the research on the support effect mainly used numerical simulation software to analyze the bolt support of coal roadways, obtain the stress distribution of the surrounding rock of the bolt support in the roadway and the law of mine pressure manifestation, so as to verify the rationality of the support and provide a theoretical basis for optimizing the bolt support parameters of the coal roadway and controlling the deformation of the surrounding rock. There are few reports on the design of support forms using artificial intelligence prediction methods.

[0003] The so-called intelligent support of coal mines refers to using basic parameters such as the characteristics of coal mine roadways and the characteristics of the surrounding rock around them, which are convenient to measure, and through the support form prediction method based on multi-scale density peak clustering of the present invention, predicting parameters such as the diameter, length, and spacing of roof bolts, rib bolts, and cable bolts, and finally designing a feasible support plan according to the prediction results.

[0004] The density peak clustering algorithm can effectively identify clusters with arbitrary shapes, is suitable for large-scale data sets and does not require presetting the number of clusters, has the characteristics of simplicity and high efficiency, and is widely used in clustering analysis tasks in various fields. Summary of the Invention

[0005] Aiming at the deficiencies of the prior art, the present invention proposes a prediction method and system for support forms based on multi-scale density peak clustering, predicting parameters such as the diameter, length, and spacing of roof bolts, rib bolts, and cable bolts, and designing a feasible support plan according to the prediction results.

[0006] To achieve the above object, the present invention provides the following solutions:

[0007] A prediction method for support forms based on multi-scale density peak clustering, comprising the following steps:

[0008] Using the coal mine support parameter data collected on the spot, calculate the similarity of multi-scale support forms of different coal mines, as well as the semantic similarity of roadway attributes that affect the decision of support forms;

[0009] Based on the similarity of multi-scale support forms of different coal mines and the semantic similarity of roadway attributes, construct a hypergraph of roadway attributes - support forms;

[0010] On the hypergraph of roadway attributes - support forms, apply the roadway attribute density peak mechanism and community detection method to identify the overlapping communities of attribute hotspots;

[0011] Analyze the distribution of the given attributes in the attribute hotspot overlapping community to complete the prediction of the support form.

[0012] Preferably, the coal mine support parameter data is expressed as:

[0013] ,

[0014] where, represents the relative importance of attribute in the feature set .

[0015] Preferably, the method for calculating the similarity of multi-scale support forms of different coal mines includes:

[0016] ,

[0017] where, and are both roadways, represents the influence score of attribute t on the support form of roadway , represents the influence score of attribute t on the support form of roadway .

[0018] Preferably, the method for calculating the semantic similarity of roadway attributes that affect the support form decision includes:

[0019] and are in the same connected component of the graph , and the connected component is a directed acyclic graph, that is, there is no and circular reference between them, then and The semantic similarity is defined as:

[0020] ;

[0021] and are in the same connected component of the graph , and are on a cycle in the connected component, that is, there is and circular reference between them, then and The semantic similarity is defined as:

[0022] ;

[0023] and In different connected components of Figure , that is, and there is no explicit association between them, then and the semantic similarity is defined as:

[0024] .

[0025] Preferably, the method for constructing a hypergraph of roadway attributes - support forms includes:

[0026] Using to represent a hypergraph, where is the set of roadways, that is, the set of vertices of the hypergraph ; is the set of edges, representing the equal - value association existing between any two points and or the association existing on the attribute , and T represents the set of attributes; is the set of weights, representing the degree of association.

[0027] Preferably, the method for identifying overlapping communities of attribute hotspots by applying the density - peak mechanism of roadway attributes and the community detection method includes:

[0028] Calculating the local density of the roadway ;

[0029] Based on the local density , calculating the average density on the hypergraph of roadway attributes - support forms;

[0030] Calculating the density deviation degree of the roadway ;

[0031] Based on the average density on the hypergraph of roadway attributes - support forms and the density deviation degree of the roadway , obtaining a decision graph with the local density as the x - axis and the density deviation degree as the y - axis;

[0032] Based on the decision graph, obtaining diverse density - peak nodes;

[0033] Initializing the density - peak nodes as initial community cores, and using the existing density - peak clustering algorithm to divide the hypergraph of roadway attributes - support forms into several dense sub - graphs;

[0034] The algorithm stops when all roadways are assigned to at least one community;

[0035] For the community core set , the detected overlapping communities are obtained.

[0036] Preferably, analyzing the distribution of a given attribute in the overlapping communities of the attribute hotspots, the method for completing the prediction of the support form includes:

[0037] Using a probability vector to represent the probability that a roadway belongs to each community. For community , there is:

[0038] , where is a set composed of and adjacent nodes, represents the result of normalizing the degree of attribute deviation of roadway , represents the result of normalizing the degree of attribute deviation of roadway ;

[0039] Using the vector to represent the influence of attribute t, where ;

[0040] For roadway , it belongs to each community in , and attribute t is also distributed in each community. The influence score of attribute t in is calculated as ;

[0041] Calculate the attributes of the influence score top-k of roadway . Then, among the known roadway attributes, the support form with the highest frequency of having the same top-k attributes is the prediction of the support form for roadway .

[0042] The present invention also discloses a support form prediction system based on multi-scale density peak clustering, including: a calculation module, a construction module, an identification module, and a prediction module;

[0043] The calculation module is used to calculate the similarity of multi-scale support forms of different coal mines and the semantic similarity of roadway attributes that affect the decision of the support form by using the coal mine support parameter data collected on the spot;

[0044] The building module is used to construct a hypergraph of roadway attributes - support forms based on the similarity of multi - scale support forms of different coal mines and the semantic similarity of roadway attributes;

[0045] The identification module is used to apply the roadway attribute density peak mechanism and community detection method on the hypergraph of roadway attributes - support forms to identify attribute hot - spot overlapping communities;

[0046] The prediction module is used to analyze the distribution of given attributes in the attribute hot - spot overlapping communities to complete the support form prediction.

[0047] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0048] 1. The multi - scale density peak clustering algorithm can more accurately identify and classify different features and patterns in roadway support. By analyzing data at different scales, more details and complex structures can be captured, improving the accuracy of support prediction. This multi - scale analysis method can better adapt to complex roadway environments and effectively enhance the reliability and safety of support schemes.

[0049] 2. The multi - scale density peak clustering algorithm has strong adaptability and robustness and can process different types and scales of data. Whether it is large - scale data or data with high noise, the algorithm can effectively identify key patterns and trends in the data. This is particularly important for roadway support prediction because the roadway environment is complex and changeable, and the data quality is uneven. The robustness of the algorithm makes it perform well in practical applications and can provide reliable prediction results in various situations.

[0050] 3. The algorithm determines the clustering centers by effectively finding density peaks, avoiding a large number of iterations and complex calculation processes, thus greatly reducing the computational complexity and time cost. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] In order to more clearly illustrate the technical solutions of the present invention, the following briefly introduces the drawings required in the embodiments. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, other drawings can be obtained based on these drawings without creative efforts.

[0052] Figure 1 It is a schematic flow chart of a support form prediction method based on multi - scale density peak clustering according to an embodiment of the present invention. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0053] Next, the technical solutions in the embodiments of the present invention will be clearly and completely described in conjunction with the accompanying 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. Based on the embodiments of the present invention, all other embodiments obtained by those of ordinary skill in the art without creative efforts shall fall within the protection scope of the present invention.

[0054] To make the above objects, features, and advantages of the present invention more obvious and understandable, the present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments.

[0055] Embodiment 1

[0056] As Figure 1 shown, the present invention provides a prediction method for support forms based on multi-scale density peak clustering, including the following steps:

[0057] Using the coal mine support parameter data collected on-site, calculate the similarity of multi-scale support forms of different coal mines, as well as the semantic similarity of various roadway attributes affecting the support form decision-making;

[0058] Based on the similarity of multi-scale support forms of different coal mines and the semantic similarity of the roadway attributes, construct a hypergraph of roadway attributes - support forms;

[0059] On the hypergraph of roadway attributes - support forms, apply the roadway attribute density peak mechanism and community detection method to identify the attribute hot spot overlapping communities;

[0060] Analyze the distribution of the given attributes in the attribute hot spot overlapping communities to complete the prediction of the support form.

[0061] After preliminary on-site research, on-site survey, and investigation interviews, the present invention stores the finally obtained 295 pieces of data in the SQLite database. The fields include: coal seam thickness, immediate roof lithology, immediate roof thickness, main roof lithology, main roof thickness, immediate floor lithology, immediate floor thickness, floor lithology, floor thickness, coal pillar width, cross-section shape, roadway burial depth, and support form. Except for the last support form, the rest are input parameters of the prediction method, that is, roadway attribute features. After removing the samples with missing values, 270 pieces of data can be obtained finally.

[0062] In a coal mine intelligent support system, a coal mine whose support form needs to be predicted usually includes a variety of different attributes (such as geographical location represented by longitude and latitude, immediate roof lithology, immediate roof thickness, etc., and the total number of attributes ranges from a dozen to dozens), and these attributes jointly affect the support form. Use roadway attribute features (attribute weight scheme) to characterize the characteristics of the coal mine. By extracting these attributes, the feature set of a roadway is represented as , that is, a set of key-value pairs of an attribute - weight value. Indicates an attribute In the feature set The relative importance is calculated using the term frequency - inverse document frequency (TF - IDF) algorithm, and the specific calculation method is as follows:

[0063] ,

[0064] Among them, is the term frequency of the attribute For the attribute - attribute value (the attribute value is a set) pair , , numerically equal to the size of the attribute value set; Indicates The term frequency of the attribute with the largest term frequency in is the total number of records of the coal mine support form, is the number of records of the roadway support form that contains the attribute . The weight can describe the importance of the roadway attribute for predicting the roadway support form.

[0065] Furthermore, all possible attributes are represented as a set , and the following formula is used to calculate the influence score (Content Impact Degree, CID) of the attribute in the support data of any roadway

[0066] ,

[0067] Among them, when , , otherwise it is 0.

[0068] The above analysis can be used to calculate the multi - scale support form similarity of different coal mine roadways, and to calculate the attribute semantic similarity of various attributes that affect the roadway support form decision.

[0069] If the content of the attribute t of two roadways is exactly the same, then their support form similarity should be greater than that of those roadways that are completely different. Therefore, the following formula is used to model the multi - scale support form similarity (Content Similarity, CSim) of different coal mine roadways:

[0070] ,

[0071] The above formula uses the attribute t for the roadway and the roadway The influence degree of the support form was calculated, and the similarity of the support forms of two roadways was calculated, where i and j represent the numbers of different roadways; since the attribute t comes from the attribute set T, the calculation process involving multiple attributes is the calculation of the multi-scale support form similarity. There is a semantic association between the attribute values of the roadways. Specifically, there is an attribute

[0072] whose value range of the attribute value is where n represents the number of features included in the attribute a ; there is an attribute whose value range of the attribute value is where n represents the number of features included in the attribute b ; for the roadway its for there is a definite set of attribute values such that ; whether the attributes and are associated and the constraints on their respective value ranges belong to prior knowledge. For the roadways in the roadway set if the same constraint conditions appear in the respective attributes of the roadways and they are considered relevant and there is an edge and between them. Based on this, a graph can be obtained. Then, for and and in different situations in the graph there are the following three calculations of semantic similarity (Semantic Similarity, SSim):

[0073] and are in the same connected component of the graph and this connected component is a directed acyclic graph, that is, there is no and circular reference between them, then the semantic similarity between and is defined as:

[0074] ;

[0075] and are in the same connected component of the graph ; and on a loop within this connected component, that is, there exists and a cyclic reference between and then the semantic similarity between

[0076] ,

[0077] and are in different connected components of the graph , that is, and there is no explicit association between and then the semantic similarity between

[0078] ,

[0079] Finally, for the attribute t, the similarity between roadway support attributes is obtained by weighting the multi-scale support form similarity and the semantic similarity

[0080] ,

[0081] where is a hyperparameter that reflects the relative importance of the single roadway attribute and the semantic association between attributes for the support form.

[0082] If any two roadways have equal attribute values, they are considered to have an equal-value association. To calculate this association, for roadways and , use and to represent the sets of roadways associated with roadways and respectively. The degree of equal-value association between roadways and is:

[0083] ,

[0084] Use to represent a hypergraph, where: is the set of roadways, that is, the set of vertices of the hypergraph ; is the set of edges, representing the equal-value association existing between any two points and or the association existing on the attribute ; is the set of weights, representing the degree of association, that is, Use to represent the roadway degree. If is an endpoint of the edge , , otherwise it is .

[0085] Based on the above definitions of hypergraph and association degree, the attribute deviation degree of the roadway is calculated as follows:

[0086] ,

[0087] Normalize the attribute deviation degree to obtain :

[0088] ,

[0089] Obviously, there exists , that is, the association between roadways is mutual and undirected.

[0090] The number of connections between vertices is not uniform, reflecting different degrees of association between different roadways. The density of each vertex is different, reflecting that the number of attributes owned by the roadways is not exactly the same. Design a density peak clustering method for classifying objects into local maxima of the density field. This method has a basic assumption that the clustering core is found by relatively high local link density and is relatively far from any point with high local density. Use the existing density peak idea to find the core of the hypergraph and then perform overlapping community detection.

[0091] The local density of the roadway is calculated as:

[0092] ,

[0093] where is a set composed of and its adjacent nodes. For binarization:

[0094] ,

[0095] The average density on the graph is:

[0096] ,

[0097] The density deviation degree of The calculation method is as follows:

[0098] ,

[0099] Based on the definitions of density and deviation degree, a decision diagram can be obtained with density as the x-axis and deviation degree as the y-axis. Nodes with higher local density and deviation degree can be regarded as diverse density peak nodes. Initialize these density peak nodes as the initial community cores, and then use the existing Density Peaks Clustering (DPC) algorithm to partition the hypergraph into several robust dense subgraphs. The algorithm stops when all vertices are assigned to at least one community. According to the above idea, for the community core set , where k is the number of communities and c i represents the core of the i-th community, we can obtain the monitored overlapping communities . Through covering search, the nodes of each community either overlap with other communities or do not overlap. That is, the roadway may belong to multiple communities, and two communities may have many overlapping roadways. The overlap coefficient of two communities is calculated as :

[0100] ,

[0101] Then continuously merge pairwise the communities in whose overlap coefficient is greater than the threshold until the overlap coefficient between all communities in is less than the threshold .

[0102] After community merging, there are communities, . First, use a probability vector to represent the probability that the roadway belongs to each community, where p ij represents the probability that the roadway belongs to the j-th community. For community , p ij is calculated as follows:

[0103] , where represents the result of normalizing the attribute deviation degree of the roadway , and represents the roadway The result of normalizing the degree of deviation of the attributes;

[0104] Then use the vector to represent the influence of attribute t, where , where represents the influence score of any element v in the community on the community Influence score.

[0105] For the roadway , it may belong to each community in, and attribute t is also distributed in each community. The influence score of attribute t in is calculated as . Calculate the attributes of the influence score top-k of the roadway . Among the known roadway attributes, the support form with the highest frequency of the same top-k attributes is the prediction of the support form for the roadway .

[0106] Embodiment 2

[0107] The present invention also discloses a support form prediction system based on multi-scale density peak clustering, including: a calculation module, a construction module, an identification module, and a prediction module;

[0108] The calculation module is used to calculate the similarity of multi-scale support forms of different coal mines and the semantic similarity of roadway attributes that affect the support form decision-making by using the coal mine support parameter data collected on the spot;

[0109] The construction module is used to construct a hypergraph of roadway attributes - support forms based on the similarity of multi-scale support forms of different coal mines and the semantic similarity of roadway attributes;

[0110] The identification module is used to apply the roadway attribute density peak mechanism and the community detection method on the hypergraph of roadway attributes - support forms to identify the attribute hot spot overlapping communities;

[0111] The prediction module is used to analyze the distribution of given attributes in the attribute hot spot overlapping communities to complete the support form prediction.

[0112] In this embodiment, the coal mine support parameter data is expressed as:

[0113] ,

[0114] where represents the relative importance of attribute in the feature set .

[0115] In this embodiment, the process of calculating the similarity of multi-scale support forms of different coal mines includes:

[0116] ,

[0117] Among them, and are both roadways, represents the influence score of attribute t on the support form of roadway ; represents the influence score of attribute t on the support form of roadway ;

[0118] In this embodiment, the method for calculating the semantic similarity of roadway attributes that affect the support form decision includes:

[0119] and are in the same connected component of the graph , and the connected component is a directed acyclic graph, that is, there is no and circular reference between them, then and The semantic similarity is defined as:

[0120] ;

[0121] and are in the same connected component of the graph , and are on a loop in the connected component, that is, there is a and circular reference between them, then and The semantic similarity is defined as:

[0122] ;

[0123] and are in different connected components of the graph , that is, there is no explicit association between and , then and The semantic similarity is defined as:

[0124] .

[0125] In this embodiment, the method for constructing a hypergraph of roadway attributes - support form includes:

[0126] Use to represent a hypergraph, where is a set of roadways, i.e., a hypergraph a set of vertices; is a set of edges, indicating the equivalent association existing between any two points and or the association existing in the attribute where T represents the set of attributes; is a set of weights, indicating the degree of association.

[0127] In this embodiment, the method for identifying the overlapping communities of attribute hotspots by applying the roadway attribute density peak mechanism and the community detection method includes:

[0128] Calculate the local density of the roadway ; ;

[0129] Based on the local density , calculate the average density on the hypergraph of roadway attribute - support form ;

[0130] Calculate the density deviation degree of the roadway ; ;

[0131] Based on the average density on the hypergraph of the roadway attribute - support form and the density deviation degree of the roadway , obtain a decision graph with the local density as the x - axis and the density deviation degree as the y - axis;

[0132] Based on the decision graph, obtain diverse density peak nodes;

[0133] Initialize the density peak nodes as the initial community cores, and use the existing density peak clustering algorithm to divide the hypergraph of the roadway attribute - support form into several dense sub - graphs;

[0134] When all roadways are assigned to at least one community, the algorithm stops;

[0135] For the community core set , obtain the detected overlapping communities .

[0136] In this embodiment, the method for completing the support form prediction by analyzing the distribution of a given attribute in the overlapping communities of attribute hotspots includes:

[0137] Use a probability vector to represent the roadway The probability of belonging to each community, for the community , there is:

[0138] , where is a set composed of and adjacent nodes, represents the result of normalizing the degree of attribute deviation of the roadway , represents the result of normalizing the degree of attribute deviation of the roadway ;

[0139] Use the vector to represent the influence of attribute t, where ;

[0140] For the roadway , it belongs to each community in, and attribute t is also distributed in each community. The influence score of attribute t in is calculated as ;

[0141] Calculate the attributes of the influence score top-k of the roadway . Then among the known roadway attributes, the support form with the highest frequency of the same top-k attributes is the prediction of the support form of the roadway .

[0142] The embodiments described above are only descriptions of the preferred embodiments of the present invention, and do not limit the scope of the present invention. Without departing from the design spirit of the present invention, various deformations and improvements made by those of ordinary skill in the art to the technical solutions of the present invention should fall within the protection scope determined by the claims of the present invention.

Claims

1. A prediction method for support forms based on multi-scale density peak clustering, characterized in that, Including the following steps: Using the coal mine support parameter data collected on-site, calculate the similarity of multi-scale support forms in different coal mines, as well as the semantic similarity of roadway attributes that affect the decision-making of support forms; Based on the similarity of multi-scale support forms in different coal mines and the semantic similarity of roadway attributes, construct a hypergraph of roadway attributes - support forms; On the hypergraph of roadway attributes - support forms, apply the density peak mechanism of roadway attributes and the community detection method to identify the overlapping communities of attribute hotspots; Analyze the distribution of a given attribute in the overlapping communities of attribute hotspots to complete the prediction of support forms; The method of applying the density peak mechanism of roadway attributes and the community detection method to identify the overlapping communities of attribute hotspots includes: Calculation roadway of local density ; Based on local density , calculate the average density on the hypergraph of roadway attribute - support form ; Calculation roadway Degree of density deviation ; Hypergraph based on the roadway attribute - support form On the average density and the roadway Of the density deviation degree, a decision diagram is obtained with the local density As the x-axis and the density deviation degree As the y-axis; Based on the decision graph, obtain diverse density peak nodes; Initialize the density peak nodes as the initial community cores, and use the existing density peak clustering algorithm to divide the hypergraph of the roadway attribute - support form into several dense subgraphs; When all roadways are assigned to at least one community, the algorithm stops; For the community core set to obtain the detected overlapping communities .

2. The support form prediction method based on multi-scale density peak clustering according to claim 1, characterized in that, The coal mine support parameter data is represented as: ， Among them, represents an attribute in the feature set of relative importance.

3. The support form prediction method based on multi-scale density peak clustering according to claim 2, wherein, The method of calculating the similarity of multi-scale support forms in different coal mines includes: ， Among them, and are both roadways, represents the influence score of attribute t on the support form of roadway , and represents the influence score of attribute t on the support form of roadway .

4. The support form prediction method based on multi-scale density peak clustering according to claim 3, characterized in that The method of calculating the semantic similarity of roadway attributes that affect the decision-making of support forms includes: and are in the same connected component of the graph shown in . The connected component is a directed acyclic graph, that is, there is no and circular reference between them. Then and the semantic similarity is defined as: ； and are in the same connected component of the graph , and and are on a cycle in the said connected component, that is, there is a cyclic reference between and , then and The semantic similarity is defined as: ； and are in different connected components of Figure , that is and there is no explicit association between them, then and the semantic similarity of is defined as: 。 5. The support form prediction method based on multi-scale density peak clustering according to claim 1, characterized in that The method of constructing a hypergraph of roadway attributes - support forms includes: Usage represents a hypergraph, where is a set of roadways, i.e., the set of vertices of the hypergraph ; is a set of edges, representing the equivalent association existing between any two points and or the association existing on the attribute , and T represents the set of attributes; is a set of weights, representing the degree of association 6. The prediction method of the support form based on multi-scale density peak clustering according to claim 1, characterized in that The method of analyzing the distribution of a given attribute in the overlapping communities of attribute hotspots to complete the prediction of support forms includes: Use a probability vector , representing the probability that the roadway belongs to each community. For community , there is: , where is a set composed of and adjacent nodes, represents the result of normalizing the degree of attribute deviation of the roadway , represents the result of normalizing the degree of attribute deviation of the roadway ; Use a vector to represent the influence of attribute t, where ; For the roadway , it belongs to each community in, and the attribute t is also distributed in each community. The influence score of the attribute t in is calculated as ; Calculation roadway For the attributes of the influence score top-k of, among the known roadway attributes, the support form with the highest frequency of the same top-k attributes is the prediction of the support form for the roadway form of support.

7. A support form prediction system based on multi-scale density peak clustering, the system is used to implement the support form prediction method based on multi-scale density peak clustering described in any one of claims 1-6, characterized in that, Including: A calculation module, a construction module, an identification module, and a prediction module; The calculation module is used to calculate the similarity of multi-scale support forms in different coal mines and the semantic similarity of roadway attributes that affect the decision-making of support forms by using the coal mine support parameter data collected on-site; The construction module is used to construct a hypergraph of roadway attributes - support forms based on the similarity of multi-scale support forms in different coal mines and the semantic similarity of roadway attributes; The identification module is used to apply the density peak mechanism of roadway attributes and the community detection method on the hypergraph of roadway attributes - support forms to identify the overlapping communities of attribute hotspots; The prediction module is used to analyze the distribution of a given attribute in the overlapping communities of attribute hotspots to complete the prediction of support forms.

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