A hypergraph-based reordering method for three-dimensional assembly model

Abstract

The present application aims at the problem that the overall correlation in the model library is generally ignored in the existing assembly model retrieval method, and proposes a three-dimensional assembly model reordering method based on hypergraph. The hypergraph of part co-occurrence is established according to the similar parts existing between the assembly models, so as to realize the quantitative expression of the assembly design correlation. The vertex of the hypergraph corresponds to an assembly model, and the hyperedge corresponds to the set of assembly vertices containing a similar part. Given a query assembly model, firstly, the most similar target assembly model in the model library is found. Then, the random walk algorithm of hypergraph is adopted to calculate the walk probability of other vertices as the correlation degree between the query assembly model and the target assembly model, and the retrieval of the assembly model is realized through the correlation degree sorting.

Description

Technical Field

[0001] This invention belongs to the field of computer-aided design, specifically a method for reordering 3D assembly models based on hypergraphs. Background Technology

[0002] Assembly models, as a carrier of product design knowledge, integrate most of the product's process, assembly, and simulation information, and are an important form of accumulating enterprise experience and knowledge. Therefore, establishing retrieval technologies for assembly models, retrieving related assemblies based on their characteristics, and reusing the knowledge contained within them is an effective means to reduce design work and improve product development efficiency. Several retrieval technologies for assembly models have already emerged:

[0003] The patent “Quantitative Description Method of Assembly Model Oriented to Model Retrieval (CN105574265A, Publication Date: 20160511)” proposes an assembly description and retrieval method based on part shape matching. This method describes the part shape distribution information in a multi-dimensional space and describes the assembly in the form of a set of parts.

[0004] The patent “A method for retrieving assembly model similarity based on spatial point set matching (CN111539485A, publication date: 20200814)” proposes an assembly model retrieval method based on spatial point set matching. This method calculates the comprehensive similarity of parts from two aspects: attribute similarity and spatial position similarity. It sums the elements of the corresponding positions of the matching part set and the model similarity matrix, and the value with the highest similarity of the matching part set is the similarity between the model and the reference body.

[0005] These methods calculate the similarity between assembly models in the model library and the queried assembly models by comparing them pairwise, but they ignore the high-level relationships formed by all assemblies during the design process. Summary of the Invention

[0006] To address the shortcomings of existing assembly model retrieval technologies, the applicant considers the design relationships between assembly models, recognizing that the entire model library is a tightly interconnected whole. If the relationships between models can be extracted and mined to reveal the correlation patterns between existing products, the retrieval accuracy of assembly models can be improved. Therefore, this invention proposes a hypergraph-based 3D assembly model reordering method. This method uses a hypergraph to quantify the design relationships existing in the assembly model library. For a given query model, it finds the assembly model most similar to the query model through pairwise comparisons. Based on this, the similarity between assembly models is calculated according to the hypergraph relationships to reorder them, thereby supporting assembly retrieval and improving retrieval accuracy.

[0007] The technical solution of this invention is as follows:

[0008] The aforementioned method for reordering 3D assembly models based on hypergraphs includes the following steps:

[0009] Step 1: For each assembly model in the model library, extract the shape information of the parts in the assembly model and establish the corresponding part shape vector;

[0010] Step 2: For the parts in the model library, cluster them using the shape vectors of the parts to obtain K clusters {pf1, pf2, ..., pf...} K}, where K represents the number of clusters;

[0011] Step 3: Build a hypergraph network based on the assembly models and part clusters in the model library, and obtain the corresponding parameter matrix of the hypergraph network:

[0012] Step 3.1: For each part, cluster pf i Initialize the corresponding hyperedge e i It is an empty set;

[0013] Step 3.2: Traverse all parts in the model library. If part p∈pf i If p∈a, then add assembly a from the model library to hyperedge e. i Based on this, a hypergraph network is established.

[0014] G = {A, E}

[0015] Where A = {a1, a1, ..., a1} N} represents the set of vertices in the hypergraph, where each vertex represents an assembly model, and N is the size of the assembly model library; E = {e1, e2, ..., e K} represents the set of hyperedges, where each hyperedge represents a component cluster, and K is the number of component clusters;

[0016] Step 3.3: Calculate the hyperedge weight, membership degree, vertex degree, and hyperedge degree of the hypergraph based on the relationship between the assemblies and part clusters in the hypergraph network:

[0017] The weight of each hyperedge is determined by the number of all assembly models within it.

[0018] w(e) = |e|

[0019] Calculate the similarity of each part p in assembly a with respect to hyperedge e, and sum them up to obtain the membership degree of assembly a with respect to hyperedge e:

[0020]

[0021] Where pf is the cluster of parts corresponding to hyperedge e, and dis(p,pf) is the Euclidean distance between the cluster centers of part p and the cluster of part pf;

[0022] For the assembly model v, calculate the sum of the weighted membership degrees of all its hyperedges as the hypergraph vertex degree:

[0023] d(v)=∑w(e)h(v,e)

[0024] For hyperedge e, the sum of the membership degrees of all assembly models within that hyperedge is calculated as the hyperedge degree:

[0025] δ(e)=∑h(v,e)

[0026] Step 3.4: Based on the hypergraph calculation results in Step 3.3, establish the corresponding hyperedge weight matrix W, membership matrix H, and vertex degree matrix D. v Hypermarginality matrix D e :

[0027]

[0028]

[0029]

[0030]

[0031] Step 4: For the assembly model to be queried, find the most similar assembly model in the model library through the following steps:

[0032] Step 4.1: For a given query assembly model q, calculate the initial similarity dis(q,a) between q and each assembly model a in the model library.

[0033]

[0034] Where p1 and p2 are parts in assemblies q and a respectively, and L1(p1,p2) is the shape vector similarity between parts p1 and p2, which is calculated using Manhattan distance;

[0035] Step 4.2: Based on the initial similarity, obtain the set C of the top M assembly models C in the model library that are most similar to q. M ;

[0036] Step 4.3: Initialize the N-dimensional zero vector Y, where N is the number of assembly models in the model library. If the i-th assembly model a in the model library... i ∈C M Then the value of the i-th dimension of vector Y is Y i =1-dis(q,a)i );

[0037] Step 4.4: The following iterative algorithm is used to calculate the relevance vector of the assembly model:

[0038]

[0039] Where S is the Laplacian matrix of the hypergraph: α is an adjustment parameter;

[0040] Step 4.5: Set a deviation threshold ε. When the iteration deviation in step 4.4 is less than ε, F... (t) As the final steady-state distribution probability F * ;

[0041] Step 4.6: According to the formula

[0042]

[0043] Get the query assembly q and each assembly a in the model library i Correlation vector between:

[0044] I_SIM=[isim(q,a1),isim(q,a2),...,isim(q,a N )]

[0045] Step 4.7: Based on the correlation vector, reorder the assembly models in the model library in descending order of correlation.

[0046] Furthermore, in step 1, the process of establishing the part shape vector is as follows:

[0047] Step 1.1: For the assembly model a, decompose it into n part models p, and represent a as a set of p a = [p1, p2, ..., p n ], where n represents the total number of parts in a;

[0048] Step 1.2: For part p in assembly model a i If 1 ≤ i ≤ n, extract the shape information of the part and transform the part into a k-dimensional shape vector p. i =[l1,l2,…,l k ], where l j Indicates part p i The shape distribution probability value of the j-th dimension, 1≤j≤k;

[0049] Steps 1-3: Repeat steps 1-1 and 1-2 until all assembly and part models in the model library have been traversed.

[0050] Beneficial effects

[0051] The assembly model reordering and further retrieval method proposed in this invention first analyzes the relationships between all assembly models before retrieval and then uses graph theory to transform these relationships into a hypergraph. For a given query model, this method implements retrieval in two stages: first, it finds the assembly model most similar to the query model through pairwise comparisons; then, it calculates the relationship strength between the most similar assembly model and other assembly models. Compared with existing methods, when the query assembly model is incomplete, this method can infer the correlation between the query model and existing assembly models through relational reasoning, and ultimately obtains more accurate retrieval results.

[0052] Additional aspects and advantages of the invention will be set forth in part in the description which follows, and in part will be obvious from the description, or may be learned by practice of the invention. Attached Figure Description

[0053] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0054] Figure 1 This is a flowchart of the assembly model retrieval method of the present invention.

[0055] Figure 2 This is a partial assembly model of the model library in a specific embodiment of the method of the present invention.

[0056] Figure 3 This is an example of a cardboard assembly model in a specific embodiment of the method of the present invention.

[0057] Figure 4 These are shape descriptors for some part models in specific embodiments of the method of the present invention.

[0058] Figure 5 This refers to the cluster of parts in the cardboard assembly model in a specific embodiment of the method of the present invention.

[0059] Figure 6 This is the query assembly model in a specific embodiment of the method of the present invention.

[0060] Figure 7 This is the assembly correlation ranking result in a specific embodiment of the method of the present invention.

[0061] Figure 8 This is a comparison of the search results in a specific embodiment of the present invention with those of existing methods. Detailed Implementation

[0062] This invention addresses the common problem in existing assembly model retrieval methods that neglect the overall association within the model library. It proposes a hypergraph-based method for reordering 3D assembly models. This method establishes a part co-occurrence hypergraph based on similar parts among assembly models, enabling a quantitative expression of assembly design associations. Each vertex in this hypergraph corresponds to an assembly model, and each hyperedge corresponds to a set of vertices in an assembly containing a similar part. Given a query assembly model, the method first searches the model library for the most similar target assembly model. Using the target assembly model as the initial point, a hypergraph random walk algorithm is used to calculate the walk probability of other vertices as their relevance to the query assembly model. Finally, assembly models are retrieved by ranking them based on their relevance.

[0063] The embodiments of the present invention are described in detail below. These embodiments are exemplary and intended to explain the present invention, and should not be construed as limiting the present invention.

[0064] Step 1: For Figure 2 The model library contains 100 assembly models. Descriptors are created by extracting the shape information of the parts within the assembly models. This process includes the following steps:

[0065] Step 1-1: From Figure 2 We randomly select an assembly model 'a' and decompose it into n part models 'p'. Therefore, 'a' can be represented as a set of 'p': a = [p1, p2, ..., p...]. n ], where n represents the total number of parts in a;

[0066] Step 1-2: Randomly select a part p from a. i (1≤i≤n), the shape information of the part can be extracted using the shaped distribution algorithm, which can transform the part into a 50-dimensional vector p. i =[l1,l2,…,l 50 ], where l j (1≤j≤50) represents the shape distribution probability value of the j-th dimension.

[0067] exist Figure 4 The shape distribution vectors of the three parts are [0.12, 0.20, 0.32, 0.41, ... 0.68] × 10. -2 [0.90, 1.82, 2.53, 2.97, ... 0.06] × 10 -2 And [0.48, 0.76, 1.42, 1.94, ..., 0.48] × 10 -2 .

[0068] Steps 1-3: Repeat steps 1-1 and 1-2 until all assembly and part models in the model library have been traversed.

[0069] Step 2: Set K=60. For all part models in the model library, use the K-Means algorithm to cluster the shape vectors of the part models, obtaining 60 clusters {pf1, pf2, ..., pf...}. 120}.for Figure 3 The eight pallet assembly models contain clusters such as... Figure 5 As shown.

[0070] Step 3: Establish a hypergraph network based on the assembly model and part clusters;

[0071] Step 3-1: For each part, cluster pf i (1≤i≤60), initialize the hyperedge to e. i An empty set. If part p∈pf i If p∈a, then add assembly a to hyperedge e. i .

[0072] Step 3-2: Traverse all parts and construct 60 hyperedges. Based on this, build a hypergraph network, which can be represented as:

[0073] G={A,E} (1)

[0074] In the formula:

[0075] A = {a1, a1, ..., a1} 100} — represents the set of vertices of the hypergraph, i.e., the set of assembly models;

[0076] E = {e1,e2,…,e} 60} — represents a set of superedges, where each superedge represents a cluster of parts.

[0077] Step 3-3: Calculate the hyperedge weights, membership degrees, vertex degrees, and hyperedge degrees of the hypergraph based on the relationships between assembly and part clusters in the hypergraph network. This includes the following steps:

[0078] Step 3-3-1: Count the number of all assembly models in each hyperedge and use this count as the weight of the hyperedge:

[0079] w(e)=|e| (2)

[0080] Step 3-3-2: Calculate the similarity of each part p in assembly a with respect to hyperedge e, and sum these similarities to obtain the membership degree of assembly a with respect to hyperedge e. The calculation method is as follows:

[0081]

[0082] In the formula:

[0083] pf — the cluster of parts corresponding to the superedge e;

[0084] dis(p,pf) — Euclidean distance between the cluster centers of part p and the cluster pf of parts.

[0085] Step 3-3-3: For each assembly model, calculate the sum of the weighted membership degrees of all its hyperedges as the hypergraph vertex degree:

[0086] d(v)=∑w(e)h(v,e) (4)

[0087] Step 3-3-4: For each hyperedge, calculate the sum of the membership degrees of all assembly models within that hyperedge as the hyperedge degree:

[0088] δ(e)=∑h(v,e) (5)

[0089] Step 3-3-5: Based on the above calculation results, establish the corresponding hyperedge weight matrix W, membership matrix H, and vertex degree matrix D. v Hypermarginality matrix D e :

[0090]

[0091]

[0092]

[0093]

[0094] Step 4: Select as follows Figure 6 The assembly model shown is used as the query assembly model. Based on the relationship strength in the hypergraph, the correlation between assembly models is inferred to find the most similar assembly model in the model library, thus achieving assembly model retrieval. Specifically, the following steps are included:

[0095] Step 4-1: For a given query assembly model q, calculate the initial similarity dis(q,a) between q and each assembly model a in the model library. The calculation method is as follows:

[0096]

[0097] In the formula:

[0098] p1, p2 — One of the parts in assembly q and a;

[0099] L1(p1,p2) represents the shape vector similarity between parts p1 and p2, calculated using Manhattan distance;

[0100] Step 4-2: Set parameter M=2, and obtain the set C of the two assembly models with the smallest similarity value to q in the model library. M After calculation C M ={a1,a3};

[0101] Step 4-3: Initialize a 100-dimensional zero vector Y; if the i-th assembly model a in the model library i ∈C M Then the value of the i-th dimension of vector Y is Y i =1-dis(q,a);

[0102] Step 4-4: Set α = 0.5, and use the following iterative algorithm to calculate the relevance vector of the assembly model:

[0103]

[0104] In the formula:

[0105] S—the Laplacian matrix of the hypergraph, which is calculated as follows:

[0106] Step 4-5: Set the deviation threshold ε = 0.01. When the iteration deviation in step 4-4 is less than ε, F... (t) As the final steady-state distribution probability F * The iteration deviation for the t-th iteration is calculated as follows:

[0107]

[0108] In the formula:

[0109] F i (t) —The probability of walking to the i-th (1≤i≤N) vertex calculated in the t-th iteration;

[0110] Steps 4-6: Calculate the query assembly model q and each assembly a in the model library. i The correlation isim(q,a) i The calculation method is as follows:

[0111]

[0112] In the formula:

[0113] I_SIM=[isim(q,a1),isim(q,a2),...,isim(q,a N )]—— Represents the correlation vector between the query assembly and each model in the model library.

[0114] Steps 4-7: Sort the assembly models in descending order of relevance and output the results as the calculation results, thereby realizing the retrieval of assembly models. The final retrieval results are as follows: Figure 7 As shown.

[0115] For the same query model, the result calculated using patent (CN111539485A) is as follows: Figure 8 As shown. Since the query model only appears in the 5 cardboard models, this method can only return 5 correct results, while the other cardboard models are considered dissimilar. Figure 7 In the search results, some cardboard models do not actually contain the query assembly model, such as the 7th and 8th search results. However, the calculation results show that these models still have a high relevance to the query. This is because the present invention considers the association between assembly models. During the retrieval process, if one assembly model is retrieved as a similar model to the query, other related assembly models may also be considered similar, which is consistent with human thinking. This implementation example shows that the assembly retrieval method proposed in this invention can achieve good retrieval results.

[0116] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention without departing from the principles and spirit of the present invention.

Claims

1. A method for reordering 3D assembly models based on hypergraphs, characterized in that: Includes the following steps: Step 1: For each assembly model in the model library, extract the shape information of the parts in the assembly model and establish the corresponding part shape vector; Step 2: For the parts in the model library, cluster them using the shape vectors of the parts to obtain K clusters {pf1, pf2, ..., pf...} K }, where K represents the number of clusters; Step 3: Build a hypergraph network based on the assembly models and part clusters in the model library, and obtain the corresponding parameter matrix of the hypergraph network: Step 3.1: For each part cluster pf i Initialize the corresponding hyperedge e i It is an empty set; Step 3.2: Traverse all parts in the model library. If part p∈pf i If p∈a, then add assembly a from the model library to hyperedge e. i Based on this, a hypergraph network is established. G = {A, E} Where A = {a1, a2, ..., a} N } represents the set of vertices in the hypergraph, where each vertex represents an assembly model, and N is the size of the assembly model library; E = {e1, e2, ..., e K } represents the set of hyperedges, where each hyperedge represents a component cluster, and K is the number of component clusters; Step 3.3: Calculate the hyperedge weight, membership degree, vertex degree, and hyperedge degree of the hypergraph based on the relationship between the assemblies and part clusters in the hypergraph network: The weight of each hyperedge is determined by the number of all assembly models within it. w(e) = |e| Calculate the similarity of each part p in assembly a with respect to hyperedge e, and sum them up to obtain the membership degree of assembly a with respect to hyperedge e: Where pf is the cluster of parts corresponding to hyperedge e, and dis(p,pf) is the Euclidean distance between the cluster centers of part p and the cluster of part pf; For the assembly model v, calculate the sum of the weighted membership degrees of all its hyperedges as the hypergraph vertex degree: d(v)=∑w(e)h(v,e) For hyperedge e, the sum of the membership degrees of all assembly models within that hyperedge is calculated as the hyperedge degree: δ(e)=∑h(v,e) Step 3.4: Based on the hypergraph calculation results in Step 3.3, establish the corresponding hyperedge weight matrix W, membership matrix H, and vertex degree matrix D. v Hypermarginality matrix D e : Step 4: For the assembly model to be queried, find the most similar assembly model in the model library through the following steps: Step 4.1: For a given query assembly model q, calculate the initial similarity dis(q,a) between q and each assembly model a in the model library. Where p1 and p2 are parts in assemblies q and a respectively, and L1(p1,p2) is the shape vector similarity between parts p1 and p2; Step 4.2: Based on the initial similarity, obtain the set C of the top M assembly models C in the model library that are most similar to q. M ; Step 4.3: Initialize the N-dimensional zero vector Y, where N is the number of assembly models in the model library. If the i-th assembly model a in the model library... i ∈C M Then the value of the i-th dimension of vector Y is Y i =1-dis(q,a) i ); Step 4.4: The following iterative algorithm is used to calculate the relevance vector of the assembly model: Where S is the Laplacian matrix of the hypergraph: α is an adjustment parameter; Step 4.5: Set a deviation threshold ε. When the iteration deviation in step 4.4 is less than ε, F... (t) As the final steady-state distribution probability F * ; Step 4.6: According to the formula Get the query assembly q and each assembly a in the model library i Correlation vector between: I_SIM=[isim(q,a1),isim(q,a2),...,isim(q,a N )] Step 4.7: Based on the correlation vector, reorder the assembly models in the model library in descending order of correlation.

2. The method for reordering 3D assembly models based on hypergraphs according to claim 1, characterized in that: In step 1, the process of establishing the part shape vector is as follows: Step 1.1: For the assembly model a, decompose it into n part models p, and represent a as a set of p a = [p1, p2, ..., p n ], where n represents the total number of parts in a; Step 1.2: For part p in assembly model a i If 1 ≤ i ≤ n, extract the shape information of the part and transform the part into a k-dimensional shape vector p. i =[l1,l2,…,l k ], where l j Indicates part p i The shape distribution probability value of the j-th dimension, 1≤j≤k; Steps 1-3: Repeat steps 1-1 and 1-2 until all assembly and part models in the model library have been traversed.

3. The method for reordering 3D assembly models based on hypergraphs according to claim 1, characterized in that: In step 2, the K-Means algorithm is used to cluster the parts in the model library using the shape vectors of the parts.

4. The method for reordering 3D assembly models based on hypergraphs according to claim 1, characterized in that: In step 4.1, the shape vector similarity is calculated using Manhattan distance.

5. The method for reordering 3D assembly models based on hypergraphs according to claim 1, characterized in that: In step 4.4, the parameter α∈[0,1] is adjusted.

6. The method for reordering 3D assembly models based on hypergraphs according to claim 1, characterized in that: In step 4.5, the iteration deviation for the t-th iteration is: in Let be the walk probability of the i-th vertex calculated in the t-th iteration.

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