CN110930028A - Machining manufacturing resource allocation method based on cluster analysis method - Google Patents

Machining manufacturing resource allocation method based on cluster analysis method Download PDF

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CN110930028A
CN110930028A CN201911153125.7A CN201911153125A CN110930028A CN 110930028 A CN110930028 A CN 110930028A CN 201911153125 A CN201911153125 A CN 201911153125A CN 110930028 A CN110930028 A CN 110930028A
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孙群
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Abstract

The invention provides a method for allocating machining manufacturing resources based on a cluster analysis method, which comprises the following 3 main contents on the basis of extracting static process characteristics of a product: classification, determination of metric index and cluster analysis. The invention allocates the manufacturing resources according to the static process requirements (such as precision requirements, roughness requirements and the like) of the product. And clustering analysis is carried out on the processing capacity of the manufacturing resources, and the available manufacturing resources of the workshop are pre-configured in the aspects of processing performance, process characteristics and the like. In the stage, corresponding indexes such as a process method, machining precision, overall dimension and machining capacity of manufacturing resources of the product are mainly considered for matching, and a foundation is laid for quickly searching machining equipment and tools.

Description

Machining manufacturing resource allocation method based on cluster analysis method
Technical Field
The invention belongs to the field of planning of mechanical manufacturing processes, and relates to a method for allocating machining manufacturing resources based on a cluster analysis method for low-carbon process planning, aiming at comprehensively considering low-carbon emission constraint and product process quality requirements in the manufacturing process and providing theoretical and method support for quickly and reasonably selecting manufacturing resources.
Background
The manufacturing resources are used as the important material basis of the process planning system, and the configuration problem plays a significant role in the aspect of realizing the function of the process planning. The manufacturing resource allocation problem in the process planning mainly surrounds the information and design requirements of the product, and the manufacturing resources are scientifically and reasonably selected under the target constraint according to the resource condition and the process capability of each manufacturing unit and the accumulated process knowledge, so that the maximization of the economic benefit, the technical benefit and the environmental benefit is realized.
At present, the research on the optimal configuration of manufacturing resources mainly focuses on both the optimal configuration model of manufacturing resources and the optimal configuration method. In the aspect of resource optimization configuration model research, the research on workshop production planning and scheduling, the problem on cooperative allocation of resources in a networked manufacturing background, the research on manufacturing resource optimization adapting to the requirements of multiple varieties and multiple processes of a flexible manufacturing system is carried out to completely release the capability of manufacturing resources, or the research is carried out from the perspective of a virtual enterprise, a manufacturing resource optimization model is established from the perspective of selecting carriers (manufacturing units or enterprises) of the manufacturing resources, and resource evaluation and selection are carried out. The evaluation index system mainly comprises delivery date (T), cost (C), quality (Q), service (S) and the like; in the aspect of optimizing configuration method research: currently, decision method research is mainly performed from the viewpoint of multi-objective optimization. The main methods are as follows: 1) the mathematical integer programming method has the main idea that an integer programming method is used for establishing an optimized configuration model of resources, but the algorithm cannot well quantize some optimized indexes; 2) although the analytic hierarchy process can well quantify certain qualitative indexes, the requirement for the consistency of the judgment matrix is often repeatedly adjusted and is carried out by rough estimation, the blindness is very high, and the consistency of the judgment matrix is often different from the consistency of decision thinking of people; 3) the method can well solve the multi-objective optimization problem through a genetic algorithm. In general, the problem of allocating manufacturing resources in process planning has been a great concern, and related research efforts have been on the rise.
At present, research related to carbon emission and resource allocation in the process has made some breakthrough progresses respectively, and a corresponding solution and an evaluation method are provided. However, due to the complexity of the machining system in consuming manufacturing resources, the diversity of product manufacturing environments, the imperfection of evaluation criteria, and the like, the impact of low carbon constraints on the configuration of manufacturing resources in process planning is less involved. At present, the optimization research of manufacturing resource allocation in the process mainly takes quality, cost, time, profit or the like as optimization targets, although some researches focus on energy consumption targets, most of the researches only consider single-target optimization methods, and few researches considering multiple targets also consider traditional target optimization methods such as cost, time, quality and the like, ecological environment influence indexes which are less related to the processing process are taken as optimization targets, and resource allocation optimization facing low-carbon emission needs to be further deeply researched.
Traditional Computer Aided Process Planning (CAPP) systems tend to focus on pure Process technology design, do not consider the manufacturing resource processing capacity and the manufacturing resource allocation optimization problem of carbon emission information, and rarely relate to implementation methods related to carbon emission in an integrated model of CAPP and Production Planning Control (PPC).
In the machining process, the selected manufacturing resources are different, so that the machining quality, the production efficiency and the like of the product are influenced, and the energy consumption and the environmental pollution degree are different. The reasonable selection of manufacturing resources can effectively utilize resources, shorten the processing time and improve the production efficiency, so that necessary research needs to be carried out on the configuration of the manufacturing resources in the low-carbon processing and manufacturing process to reduce the resource consumption and the environmental influence in the production process of a machining system.
In the production process, a plurality of processes are usually required to realize the processing of the product. How to select the manufacturing resources and the optimized configuration available for the manufacturing shop under the processing conditions of the manufacturing shop so as to maximize the comprehensive benefits of the factors such as the processing quality (Q), the processing time (T) and the processing cost (C) of the product, and the like, has become a problem generally concerned by the majority of manufacturing enterprises. The traditional process scheme mainly takes time, quality, cost and the like as optimization targets, and multiple targets of resource consumption and carbon emission must be considered simultaneously for a low-carbon processing and manufacturing process. On the premise of meeting the processing quality of products, the problem to be solved is to reduce the resource consumption generated in the machining process through reasonable manufacturing resource scheduling configuration and further reduce the carbon emission of enterprises.
The invention aims to research a manufacturing resource allocation evaluation and optimization method oriented to low-carbon process planning by establishing a carbon emission quantitative model and an evaluation mechanism of process elements so as to realize quantitative analysis of carbon emission in the product process and reasonable allocation of manufacturing resources under the constraint of a low-carbon target.
Disclosure of Invention
The invention aims to provide a manufacturing resource allocation decision oriented to low-carbon process planning, which is based on the premise of meeting the processing quality, and screens available manufacturing resources according to the static process requirements (such as precision requirements, roughness requirements and the like) of products so as to pre-allocate the manufacturing resources. On the basis, the influence of constraints such as processing time, carbon emission cost and the like on the selection of manufacturing resources is considered in the dynamic optimization configuration. The specific scheme is as follows:
a method for allocating machining and manufacturing resources based on a cluster analysis method comprises the following steps,
s1, classification: classifying all objects in the resource set O into S groups according to different machining modes required by the mechanical part;
s2, determining the measurement index: extracting common processing capacity characteristics of each class group as a measurement index, forming a characteristic vector to describe each object of the class group, and establishing a measurement index mathematical expression of the class group;
s3, cluster analysis: group O ofKAs a clustered sample space, assume a clustered sample space OKContaining r processing features, the vector being represented as
Figure BDA0002284107630000031
Class group OKThe object in (1)
Figure BDA0002284107630000032
Is a clustered sample, and is linked by a set of logical associations "feature-value" to OKCluster samples in (1)
Figure BDA0002284107630000033
Converting into a measurement index numerical value vector expression form, and logically connecting mathematical description of 'characteristic-value' as follows:
Figure BDA0002284107630000034
in the formula 1, i and j are positive integers or natural numbers, i is more than or equal to 1 and less than or equal to m, and j is more than or equal to 1 and less than or equal to r;
will cluster sample space OKGet each cluster sample OKIs/are as follows
Figure BDA0002284107630000035
Each metric index of (a) is mapped to a matrix of eigenvalues VKEach element of
Figure BDA0002284107630000041
The mathematical description is as follows:
Figure BDA0002284107630000042
in the formula 2, i, j and K are positive integers, i is more than or equal to 1 and less than or equal to m, j is more than or equal to 1 and less than or equal to r, and K is more than or equal to 1 and less than or equal to S;
according to the eigenvalue matrix VKWill cluster the sample space OKEach cluster sample in (1)
Figure BDA0002284107630000043
Clustering is carried out, and resource clusters for clustering results are used
Figure BDA0002284107630000044
The specific mathematics are described as follows:
Figure BDA0002284107630000045
Figure BDA0002284107630000046
……
Figure BDA0002284107630000047
……
Figure BDA0002284107630000048
s4, performing cluster calculation of manufacturing resources, wherein the calculation process sequentially comprises the following steps: normalization processing, sample distance calculation, similarity degree and similarity matrix determination, cluster analysis and cluster granularity parameter calculation;
s5, determining the uniqueness of the attribution: judging the uniqueness of the attribution, determining a clustering sample and carrying out clustering analysis.
Further, in step S1, the mathematical expressions of the S class groups are:
Figure BDA0002284107630000049
Figure BDA00022841076300000410
……
Figure BDA00022841076300000411
……
Figure BDA00022841076300000412
wherein, a + b +. c +. d + N, S, a, b, c, d are all positive integers or natural numbers.
Further, in step S2, the class group O is setKThe corresponding feature vector is AKK — 1,2, …, S, the class group metric is mathematically expressed as:
Figure BDA00022841076300000413
Figure BDA0002284107630000051
……
Figure BDA0002284107630000052
……
Figure BDA0002284107630000053
further, in step S4, the mathematical expression of the normalization process is:
Figure BDA0002284107630000054
Figure BDA0002284107630000055
through normalization processing, the matrix V in the formula 2KMapped to a matrix v, which is mathematically described as:
Figure BDA0002284107630000056
further, in step S4, the distance between samples is calculated by using the formula of the distance between the reference points, which is as follows:
Figure BDA0002284107630000057
wherein, the sample satisfies the following conditions: when d (i, j) is larger than or equal to 0, the distance between the sample and the sample is not negative, when d (i, j) is 0, the distance function has symmetry when d (i, j) is d (j, i), and when d (i, j) is larger than or equal to d (i, h) + d (h, j), the distance between the sample i and the sample j is smaller than or equal to the sum of the distances of other objects h;
wherein the michelson distance formula is the manhattan distance formula when q is 1, that is:
Figure BDA0002284107630000058
when q is 2, the formula is a euclidean distance formula, i.e.:
Figure BDA0002284107630000059
Figure BDA0002284107630000061
and (3) performing function calculation on the distance between the samples and performing normalization processing on the Euclidean distance by adopting an Euclidean method, wherein the mathematical form of the Euclidean distance is as follows:
Figure BDA0002284107630000062
in the formula 8, r, c, i, j are all positive integers, and p is a clustering sample space OKC is the cluster sample space OKI is more than or equal to 1, and l is more than or equal to c.
Further, in step S4, the step of determining the similarity and the similarity matrix includes:
calculating OKAnd (3) the similarity between the middle cluster samples is defined by the calculation formula:
Figure BDA0002284107630000063
in the formula 9, F is a normalization constant and is larger than Max (D)il)，
Figure BDA0002284107630000064
I is more than or equal to 1 and l is more than or equal to c;
similarity matrix SKRepresenting the similarity between all the clustered samples, mapping each similarity value to a similarity matrix SKTo obtain a similarity matrix SKIts mathematical form is expressed as follows:
Figure BDA0002284107630000065
due to the fact that
Figure BDA0002284107630000066
And 1 is less than or equal to i, l is less than or equal to c, so that the matrix SKHas reflexibility and symmetry, and the mathematical form of the reflexibility and symmetry is expressed as follows:
Figure BDA0002284107630000067
in equation 11, matrix (S)K)TIs a matrix SKAccording to the contents of the discrete mathematical theorem, SKοSK＝SKThe known matrix SKHas transferability.
Further, in step S4, the step of cluster analysis is:
according to the similarity matrix SKWill cluster sample space OKClustering the obtained elements, dividing the obtained elements into a plurality of resource clusters, and obtaining the resource clusters according to the matrix Sθ＝θ'If the following conditions are met:
Figure BDA0002284107630000071
then
Figure BDA0002284107630000072
Belonging to the same resource cluster, the mathematical form can be simplified into a triangular matrix, and the expression is as follows:
Figure BDA0002284107630000073
will matrix Sθ＝θ'And performing logical partitioning, wherein the elements forming the logical triangular area are all 1, and clustering samples in the same logical triangular area belong to the same resource cluster.
Further, in step S4, the step of calculating the cluster size parameter is:
suppose manufacturing resource X ═ X1,X2,...Xm}
Figure BDA0002284107630000074
Into t resource class groups (c)i)O＝{O1,O2,...OmThe number of resources in each resource class group is ciI.e. by
Figure BDA0002284107630000075
Then C (O)i)C(Oi) As a resource class group OiThe degree of polymerization of (a) is,
in the clustering process, clustering results with different densities are obtained by defining different granularities from coarse to fine or from fine to coarse, a clustering granularity parameter theta is closely related to the similarity, theta is a real number and belongs to [0,1 ]]The clustering result is determined by theta, if a specific theta' value is given, if
Figure BDA0002284107630000076
Then order
Figure BDA0002284107630000077
Figure BDA0002284107630000078
j is 1,2, c, the remainder being 0, thus forming a matrix SKIs converted into a corresponding matrix Sθ＝θ'；
Is provided with
Figure BDA0002284107630000079
Figure BDA00022841076300000710
The average value of the similarity is taken as the value of the granularity parameter theta,
Figure BDA00022841076300000711
the expression of (a) is:
Figure BDA00022841076300000712
further, step S5 specifically includes:
s51, attribution uniqueness judgment: firstly, judging whether a common element exists in a resource cluster of a clustering result, if the common element does not exist, stopping the process, and obtaining a final unique clustering result; if the common element exists, finding the common element and proceeding to S52;
s52, determining clustering samples: taking the common elements of the resource clusters as clustering samples, finding out the resource clusters where the common elements are located, determining the core values of the measurement indexes, taking the average value of the measurement indexes as the core value representing the resource clusters, taking the core value as the reference value of the corresponding measurement indexes in the resource clusters, forming new clustering samples, and forming a temporary clustering sample space omega together with the common elements;
s53, cluster analysis: and re-clustering the temporary clustering sample space omega to obtain a new clustering result, and then continuing to execute S51.
The resource allocation method of mechanical products in the manufacturing process is mainly researched, and particularly, the manufacturing resource optimization allocation in the process mainly based on cutting is realized, so that on one hand, the effective implementation of a low-carbon technology in the manufacturing field is objectively promoted, and the transition from a modeling enterprise to low-carbon manufacturing is actively promoted; on the other hand, the research result of the subject can provide theoretical support for carbon emission evaluation in the production stage of the product, the manufacturing resource with less carbon emission is selected from the process planning level, the carbon emission generated in the machining process is reduced, reference is further provided for carbon emission evaluation of mechanical products in China, and the method has promotion significance for formulating product carbon emission standards, carbon identification, dealing with trade barriers such as carbon customs and the like in China.
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In order to more clearly illustrate the technical solutions in the embodiments of the present invention, the drawings needed to be used in the embodiments or the prior art descriptions will be briefly described below, and it is obvious that the drawings in the following description are only some embodiments of the present invention, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without inventive exercise.
Fig. 1 is a manufacturing resource classification model, and the energy consumption and resource consumption involved in the cutting process are collectively referred to as manufacturing resource consumption, and specifically include manufacturing resources such as machine tool equipment, tools, cutting fluid, and lubricating oil available in a manufacturing shop.
Fig. 2 is a schematic diagram of a mapping relationship between process characteristics, a method, and manufacturing resources, where static process characteristics of a product correspond to an appropriate process method, and the process method and the manufacturing resources are restricted from each other, and on the premise of establishing the mapping relationship between the process characteristics, the process method, and the manufacturing resources, a constraint on selection of the manufacturing resources can be realized through some association, so as to improve the rationality of resource allocation.
Fig. 3 is a schematic diagram of a cluster analysis method of manufacturing resources, which includes 3 main contents on the basis of extracting static process features of a product: classification, determination of metric index and cluster analysis.
Detailed Description
In the following description, numerous specific details are set forth in order to provide a more thorough understanding of the present invention. It will be apparent, however, to one skilled in the art, that the present invention may be practiced without one or more of these specific details. In other instances, well-known features have not been described in order to avoid obscuring the invention.
In the following description, for the purposes of explanation, numerous specific details are set forth in order to provide a thorough understanding of the present invention. The following detailed description of the preferred embodiments of the invention, however, the invention is capable of other embodiments in addition to those detailed.
The "resource" in the manufacturing system is also called manufacturing resource, which is a general name of the physical elements of the enterprise completing all production activities in the whole life cycle of the product, and is the basis of normal operation of the manufacturing enterprise. As used herein, "manufacturing resources" refers to physical energy resources, including electrical energy consumption, resource consumption associated with process elements in the processing activities of a product. For the sake of simplicity, the energy consumption and resource consumption involved in the processing are collectively referred to as manufacturing resource consumption (see fig. 1). Meanwhile, the carbon footprints generated by auxiliary logistics and the like due to tooling fixture and process conversion in manufacturing resources have diversity and complexity, and the research boundaries of the carbon footprints need to be defined in detail and definitely, so that the analysis of the carbon footprints generated by the tooling fixture and the auxiliary logistics and the like is not considered at this time. The invention mainly researches the resource selection problem of process elements related to manufacturing objects, process methods and processing time in the process of products, and particularly comprises the configuration of manufacturing resources of machine tool equipment, cutters, cutting fluid, lubricating oil and the like available in a manufacturing workshop.
From the manufacturing point of view, the manufacturing process of the product is a combination of processing the basic geometric shapes of the product one by one, and the unit elements of the basic geometric shapes are the shape characteristics of the product. The static process characteristics of the product correspond to appropriate process methods, and the process methods and manufacturing resources are restricted with each other, so that on the premise of establishing a mapping relationship of the process characteristics, the process methods and the manufacturing resources (see fig. 2), the restriction of manufacturing resource selection can be realized through some association, thereby improving the rationality of resource allocation.
In conclusion, the reasonable pre-configuration of manufacturing resources is researched on the premise of meeting the processing quality of the product by taking the requirement of meeting the static process characteristic of the product as a target. The cluster analysis is used as a manufacturing resource searching method, and based on the static process characteristic requirements of products, a proper process method and manufacturing resource allocation are selected, so that the manufacturing resource allocation searching space is reduced, and a research object is provided for resource optimization allocation facing low-carbon process planning.
On the basis of extracting the static process characteristics of the product, the cluster analysis method of the manufacturing resources comprises 3 main contents: classification, determination of metrics and cluster analysis (as shown in fig. 3).
The process steps of the present invention are described in detail below:
step S1, classification: all the objects in the resource set O are classified according to different machining modes required by the mechanical part, and are assumed to be divided into S groups according to the machining modes. Generally, these machining methods are turning, milling, drilling, grinding, boring, and the like. The mathematical representation of the S class groups is:
Figure BDA0002284107630000101
Figure BDA0002284107630000102
……
Figure BDA0002284107630000103
……
Figure BDA0002284107630000104
wherein, a + b +. c +. d + N, S, a, b, c, d are all positive integers or natural numbers, and the numerical values are closely related to the manufacturing resources of a specific workshop or factory and enterprise.
Step S2, determining a metric: and extracting the common processing capacity characteristics of each class group as a measurement index, and forming a characteristic vector to describe each object of the class group. Because the objects are divided into different groups O according to different processing modes1,O2,...,OK,...,OSThus elements of the same group have some specific common characteristics. For example, the milling amount (cutting speed, feed amount and tool depth) is one of common machining capability characteristics of milling, and the spindle rotation speed is one of common characteristic indexes of the machining capability of the machine tool. The characteristic index as a measure of the process element metric must meet the following requirements:
(1) can represent the processing characteristics and capabilities of a certain group of objects;
(2) one of the key feature specifications or features representing objects in the class group;
(3) is a quantitative index which can be quantified and has a determined value or value range;
(4) high dimensional property. A database or data warehouse may contain only a few dimensions, and many clustering algorithms involve only two to three dimensions. Human beings have a judgment to data within three dimensions, and the data clustering higher than three dimensions is very challenging, and the data may be very sparse or highly skewed.
(5) Constraint-based clustering. The manufacturing resources of an actual process may be clustered under constraints, which requires data groupings that satisfy process-specific constraints and have good clustering characteristics.
The measurement index value varies depending on the object to be processed. For example, the maximum cutting speed that different models of numerically controlled milling machines can process may be the same or different. And group OKThe corresponding feature vector is AKK is 1,2, …, S. The metric indices of the class group are mathematically expressed as:
Figure BDA0002284107630000111
Figure BDA0002284107630000112
……
Figure BDA0002284107630000113
……
Figure BDA0002284107630000114
step S3, cluster analysis: the clustering method is not general, although different groups have different features. Group O ofKAs a clustered sample space. Assume clustered sample space OKContaining r processing features, the vector being represented as
Figure BDA0002284107630000115
Class group OKThe object in (1)
Figure BDA0002284107630000116
Are clustered samples. O is represented by a set of logical association pairs "feature-Value" (Attribute-Value)KCluster samples in (1)
Figure BDA0002284107630000117
And converting into a metric value vector expression form. The mathematical description of the logical association "feature-value" is:
Figure BDA0002284107630000118
in the formula 1, i and j are positive integers or natural numbers, i is more than or equal to 1 and less than or equal to m, and j is more than or equal to 1 and less than or equal to r.
Will cluster sample space OKGet each cluster sample OKIs/are as follows
Figure BDA0002284107630000119
Each metric index of (a) is mapped to a matrix of eigenvalues VKEach element of
Figure BDA00022841076300001110
The mathematical description is as follows:
Figure BDA0002284107630000121
in the formula 2, i, j and K are positive integers, i is more than or equal to 1 and less than or equal to m, j is more than or equal to 1 and less than or equal to r, and K is more than or equal to 1 and less than or equal to S.
According to the eigenvalue matrix VKWill cluster the sample space OKEach cluster sample in (1)
Figure BDA0002284107630000122
And (6) clustering. Clustering resource clusters for results
Figure BDA0002284107630000123
The specific mathematics are described as follows:
Figure BDA0002284107630000124
Figure BDA0002284107630000125
……
Figure BDA0002284107630000126
……
Figure BDA0002284107630000127
and step S4, clustering algorithm process of manufacturing resources. The clustering algorithm process includes the following 5 steps S41: and (6) normalization processing. Due to different properties of the measurement indexes, the measurement indexes may have different dimensions, so that clustering analysis cannot be performed. Therefore, to eliminate the difference in the dimensions, the different dimensions need to be normalized. The normalization method can adopt two methods of averaging and normalizing, as shown in formulas (4) and (5).
Figure BDA0002284107630000128
Figure BDA0002284107630000129
By normalization, the matrix V isK(as shown in equation 2) to a matrix v, which is mathematically described as:
Figure BDA00022841076300001210
s42: and calculating the sample distance. The dissimilarity between different clustered samples is calculated based on the distance between samples. Common measurement methods are euclidean distance, manhattan distance, and michelson distance. The formula for the distance from the Minkowski is as follows:
Figure BDA0002284107630000131
wherein, the sample needs to satisfy the following conditions:
d (i, j) ≥ 0: the sample distance is non-negative;
d (i, j) ═ 0: the distance between the sample and the sample is 0;
d (i, j) ═ d (j, i): the distance function has symmetry;
d (i, j) is less than or equal to d (i, h) + d (h, j): the distance from the sample i to the sample j is less than or equal to the sum of the distances of any other objects h.
Obviously, the formula is the manhattan distance formula when q is 1, that is:
Figure BDA0002284107630000132
when q is 2, it is the euclidean distance formula, i.e.:
Figure BDA0002284107630000133
the most common euclidean method is used herein to perform a function calculation on the inter-sample distances. The Euclidean distance is normalized, and the mathematical form is as follows:
Figure BDA0002284107630000134
wherein r, c, i, j are all positive integers, and p is a clustering sample space OKC is the cluster sample space OKI is more than or equal to 1, and l is more than or equal to c.
S43: and determining the similarity and the similarity matrix. Calculating OKAnd (3) the similarity between the middle cluster samples is defined by the calculation formula:
Figure BDA0002284107630000135
wherein F is a normalization constant and is greater than Max (D)il)，
Figure BDA0002284107630000141
I is more than or equal to 1, and l is more than or equal to c.
Similarity matrix SKRepresenting the similarity between all the clustered samples, mapping each similarity value to a similarity matrix SKTo obtain a similarity matrix SK. Its mathematical form is expressed as follows:
Figure BDA0002284107630000142
because of the fact that
Figure BDA0002284107630000143
And 1 is less than or equal to i, l is less than or equal to c, so that the matrix SKHas self-reflexibility and symmetry.
Its mathematical form is expressed as follows:
Figure BDA0002284107630000144
in the formula, matrix (S)K)TIs a matrix SKThe transposed matrix of (2). According to the contents of the discrete mathematical theorem, SKοSK＝SKThe known matrix SKHas transferability, namely: matrix SKHas reflexibility, symmetry and transitivity.
S44: and (5) clustering analysis. According to the similarity matrix SKWill cluster the sample space OKAnd clustering the obtained elements, and dividing the obtained elements into a plurality of resource clusters. According to matrix Sθ＝θ'If the following conditions are met:
Figure BDA0002284107630000145
then
Figure BDA0002284107630000146
Belonging to the same resource cluster. The mathematical form can be simplified into a triangular array, so that the data processing amount can be reduced, and the data processing efficiency can be improved. Is expressed as follows：
Figure BDA0002284107630000147
Will matrix Sθ＝θ'And performing logical partitioning, wherein the elements forming the logical triangular area are all 1, and clustering samples in the same logical triangular area belong to the same resource cluster.
S45: and calculating a clustering granularity parameter.
Suppose manufacturing resource X ═ X1,X2,...Xm}
Figure BDA0002284107630000151
Can be divided into t resource class groups (c)i)O＝{O1,O2,...OmThe number of resources in each resource class group is ciI.e. by
Figure BDA0002284107630000152
Then is called C (O)i)C(Oi) As a resource class group OiDegree of polymerization of (2). In the clustering process, clustering results with different densities can be obtained by defining different granularities from coarse granularity to fine granularity or from fine granularity to coarse granularity. The cluster granularity parameter theta is closely related to the similarity, directly influences the distance between resource clusters and the distance between elements in the clusters, and determines the clustering result. Theta is a real number and theta ∈ [0,1 ]]And the clustering result is determined by theta. If a specific value of θ' is given, if
Figure BDA0002284107630000153
Then order
Figure BDA0002284107630000154
The others are 0. From this matrix SKIs converted into a corresponding matrix Sθ＝θ'。
If the value of the granularity parameter θ is too large (e.g., θ equals 1) or too small (e.g., θ equals 0), the clustering result will lose the practical meaning. Therefore, the average value of the similarity is selected as a reference value of the particle size parameter θ, so that θ is not too large or too small. As used herein
Figure BDA0002284107630000155
Figure BDA0002284107630000156
Is the average of the similarity:
Figure BDA0002284107630000157
and step S5, determining the attribution uniqueness. A clustered sample may be a common element of two or several resource clusters. If the attribution uniqueness of each clustering sample is uncertain, the clustering result loses significance for the evaluation of manufacturing resources. Therefore, each cluster sample can only belong to one resource cluster. For two resource clusters, they either completely coincide or do not intersect each other, either of them. In other words, if an object belongs to resource cluster a, it cannot belong to any other resource cluster except resource cluster a. Since a clustered sample may belong to two or more clusters, an averaging method is combined with a cluster analysis method to determine the uniqueness of attribution of the clustered sample. The method comprises the following 3 steps.
S51: and determining attribution uniqueness. Firstly, whether the resource cluster of the clustering result has a common element is judged. If no public element exists, stopping the process to obtain a final unique clustering result; if there is a common element, the common element is found and execution continues with S52.
S52: and determining a clustering sample. And taking the common elements of the resource clusters as clustering samples, finding out the resource clusters where the common elements are located, and determining the core values of the measurement indexes of the resource clusters. The average value of the measurement indexes is used as a core value representing the resource cluster, the core value is used as a reference value of the corresponding measurement indexes in the resource cluster, a new clustering sample is formed, and the new clustering sample and the common elements form a temporary clustering sample space omega.
S53: and (5) clustering analysis. And aiming at the temporary clustering sample space omega, re-clustering by adopting the method of the invention to obtain a new clustering result, and then continuously executing S51.
The manufacturing resource allocation decision oriented to the low-carbon process planning is to allocate manufacturing resources according to the static process requirements (such as precision requirements, roughness requirements and the like) of products on the premise of meeting the processing quality. And clustering analysis is carried out on the processing capacity of the manufacturing resources, and the available manufacturing resources of the workshop are pre-configured in the aspects of processing performance, process characteristics and the like. In the stage, corresponding indexes such as a process method, machining precision, overall dimension and machining capacity of manufacturing resources of the product are mainly considered for matching, and a foundation is laid for quickly searching machining equipment and tools.
Carbon emission analysis and evaluation of a process system under different processing strategies and processing conditions and related relation with resource allocation are important components of low-carbon manufacturing, but a systematic theoretical research system is still lacking at present. Therefore, the research provided by the invention not only deeply expands the efficient utilization of resources and the low-carbon emission, but also effectively implements the low-carbon manufacturing, and provides reference for carbon emission evaluation of mechanical products in China and carbon footprint label making methods of the mechanical products.
The above description is of the preferred embodiment of the invention. It is to be understood that the invention is not limited to the particular embodiments described above, in that devices and structures not described in detail are understood to be implemented in a manner common in the art; those skilled in the art can make many possible variations and modifications to the disclosed embodiments, or modify equivalent embodiments to equivalent variations, without departing from the spirit of the invention, using the methods and techniques disclosed above. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present invention are still within the scope of the protection of the technical solution of the present invention, unless the contents of the technical solution of the present invention are departed.

Claims (9)

1. A method for allocating machining manufacturing resources based on a cluster analysis method is characterized by comprising the following steps,
s1, classification: classifying all objects in the resource set O into S groups according to different machining modes required by the mechanical part;
s2, determining the measurement index: extracting common processing capacity characteristics of each class group as a measurement index, forming a characteristic vector to describe each object of the class group, and establishing a measurement index mathematical expression of the class group;
s3, cluster analysis: group O ofKAs a clustered sample space, assume a clustered sample space OKContaining r processing features, the vector being represented as
Figure FDA0002284107620000011
Class group OKThe object in (1)
Figure FDA0002284107620000012
Is a clustered sample, and is linked by a set of logical associations "feature-value" to OKCluster samples in (1)
Figure FDA0002284107620000013
Converting into a measurement index numerical value vector expression form, and logically connecting mathematical description of 'characteristic-value' as follows:
Figure FDA0002284107620000014
in the formula 1, i and j are positive integers or natural numbers, i is more than or equal to 1 and less than or equal to m, and j is more than or equal to 1 and less than or equal to r;
will cluster sample space OKGet each cluster sample OKIs/are as follows
Figure FDA0002284107620000015
Each metric index of (a) is mapped to a matrix of eigenvalues VKEach element of
Figure FDA0002284107620000016
The mathematical description is as follows:
Figure FDA0002284107620000017
in the formula 2, i, j and K are positive integers, i is more than or equal to 1 and less than or equal to m, j is more than or equal to 1 and less than or equal to r, and K is more than or equal to 1 and less than or equal to S;
according to the eigenvalue matrix VKWill cluster the sample space OKEach cluster sample in (1)
Figure FDA0002284107620000018
Clustering is carried out, and resource clusters for clustering results are used
Figure FDA0002284107620000019
The specific mathematics are described as follows:
Figure FDA00022841076200000110
Figure FDA00022841076200000111
……
Figure FDA00022841076200000112
……
Figure FDA0002284107620000021
s4, performing cluster calculation of manufacturing resources, wherein the calculation process sequentially comprises the following steps: normalization processing, sample distance calculation, similarity degree and similarity matrix determination, cluster analysis and cluster granularity parameter calculation;
s5, determining the uniqueness of the attribution: judging the uniqueness of the attribution, determining a clustering sample and carrying out clustering analysis.
2. The cluster analysis based machining manufacturing resource allocation method according to claim 1, wherein in step S1, the mathematical expressions of the S class groups are expressed as:
Figure FDA0002284107620000022
Figure FDA0002284107620000023
……
Figure FDA0002284107620000024
……
Figure FDA0002284107620000025
wherein, a + b +. c +. d + N, S, a, b, c, d are all positive integers or natural numbers.
3. The method of claim 1, wherein in step S2, a class group O is definedKThe corresponding feature vector is AKK — 1,2, …, S, the class group metric is mathematically expressed as:
Figure FDA0002284107620000026
Figure FDA0002284107620000027
……
Figure FDA0002284107620000028
……
Figure FDA0002284107620000029
4. the cluster analysis based machining manufacturing resource allocation method according to claim 1, wherein in step S4, the mathematical expression of the normalization process is:
Figure FDA00022841076200000210
Figure FDA00022841076200000211
through normalization processing, the matrix V in the formula 2KMapped to a matrix v, which is mathematically described as:
Figure FDA0002284107620000031
5. the method for allocating resources for manufacturing a machine according to claim 4, wherein in step S4, the distance between samples is calculated using the distance formula of Minkowski, which is as follows:
Figure FDA0002284107620000032
wherein, the sample satisfies the following conditions: when d (i, j) is larger than or equal to 0, the distance between the sample and the sample is not negative, when d (i, j) is 0, the distance function has symmetry when d (i, j) is d (j, i), and when d (i, j) is larger than or equal to d (i, h) + d (h, j), the distance between the sample i and the sample j is smaller than or equal to the sum of the distances of other objects h;
wherein the michelson distance formula is the manhattan distance formula when q is 1, that is:
Figure FDA0002284107620000033
when q is 2, the formula is a euclidean distance formula, i.e.:
Figure FDA0002284107620000034
and (3) performing function calculation on the distance between the samples and performing normalization processing on the Euclidean distance by adopting an Euclidean method, wherein the mathematical form of the Euclidean distance is as follows:
Figure FDA0002284107620000035
in the formula 8, r, c, i, j are all positive integers, and p is a clustering sample space OKC is the cluster sample space OKI is more than or equal to 1, and l is more than or equal to c.
6. The method for allocating resources in manufacturing machines based on cluster analysis of claim 5, wherein in step S4, the step of determining the similarity and the similarity matrix comprises:
calculating OKAnd (3) the similarity between the middle cluster samples is defined by the calculation formula:
Figure FDA0002284107620000041
in the formula 9, F is a normalization constant and is larger than Max (D)il)，
Figure FDA0002284107620000042
I is more than or equal to 1 and l is more than or equal to c;
similarity matrix SKRepresenting the similarity between all the clustered samples, mapping each similarity value to a similarity matrix SKTo obtain a similarity matrix SKIts mathematical form is expressed as follows:
Figure FDA0002284107620000043
due to the fact that
Figure FDA0002284107620000044
And 1 is less than or equal to i, l is less than or equal to c, so that the matrix SKHas reflexibility and symmetry, and the mathematical form of the reflexibility and symmetry is expressed as follows:
Figure FDA0002284107620000045
in equation 11, matrix (S)K)TIs a matrix SKThe transposed matrix of (a), according to the contents of the discrete mathematical theorem,
Figure FDA0002284107620000046
knowing the matrix SKHas transferability.
7. The method for allocating resources for manufacturing a machine according to claim 6, wherein in step S4, the step of cluster analysis comprises:
according to the similarity matrix SKWill cluster sample space OKClustering the obtained elements, dividing the obtained elements into a plurality of resource clusters, and obtaining the resource clusters according to the matrix Sθ＝θ'If the following conditions are met:
Figure FDA0002284107620000047
then
Figure FDA0002284107620000048
Belonging to the same resource cluster, the mathematical form can be simplified into a triangular matrix, and the expression is as follows:
Figure FDA0002284107620000051
will matrix Sθ＝θ'And performing logical partitioning, wherein the elements forming the logical triangular area are all 1, and clustering samples in the same logical triangular area belong to the same resource cluster.
8. The method for allocating resources for machining and manufacturing based on cluster analysis of claim 7, wherein in step S4, the step of calculating the cluster size parameter is:
assuming manufacturing resources
Figure FDA0002284107620000052
Into t resource class groups (c)i)O＝{O1,O2,...OmThe number of resources in each resource class group is ciI.e. by
Figure FDA0002284107620000053
Then C (O)i)C(Oi) As a resource class group OiThe degree of polymerization of (a) is,
in the clustering process, clustering results with different densities are obtained by defining different granularities from coarse to fine or from fine to coarse, a clustering granularity parameter theta is closely related to the similarity, theta is a real number and belongs to [0,1 ]]The clustering result is determined by theta, if a specific theta' value is given, if
Figure FDA0002284107620000054
Then order
Figure FDA0002284107620000055
The others are 0, thus the matrix SKIs converted into a corresponding matrix Sθ＝θ'；
Is provided with
Figure FDA0002284107620000056
Figure FDA0002284107620000057
The average value of the similarity is taken as the value of the granularity parameter theta,
Figure FDA0002284107620000058
the expression of (a) is:
Figure FDA0002284107620000059
9. the cluster analysis method-based machining manufacturing resource allocation method according to claim 8, wherein the step S5 specifically includes:
s51, attribution uniqueness judgment: firstly, judging whether a common element exists in a resource cluster of a clustering result, if the common element does not exist, stopping the process, and obtaining a final unique clustering result; if the common element exists, finding the common element and proceeding to S52;
s52, determining clustering samples: taking the common elements of the resource clusters as clustering samples, finding out the resource clusters where the common elements are located, determining the core values of the measurement indexes, taking the average value of the measurement indexes as the core value representing the resource clusters, taking the core value as the reference value of the corresponding measurement indexes in the resource clusters, forming new clustering samples, and forming a temporary clustering sample space omega together with the common elements;
s53, cluster analysis: and re-clustering the temporary clustering sample space omega to obtain a new clustering result, and then continuing to execute S51.
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