A Business-Model-Driven Approach to Task-Planning Knowledge Graph Construction

Abstract

As the complexity of mission planning increases, relying on the subjective experience of planners is no longer sufficient to meet the needs of modern mission planning. Knowledge mapping, as a structured knowledge management technique, provides an effective solution for systematically integrating knowledge in the task-planning domain. The mission-planning business model is able to systematically capture and portray domain knowledge in mission planning through a formal representation of mission planning processes, rules, and constraints. Thus, it becomes an important source of knowledge for mission-planning knowledge mapping. This paper proposes a business-model-driven knowledge graph construction method for mission planning. First, under the support of conceptual business knowledge, the multidimensional task-planning ontology network expression method is utilized to construct the task-planning ontology network, and then the data-based business knowledge is structured to transform it into business data mapping to complete the acquisition of business knowledge. Then, the task-planning ontology network is constructed using the multidimensional task-planning ontology network representation method under the support of conceptual knowledge. Subsequently, a domain knowledge categorization algorithm based on Ullman subgraph matching is used to realize the matching mapping between the ontology network and business data mapping to complete the categorization of task-planning domain knowledge. Finally, the generated task-planning domain knowledge graph is stored in the Neo4j graph database. In order to ensure the completeness of the knowledge graph, an adaptive adjustment method based on its actual effectiveness is conceived, which is able to detect and adjust the completeness of the knowledge graph. The effectiveness of the proposed methodology is validated by constructing a space-station mission-planning knowledge graph driven by a space-station mission-planning business model.

1. Introduction

This section discusses the current status as well as the characteristics of two different types of knowledge graphs, pointing out that task-planning knowledge graphs are a type of domain knowledge graphs that integrate and mine knowledge for a specific task-planning domain. Based on the status quo that most of the existing related research focuses on specific applications and the lack of standardized frameworks, this paper proposes a framework for constructing a knowledge graph for mission planning based on a business model, proposes a multi-dimensional mission-planning ontology network expression method and a domain class knowledge categorization algorithm, and verifies the effectiveness of the method in space-station mission planning.

Despite the wide range of applications of knowledge graphs in several domains, the existing research is still insufficient to face the specific needs of the task-planning domain. Based on this, this paper will propose a new knowledge graph construction method in the next section, aiming to effectively integrate task-planning knowledge through a business model driven to optimize the construction efficiency and completeness of a task-planning knowledge graph.

Task planning is the process of breaking down a large and complex task into a series of orderly small steps, rationally arranging the order and priority of execution, allocating the necessary resources, and defining the task executor and execution equipment so as to accomplish the goal in an efficient and orderly manner [1]. Task planning is a key step in improving production efficiency, optimizing resource utilization, enhancing production quality, and promoting production automation in order to achieve high efficiency, high quality, stability, and sustainability in industrial production [2].

From this, we can see, with the continuous progress of modern production technology and production tools, the complexity and diversity of the production process continues to increase, and this has led to an increasing number of factors that need to be weighed in mission planning, resulting in ever-increasing difficulty in mission planning. Currently, most of the model modeling processes involved in the various steps of mission planning are performed by planners with subjective experience. Due to the limitations of the planner’s personal experience, the modeling approach that relies on subjective experience cannot fully reflect the actual situation and is difficult to meet the complex and changing needs.

With the advent of the information age, the management technology of knowledge is constantly updated, especially the emergence of knowledge-mapping technology, which provides an effective solution for knowledge integration in the field of mission planning. In 2012, Google officially proposed the concept of knowledge graphs as the most important method for managing massive amounts of knowledge [3]. In essence, a knowledge graph is a semantic network and knowledge base with a directed graph structure [4]. It describes entities (concepts) and their relationships in the physical world in the form of triplets. Knowledge graphs can support applications such as knowledge retrieval, knowledge quiz, knowledge recommendation, knowledge visualization, etc. [5]. In the field of mission planning, knowledge mapping can systematically integrate dispersed knowledge, break the traditional “knowledge island” problem, and improve the intelligence and automation of the mission-planning process. However, there is often a lack of knowledge resources that can be directly utilized in the construction of scenario-specific knowledge graphs for task planning. As a result, much of the construction relies on expert experience, but this manual construction is limited by the one-sided nature of expert knowledge, which makes it difficult to comprehensively cover all the knowledge elements of task planning. In addition, the ontology construction of task-planning knowledge graphs often lacks a systematic and standardized approach, resulting in the inability to completely express domain knowledge. These problems limit the effectiveness of task-planning knowledge graphs, and there is an urgent need for a more efficient, reliable, and domain-specialized construction method.

Currently, the construction of domain knowledge graphs faces three prominent problems [6,7,8]. First, there is a lack of reliable data sources, and the existing methods lack high-quality and systematic data support; second, ontology construction mainly relies on the experience of domain experts, but it is difficult to comprehensively cover the multi-level and multi-dimensional knowledge elements in the process of task planning due to the one-sidedness of experts’ knowledge; and third, the filling of the data layer is based on the manual operation of the domain experts by virtue of their subjective experience, which is inefficient and with a limited scope of coverage, further restricting the data. This further limits the application effect of knowledge mapping. Aiming at these problems and combining the characteristics of multi-level and multi-dimensional knowledge in the task-planning domain, this paper proposes a business-model-driven task-planning knowledge graph construction method to realize the systematic integration and deep mining of task planning knowledge in a certain domain so as to construct a task-planning knowledge graph that can support planning modeling and simulation modeling. The main contributions of this work are as follows:

(1)

A business-model-driven task-planning knowledge graph construction framework is proposed. The framework uses the business knowledge utilized in the operation of the business model for mission planning in a particular domain as the basic data source for knowledge graph construction. After the business knowledge acquisition, domain knowledge categorization, knowledge integrity testing, and knowledge graph storage, the task-planning knowledge graph with the ability to support planning modeling and simulation modeling is generated. After steps such as business data graph generation, knowledge-matching mapping, knowledge fusion, and knowledge integrity check, it generates a task-planning knowledge graph that has the ability to support planning modeling and simulation modeling. This framework can effectively solve the problem of the lack of high-quality knowledge sources in specific mission-planning domains and provides an efficient and reliable solution for building high-quality mission-planning knowledge graphs.

(2)

A multidimensional task-planning ontology network representation method is proposed. The method divides mission-planning knowledge into five categories according to the ontological perspective: tasks, resources, processes, goals, and results. Each major category is further subdivided into three levels according to the knowledge granularity, corresponding to the macro, meso, and micro levels, respectively. At the same time, based on the “function-structure-behavior” chain of thought in cognitive science, the method portrays the knowledge of each granularity level according to the three dimensions of function, structure, and behavior and constructs a multidimensional expression of the task-planning ontology network. This expression can comprehensively summarize all kinds of knowledge elements in the task-planning process and lay the foundation for the formal modeling of knowledge in specific task-planning domains.

(3)

A domain knowledge classification algorithm based on Ullmann subgraph matching is proposed. The knowledge graph data network construction problem is regarded as the matching and classification problem of domain knowledge subgraphs: the ontology network is decomposed into subgraph templates of domain knowledge, and the improved Ullman-subgraph-matching algorithm is used to match the business data subgraph consistent with the subgraph template from the business data graph and classify it as the domain knowledge subgraph of the subgraph template. The algorithm comprehensively considers the external structural attribute features of knowledge nodes to improve the accuracy of domain knowledge recognition and classification.

The rest of this paper is organized as follows: Section 2 introduces the related work of knowledge graph construction. Section 3 introduces the business-model-driven task-planning domain knowledge graph construction framework. Section 4 describes the specific model and algorithm for task-planning domain knowledge graph construction proposed in the framework. The experimental design and experimental results are shown in Section 5. Finally, this paper is summarized in Section 6.

2. Related Work

This section discusses the current status as well as the characteristics of two different types of knowledge graphs, pointing out that task-planning knowledge graphs are a type of domain knowledge graph that integrates and mines knowledge for a specific task-planning domain. Based on the status quo that most of the existing related research focuses on specific applications and the lack of standardized frameworks, this paper proposes a framework for constructing a knowledge graph for mission planning based on a business model, proposes a multi-dimensional mission-planning ontology network expression method and a domain class knowledge categorization algorithm, and verifies the effectiveness of the method in space-station mission planning.

Knowledge graphs are divided into general knowledge graphs and domain knowledge graphs. At present, most of the research results of knowledge graphs are general knowledge graphs. In addition to the universal knowledge graph constructed by Google, famous universal knowledge graphs include the DBpedia language knowledge base jointly constructed by the University of Leipzig and Mannheim [9], YAGO comprehensive knowledge base proposed by German Marker Institute [10], Probase, a large-scale knowledge graph developed and maintained by Microsoft Research Asia [11], “Zhishi.me” [12], “CN-DBpedia” constructed by Fu dan University [13], and so on. These general knowledge graphs each contain hundreds of millions of entities and relations. For example, Google Knowledge Graph includes 500 million entities and 2.5 billion relations, and Probase contains 1.68 billion web pages and 2.7 million concepts. Generic knowledge graphs are large in scale, breadth, and automation, but the lack of domain details makes it difficult to meet the individual needs of specific tasks and cannot be directly applied to specific industries. For this reason, domain knowledge graphs need to be constructed to solve this problem.

Domain knowledge graphs usually involve a specific industry object and have deeper research depth and higher accuracy. Amazon [14] has constructed an Internet movie database called IMDb, which contains basic information about movie actors, movies, and TV shows, as well as deeper content such as movie-related footage, holes in the film, and the film’s audio track. China Academy of Traditional Chinese Medicine [15] formed a domain knowledge graph for pediatric disease prediction by combining pediatric disease prediction rules with an established weighted knowledge graph based on plain Bayes. Shanghai Jiao Tong University [16] proposed AceKG, a large-scale domain knowledge graph for academic domains based on consistent ontology, which describes 3.13 billion ternary academic facts, including necessary attributes of papers, authors, research fields, locations and institutes, and the relationships among them. Wolfram Research [17] has developed WolframAlpha, a knowledge base for the field of mathematics, which has powerful computational capabilities to help students perform better calculus tasks and contribute to mathematical calculations.

The task-planning knowledge graph belongs to the category of domain knowledge graph, which is formed through the systematic integration and mining of domain-specific task-planning knowledge. To date, research on constructing task-planning knowledge graphs is still relatively limited. Duan et al. [18] discussed the construction process of UAV mission-planning knowledge graph in detail and also proposed a knowledge inference method based on graph neural network, which utilizes the advantages of graph structure and path inference techniques to predict the missing entities or relationships in the UAV mission-planning knowledge graph, and finally verified the validity and applicability of the method through simulation. WANG et al. [19] proposed a knowledge representation method for multi-intelligent body deep space probes based on knowledge mapping for mission planning, which firstly extracts knowledge from the probe system, then associates the system devices and their states and actions through knowledge fusion, and finally employs knowledge processing to mine potential relationships between multi-intelligent bodies, which is conducive to the probe’s realization of autonomous, flexible, and accurate mission planning. Li et al. [20] proposed a tactical mission event representation framework based on a simple event model for constructing a logic diagram of tactical mission events, whose construction process mainly involves first extracting tasks from military texts through a two-stage event extraction method, then decomposing them into sub-tasks by using a hierarchical task network, and further refining them into atomic tasks; finally, a Granger causality model is used to analyze the explicit causal relationships between sub-tasks and events, as well as the implicit causal relationships between atomic task events and military resources, explicit causality between events, and implicit causality between atomic task events and military resources; this construction method helps military personnel to analyze the composition and evolution of tactical tasks. However, these research studies are targeted at domain-specific application scenarios and lack the construction framework of a unified standard for task-planning knowledge graphs, as well as the research on the corresponding expression methods and related construction algorithms, with low domain generalization, which makes it difficult to be promoted to other domains. Therefore, this paper proposes a business-model-driven task-planning knowledge graph construction framework and, at the same time, proposes a multidimensional task-planning ontology network expression method and a domain knowledge categorization algorithm based on Ullman subgraph matching, which effectively solves the problem of the lack of high-quality knowledge sources in a specific task-planning domain, and can comprehensively summarize task-planning knowledge, improve the accuracy of knowledge identification and categorization, and enhance the quality and efficiency of the task-planning knowledge graph. Finally, the effectiveness of the proposed mission-planning knowledge graph construction method is verified by constructing the space-station mission-planning knowledge graph.

However, most of the existing research focuses on domain-specific application scenarios and lacks a unified framework for constructing knowledge graphs for task planning, as well as corresponding ontology modeling methods and knowledge mapping algorithms, which leads to its low domain generality and difficulty in promoting its application. In order to solve this problem, this paper proposes a business-model-driven task-planning knowledge graph construction framework, a multidimensional task-planning ontology network expression method, and a domain knowledge categorization algorithm based on Ullman subgraph matching to accompany the framework, aiming to provide a generalized and generalizable method for constructing task-planning knowledge graphs.

3. Business-Model-Driven Task-Planning Knowledge Graph Construction Framework

A business model is a formal representation of the business processes, knowledge entities, rules, and constraints of an enterprise or an organization, which can systematically capture and portray the business logic, processes, and rules of a specific domain, allowing the domain knowledge implicit in business operations to be explicitly and structurally expressed [21]. Therefore, using their business models as a source of knowledge in a specific task-planning domain ensures that the knowledge graph is constructed with domain expertise and accuracy.

In this section, a business-model-driven knowledge graph construction framework for task planning is proposed, which consists of four modules: business knowledge acquisition, domain knowledge categorization, knowledge integrity testing, and knowledge graph storage. The framework structure of the business-model-driven knowledge graph construction method for task planning and the control flow between different modules are shown in Figure 1.

The business information acquisition module integrates business information from all parts of the mission-planning business model. First, the operation mechanism of the domain task-planning business model is analyzed to extract business conceptual knowledge and data knowledge, including tabular data, document keywords, pictures and diagrams, 3D models and attribute lists, and domain rules; then, based on the business conceptual knowledge, the developed multidimensional task-planning ontology network expression method is used to construct the task-planning ontology; finally, through manual calibration and structured processing, the business data knowledge is organized into a data atlas to provide structured data support for the domain knowledge categorization module.

The domain knowledge categorization module is used to categorize the entity knowledge described in the business data mapping to the corresponding concept nodes of the task-planning ontology network. First, according to the description information of each concept node, the task-planning ontology network is divided into multiple subgraph patterns, and subgraph templates are generated for categorization; then, using the improved Ullman-subgraph-matching algorithm, business data subgraphs with the same structure as the subgraph templates are matched from the business data mapping and categorized into corresponding domain knowledge subgraphs to achieve ontology-to-data mapping; finally, the ontology-to-data mapping is achieved by the attribute similarity weighted averaging method to fuse domain knowledge subgraphs and eliminate redundant information.

The knowledge integrity check module is used to ensure that the task-planning knowledge graph contains complete domain knowledge. First, a set of test entity collections is constructed for evaluating the completeness of the knowledge graph; then, the task-planning knowledge graph is checked for the inclusion of these entities and the coverage of the graph over the test entity collections is calculated. If all of them are included, it indicates that the mapping is complete enough to enter the knowledge graph storage module; otherwise, it returns to the business information acquisition module and continues to extract the structured business knowledge required for task planning to continuously improve the mapping. Through the closed-loop feedback established between the business knowledge acquisition module, the domain knowledge categorization module, and the knowledge integrity checking module, continuous iteration ultimately ensures the integrity of the constructed task-planning knowledge graph.

The knowledge graph storage module is used to store the task-planning knowledge graph that has been checked for knowledge integrity. In this paper, we use graph database Neo4j for storage, which is a graph-model-based NoSQL database [22] that can store and query relational data efficiently.

This section describes the framework structure of the business-model-driven task-planning knowledge graph construction method and the components of each module, providing a modular framework for the integration of domain-specific task-planning knowledge. However, the operation of the modular framework still requires efficient and accurate modeling algorithms to support specific task planning. In this paper, we will introduce in the next section the modeling algorithms that match the construction methodology, which are central to achieving efficient knowledge graph construction.

4. Model and Algorithm

This section provides a detailed description of the multidimensional task-planning ontology network representation approach and the domain knowledge categorization algorithm based on Ullman subgraph matching. First, the multidimensional task-planning ontology network expression method is used to express the multidimensional knowledge information in task planning so as to construct an ontology network that can comprehensively summarize the task-planning knowledge. Then, on this basis, through the domain knowledge categorization algorithm based on the matching of Ullman subgraphs, the business data map is mapped and categorized with the previously constructed task-planning ontology network, thus forming the task-planning knowledge mapping data network.

4.1. Representation Methods for Multidimensional Task-Planning Ontology Networks

The ontology provides a unified conceptual definition, structural framework, and semantic rules for the knowledge graph, which is the key foundation for ensuring the quality and practicality of the knowledge graph [23]. There are two ways to build an ontology: top-down and bottom-up. Most domain knowledge graph ontology construction uses a top-down approach. This method relies too heavily on the subjective experience and assumptions of experts and lacks consideration of data from the real world, resulting in an ontology that differs greatly from the real world. Meanwhile, the lack of participation of practitioners in the domain has resulted in certain limitations in the knowledge coverage. The multi-dimensional task-planning ontology network expression method provides an a priori expression model for constructing a task-planning ontology network. It structurally divides and models task-planning knowledge from an ontological perspective, solving problems, such as the top-down construction method being too reliant on experts’ subjective experience and assumptions, and lacking consideration of real-world data.

The multi-dimensional task-planning ontology network expression method divides task-planning knowledge into five categories from an ontological perspective: task, resource, process, goal, and result. Each major category of knowledge is further subdivided into three levels according to the granularity of knowledge, corresponding to the macro, meso, and micro levels. Meanwhile, the method is based on the concept of the thinking chain in cognitive science [24], and each level of granularity of knowledge is characterized according to the three dimensions of structure, behavior, and function. The model structure of this expression method is shown in Figure 2.

Figure 3 shows a multi-dimensional expression model for task knowledge in the task-planning domain. First, the task knowledge in the planning domain is divided into three levels according to granularity: multi-tasks, subtasks, and meta-tasks. Then, the dependency between tasks of different granularities is defined to characterize the knowledge structure of the task category; the logical temporal relationship between different tasks of the same granularity is defined to characterize the knowledge behavior of the task category. The logical temporal relationship is expressed by the 13 types of relationships between time periods proposed by Allen [25]; the functional description of each task category is defined to characterize the knowledge function of the task category. The functional description includes the task identity description, the task resource requirement description, and the task attribute description.

Figure 4 shows a multi-dimensional expression model for resource knowledge in the task-planning domain. First, the resource knowledge in the planning domain is divided into three levels according to granularity: global resources, partitioned resources, and unit resources. Then, the unit resources are divided into three types of knowledge: resource entity, resource available fragment, and resource mode or type for description, and the composition relationship between resources of different granularities is defined to achieve the characterization of resource class knowledge structure; then, the association between the three types of knowledge in the description unit resource to characterize the behavior of the resource type knowledge and the functional description of the three types of knowledge in the description unit resource to characterize the function of the task-related knowledge are also defined. The functional description includes the attribute description of the resource entity, the attribute description of the available fragments of the resource, and the attribute description of the resource type or mode.

Figure 5 shows a multi-dimensional expression model for process knowledge in the task-planning domain. First, process knowledge in the planning domain is divided into three levels: multi-processes, sub-processes, and meta-process according to granularity. Then, the composition relationship between processes of different granularities is defined to characterize the structure of process-related knowledge. Each process consists of four parts: end state, start state, resource occupation, and process items. The logical timing relationship between processes of the same granularity is defined to characterize the behavior of process-related knowledge. The functional description of each type of process is defined to characterize the function of process-related knowledge. The functional description includes the attribute description of process items, resource items, and states.

4.2. Domain Knowledge Classification Algorithm Based on Ullman Subgraph Matching

The specific modeling process of the multidimensional task-planning ontology network expression method under the ontological perspective is discussed in detail above, through which an a priori expression model is provided for the construction of the task-planning ontology network, and then the business conceptual knowledge is integrated and processed to construct the task-planning business data atlas in a certain domain. Then, to construct the task-planning knowledge graph, it is also necessary to categorize the task-planning business data graph of the domain with the constructed task-planning ontology network because, for the construction of knowledge graph, the knowledge categorization algorithm is the key in it [26]. In this paper, the domain knowledge categorization algorithm based on Ullman subgraph matching is used for knowledge categorization. The algorithm consists of two parts: an improved Ullman-subgraph-matching algorithm and an entity fusion algorithm based on the weighted average of attribute similarities. Take a conceptual subgraph as an example. Under the action of the domain knowledge classification algorithm based on Ullman subgraph matching, the classification process of the domain knowledge subgraphs that are isomorphic to the conceptual subgraph is shown in Figure 6.

As can be seen from the figure above, the main function of the improved Ullman-subgraph-matching algorithm is to match the domain knowledge subgraphs from the business data graph that are isomorphic to the subgraph templates defined in the ontology network; the main function of the entity fusion algorithm based on the weighted average of attribute similarities is to fuse the several domain knowledge subgraphs that characterize the same entity obtained in domain knowledge extraction into a domain knowledge subgraph that characterizes the entity more comprehensively.

4.2.1. Improved Ullman-Subgraph-Matching Algorithm

The subgraph-matching algorithm is used to find a subgraph isomorphic to a given small graph in a large graph [27]. The improved Ullmann-subgraph-matching algorithm mainly expands the generation and representation methods of the adjacency matrix on the basis of the original Ullmann-subgraph-matching algorithm [28], enabling it to express complex networks with multiple relationships, thereby achieving the matching of domain knowledge subgraphs in the business data graph that are isomorphic to the subgraph templates defined by the top-level ontology.

The improved Ullmann-subgraph-matching algorithm takes the business information graph and ontology network as input and obtains the domain knowledge subgraph corresponding to each subgraph pattern structure in the business information graph as output. The specific calculation process of the algorithm is as follows:

Step 1: Summarize and organize all the associated attributes (including object attributes and data attributes) in the ontology network to form a list of associated attributes $P$ of the ontology network.

Step 2: Divide the ontology network into a set of templates $Q=\left\{Q_1,Q_2,\dots ,Q_n\right\}$.

For each concept node $q_i$ in the ontology network, a list of associated attributes $p_i$ of the concept node is extracted from the ontology network, and the concept node or data type $v_i$ corresponding to each associated attribute in the list is obtained to form a list of associated attribute values, thereby forming a subgraph template $Q_i=\left\{q_i;p_i;v_i\right\}$ of the concept node $q_i$.

Step 3: Obtain the adjacency matrices of each subgraph template to form the set of subgraph adjacency matrices $MA=\left\{M{A}_1,M{A}_2,\dots ,M{A}_n\right\}$.

For each subgraph template $Q_i$ in the subgraph mode collection, the concept nodes and associated attribute value lists are summarized to form a subgraph adjacency matrix index list $s_i=\left[q_i,v_i\right]$. The element values in the subgraph adjacency matrix $M{A}_i$ are set according to the following rules:

$$M{A}_i\left[i\right]\left[j\right]=\left\{\begin{array}{cc}index\left[p\right],& s_i\left[i\right]\stackrel{\exists p\in P}{\to }{s}_i\left[j\right],\\ 0,& else.\end{array}\right.$$

(1)

where $s_i\left[i\right]\stackrel{\exists p\in P}{\to }{s}_i\left[j\right]$ represents that, for element $s_i\left[i\right]$, there is an associated property $p$ belonging to the associated property list $P$, which associates it with element $s_i\left[j\right]$; $index\left[p\right]$ is the index value of the relationship $p$ in the ontology network associated property list $P$.

Step 4: Obtain the adjacency matrix M of the business data graph $G$.

For the business data graph $G$, the internal concept node list $GQ$ and the associated attribute value list $GV$ are sorted and compiled to form the adjacency matrix index list $S=\left[GQ,GV\right]$ of the business data graph $G$. The internal element values of the adjacency matrix $MB$ of the business data graph $G$ are set according to the following rules:

$$MB\left[i\right]\left[j\right]=\left\{\begin{array}{cc}index\left[p\right],& S\left[i\right]\stackrel{\exists p\in P}{\to }S\left[j\right],\\ 0,& else.\end{array}\right.$$

(2)

where $S\left[i\right]\stackrel{\exists p\in P}{\to }S\left[j\right]$ represents that, for element $S\left[i\right]$, there is an associated property $p$ belonging to the associated property list $P$, which associates it with element $S\left[j\right]$; $index\left[p\right]$ is the index value of the relationship $p$ in the ontology network associated property list $P$.

Step 5: Generate the search space matrix for each subgraph pattern to form the search space matrix set $M=\left\{M_1,M_2,\dots ,M_n\right\}$.

For the domain knowledge subgraph template $Q_i$, the element values of the search space matrix $M$ are set according to the following rules:

$$M_i\left[i\right]\left[j\right]=\left\{\begin{array}{cc}1,& \left(\alpha \times n\left(s_i\left[i\right]\right)\le n\left(S\left[j\right]\right)\right)\&\left(d_{+}\left(s_i\left[i\right]\right)\le d_{+}\left(S\left[j\right]\right)\right),\\ 0,& else.\end{array}\right.$$

(3)

where $n\left(s_i\left[i\right]\right)$ is the number of related attributes of the i-th element in the subgraph template $Q_i$, and $\alpha$ is the matching relaxation coefficient, which is used to relax the matching conditions and match the subgraphs of domain knowledge with related attributes in the subgraph template $Q_i$ by default so as to improve the knowledge coverage of the matching results of the matching algorithm; $n\left(S\left[j\right]\right)$ is the number of related attributes of the $j$-th element in the business data graph; $d_{+}\left(s_i\left[i\right]\right)$ is the out-degree of the $i$-th element in the subgraph template $Q_i$, and $d_{+}\left(S\left[i\right]\right)$ is the out-degree of the $j$-th element in the business data graph.

Step 6: Generate the mapping matrix set $M_i^{\prime }$ of the search space matrix $M_i$.

Select any subgraph template from the set to obtain the search space matrix $M_i$. Check $M_i$ row by row, replacing some non-zero elements with zero so that the matrix satisfies the condition that each row has exactly one non-zero element and each column has at most one non-zero element. Sum up all matrices that satisfy the above conditions to obtain the set of mapping matrices $M_i^{\prime }$ for the search space matrix $M_i$.

Step 7: Obtain a collection $S{G}_i$ of subgraphs with isomorphic domain knowledge to the subgraph template $Q_i$.

For each mapping matrix $M_i^{\prime }$ in the set, perform the matrix operation in Equation (4):

$$M{C}_i=M^{\prime }M{B}_i{\left(M^{\prime }\right)}^T$$

(4)

If $\forall i,j:M{A}_i\left[i\right]\left[j\right]=1$, $M{C}_i\left[i\right]\left[j\right]=1$, then the mapping matrix satisfies the subgraph isomorphism theorem. Enumerate all mapping matrices that satisfy the subgraph isomorphism theorem and obtain the set of domain knowledge subgraphs corresponding to the subgraph template $Q_i$.

Step 8: Iterate Steps 6 and Step 7 to solve for all element domain knowledge subgraphs in the set of search space matrices $M$.

Step 9: Output the result $Result=\left\{S{G}_1,S{G}_2,\dots ,S{G}_n\right\}$ of the subgraph matching for domain knowledge.

It is worth mentioning that the performance of the improved Ullman-subgraph-matching algorithm mentioned above is related to the number of nodes. Here, we analyze the complexity of this algorithm, specifically, the complexity can be expressed as O(n!*m), where n denotes the number of nodes in the subgraph, and m denotes the number of nodes in the target graph, from which it can be seen that the computational complexity of this algorithm is exponential, and the computational cost becomes very large, especially when the number of nodes in both the subgraph and the target graph is high.

4.2.2. Entity Fusion Algorithm Based on Weighted Average of Attribute Similarities

Entity fusion is used to identify and merge domain knowledge subgraphs that describe the same entity under the same subgraph template to eliminate redundant information and provide a consistent and accurate representation of the entity. The entity fusion algorithm based on the weighted average of attribute similarity is a common entity fusion method [29]. It compares the similarity of attributes of entities and assigns weights to each attribute to finally calculate a comprehensive entity representation. The entity fusion algorithm based on attribute similarity weighted average is as follows:

Step 1: Load the domain knowledge subgraph set $Result=\left\{S{G}_1,S{G}_2,\dots ,S{G}_n\right\}$ and set $i=1$.

Step 2: Obtain the attribute vector ${\mathit{W}}_j$ of each element in the subgraph set $S{G}_i$ of domain knowledge subgraphs.

For each subgraph element in the domain knowledge subgraph set $S{G}_i$, read its associated attribute values as attribute information, store the attribute information in vector form, and obtain the attribute vector ${\mathit{W}}_j=\left[W_{j1},W_{j2},\dots ,W_{jm}\right]$ for each subgraph element.

Step 3: Calculate the similarity score vector $\mathit{s}\mathit{i}\mathit{m}({\mathit{W}}_p,{\mathit{W}}_q)$ between two subgraph elements in the set $S{G}_i$.

$$\mathit{s}\mathit{i}\mathit{m}\left({\mathit{W}}_p,{\mathit{W}}_q\right)=\left[\begin{array}{cccc}sim\left(W_{p1},W_{q1}\right)& sim\left(W_{p2},W_{q2}\right)& \cdots & sim\left(W_{pm},W_{qm}\right)\end{array}\right]$$

(5)

where $W_{px}$ is the ith attribute value of the x-th attribute of the subgraph element $p$, and $sim\left(W_{px},W_{qx}\right)$ is the similarity value between the subgraph element $p$ and the subgraph element $q$ at the x-th attribute component, which is calculated using the minimum edit distance algorithm [30].

Step 4: Calculate the weighted average of the similarities between the elements of the two subgraphs in the set $S{G}_i$;

$$\overline{sim}\left({\mathit{W}}_p,{\mathit{W}}_q\right)={\displaystyle \sum _{i=1}^m\frac{1}{m}\cdot sim\left(W_{pi},W_{qi}\right)}$$

(6)

Step 5: Merge the subgraph elements with $\overline{sim}\left({\mathit{W}}_p,{\mathit{W}}_q\right)\ge 0.8$ to obtain the fused subgraph set $N\_S{G}_i$.

Step 6: If $i<n$, then $i=i+1$ and go to Step 2; if $i=n$, then go to Step 7.

Step 7: Export the subgraph fusion result $Result=\left\{N\_S{G}_1,N\_S{G}_2,\dots ,N\_S{G}_n\right\}$.

The modeling algorithm proposed in this section provides an important technical support for the efficient construction of knowledge graphs for task planning. However, pure theoretical derivation cannot prove the practical value of the algorithm. In the next section, this paper will take the space-station mission-planning domain as an example to comprehensively validate the proposed business-model-driven mission-planning knowledge graph construction framework method and the practical effect of the matching algorithm, which consists of three parts, namely, experimental preparation, result validation, and analyzing and evaluating.

5. Experimentation and Verification of the Proposed Method

In this section, we take space-station mission planning as an example to construct a space-station mission-planning knowledge graph and verify the effectiveness of the proposed method. First, the business model describing the business process of space-station mission planning is constructed and the conceptual and data-based knowledge is extracted; then, under the support of the conceptual knowledge, the domain ontology of space-station mission planning is modeled by using the multidimensional mission-planning ontology network representation method, and the domain knowledge categorization algorithm based on Ullman subgraph matching is applied to complete the matching categorization of the data-based knowledge. Finally, the support capabilities of the knowledge graph and the performance of the domain knowledge categorization algorithms are evaluated.

5.1. Experimental Preparation

All the data in this paper come from the Beijing Flight Control Center and are modeled in SysML language and constructed and analyzed with the help of Enterprise Architect 15.2. Space-station mission planning refers to the process of overall planning, resource coordination, and specific arrangements for the various types of tasks to be carried out by the space station during its on-orbit operation; it is a key link in ensuring the orderly and efficient operation of the space station [31]. By analyzing the business processes of space-station mission planning, a business model for standardizing the description of space-station mission-planning business processes is constructed, as shown in Figure 7.

As can be seen from the figure above, the completion of a space-station mission-planning operation requires the collaborative operation of four departments to realize 10 business operations, such as the reception of the monthly event plan, the acquisition of the elements of the monthly event, and the modeling of the orbital scenario. Each operation generates the domain data that will be utilized in this mission-planning operation, including the monthly event plan, the monthly event components, the list of orbital resources, and so on. These domain data consist of a combination of conceptual and data-based knowledge to provide knowledge support for the construction of ontology and data networks for the space-station mission-planning knowledge graph (hereinafter referred to as SSMPKG).

5.2. Construction Results

5.2.1. Construction Results of Space-Station Mission-Planning Ontology Network

In this paper, the conceptual knowledge of the space-station mission-planning domain is modeled using the multidimensional mission-planning ontology network representation developed in Section 4.1 to obtain the space-station mission-planning ontology network, and the creation tool uses the ontology editing tool Protege [22]. The exact creation process is described below.

First, we create five knowledge categories: task, resource, process, goal, and outcome, under the thing category; then, each major category of knowledge is subdivided into three levels according to macro, meso, and micro granularity, for example, under the mission category; the space-station mission-planning task is then divided into three subcategories: “Month_event”, “Flight_control_event”, and “Command”; the mission-planning task is then divided into two subcategories: “Flight_control_event” and “Command”. For example, under the task class, the space-station planning task is divided into three subclasses: “Month_event”, “Flight_control_event”, and “Command”.

After that, for the subclass information in the task’s broad category, the subclasses at each granularity level are portrayed according to the three dimensions of structure, behavior, and function, and the object attributes and data attributes describing the nodes of the subclass are obtained. Take the three subclasses under the task category as an example, define the object attributes “monthTaskInclude” and “flyTaskInclude” to describe the structural relationship between the three subclasses and define the object attributes “monthTaskBefore”, “monthTaskAfter”, and so on. Define 9 object attributes such as “monthTaskBefore” and “monthTaskAfter” to describe the behavioral relationship of the knowledge under the task category and define “hasPriority”, “hasLightDem”, “hasDurationScope”, and the other 18 data attributes to describe the functional attributes of the three subclasses under the broad task category. The functional attributes of the three subclasses under the task category are described. Finally, define the role “Domain” and the attribute “Range” for the object attribute and the data attribute, respectively, with “Domain” indicating the class to which the attribute belongs and “Range” indicating the range of values for the attribute. The “Range” indicates the value range of the attribute. The classes, object attributes, and data attributes in the space-station mission-planning ontology network are shown in Figure 8.

The space-station mission-planning ontology network constructed based on the multidimensional mission-planning ontology network expression method contains a total of 55 class nodes, 64 object attributes, and 125 data attributes. The five broad categories of knowledge defined by Figure 8 include tasks, resources, etc., object attributes, and data attributes. These defined properties provide the underlying framework for the construction of ontology networks. Based on this framework, the different knowledge elements and their interrelationships are expressed in more detail by further refining the object attributes and data attributes. The structure of the space-station mission-planning ontology network was demonstrated using Protégé’s visual presentation function, and the structure of the ontology is shown in Figure 9.

5.2.2. Construction Results of the Space-Station Mission-Planning Knowledge Graph

The complete ontology network for space-station mission planning is shown in Figure 9, which provides a semantic model for the space-station mission-planning knowledge graph. In this section, the domain knowledge categorization algorithm based on Ullman subgraph matching developed in Section 4.2 is utilized to realize the matching mapping between the operational DATAbility knowledge and the ontology network, thus completing the construction of the space-station mission-planning knowledge graph. Before carrying out the matching mapping work, it is necessary to transform the business-data-based knowledge into business data mapping. Taking the planning of the platform function initialization monthly event and the rendezvous and docking monthly event as an example, the business data used in the planning process of these two monthly events are extracted from the business model of the space-station mission planning, including the table, the document keywords, the picture and illustration information, and the 3D model and checklist, as well as the domain rules. After manual calibration and structuring, the ternary representation of the business data in the above five items is obtained and dumped as a business data mapping.

The business data graph obtained from Figure 10 is only a structured storage of domain data, which lacks the class labels and semantic information in the domain knowledge graph, and thus can only store the data but cannot provide functions to support reasoning and semantic querying. Business data mapping can be used to view and organize the connectivity relationships of domain data but lacks the semantic level of domain knowledge mapping to enable intelligent reasoning and querying at a higher level.

Taking the constructed space-station mission-planning ontology network and business data mapping as inputs (i.e., the results obtained from Figure 9 and Figure 10 are taken as inputs), the domain knowledge categorization algorithm based on the matching of Ullman subgraphs is utilized to realize the matching mapping between business-data-study knowledge and ontology network, and the knowledge mapping of the space-station mission planning in Figure 11 is formed. The ontology network (including concepts, object attributes, data attributes, etc.) in Figure 9 is interconnected with the specific data instances of the business data mapping in Figure 10, which establishes a bridge between the specific data and the high-level domain knowledge. The knowledge mapping in Figure 11 not only retains the conceptual and relational structure of Figure 9 but also adds the business data in Figure 10, which is able to demonstrate the actual data application in mission planning. The knowledge map formed by matching mapping has visualized domain relationships and potential “knowledge island” correlations, which facilitates the discovery of implicit relationships between knowledge and supports the mining of correlation paths in task planning, providing a new way for knowledge management and application in complex tasks.

5.3. Method Assessment

5.3.1. Space-Station Mission-Planning Knowledge Graph Capability Assessment

In this section, we assess the capability of the knowledge graph for space-station mission planning. The capability assessment mainly refers to verifying the effectiveness of the knowledge graph in supporting mission planning, reasoning, and decision-making through practical application scenarios. By retrieving and reasoning about specific mission requirements, we can assess the capability of the knowledge graph in providing decision support, mission optimization, and simulation analysis to ensure that it can fully meet the needs of mission planning.

In the area of mission planning, simulation analysis helps to assess and optimize the effectiveness and feasibility of mission planning by constructing virtual environments and models that simulate real-world conditions and scenarios. The Petri net model, as a graphical and mathematical tool, can effectively capture the complex dynamic behavior in mission planning and fully support simulation analysis [32]. Compared with other mathematical methods, Petri nets have unique advantages in dealing with dynamic behaviors such as concurrency, synchronization, and conflict and thus are more suitable for describing complex systems in task planning.

Taking the construction of the Petri net model of rendezvous and docking events at the flight control level as a demand, the constructed knowledge graph of space-station mission planning is retrieved and reasoned, as shown in Figure 12 for the knowledge nodes of the Petri net model of the construction of rendezvous and docking events at the flight control level obtained by retrieval and reasoning. By modeling the knowledge nodes of the Petri net model obtained from the retrieval inference in Figure 12, the Petri net model of the rendezvous and docking event at the flight control event level constructed based on the retrieval results is obtained, as in Figure 13. The model contains eight resource repositories and four flight control event operation repositories, and there are multiple combinations between each flight control event repository and different resource repositories, which together describe the complex resource occupation and process logic relationship during the execution of rendezvous–docking events. This model meets the simulation requirements and proves that the constructed knowledge map of space-station mission planning in Figure 11 has good support for simulation modeling, solves the problems of Petri net modeling in traditional mission planning that relies on manual experience, is inefficient, has a high error rate, and provides reliable support for the subsequent space-station planning.

Taking the construction of the Petri net model of rendezvous and docking events at the flight control level as a requirement, the constructed knowledge graph of space-station mission planning is retrieved and reasoned, and the knowledge nodes of constructing Petri net model of rendezvous and docking events at the flight control level obtained by retrieval and reasoning are shown in Figure 12. The Petri net model knowledge nodes obtained by retrieval and reasoning in Figure 12 are modeled. The Petri net model of the rendezvous and docking event at the flight control event level constructed based on the retrieval results is obtained as in Figure 13. The model contains eight resource repositories and four flight control event operation repositories, and there are various combinations between each flight control event repository and different resource repositories, which together describe the complex resource occupation and process logic relationship during the execution of the rendezvous and docking event. This model meets the simulation requirements and proves that the knowledge map for space-station mission planning in Figure 11 has good support for simulation modeling, solves the problems of Petri net modeling in traditional mission planning, which relies on manual experience, is inefficient, has a high error rate, and provides reliable support for subsequent space-station planning.

5.3.2. Algorithm Performance Evaluation

This section evaluates the domain knowledge classification algorithm that implements the mapping of the space station’s operational data atlas to the mission-planning ontology network, comparing the metrics of recall, accuracy, and F-value of the method with the edit distance algorithm, the Jaccard coefficient algorithm, and the Euclidean algorithm, as defined in Equations (7)–(9).

$$\mathrm{Precision}: P={\displaystyle \frac{TP}{FP}}\times 100\%$$

(7)

$$\mathrm{Recall} \mathrm{rate}: R={\displaystyle \frac{TP}{TP+FN}}\times 100\%$$

(8)

$$\mathrm{Harmonic} \mathrm{mean} \mathrm{of} \mathrm{exact} \mathrm{and} \mathrm{recall}: F={\displaystyle \frac{2\times P\times R}{P+R}}\times 100\%$$

(9)

where $\mathrm{TP}$ is the correct number of matches, $\mathrm{FP}$ is all matches found by the method, and $\mathrm{FN}$ is the number of matches recommended by the method.

Figure 14 is the comparison result of the domain knowledge classification algorithm based on Ullman subgraph matching with the edit distance, Jaccard coefficient algorithm, and Euclidean metric algorithm. The results show that the accuracy $\mathrm{P}$, recall $\mathrm{R}$, and $\mathrm{F}$ measurements of the domain knowledge categorization algorithm based on Ullman subgraph matching are above 90%, exceeding the results of the other three algorithms. This is because the algorithm synthesizes the intrinsic semantic features and extrinsic structural attribute features of the knowledge nodes to improve the accuracy of domain knowledge recognition and categorization.

In order to further investigate the performance of the algorithm, especially the effect of subgraph size on the domain knowledge categorization results, we design comparative experiments to explore the trends of accuracy, recall, and F-value of the domain knowledge categorization algorithm based on Ullman subgraph matching under different subgraph sizes. The core of the Ullmann-subgraph-matching algorithm is matching by edges, so we use the number of attribute edges to measure the size of the graph. The results of the comparison test are shown in Figure 15.

The results show that as the number of attribute edges increases, the accuracy, recall, and F-value of the domain knowledge classification algorithm based on Ullman subgraph matching all show an upward trend. When the number of attribute edges increases to a certain extent, the increase in these indicators gradually slows down and finally stabilizes at a high level. This trend shows that as the scale of the graph increases, the performance of the algorithm in domain knowledge classification gradually optimizes, but when the number of attribute edges reaches a certain scale, the performance tends to saturate. In addition, since the computational complexity of the algorithm also grows exponentially, the larger the scale of the graph, the longer the required calculation time. Therefore, in specific applications, the two factors of accuracy and computational complexity should be comprehensively considered to make the scale of the subgraph template as reasonable as possible to achieve the effect of balancing performance and efficiency.

6. Conclusions and Future Work

This paper proposes a business-model-driven task-planning knowledge mapping construction method, which is different from the previous domain knowledge mapping construction research that relies on the experience of domain experts with one-sidedness and has a lack of a unified knowledge construction framework, etc. This method proposes a business-model-driven task-planning knowledge mapping construction framework by systematically integrating the business knowledge in the business model of the task planning of a certain domain and by deep mining. The method proposes a business-model-driven task-planning knowledge mapping construction framework and a multidimensional task-planning ontology network expression method and a domain knowledge categorization algorithm based on Ullman subgraph matching to match the framework, thus providing a task-planning knowledge mapping construction method that can support planning and simulation modelling in this domain, and its domain generality is strong enough to be promoted and applied. Specifically, the method includes the steps of business knowledge acquisition, domain knowledge categorization, knowledge integrity testing, and graph storage. First, the task-planning ontology network is constructed by using the multidimensional task-planning ontology network expression method, and then the business data are transformed into business data mapping through manual calibration and structured processing to complete the acquisition of business knowledge. Subsequently, a domain knowledge categorization algorithm based on Ullman subgraph matching is used to complete the mapping of the ontology network to the business data mapping to complete the categorization of domain knowledge. Ultimately, the generated knowledge graph of the task-planning domain is stored in the Neo4j graph database. To ensure the completeness of the knowledge graph, an adaptive adjustment method is also developed that can detect and adjust the completeness of the knowledge graph. The method is unsupervised, does not rely on deep linguistic knowledge, and can be widely applied to the construction of knowledge graphs for task planning in different domains.

Taking space-station mission planning as a research area, this paper validates the effectiveness of the proposed method by constructing a knowledge map of space-station mission planning. The experimental results show that the adoption of the multidimensional mission-planning ontology network expression method can ensure that the constructed space-station mission-planning ontology network has complete semantic expression capability and accurately describes the domain knowledge and its interrelationships. Meanwhile, the knowledge categorization algorithm based on Ullman subgraph matching ensures that the generated data network is highly accurate in terms of domain knowledge.

However, we also recognize several limitations. First, our approach still requires manual intervention in the knowledge graph construction process, including the construction of ontology networks and the generation of business data graphs, which lacks full automation. Second, complex graph-matching computations are involved in the domain knowledge categorization module, and the performance of the method degrades as the number of graph nodes increases. Therefore, in our future work, we need to explore more automated and intelligent methods to improve the efficiency and scope of our approach. In addition, future research can focus on improving graph-matching algorithms, optimizing graph storage and computation, and adopting more efficient distributed computing methods or graph parallel computing techniques to meet the challenges of large-scale datasets. In conclusion, the research in this paper provides an innovative solution for task-planning knowledge graph construction and lays the foundation for future research directions and technological advances. Future work will focus on addressing the current limitations of the method and exploring more advanced techniques and approaches. In this paper, we propose a business-model-driven task-planning knowledge graph construction method, which provides an efficient and reliable solution for constructing high-quality task-planning knowledge graphs. The method takes the business knowledge used in the operation process of a domain task-planning business model as the basic data source and generates a task-planning knowledge graph with the ability to support-planning modeling and simulation modeling through the steps of business knowledge acquisition, domain knowledge categorization, knowledge integrity testing, and knowledge graph storage. Meanwhile, a multi-dimensional task-planning ontology network expression method and a domain knowledge categorization algorithm based on Ullman subgraph matching are proposed for the modeling of task-planning ontology network and the generation of task-planning data network, respectively, to improve the quality and efficiency of task-planning knowledge graph construction. Finally, the effectiveness of the proposed method is verified by constructing SSPMKG. In future work, the business knowledge acquisition module can be further optimized to explore methods for automatically extracting structured business knowledge from unstructured data sources (e.g., natural language text) to expand the scope of knowledge acquisition.