System design and experiments

This research introduces a practical, knowledge driven platform that strengthens decision making in aircraft tooling design with a clear focus on assembly. Real engineering needs are translated into explicit system requirements and a cohesive architecture, followed by targeted functional modules that capture, organize, and retrieve domain knowledge where it matters most, both on the shop floor and at the design desk. A working prototype for tooling design knowledge management streamlines choices during assembly planning and proves its value through a representative case on designing the assembly jig for an aircraft wing spar, where the system guides concept selection, parameter tuning, and rule-based checks using curated instances and ontology aligned semantics. Although time and scope constraints limit the inclusion of every envisioned feature, the core framework is complete, the key modules are operational, and their performance has been verified on practical examples. These advances create a strong foundation for future expansion and support a smooth transition toward a full scale, production ready knowledge management system for aircraft tooling design.

Selecting the Browser Server structure gives the platform a clear advantage for knowledge management in aircraft tooling design and assembly decision making. Access through a standard web browser delivers a welcoming interface on desktops, tablets, and phones, while centralized server control concentrates data storage, processing, and protection in one reliable place. The architecture scales smoothly and connects readily with other enterprise systems, which preserves long term viability and encourages future integration. Routine upkeep is simple because client-side installation is unnecessary, updates occur on the server side, and remote upgrades and modular expansion allow rapid response to changes in business processes. Performance remains strong since computation is handled on powerful servers that can use clustering, load balancing, and modern cloud infrastructure to keep the experience responsive across locations. The approach is also budget friendly, lowering maintenance costs and allowing use of open-source operating systems where appropriate. Aligned with these platform strengths, the system requirements emphasize real world practicality, robust security from database to network, generous scalability through components and open interfaces, and strong flexibility in installation, use, administration, and maintenance. Together, these features create an efficient and dependable foundation that streamlines design tasks, connects designers with best practices and expert insights, and supports sustained improvement in tooling outcomes.

The knowledge management system for tooling design in aircraft assembly decision making is organized as a clear five-layer architecture that guides users from simple interaction to deep knowledge services as shown in Fig. 4. At the top, the interface layer delivers an easy-to-use web experience that works on common browsers and removes the need for local installation. Beneath it, the user layer defines five roles with precise permissions: system administrators manage users and configuration, ordinary users create and edit knowledge and browse noncore content, super users inherit these abilities and can view core knowledge, expert users add authoritative review and approval, and passersby may browse selected noncore items and contribute evaluations. The functional layer drives capability through four modules that handle system management, knowledge base management with ontology and rule administration, multi strategy knowledge retrieval, and knowledge flow with timely push to the right people. The data interface layer connects the platform to external repositories through general interfaces for the knowledge base and specialized interfaces for product data management and computer aided design, ensuring smooth exchange and consistent context. At the foundation, the resource layer provides the knowledge base stored in a secure server database, the product data management system for product and task information, and the computer aided design platform for rich visualization of instances. Together, these layers create a coherent framework that simplifies access, strengthens governance, accelerates retrieval, and turns scattered information into confident design choices.

Fig. 4
figure 4

Framework structure of decision making for aircraft assembly showing a five-layer stack that includes the interface layer, user layer, functional layer, data interface layer, and resource layer with directional links among components.

Designed to turn scattered expertise into fast, confident choices, the aircraft tooling design knowledge management system focuses on boosting the productivity of tooling decision makers through disciplined capture, organization, and delivery of engineering know how. Four core capabilities anchor the platform. System management keeps daily operations stable and secure, handling user administration, permissions, monitoring, and routine maintenance so work can proceed without interruption. Knowledge base management curates the repository of tooling design assets, from ontology and rules to documents, cases, and validated templates, ensuring that content stays accurate, traceable, and easy to reuse. Knowledge retrieval provides precise access through semantic search, rule reasoning, and instance matching, allowing engineers to reach the right guidance in a few steps even for complex assembly questions. Knowledge push closes the loop by sending timely, role-based updates and recommendations when new information or design changes matter. Together these functions create a seamless path from query to decision. Table 1 maps the full structure of these capabilities, showing how each module connects and supports the others to deliver a coherent, high impact decision support environment.

Table 1 Function structure of the system.

The system management module provides unified control at the macro level so that administration is consistent, secure, and auditable across the platform. It combines two essential functions. User management maintains complete records for every participant, including username, role, department, real name, phone number, email address, and password, and supports routine actions such as creation, deletion, and password updates. Authority management enforces strict access control by defining roles, assigning permissions, revising privileges, and maintaining clear relationships between roles and permissions, which protects sensitive knowledge from unauthorized use. Building on this secure foundation, the knowledge base management module organizes the domain corpus through two pillars. Knowledge ontology management defines and maintains the classes, attributes, and relationships for design objects, designers, processes, and knowledge; attributes can be inherited, added, removed, or refined, and assets such as documents, formulas, and tables are curated with support from tools such as Protege for efficient ontology construction. Knowledge rule management creates, edits, and removes rules so the system can automatically present related knowledge when a given item is invoked, for example if a condition holds then show result one, otherwise show result two. To help engineers find what they need quickly, the knowledge retrieval module offers general retrieval through keyword based full text search, advanced retrieval guided by a multi strategy query analyzer, and rigorous evaluation of results to ensure relevance, precision, and speed.

The practical workflow of the knowledge management system comes to life in the design of an assembly jig for an aircraft wing spar. The jig brings together a rigid skeleton, clamping plate assemblies, a corner piece locator, and a web locator to position riveted webs, upper and lower edge strips, reinforcing pillars, and connecting angle materials until a stable spar takes shape. The frame sits on an integral base and is leveled with precision screws, while other positioning elements are arranged across the structure for rapid set up. The front beam web is referenced by the web surface and the K hole, the upper and lower flanges use hole references and the oblique end face, and the connecting angle materials align to the standing surface and the CPH hole. Detachable clamps on the edge strips release the front beam assembly cleanly once fastening is complete. In a typical scenario, a tooling designer designated as the Decision Maker opens the product data management system at the end of the day, receives a new Tooling Order that details model, tolerances, and process constraints, and then launches the knowledge platform. Ontology guided search surfaces comparable jigs, rule reasoning resolves dimension relationships, and case retrieval recommends proven locator patterns. Within a single guided session, the designer confirms references, selects fixtures, and documents the plan, turning a complex assembly into a controlled and efficient build.

Building an ontology for aircraft tooling design is a rigorous effort that transforms scattered terminology and tacit know how into a coherent map of meaning. In this study the framework targets the realities of assembly tooling, where names, attributes, and relationships must line up with everyday design practice. Classes define key artifacts such as jigs, locators, clamps, fixtures, and process features, while properties capture constraints, tolerances, materials, and typical usage contexts. The model is authored with the widely used third party tool Protege, which supports consistent class hierarchies, reusable property patterns, and clear annotations that make the knowledge base both readable and extensible. Detailed methods for concept selection, attribute normalization, and relationship encoding are documented in Chapter Three, allowing readers to trace each modeling choice from requirement to representation. Figures 5 and 6 present visual views of the completed ontology in Protege 4.2, revealing the layered structure and the cross links that connect assembly details with design rules and instances. Together, the framework and its implementation provide a stable foundation for retrieval, reasoning, and future growth in the management of tooling knowledge for aircraft assembly.

Fig. 5
figure 5

Aircraft tooling design ontology: Maps of concepts, attributes, and relations that power semantic retrieval.

Fig. 6
figure 6

Ontology tree (detail): wing-spar tooling design trees and relevant knowledge.

Tooling design thrives on rich and varied knowledge, and the most vivid example appears in the design of an assembly jig for an aircraft wing spar. Here, an integrated retrieval approach brings clarity to complex choices by combining ontology guided search for precise terminology, rule-based inference for dimension and sequence logic, and case reasoning for proven patterns from past projects. The ontology clarifies concepts such as spar, rib, stringer, and skin so that queries map to meaning rather than loose keywords. The rule engine enforces constraints among key dimensions and tolerances to keep proposals practical and consistent. Case retrieval then compares the target task with prior jigs to surface locator schemes and clamp arrangements that worked well under similar loads and materials. Together, these complementary strategies shrink search time, raise confidence in selections, and transform scattered documents into an actionable stream of guidance that moves the wing spar jig from idea to validated design.

Ontology-Based Semantic (OBS) Retrieval Example: When the query centers on the concept wing spar, the ontology opens a wider map of meaning that naturally pulls in connected ideas such as wing rib, stringer, wing skin, and fuselage frame. Each of these related concepts can be searched as a keyword to broaden discovery beyond a single term, which raises recall without sacrificing clarity. The same ontology also sharpens focus when precision matters. For a request like section size of aluminum pallet, the system accepts attribute values that define intent, for example stiffness marked as strong or general, and it can confine unit length within a selected weight range. By pairing semantic expansion with targeted attribute constraints, the search moves effortlessly from broad exploration to disciplined filtering. The result is a streamlined path to the most relevant guidance, where rich context reveals what to consider and smart limits deliver exact matches for the design task at hand.

Example of Rule-Based Inference (RBI) Retrieval: When the user inquiries about the “dimension relationship of the quadrilateral frame of the assembly jig of the wing spar,” the knowledge type item in the query information model is “method and rule class.” Therefore, the rule-based inferential retrieval is selected. Since the three dimensions of the quadrilateral frame are relevant, the following rules are established in advance in the knowledge base: if \(A \in \left( {0,a} \right)\) then B, C, else if \(A \in \left( {a,b} \right)\) then B, C,……..,else B, C. When searching, the user can limit the range of parameters so that relatively accurate results can be obtained quickly, and the retrieval example is shown in Table 2.

Table 2 Example of reasoning retrieval based on rules.

Table 2 illustrates how rule-based retrieval narrows candidates for the wing spar jig by linking dimensional rules with user constraints. The query is split by model families I and II, and each family lists frame series such as 14a, 16a, 16b, 18a, and so on. For several entries, dimensions A and B are known while C is left to be calculated by the rule engine, which applies the relations among the three sides to complete the geometry. The table also records the load class as weight one or weight two under a standard test load of one-hundred-kilogram force, and returns a test value that reflects predicted performance for the chosen geometry. Within Model I, moving from lighter to heavier load classes generally raises the test value, while parameter choices that increase span or section tend to lower or stabilize the result across the series. Model II entries show lower test values under comparable conditions, which suggests greater stiffness or better compliance with the design rules for larger frames. In practice, a designer can set ranges for A and B, select a weight class, and let the system infer C and return the best fitting candidates with their expected test values.

Case-Based Reasoning Instance (CBRI) Retrieval: When the user queries “an example of the structural form of the skeleton of the aircraft wing spar jig frame,” the query analyzer converts it into a query information model as:

IM=<

RF = {“Instance” “Model”},

KT=“Design Instance Class”,

CS= {“Aircraft Wing Spar” “Jig Frame” “Clamp” “Positioner” “Skeleton” “Structure”},

CV=“ ”,

AC=“ ”>

Since the knowledge type (KT) is “design instance class,” the retrieval method based on case reasoning will be triggered. The system will calculate the similarity between the target instance and the attributes of existing cases, including work opening, stiffness, size, etc., and return the instance with the most considerable similarity to the user. The architecture of the knowledge management system for aircraft assembly decision making using KRP shown in Fig. 7.

Fig. 7
figure 7

KRP-enabled decision architecture for aircraft assembly: The query analyzer maps requests to an information model and, when the knowledge type is design instance class, routes them to case-based reasoning (CBRI).

Performance analysis

Data collection followed a multi-source design tailored to wing-spar tooling decisions. Primary materials comprised PDM exports (part metadata, bills of materials, revision histories), CAD-linked drawings (PDF/DXF), process sheets and work instructions, torque and tolerance tables, non-conformance reports with dispositions, lessons-learned logs, and prior tooling design reports; a domain-agnostic literature set on cloud databases was added to stress-test generalization. Stratified sampling by document type, recency, and metadata completeness guided inclusion, which required machine-legible text or successful OCR, identifiable part or process context, and resolvable provenance. Graded corpora of 100, 150, 270, 350, and 420 documents supported scalability analyses, while a separate set of 500–900 documents underpinned stress testing. The dataset comprises twenty targeted content searches that simulate real decisions in aircraft assembly and tooling design. Eight searches use ontology based semantic retrieval, six use rule-based inference, five use case-based reasoning, and one blends case reasoning with rule inference as shown in Table 3. Accuracy is computed as the proportion of retrieved items or computed values that match verified references from the knowledge base and validated design records. The overall mean accuracy reaches 93.09 percent with a median of 93.5 percent, indicating stable performance across diverse query types. Notable high points include determination of aperture definitions for five-hole categories at 96.1 percent and the derived solution for the unknown frame dimension C at 96.5 percent. The hybrid integration delivers the top score at 96.9 percent when generating a composite fixture recommendation. The lowest accuracy appears in historical material selection for the jig frame at 87.6 percent, which reflects legacy records that predate current ontology terms. Ontology expansion improves recall for extended queries such as design of wing assembly at 93.8 percent, while structured constraints narrow deviations in alignment and clamp parameters to within precise ranges.

Table 3 Outcomes from KRP driven content search supporting aircraft assembly decisions.

Method level trends show average accuracy of 92.24 percent for ontology guided searches, 93.72 percent for rule inference, 92.94 percent for case reasoning, and 96.9 percent for the integrated approach. These figures suggest that explicit rules excel when dimensions, loads, and sequences are tightly constrained, as seen in the consistent rise of test values with increasing load and in fast computation of missing geometric variables. Ontology led queries perform strongly for conceptual, structural, and attribute questions, especially where hierarchical relations and controlled vocabularies reduce ambiguity, exemplified by reliable ranges for wing skin clamping and hole alignment deviation. Case reasoning proves most valuable for structural exemplars and adjustment tasks, such as locator pin offsets within zero point zero five millimeters, where similarity scoring on quantitative and qualitative attributes guides reuse with minimal revision. The hybrid path capitalizes on complementary strengths by using case similarity to frame design intent and rules to finalize admissible values, which explains the highest confidence outcome. Together, these results indicate that an adaptive retrieval strategy can deliver accurate and explainable guidance for aircraft assembly decisions while highlighting specific areas, such as legacy material records, where curation will further raise precision.

This study has meticulously assessed the accuracy of the proposed KRP by employing key metrics, namely precision, recall, and F-measure52. These metrics serve as crucial indicators of accuracy, encapsulating various factors that influence the effectiveness of the retrieval system. By evaluating accuracy through these metrics, this research aims to provide a comprehensive understanding of the proposed KRP’s efficacy in retrieving relevant knowledge, thereby contributing to advancements in KRP.

(1) Precision: Precision is an essential metric in data analysis, representing the ratio of relevant data to the overall data set conditioned for detection. This metric provides crucial insights into the accuracy and reliability of a detection system or algorithm. Precision is calculated by dividing the number of relevant data points by the total number of data points under consideration, offering a quantifiable measure of how effectively a system identifies pertinent knowledge.

$${\text{Precision = }}\frac{{\text{Number of Retrieved Relevant Document}}}{{\text{Number of Document Retrieved}}}$$

(20)

(2) Recall: Recall, an essential metric in data analysis and detection systems, encapsulates the ratio between relevant data successfully identified by a detection process and the total relevant data available. This metric provides critical insights into the comprehensiveness and effectiveness of a detection system’s ability to capture all pertinent knowledge. Calculated by dividing the number of relevant data points correctly identified by the total number of relevant data points, recall quantifies the system’s capability to avoid missing important knowledge.

$${\text{Recall = }}\frac{{\text{Number of Retrieved Relevant Document}}}{{\text{Total Number of Document Retrieved in Collection}}}$$

(21)

(3) F-Measure: The F-Measure, a fundamental metric in data analysis and evaluation, harmonizes precision and recall into a single composite value. Derived from the harmonic mean of precision and recall, the F-Measure encapsulates the balance between these two critical aspects of detection performance. Typically, the value of beta in the F-Measure formula is set to 1, emphasizing equal importance between precision and recall. By considering both precision and recall simultaneously, the F-Measure provides a comprehensive assessment of a detection system’s overall effectiveness.

$${\rm{F – Measure = 2 \times }}\frac{{{\rm{Precision \times Recall}}}}{{\rm{Precision + Recall}}}$$

(22)

Five carefully designed experiments evaluated the effectiveness of the proposed KRP across collections that document the tooling design of the aircraft wing spar. Table 4 and Fig. 8 summarize performance on these corpora and reveals how the approach scales from modest libraries of one hundred documents to extensive repositories of four hundred and twenty documents. Each collection contains design principles, dimensional constraints, process notes, and validated cases that together represent the practical knowledge used in aircraft assembly. The evaluation focuses on the system’s ability to surface relevant guidance with clarity, maintain precision when terminology varies across sources, and preserve context when queries span multiple design concerns. Results show consistent improvements in relevance and retrieval precision as the framework adapts its use of ontology guided semantics, rule-based reasoning, and case informed evidence to the size and heterogeneity of the corpus. By testing across varied document volumes, the study demonstrates robust performance in both narrow and broad searches and establishes a dependable foundation for future refinement of retrieval strategies tailored to aerospace tooling design. These findings support more confident and timely decisions in wing spar assembly and point to meaningful advances in aircraft manufacturing methodology.

Table 4 Performance analysis of the proposed KRP over the tooling design of aircraft wing spar concept.
Fig. 8
figure 8

Performance analysis (Number of Documents vs Accuracy).

Table 5 and Fig. 9 present a rigorous performance analysis of an innovative knowledge retrieval algorithm applied to literature on cloud databases. The evaluation spans collections that range from five hundred to nine hundred documents, allowing the study to probe both moderate scale corpora and larger, more varied repositories. Within each collection the algorithm identifies definitions, architectural patterns, consistency models, indexing strategies, and security practices that are central to cloud database management. The analysis emphasizes two outcomes that matter most to practitioners and researchers alike, namely the ability to return highly relevant passages with minimal noise and the stability of precision as the document volume grows. Results indicate that relevance remains strong across all tested sizes and that precision degrades only marginally as collections expand, which suggests sound generalization beyond narrow test sets. By mapping performance across graded volumes, the investigation offers clear guidance on where the algorithm excels and where tuning may yield further gains, laying a practical foundation for refined retrieval techniques in cloud database management and meaningful progress in cloud computing practice.

Table 5 Performance Analysis of the proposed KRP over the documents.
Figure 9
figure 9

KRP performance (Accuracy) analysis compare with traditional method.

Insights from Table 5 and Fig. 9 show that the accuracy of the proposed knowledge retrieval algorithm varies clearly with the number of documents used in the experiments. Performance shifts as the corpus grows from one hundred to five hundred items, reflecting how larger and more diverse collections challenge matching, ranking, and consolidation of results. Figure 10 deepens this view with a relevance score comparison of three retrieval practices: Ontology Based Semantic (OBS), Ontology Based Semantic with Rule Based Inference (OBS+RBI), and the full integration of Ontology Based Semantic with Rule Based Inference and Case Based Reasoning Instance (OBS+RBI+CBRI). Across all five corpus sizes, the integrated approach delivers the highest relevance scores, the pair of Ontology Based Semantic with Rule Based Inference follows closely, and Ontology Based Semantic alone trails by a measurable margin. The widening advantage at larger document counts suggests that the combination of semantic context, explicit rules, and instance evidence provides stronger guidance when documents span multiple levels of detail and vocabulary, leading to more reliable retrieval for complex engineering content.

Fig. 10
figure 10

Relevance score analysis between OBS, OBS+RBI and OBS+RBI+CBRI.

Figure 10 presents a clear comparison of KRP that combines Ontology Based Semantic (OBS), Rule Based Inference (RBI), and Case Based Reasoning Instance (CBRI) with approaches that use only Ontology Based Semantic or the pair of OBS and RBI. The blended strategy that unites all three techniques delivers the strongest performance, as shown by consistently higher relevance scores across a representative set of assembly queries. Ontology Based Semantic anchors the meaning of terms and reduces ambiguity, RBI enforces design logic and dimensional constraints, and Case Based Reasoning Instance supplies proven solutions from similar projects. When these elements operate together, the system retrieves guidance that is both context aware and decision ready, outperforming the other configurations that lack either rule reasoning or instance evidence. The relevance score analysis in Fig. 10 underscores this advantage, demonstrating reliable gains in precision and usefulness for aircraft tooling design decisions.

The study evaluates knowledge retrieval across carefully assembled document sets that range from one hundred to five hundred items, creating a thorough testbed for understanding performance under changing corpus sizes. By varying the number of documents, the analysis reveals how configuration choices influence recall, precision, and the stability of relevance rankings when queries span conceptual definitions, procedural guidance, and detailed design evidence. Smaller collections highlight sensitivity to vocabulary coverage and synonym handling, while larger collections expose the importance of robust indexing, clear ontology alignment, and resilient ranking strategies that can separate useful guidance from background noise. The results show that tuning query interpretation and attribute constraints has a measurable effect on both accuracy and response time, and that balanced weighting of semantic cues, rule logic, and instance evidence provides consistent gains as volume grows. This graded evaluation produces practical design rules for future systems, indicating which parameter settings and data curation practices deliver the most reliable outcomes for specific engineering domains. In doing so, the study establishes a clear path toward optimized retrieval practices that remain effective as repositories expand and diversify.

Analysis in Table 6 shows clear gains in precision, recall, F measure, and overall accuracy delivered by the proposed system when compared with established alternatives. The advantage arises from a mature knowledge management practice that orders documents through coordinated syntax oriented and semantic oriented strategies, so that meaning, terminology, and structure align before ranking and retrieval occur. This orchestration reduces noise, strengthens query intent matching, and elevates the most informative passages for aircraft tooling design and related engineering topics. Precision improves because irrelevant items are screened early, recall rises as concept expansion and relation mapping surface valid variants, and F measure benefits from the balanced rise in both dimensions. Overall accuracy follows the same positive trend, reflecting stable performance across different corpus sizes and content types. Beyond metrics, the result is a collection that feels organized and accessible, where targeted guidance appears quickly and consistently. Such performance marks a meaningful advance in knowledge retrieval methodology and sets a practical foundation for efficient knowledge management across diverse technical applications.

Table 6 Performance analysis.

Figure 11 compares the average inference time of the baseline knowledge-based system and the proposed KRP-based decision-making system as the knowledge base size \(\mid K\mid\) increases from 1,000 to 20,000 rules and facts. Across the entire range of \(\mid K\mid\), the KRP-based system exhibits a markedly lower growth in inference time, suggesting a more favorable computational behavior for aircraft assembly tooling design queries. In general, the inference time can be expressed as a function of the knowledge base size and the input data size \(\mid D\mid\), i.e:

$$T = f(\rm{\mid }K\rm{\mid },\rm{\mid }D\rm{\mid }),$$

(23)

where \(T\) denotes the average inference time. Empirically, the results indicate that:

$$T_{KRP} (\rm{\mid }K\rm{\mid },\rm{\mid }D\rm{\mid }) < T_{base} (\rm{\mid }K\rm{\mid },\rm{\mid }D\rm{\mid }) \, \forall \rm{\mid }K\rm{\mid } \in [1000,20000],$$

(24)

Fig. 11
figure 11

Inference time vs. knowledge base size Al-based decision-making for aircraft tooling design.

Which demonstrates that the proposed KRP algorithm achieves improved scalability and more efficient handling of complex, knowledge-intensive queries in the context of aircraft product assembly decision-making.

Figure 12 presents the throughput characteristics of the AI-based decision-making system as the number of concurrent users increases, highlighting a clear performance gap between the baseline architecture and the proposed KRP-based framework. The baseline system exhibits a pronounced degradation in throughput beyond approximately 20 users, indicating limited scalability under multi-user conditions. In contrast, the KRP-based architecture sustains a higher query processing capacity across the entire evaluated load range, thereby offering more robust support for near real-time aircraft product assembly decisions. This behavior can be expressed as:

$$\Theta_{KRP} (u)> \Theta_{base} (u) \, \forall u \ge 20$$

(25)

Fig. 12
figure 12

Throughput vs. concurrent users Al-based knowledge retrieval for aircraft assembly.

Where, \({\Theta }_{\text{KRP}}(u)\) and \({\Theta }_{\text{base}}(u)\) denote the throughput (queries per second) of the KRP-based and baseline systems, respectively, as a function of the number of concurrent users \(u\). The superior throughput profile of the KRP-based system underscores the effectiveness of the developed knowledge retrieval algorithm in mitigating contention, optimizing resource utilization, and sustaining responsive decision support in collaborative aircraft tooling design environments.

Figure 13 compares the memory consumption of the baseline knowledge-based system and the proposed KRP-based knowledge retrieval architecture as a function of the knowledge base size \(\mid K\mid\) (number of rules/facts). For all evaluated configurations, the KRP-based system consistently requires less RAM than the baseline for the same \(\mid K\mid\), indicating more compact internal representations of rules, facts, and ontological entities. This improvement can be expressed as:

$$M_{KRP} (|K|) < M_{base} (|K|) \, \forall |K| \in [|K_{\min } |,|K_{\max } ]$$

(26)

where \({M}_{\text{KRP}}(\mid K\mid )\) and \({M}_{\text{base}}(\mid K\mid )\) denote the memory usage of the KRP-based and baseline systems, respectively. The observed reduction in memory footprint is attributed to optimized indexing structures and more efficient working memory management during ontology-based retrieval, rule firing, and case-based reasoning, which together enhance the scalability of the AI-based decision-making system for aircraft tooling design.

Fig. 13
figure 13

Memory usage vs. knowledge base size Al-based decision-making system with KRP.



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