Overview of the research approach

As illustrated in Figure 1, this research started with identifying the research topic through examining the literature, and then built the translation method based on NLP techniques followed by evaluations. Figure 1 shows the logical sequence of the steps, the research was carried out with iterations where the evaluation led to improvement in the method.

Figure 1. Research overview.

The method development started with the analysis of the two languages and the analysis of the structure of reference manuals. This informed the selection of NLP techniques. Figure 2 gives an overview of the steps taken in developing the method.

Figure 2. The steps of developing the mapping method.

The method evaluation and application was on three levels:

• • Level 1: evaluates the performance of the method . The Pearson correlation coefficient and the Spearman correlation coefficient were used to measure the capability of NLP-based models for calculating the similarity. Three datasets (MC, RG, and Agirre) were used for word mappings and the STSBenchmark dataset for sentences mapping (see Sections “The combined RW and GloVe models” and “The DeBERTa ensemble”).

• • Level 2: checks the mapping results of the language elements of EXPRESS and OWL were carried out and compared to the literature (see Section “The mapping results of language elements and discussion”).

• • Level 3: applies the proposed method to a data model which presents the mapping results for 12 EXPRESS declarations about high-level product definition (see Section “Application to the mapping of data models”).

The language reference manual analysis

The mapping process finds the pairs of similar language expressions, and thus, the documents that describe the definitions and usage of the two languages are analyzed. The language reference manuals compared in this research are “Industrial automation systems and Integration – Product data representation and exchange – Part 11: Description methods: The EXPRESS language reference manual” (ref. no. ISO 10303-11:2004(E)) and “OWL 2 Web Ontology Language Structural Specification and Functional – Style Syntax” (2nd Edition). Both documents define the languages, specifying their elements in terms of representation, meaning, and usage. The two manuals are the input of the proposed method for the semantic similarity analysis.

The EXPRESS manual consists of 16 sections and the OWL 2 manual has 11 sections, excluding the appendix. Section/subsection headings and the descriptive text under these headings are analyzed for each language and subsequently compared. The headings consist of words and short phrases, reflecting not only the essence of the sections’ content but also the language elements that allow an unambiguous data definition and specification of constraints to construct the syntax. For example, both headings “Data types” in the EXPRESS document and “Datatype Maps” in the OWL 2 document show that the sections define the data types. Their subheadings “String data type” and “Strings”, respectively, describe a particular data type – String. The semantic similarity of the heading directly points out the mapping between the elements.

The descriptive text under each section/subsection describes the language elements in detail. Take subtype in EXPRESS and subclass in OWL 2 for example. From the two words, it is not obvious that the two can be mapped to each other. The following two paragraphs from the manuals suggest a possible mapping because both indicate a “child–parent” hierarchical relation.

Both the headings and the text can be analyzed by NLP techniques but need different models, because headings are short whereas text consists of sentences. An examination of the manuals revealed that for the elements with similar functions their headings are also at similar levels of hierarchy, for example subtype and subclass. The heading hierarchy is, therefore, used as an extra dimension for mapping analysis.

RW and GloVe for heading similarity analysis

The headings of the manual sections are composed of single or few words. The semantic matching of two headings can be handled by NLP models for word similarity tasks. Random Walks (RW) (Goikoetxea et al., Reference Goikoetxea, Soroa and Agirre2015) and Global Vectors for Word Representation (GloVe) (Pennington et al., Reference Pennington, Socher and Manning2014) are two such models with outstanding performance.

The RW model

The RW model is obtained through two stages, that is establishing the corpus by random walk in WordNet (Miller, Reference Miller1995) and training on the established corpus using Word2Vec (Mikolov et al., Reference Mikolov, Chen, Corrado and Dean2013). WordNet is a large lexical database of English designed at Princeton University, which is a network of meaningfully related words and concepts. Nouns, verbs, adjectives, and adverbs are grouped into sets of cognitive synonyms (synsets) and these synsets are further interrelated by means of conceptual-semantic and lexical relations. In this sense, the adjacent words in the established corpus from WordNet are interlinked with semantics and thus the word vectors trained on the corpus can better capture the semantic relationship between words. The random walk algorithm for establishing the corpus is described in Algorithm 1 based on Goikoetxea et al. (Reference Goikoetxea, Soroa and Agirre2015).

Two neural network models from Word2Vec, that is CBOW and Skip-gram, are then trained with several iterations of random walks over WordNet (Mikolov et al., Reference Mikolov, Chen, Corrado and Dean2013). CBOW predicts the current word based on the context, whereas Skip-gram predicts surrounding words given the current word (Mikolov et al., Reference Mikolov, Chen, Corrado and Dean2013).

DeBERTa for text similarity analysis

DeBERTa (He et al., Reference He, Liu, Gao and Chen2021) is a pre-trained neural language model, which enhances the BERT (Devlin et al., Reference Devlin, Chang, Lee and Toutanova2019) model using two novel techniques: a disentangled attention mechanism and an enhanced mask decoder. Two main stages can be summarized for establishing the model.

• Stage 1: improve the architecture of BERT. The disentangled attention mechanism makes use of relative positions as well as the contents of a word pair. It represents each word in two vectors encoding its content and position, and computes the attention weights among words using disentangled matrices. The disentangled self-attention with relative position bias is calculated using Eq. (3). $\tilde{A}_{i, j}$ is the attention score from token i to token j. Q_i^c and K_j^c are the i-th and j-th rows of Q^c and K^c which are two projected content vectors. Q_δ^r _(i.j) and K_δ^r _(j.i) are the δ(i,j)-th and δ(j,i)-th rows of Q^r and K^r which are two projected relative position vectors, regarding the relative distances δ(i,j) and δ(j,i).

  (3)$$\eqalign{ {\widetilde{A}} _{i, j} &= Q_i^c K_j^{cT} + {Q_i^c K_{\delta ( i, j) }^r}^T + Q_{\delta ( j, i) }^r K_j^{cT}, \cr H_o &= {\rm softmax}\left({\displaystyle{{\widetilde A } \over {\sqrt {3{d}} }}} \right)V_c.} $$

• As the decoding component of DeBERTa, the enhanced mask decoder then captures the absolute positions of words as complementary information when decoding the masked words. In this way, both relative and absolute positions as well as contents are used in the training stage.

• Stage 2: train the model. A virtual adversarial training algorithm, namely Scale-invariant-Fine-Tuning, is used for the training, which applies the perturbations to the normalized word embeddings to improve the stability.

Document preprocessing

In both manuals, language elements are mainly described by text. There are also figures, tables, and codes which are mostly examples to help understanding. These have been removed from the documents for this research.

Each section or subsection targets a particular language element type or language element. The length of the text for each section/subsection varies by up to more than 500 words (seen in Fig. 4a). This increases the difficulty of semantic similarity calculation by NLP models, as a very long text could lead to inaccurate semantic extraction. To make the length of each section/subsection text in the two manuals relatively short and balanced, this research adopts Lead-3 algorithm to extract the representative text without losing semantic information. Lead-3 is a baseline method for text summarization and relies on the observation of the semantic distribution of the text that the first three sentences of a text can generally summarize the main semantic information of the whole text. Lead-3 was chosen because it is simple to implement and capable of obtaining effective results (Nallapati et al., Reference Nallapati, Zhai and Zhou2017). After processing the manuals, most of the texts are within 100 words, as shown in Figure 4b.

Figure 4. Words count of (a) before and (b) after text summarization.

The preprocessed documents from the two manuals are used for analyzing semantic similarities. The words of the headings are collected as input to the heading similarity analysis model; the summarized paragraphs are the input to the text similarity analysis model; and heading levels are the input to the heading hierarchical similarity analysis model.

Analysis of heading similarity based on RW and GloVe

Two aspects of a language element impact the translation of manual headings:

• • Keywords: RW focuses on analyzing words through their embedded context. For example, both subtype and subclass indicate a hierarchical relation.

• • Synonyms: GloVe performs well on these word analogies, such as subtype and subclass or entity and class.

To include both aspects, this paper combines RW and GloVE to analyze the semantic similarities of headings. The headings from both documents are the input to the RW and GloVe models. Two word-embedding matrices are then generated, denoted W ^RW and W ^GloVe, respectively. Given two words w_i and w_j, their similarity is calculated as follows.

• Step 1: locate the word in the word-embedding matrix. As Eq. (4) indicates, the word vectors of the two input words are found from the matrices W ^RW and W ^GloVe.

  (4)$$\eqalign{& vec_i^{{\rm RW}} = W^{{\rm RW}}( w_i) , \;vec_j^{{\rm RW}} = W^{{\rm RW}}( w_j) , \;\cr & vec_i^{{\rm GloVe}} = W^{{\rm GloVe}}( w_i) , \;vec_j^{{\rm GloVe}} = W^{{\rm GloVe}}( w_j), } $$

where vec_i ^RW and vec_j ^RW are the word vectors of w_i and w_j in the matrix W ^RW, and vec_i ^GloVe and vec_j ^GloVe are the word vectors of w_i and w_j in the matrix W^GloVe.

• Step 2: compute the similarity in the individual model. For element i in EXPRESS and element j in OWL 2, two semantic similarity values of comparing their headings are computed by Eq. (5). sim _RW and sim _GloVe denote the values from the RW model and GloVe model, respectively.

  (5)$$\eqalign{& sim_{_{{\rm RW}} }^{ij} = {\rm cosin}( vec_i^{{\rm RW}} , \;vec_j^{{\rm RW}} ), \cr & sim_{_{{\rm GloVe}} }^{ij} = {\rm cosin}( vec_i^{{\rm GloVe}} , \;vec_j^{{\rm GloVe}} ), } $$

where cosin(v_i,v_j) is the function calculating the cosine similarity between the two vectors v_i and v_j.

• Step 3: compute the final heading similarity by averaging the two semantic similarity values from step 2.

  (6)$${ HSim}_{ij} = \displaystyle{1 \over 2}( {sim}_{{\rm RW}}^{ij} + {sim}_{_{{\rm GloVe}} }^{ij} ). $$

When there are multiple words in the headings, the word vectors in step 1 are the averaged vectors of all the words.

Text similarity analysis based on DeBERTa

The text under the headings explains the language elements in terms of their definitions, usage, and characteristics. After preprocessing the documents with the Lead-3 algorithm, the length of the text in each section/subsection is within 100 words. Similarity analysis on sentence level is carried out with a DeBERTa model. DeBERTa model performs well in classification and regression tasks but tends to produce overconfidence predication when handling samples out of the distribution. To overcome this problem and produce accurate text similarity results, the DeBERTa ensemble proposed by Jian and Liu (Reference Jian and Liu2021) is applied, which adds a predication layer to the original DeBERTa. This additional layer is setup with two neurons, the outputs of which are the mean of the predicated values and the variance. To enhance the discrimination of learned results, the negative log-likelihood loss function shown as Eq. (7) is employed, where σ² is the variance, μ is the mean of the predicated values, and y is the actual labeled value.

(7)$${\rm NLL} = \displaystyle{{\log \sigma ^2} \over 2} + \displaystyle{{( y-\mu ) } \over {2\sigma ^2}}^2.$$

The models with added layer are further gathered to build an ensemble to improve the reliability, which are trained with the same data but set with different initial weights. As illustrated in the framework (referred to Fig. 3), the ensemble consists of five models of the same structure to balance the consumed resource and the expected performance. In this case, the text similarity is the aggregated result of the five models, as shown in Eq. (8). TSim_t^ij is the similarity score of the two sentences i and j from the t-th model.

(8)$${TSim}_{ij} = \displaystyle{1 \over 5}\sum\limits_{t = 1}^5 {{TSim}_t^{ij} }. $$

Heading hierarchical similarity analysis

The heading hierarchy reflects the granularity of language elements. According to the examination of the documents, if the functions of a pair of elements from the two languages are similar, their headings are usually at similar levels. In this case, this paper suggests taking the heading hierarchical similarity into consideration for the mapping between EXPRESS and OWL 2. The analysis follows three steps.

• Step 1: obtain the heading hierarchy sets. Through the statistics of the official documents, two sets (denoted headinglevel_EXPRESS for EXPRESS and headinglevel_OWL for OWL 2 separately) are established, which consists of the heading levels of all the sections/subsections.

• Step 2: compute the heading level difference. Given element i in EXPRESS and element j in OWL 2, the difference is computed by Eq. (9), where headinglevel_EXPRESS[i] and headinglevel_OWL[j] are the heading levels of the sections that describe element i and j, respectively.

  (9)$${diff}_{ij} = \vert {headinglevel_{EXPRESS}[ i] -headinglevel_{OWL}[ j] } \vert. $$

• Step 3: calculate the heading hierarchical similarity. Linear normalization is used to limit the value to [0,1]. The similarity is calculated by Eq. (10) where d⁺ is the maximum level difference and d ⁻ is the minimum level difference.

  (10)$${LSim}_{ij} = \displaystyle{{d^ + {-}{diff}_{ij}} \over {d^ + {-}d^-}}.$$

Similarity aggregation based on fuzzy AHP-SAW

The three types of similarity values contribute to the overall similarity between the language elements, but their contributions are not of equal importance. Thus, their weights are determined by Analytic Hierarchy Process (AHP) (Saaty, Reference Saaty1980) first and then aggregated by a simple additive weighting (SAW) method. Both AHP and SAW are multiple criteria decision-making (MCDM) methods. AHP calculates the weights by pairwise comparison which makes it outperform most other methods. SAW produces an aggregated result by combining the weights of the criteria and the values under the criteria. It is a simple and practical method, which offers a transparent and understandable calculation process for the ranking results (Kaliszewski and Podkopaev, Reference Kaliszewski and Podkopaev2016; Wang, Reference Wang2019). The following steps calculate the weights of the three types of similarities and the overall similarity values of the language elements. Steps 1 and 2 come from AHP, while step 3 draws on SAW.

• Step 1: establish the similarity pairwise comparison matrix F = [c_st]_n × n. n is the number of types of similarities (n = 3 in our case), and s_st is a value from 1 to 9 representing the relative importance of type s over type t.

• Step 2: obtain the weights of the similarity types. The weight of similarity type i is computed by Eq. (11) where geometric mean is applied.

  (11)$$w_s = \displaystyle{{\root n \of {\prod\nolimits_{t = 1}^n {c_{st}} } } \over {\sum\nolimits_{s = 1}^n {\root n \of {\prod\nolimits_{t = 1}^n {c_{st}} } } }}.$$

• Step 3: calculate the overall similarity values. Given element i in EXPRESS and element j in OWL 2, their similarity value is calculated by the SAW method shown in Eq. (12). The result is further translated by Eq. (13) with the three types of similarity in this research, where w _head, w _text, and w _level are the weights of heading, text, and hierarchy, respectively.

  (12)$${OSim}_{ij} = \sum\limits_{s = 1}^n {w_s \times {sim}_s^{ij} }, $$
  (13)$${OSim}_{ij} = w_{{\rm head}}{HSim}_{ij} + w_{{\rm text}}{TSim}_{ij} + w_{{\rm level}}{LSim}_{ij}.$$

The combined RW and GloVe models

As the headings in the language manuals consist of nouns, three datasets targeted at the similarities of nouns were used to verify the performance of the model:

• • MC consists of 30 pairs of nouns with their semantic similarities that were judged by 38 native English speakers (Miller and Charles, Reference Miller and Charles1991).

• • RG contains 65 word pairs collected, each associated with 51 human subject for the judgement on their similarity (Rubenstein and Goodenough, Reference Rubenstein and Goodenough1965).

• • Agirre includes 203 word pairs using search engine methods to calculate the similarities (Agirre et al., Reference Agirre, Alfonseca, Hall, Kravalova, Pasca and Soroa2009).

Tables 2 and 3 show the Pearson correlation coefficient and the Spearman correlation coefficient obtained on the three datasets. The two indicators are often used to measure the capability of NLP models for calculating the similarity. The last column lists the mean value. With a Pearson correlation value of 0.854 and a Spearman correlation value of 0.880, it can be seen that the combined model performs better than individual RW and GloVe on the three datasets of nouns.

Table 2. Pearson correlation results

Table 3. Spearman correlation results

The DeBERTa ensemble

The efficiency of the DeBERTa ensemble for text similarity has been proved by comparing with BERT, DeBERTa, and M-MaxLSTM-CNN (Tien et al., Reference Tien, Le, Tomohiro and Tatsuya2019) models on STSBenchmark dataset. This dataset contains 8628 labeled sentence pairs which have been extracted from image captions, news headlines, and user forums (Cer et al., Reference Cer, Diab, Agirre and Specia2017). Each sentence pair is labeled with a score from 0 to 5, denoting how similar the two sentences are in terms of semantic meaning.

Table 4 shows the Spearman correlation coefficient and Pearson correlation coefficient scores. It can be seen that the performance of the proposed model is close to DeBERTa and better than the rest two models.

Table 4. The scores of the DeBERTa ensemble

The mapping results of language elements and discussion

Table 5 shows the mapping results of EXPRESS to OWL 2 by applying the proposed multiple similarity-based method. The first column lists the language elements of EXPRESS. The second column presents the OWL 2 mappings from Krima et al. (Reference Krima, Barbau, Fiorentini, Sudarsan and Sriram2009) and Barbau et al. (Reference Barbau, Krima, Rachuri, Narayanan, Fiorentini, Foufou and Sriram2012). Their work provides the most mappings among the reviewed research (as seen in Table 1) and thus was chosen by this research to validate the method. The third column presents the four OWL sections of the top similarity scores as the mapping candidates. The remaining columns show the similarity scores of the headings (HSim), text (TSim), heading hierarchies (LSim), and the overall (OSim) with their weights below. Three digits are shown in Table 5, but more were used for calculation.

Table 5. Mapping results for simple elements

For some EXPRESS elements that express complex information, for example bag and set, no one-to-one mapping in OWL exists and a combination of several OWL elements is required. The existence of multiple candidates makes the combination feasible. The results are shown in Table 6.

Table 6. Mapping results for complex elements

It can be seen from the tables that most mapped OWL 2 elements from Krima's work are covered by the top four identified candidates of this research (as highlighted in bold) except array, select, and AND. Their mapping candidate sections have a lower rank. The method also finds the potential mapping sections for elements that are not included in Krima, as highlighted in italics in the table. For example, the top candidate for 4.5 Binary Data was the language element xsd:hexBinary locates. The mappings of INVERSE and CONSTANT are another two examples. For the logical data type, despite no feasible mapping in the first four candidate sections, the follow-up candidate “4.4 Boolean Values” provides a solution that both have TRUE and FALSE values as their domain. Because OWL 2 follows the Open World Assumption that every undefined item is considered as unknown, which corresponds to the third domain value of logical data type in EXPRESS, that is UNKNOWN.

Application to the mapping of data models

The language elements are used to establish data models. ISO 10303 provides a representation of product information with EXPRESS declarations to enable data exchange. For example, ISO 10303-41: Integrated generic resources: Fundamentals of product description and support (Part41 for short hereafter) specifies the generic product description resources, generic management resources, and support resources. The following entity is extracted from Part41. It is a collector of definitions of a product.

ENTITY product_definition_formation;

id : identifier;

description : OPTIONAL text;

of_product : product;

UNIQUE

UR1 : id, of_product;

END_ENTITY;

OWL has no standards for their definitions of product data. This allows users to define their own models but also leads to the difficulty of mapping an EXPRESS data model to an OWL data model. A solution is to extract the parts with similar semantics to EXPRESS declarations from OWL files. This research applies the proposed model to comparing the similarities in an example of a linear bearing in stamping outer ring (see the right upper part of Fig. 5). The STEP file was downloaded from an online CAD part database – LinkAble PARTcommunity (https://linkable.partcommunity.com/3d-cad-models/sso/khm-%E5%86%B2%E5%8E%8B%E5%A4%96%E5%9C%88%E5%9E%8B%E7%9B%B4%E7%BA%BF%E8%BD%B4%E6%89%BF-%E4%B8%8A%E9%9A%86samlo?info=samlo%2Flinear_bushings_ball_retainers%2Fkhm.prj&cwid=7526), which describes the category and geometry of a linear bearing. Its description conformed to the predefined data models provided by ISO 10303 series standards. The file was encoded in the format of ISO 10303-21: Implementation methods: Clear text encoding of the exchange structure (Part 21 for short), which is described according to ISO 10303-203: Application protocol: Configuration controlled design. ISO 10303-203 specifies an application protocol for exchanging configuration-controlled 3D product design data of mechanical parts and assemblies. Other parts of ISO 10303 such as Part41 constitute provisions of this standard. Figure 5 shows a segment of the file. This research takes use of the EXPRESS declarations in the example file, for example entities such as product_definition_formation as inputs of EXPRESS side.

Figure 5. A segment of the STEP file of the example product bearing.

The ontologies of the part were defined in OWL. Since there is no fixed format to describe a product, different descriptions could exist. For example, property of id: identifier can either be defined in OWL as an object data property linking to a class named identifier (as indicated in Fig. 6a) or as a data property in string type (as indicated in Fig. 6b). This research takes the two types of definition as the inputs from the OWL side.

Figure 6. Examples OWL expressions for Entity product_definition_formation: (a) using object property and (b) using data property.

The proposed model was run to match the segments in OWL to the EXPRESS declarations. In the first round, the OWL file defined in the way of Figure 6a was considered. Table 7 shows the OWL segments of top 4 similarities for entity product_definition_formation and entity product_definition_formation_with_specified _source. Appendix A presents the mapping results for 12 EXPRESS declarations about high-level product definition. In the second round, the OWL file defined as Figure 6b was considered (the result is listed in Appendix B). The results indicate that the best matched OWL segments have the highest similarities. In most cases, the parent-class or sub-class (e.g., product_definition_formation to product_definition_formation_with_specified_source or vice versa) or sibling-class (product_definition_context and product_concept_context) are identified as the secondary mapping. This is followed by those classes with similar properties, for example product_definition_formation and product both have property id and the former is also linked to the later via property of_product.

Table 7. Mapping result of OWL segments to two EXPRESS entities in the example