=Paper=
{{Paper
|id=Vol-3355/richardnordsieck
|storemode=property
|title=Towards Models of Conceptual and Procedural Operator Knowledge
|pdfUrl=https://ceur-ws.org/Vol-3355/richardnordsieck.pdf
|volume=Vol-3355
|authors=Richard Nordsieck,Michael Heider,Anton Hummel,Alwin Hoffmann,Jörg Hähner
|dblpUrl=https://dblp.org/rec/conf/semiim/NordsieckHHHH22
}}
==Towards Models of Conceptual and Procedural Operator Knowledge==
https://ceur-ws.org/Vol-3355/richardnordsieck.pdf
Towards Models of Conceptual and Procedural
Operator Knowledge
Richard Nordsieck1,* , Michael Heider2 , Anton Hummel1 , Alwin Hoffmann1 and
Jörg Hähner2
1
XITASO GmbH IT & Software Solutions, Austraße 35, 86153 Augsburg, Germany
2
Organic Computing Group, University of Augsburg, Am Technologiezentrum 8, 86159 Augsburg, Germany
Abstract
To increase the utility of semantic industrial information models we propose a methodology to incorporate
extracted operator knowledge, which we assume to be present in the form of rules, in knowledge
graphs. To this end, we present multiple modelling patterns that can be combined depending on the
required complexity. Aiming to combine information models with learning systems we contemplate
desired behaviours of embeddings from a predictive quality perspective and provide a suited embedding
methodology. This methodology is evaluated on a real world dataset of a fused deposition modelling
process.
Keywords
expert knowledge, information model, graph embedding
1. Introduction
On the one hand, standardised semantic information models (IMs) and standards for their hosting,
such as the Industry 4.0 asset administration shell, are gaining traction in the industrial internet
of things where they can be used to facilitate interoperability and data interchange between
different companies, production plants, lines or machines [1, 2, 3]. On the other, knowledge
graphs (KGs) are a popular data structure to integrate knowledge of multiple heterogeneous
sources [4, 5, 6]. Combined with approaches that allow reasoning over knowledge graphs,
e. g. for link prediction to facilitate knowledge graph completion, they are a logical choice for
semantic industrial information models [7, 8, 9]. However, the knowledge typically represented
in these industrial information models is of mostly factual and conceptual nature, reaching
the level of “knowledge of principles and generalizations” of Krathwohl’s taxonomy [10].
It concerns equipment [7, 9], material [7], process segments [7], parts [5], products [5, 7],
events [9], underlying measurements [11] and geospatial information [12] as well as relations
interconnecting these entities. Based on this information, use cases addressed range from
SemIIM’22: 1st International Workshop on Semantic Industrial Information Modelling, 30th May 2022, Hersonissos,
Greece, co-located with 19th Extended Semantic Web Conference (ESWC 2022)
*
Corresponding author.
$ richard.nordsieck@xitaso.com (R. Nordsieck); michael.heider@informatik.uni-augsburg.de (M. Heider);
anton.hummel@xitaso.com (A. Hummel); alwin.hoffmann@xitaso.com (A. Hoffmann);
joerg.haehner@informatik.uni-augsburg.de (J. Hähner)
0000-0003-3140-1993 (M. Heider); 0000-0003-0107-264X (J. Hähner)
© 2022 Copyright for this paper by its authors. Use permitted under Creative Commons License Attribution 4.0 International (CC BY 4.0).
CEUR
Workshop
Proceedings
http://ceur-ws.org
ISSN 1613-0073
CEUR Workshop Proceedings (CEUR-WS.org)
anomaly detection [8] over process monitoring [13, 8] to locating parts and equipment in plants
[12] and risk management [13]. We are not aware of the use of industrial IMs containing
extracted expert knowledge, which belongs to the more advanced conceptual, i. e. “knowledge
of models, theories, structure” [10], and procedural categories of knowledge. This knowledge
is of heuristics-like nature and usually obtained through multiple years of expertise. A more
detailed explanation of expert knowledge and procedural knowledge for the manufacturing
scenario investigated in this paper is given in Section 3.
Since expert knoweldge is playing a crucial role in many industrial day to day processes—
from the design of components to reparametrisation processes necessary to deal with quality
defects during production—and only available to a limited number of people, representing it
in a standardised way would be of great interest for the industry. Therefore, we propose that
including procedural knowledge would enhance the applicability of IMs in several ways:
1. a semantic integration between the what of given machinery and the how to operate it
2. suitability for predictive quality use cases, e. g. by utilizing the resulting knowledge
graphs, which would contain quantified knowledge, to increase the performance of
learning systems. This could lead to an increase in the ability to generalize and cope with
coarse data—both frequent challenges in industrial contexts
3. a standardised representation of procedural knowledge which would (1) enable the cre-
ation of digital process twins that could be supplied alongside machinery for operating
and training purposes, thereby reducing the impact of changes in a production line, (2)
provide a standardised way to combine it with varying kinds of knowledge from different
sources, e. g. physical limits of machinery provided by process engineering and (3) enable
the fusion of knowledge extracted by traditional [14] as well as data-based [15] methods
Based on an overview of related work (see Section 2) we explore how extracted tacit operator
knowledge available as rules can be incorporated in KGs serving as IMs by modelling patterns
(Section 3). Section 4 tries to answer the question whether these KGs are able to be embedded
in a form that benefits predictive quality use cases. Section 5 provides an outlook describing
the next steps towards realizing our vision of knowledge graphs containing extracted expert
knowledge as actionable rules while Section 6 concludes this paper.
2. Related Work
Characteristics of established industrial information models and the expected benefits of incor-
porating rules in these models are described in Section 1. While rules have, to the best of our
knowledge, not been directly represented in knowledge graphs used as industrial information
models, they have been frequently used in different semantic contexts.
Rule representation in graphs Representations of rules in graphs have been addressed by
Chein and Mugnier [16]. They explored how bi-coloured graphs can be used to encode condition
and conclusion of rules on both a general level as well as, optionally, for specific entities encoded
via attributes. However, their approach does not offer a way to provide quantifications to either
conditions or conclusions. Also, established embedding methods are not directly applicable
to bi-coloured graphs, which limits the usability of their approach for e. g. knowledge infused
learning.
Assisted Embeddings More often than being directly represented in graphs, logical rules
are used as auxiliary information for knowledge graph embeddings [17, 18]. Here, rules are
either provided by algorithm designers or domain experts to capture common sense knowledge
or automatically mined from knowledge graphs [18]. Zhang et al. [19] create relations based
on rules that load to an increase in embedding performance. Ringsquandl et al. [20] conclude
that the performance of KG completion can be increased by utilizing embeddings of events,
i. e. time-series data [9] during KG embedding. However, in contrast to the events or logical
rules employed in these approaches, rules founded on extracted operator knowledge frequently
contain quantifications of conditions or quantifications which makes them more complex and
unsuited to the described approaches.
Rule Representations in Embeddings It has been shown that “existential rules can be
exactly represented using convex regions of knowledge graph embeddings” [21]. While a
methodology that provides exact representation of general rules in embeddings would pro-
vide greatly helpful in evaluating the suitability of different methodological choices of rule
representation in knowledge graphs we cannot rely on Gutierrez’s methodology since the
rules containing the experts’ extracted knowledge are more complex than the existential rules
considered. Furthermore, representing rules in knowledge graphs as opposed to embeddings,
provides a significant benefit for information models as the representation is more direct and
can be independently accessed.
Establishing Embedding Quality Link prediction and entity classification are the standard
scenarios to evaluate embedding methods [22, 23, 24, 25, 19, 26, 27, 28, 29]. However, doubt has
been cast both on biases in the used datasets [30, 31, 32] as well as on the more general capability
of KG embeddings to capture semantics [33]. Therefore, behavioural testing of embedding
methodologies is gaining attention [34]. Since we are aiming at using embeddings not only
for link prediction but to improve the performance of learning systems, an evaluation of the
embeddings’ encoding of the required semantic information is necessary in our case.
3. Representations of Operator Knowledge in Industrial
Information Models
Based on a manufacturing scenario, this section will introduce modelling patterns for different
representations of expert knowledge along with an overview of their properties.
3.1. Representations
In manufacturing use cases, a high proportion of expert knowledge is tacit operator knowledge
which pertains to parametrisation of machinery. As such, it contains knowledge about both
conceptual relationships between process parameters and quality characterisitcs as well as
procedural behaviours that lead to the achievement of goals, i. e. how and in what order to adapt
process parameters to mitigate occurring quality defects and achieve a perfect parametrisation.
In this paper we focus on the aspect of how parameters are adjusted. This tacit operator
knowledge can be extracted by various methodologies [e.g. 14, 15] leading to rules at different
levels of abstraction. Also, information concerning the same problem might be available from
alternative sources such as process engineering documents or handbooks which could be
combined or contrasted with knowledge operators gained in practice. As such, adapting and
building on definitions for operator knowledge presented in [35], we inspect several modelling
patterns for representing the underlying knowledge at different abstraction levels that can be
combined at will. In the following, we will align our terminology with manufacturing scenarios
to increase the readability of examples.
From these modelling patterns, a fitting degree of abstraction can be chosen to either reflect
the kind of knowledge that is available or of the information models’ specific domain. This is
relevant since we expect that the higher complexity, i. e. through hierarchies, provides challenges
for embedding approaches. Avoiding unneeded complexity in the representation is therefore
likely to achieve better results. As such, we recommend choosing the highest abstraction level,
that is able to encode all present information. Note that the representations of higher abstraction
levels can be easily converted to representations of lower abstraction levels. Therefore including
operator knowledge of a different source which utilises a different abstraction level is still
possible.
3.1.1. Unquantified Rules
A rule at the highest level of abstraction, i. e. an unquantified rule, could be verbalised as If
quality characteristic q is unsatisfactory then adjust process parameter p. It can be viewed as an
implies relation between the condition quality characteristic q and the conclusion parameter p.
This corresponds to the triple notation of (head, relation, tail) common in knowledge graphs.
Adapting the definitions of [35] we define parameters 𝑝 ∈ 𝑃 and quality characteristics 𝑞 ∈ 𝑄.
This yields the triple 𝑟𝜂 = (𝑞, ⟨implies⟩, 𝑝). Whereas in [35] an index for the process iteration
was included, we omit it here for the sake of readability as it is not relevant for the contents
of this paper. A graphical representation of 𝑟𝜂 is shown in Figure 1a. A modelling alternative
would be a is a relation between 𝑞 and the semantic meaning of quality characteristics. However,
this semantic information is already encoded by the directed relation. Making it explicit would
only increase syntactic complexity and hierarchy.
3.1.2. Quantified Conclusions
Rules with quantified conclusions, i. e. parameters, 𝑟𝜌^ can be verbalised as If quality char-
acteristic q is unsatisfactory then adjust process parameter p by 𝜈 with 𝜈 ∈ R. Therefore,
𝑟𝜌^ = (𝜂𝑞,𝑝 , 𝜈) = (𝑞, ⟨implies⟩, 𝑝, 𝜈). Generally, we want to keep the representation as suc-
cinct as possible. Therefore, the representation of unquantified rules is extended to use 𝜈 as
a weight of the implies relation (cf. Figure 1b). Here, the quantified parameter 𝜌 ∈ P, where
P = {(𝜈, ⟨quantifies⟩, 𝑝) | 𝑝 ∈ 𝑃 and 𝜈 ∈ R} is implicitly modelled. We denote the rules of
quantified conclusions as 𝑟𝜌^ since several observations are aggregated into the quantification.
: process implies : quality : process implies : quality
parameter characteristic parameter : quantified process characteristic
parameter
(a) Graphical representation of 𝑟𝜂 , i. e. implies rela- (b) Graphical representation of 𝑟𝜌^ with weighted
tion between a quality characteristic and param- implies relation.
eter.
Figure 1: Graphical representation of modelling patterns for unquantified rules 𝑟𝜂 and rules with
quantified conclusions 𝑟𝜌^ .
3.1.3. Quantified Conditions
In addition to quantified parameters that serve as actionable recommendations for operators, the
conditions, i. e. quality characteristics, can also be quantified to arrive at more descriptive rules.
With quantified conditions, it is possible to represent more advanced concepts, e. g. for higher
defects in a specific quality characteristic, parameters need to be adjusted more substantially.
While in theory quantified quality characteristics could be used without quantified parameters,
it is not beneficial in practice since the conclusion of the rule would remain the same. As
such, we consider quantified parameters as a prerequisite of quantified quality characteristics.
Rules with aggregated quantified quality characteristics and parameters 𝑟o^,𝜌^ can therefore be
verbalised as If quality characteristic q is within 𝜇, then adjust process parameter p by 𝜈, where
𝜇 ∈ [𝑔, ℎ]. This results in the 5-tuple 𝑟o^,𝜌^ = (𝑞, 𝜇, ⟨implies⟩, 𝑝, 𝜈), that can be represented
as shown in Figure 2. Here, an explicit modelling of quantified parameters o ∈ O, with
O = {(𝜇, ⟨quantifies⟩, 𝑞) | 𝑞 ∈ 𝑄 and 𝜇 ∈ R} becomes necessary.
Strictly speaking this leads to a further indirection, since the implies relation now connects
the actual value of quantified parameter and quality characteristic, which are decoupled from
their semantic interpretation by a quantifies relation. Transformed into hierarchical triples this
yields:
𝑟o^,𝜌^ = ((𝜇, ⟨quantifies⟩, 𝑞), ⟨implies⟩, (𝜈, ⟨quantifies⟩, 𝑝))
3.1.4. Multiple Conditions
Sometimes a specific parametrisation is only relevant if multiple conditions align. These rules,
𝑟𝑞𝑛 , could be verbalised as If quality characteristic x and quality characteristic z are unsatisfactory,
then adjust process parameter p. For this modelling pattern, we omitted quantifications for the
sake of brevity. 𝑟𝑞𝑛 could be trivially encoded by having multiple separate rules for each quality
characteristic influencing the same process parameter in the IM, e. g. 𝑟𝜂𝑞,𝑝 and 𝑟𝜂𝑠,𝑝 , with 𝑞, 𝑠 ∈ 𝑄
and 𝑝 ∈ 𝑃 . However, in this case it would not be clear whether the rules are related according to
a logical AND, OR, or a different operator altogether. As such, we propose the introduction of a
relator vertex representing the logical operator required by the 𝑟𝑞𝑛 in question. For the example
of an AND-relator shown in Figure 3 this yields 𝑟𝑞𝑛 = {(𝑞, ⟨implies⟩, 𝑝), (𝑠, ⟨implies⟩, 𝑝)}AND ,
where {}AND denotes the set of all relations combined by the respective AND-relator 𝑙. This can
: process : quality
parameter characteristic
quantifies quantifies
: quantified : quantified
process implies quality
parameter characteristic
Figure 2: Graphical representation of 𝑟^o,𝜌^ with explicit modelling of quantified parameter and quality.
: quality
characteristic
combined by
: process
implies : AND-Relator
parameter
combined by
: quality
characteristic
Figure 3: Graphical representation of modelling pattern 𝑟𝑞𝑛 , i. e. an implies relation indirectly spanning
multiple conditions, that are connected by a relator vertex.
be expanded to the following hierarchical triple:
𝑟𝑞𝑛 = {((𝑞, ⟨combined by⟩, 𝑙), ⟨implies⟩, 𝑝), ((𝑠, ⟨combined by⟩, 𝑙), ⟨implies⟩, 𝑝)}AND
In theory, there is no limit to the number of relations being combined by a relator, the definitions
here are based on the example in Figure 3.
The case of one condition influencing several conclusions can be unambiguously represented
by adding a separate rule for each of the conclusions. Therefore, this case does not require a
special relator vertex.
3.1.5. Inclusion of Process Data
Noy et al. make the point that “it is critical not to lose the linkage between the relation-
ships stored in the graph and where those relationships come from” [5]. While they refer
to the discovery process, we assume that capturing semantics of operator knowledge in IMs
could be aided by including process knowledge, especially since Ringsquandl et al. [20] have
achieved promising results in knowledge graph completion by considering event embeddings.
In manufacturing, orders Ω, which can be viewed as compositions of process iterations 𝐼, are
produced for certain amounts of time. We propose to explicitly model this process data as
(𝑖, ⟨belongs to⟩, 𝜔), where 𝑖 ∈ 𝐼 and 𝑜 ∈ 𝑂. The process iterations can be connected with
the resulting quantified parameters, (𝜌𝑖 , ⟨chosen in⟩, 𝑖), where 𝜌 ∈ P, quantified quality char-
acteristics (𝑎𝑖 , ⟨is exhibited after⟩, 𝑖), and quantified influences (𝑏𝑖−1 , ⟨influences⟩, 𝑖), where
𝑎, 𝑏 ∈ O and (𝑏𝑖−1 , ⟨is exhibited after⟩, 𝑖 − 1). P and O are defined in the modelling patterns for
quantified parameters and quantified conditions, respectively. We note that process iteration 𝑖 is
preceded by 𝑖 − 1 in order 𝜔, i. e. the quality characteristic 𝑏𝑖−1 is exhibited after the conclusion
of the preceding process iteration.
Connecting the process data with the modelling patterns described above is beneficial,
especially in the case of data-based knowledge extraction, since it allows explanation by example.
The definition is analogous for parameters 𝑝. Using this, we can denote a relationship between
process data and aggregate as (𝑎𝑖 , ⟨contributes to⟩, 𝑎 ^), where 𝑎^ is an aggregation of quantified
quality characteristic expressed in a specific rule. Both, 𝑎𝑖 and 𝑎 ^, are expressed values of a
quality characteristic and as such are equivalent in regards to their hierarchical level. The only
difference is that the value of 𝑎𝑖 is sampled from the real world process whereas 𝑎 ^ is calculated
based on a set of observations.
If all process data is included in the IM, a supports relation could also be defined following the
quality metric used in rule mining [36, 37]. However, since data-based rules rely on aggregates, a
direct comparison between ^𝑞 𝑗 and 𝑞𝑖 , as well as 𝑝^𝑗 and 𝑝𝑖 would fail and need to be relaxed by an
interval in which they are considered equal. Also, since the rules are split between parameters
and quality characteristics there would have to be two separate relations.
3.2. Properties
Here, we will give an overview of the properties shown by different modelling patterns. Firstly,
with exceeding expressiveness of and information contained in the representation its complexity
is increasing. This increase of abstraction can be seen in the increase in hierarchy hierarchy
for each additional quantification or multiple conditions. Secondly, if process data is included
in the IM it is likely to lead to a strong imbalance, since process data is much more readily
available than extracted operator knowledge. Both aspects highlight the challenges embedding
methodologies for IMs with operator knowledge have to address. As most of the relations
described in Section 3 are not symmetric it would be easy to generate inverse relations, e. g.
implied by for implies, which could be beneficial in knowledge graph completion settings.
4. Embedding Industrial Information Models containing
Operator Knowledge
In this section we aim to give a first indication whether it is possible to embed knowledge
graphs containing extracted operator knowledge available as rules. As such, we present a first
step towards a methodology for constructing such an embedding and provide a preliminary
evaluation. To this end, we utilize the dataset presented in [35] of a fused deposition modelling
(FDM) process. We choose to model the knowledge with the pattern of quantified conclusions,
since the dataset does not provide the data for more complex patterns, i. e. quantified conditions.
: process : quality : quality
parameter characteristic characteristic
quantifies quantifies
: aggregated implies : aggregated
quantified process quantified quality quantifies
quantifies parameter characteristic quantifies
contributes to contributes to
: quantified : quantified
quantified
process quality
quality
parameter characteristic
characteristic
chosen in exhibited by
influences
exhibited by
: process belongs to : process
belongs to : order
iteration iteration
Figure 4: Information Model for process data, i. e. parametrisation processes and their iterations, as
well as a rule. The rule’s condition and conclusion is quantified relying on aggregations of quantified
process parameters and quality characteristics that result from the iteration processes.
The accompanying code is available on github1 .
4.1. Embedding Methodology
To embed operator knowledge that is intended to assist learning systems instead of knowledge
graph completion, subgraphs containing the knowledge that is particularly relevant for the
given input should be embedded. In our case, the input is a defective quality characteristic, e. g.
stringing, a common problem in FDM, that can be alleviated through a fitting parametrisation
by the operator or learning system. Our embedding methodology (cf. Figure 5) is loosely based
on the methodology outlined in Kursuncu et al. [38] that is an approach towards embeddings
for learning systems addressing classification in an natural language processing (NLP) setting,
rather than KG completion or predictive quality scenarios.
We follow a sum-based approach [39] that aggregates individual node embeddings, that are
particularly relevant to the input quality characteristic. To identify the fitting subgraph 𝒮, the
1
https://github.com/0x14d/embedding-operator-knowledge
Graph
Propagation
Knowledge Graph Subgraph Node Embedding
Quality Characteristic Subgraph Embedding
Figure 5: Illustration of the embedding methodology. The quality characteristic 𝑞 is used to determine
the starting node to propagate from. Each parameter node of the resulting subgraph 𝒮 then individu-
ally embedded as node embedding, e. g. parameter node 𝑣𝑗 is embedded as 𝑧𝑗 . The parameter node
embeddings are then aggregated to one subgraph embedding 𝑧𝒮 .
input is mapped to the respective node in the knowledge graph. Then, this node is propagated
by one step for all outgoing edges to arrive at the parameters adjusted to alleviate this quality
defect.∑︀Based on this, the propagated nodes, embedded by TransH [29], 𝑧 are aggregated by
𝑧𝒮 = 𝑣𝑖 ,𝑣𝑗 ∈𝒮 𝑧𝑗 ⊗ 𝐷(𝑧𝑖 , 𝑧𝑗 ) to form the subgraph embedding 𝑧𝑆 . Here, 𝑣𝑖 , 𝑣𝑗 are the pairs of
head and tail nodes resulting from the graph propagation and 𝐷(𝑧𝑖 , 𝑧𝑗 ) is the euclidean distance
between the node embeddings of 𝑣𝑖 and 𝑣𝑗 . Dependent on which semantic information should
be represented in the subgraph embedding, it must be decided which node embeddings to
aggregate in 𝑧𝒮 . If the head node does not hold semantic information, we suggest ignoring the
head node in the subgraph embedding. As this is the case in our scenario, we only aggregated
the node embeddings for the parameters. If a modelling pattern for a different abstraction level
is used, e. g. quantified conditions, the propagation step has to be increased to deal with the
introduced indirections.
4.2. Evaluation
4.2.1. Evaluation Metric
Metrics commonly used to evaluate embeddings in knowledge graph completion settings, e. g.
mean reciprocal rank and hits@k, are unsuited to establish the quality of embeddings of operator
knowledge in our scenario since the required ground truth is not present. Instead, we propose
that the fundamental behaviour of rule embeddings in predictive quality scenarios should
be that the parameters adjusted for similar quality characteristics in the (sub)graph, should
be as equal as possible to those in the embedding space. Therefore, we define a metric in
analogy to hits@k, matches@k, based on the amount of overlap between the K closest quality
characteristics in embedding and graph space. To be able to establish the amount of overlap, a
set of the 𝐾 closest quality characteristics is prepared by ordering them descendingly according
to their similarity—amount of overlapping parameters adjusted (higher is better) and euclidean
distance (lower is better) for graph and embedding space, respectively. Then, the number of
R F F X U H Q F H
R F F X U H Q F H
P D W F K H V P D W F K H V
(a) Two dimensional kernel density estimate plot for (b) Scatterplot showing the actual results achieved
#matches and occurrence. for the respective quality characteristics
Figure 6: All quality characteristics evaluated by matches@K for 𝐾 = 3 against their respective
occurrences.
matches, #matches, between the respective sets is calculated for each quality characteristic.
By conducting the comparison on a set, we ensure that small differences in similarity are not
unduly exaggerated in the overall metric since the order is not important to determine a match.
For matches@k, 𝐾 has to be chosen according to the respective dataset. It decreases in
expressiveness with increasing size since the unordered nature of the comparison leads to
number of matches equalling the number of quality characteristics |𝑄| if 𝐾 = |𝑄|, which
would equal an overlap of 100 %. Therefore, inspecting the actual similarities between quality
characteristics in the graph space is necessary to determine the 𝐾 which is representative for
real world similarity. This can either be done by relying on domain knowledge or by determining
the point at which the similarities are abruptly decreasing. In the following experiment we
use 𝐾 = 3 since we established experimentally that for greater 𝐾 the similarities between the
quality characteristics are rapidly increasing.
4.2.2. Experimental Evaluation
To determine whether it is possible to embed knowledge graphs containing explicit operator
knowledge we conduct an experiment on the dataset described in [35]. After preprocessing and
removing categorical parameters, it contains ratings of 13 quality characteristics and a total
of 46 parameters that are adjusted to optimise the quality characteristics. The distribution of
quality characteristics is skewed with more operator knowledge being present for those that
occur more often.
Applying the methodology and metric described above we receive a mean #matches of
2.85 ± 0.38 (95.00 % ± 12.67 %) for 𝐾 = 3 over all quality characteristics for 46 dimensional
embeddings. While this indicates a relatively high overlap, we investigate its distribution for
the individual quality characteristics combined with their occurrence in Figure 6. In Figure 6a
we can see that that the performance seems to generally increase with increasing occurrence
of quality characteristics in the dataset. However, there seems to be a second cluster of well
performing quality characteristics with relatively low occurrence that yields good results.
Inspecting Figure 6b confirms this notion. Since we assume more operator knowledge to be
present in the graph for quality characteristics with higher occurrence the fact that higher
occurring quality characteristics lead to better results seems to underpin the conclusion that
extracted operator knowledge in embeddings can be represented by embeddings. However, a
significant portion of quality characteristics with low occurrence also leads to good results.
5. Future Work
While the presented preliminary evaluation strengthens our hypothesis, a more thorough
evaluation is needed to arrive at a firm conclusion. This includes a comparison of the proposed
embedding method on the different modelling patterns. Also, the influence of increasing
hierarchies, due to increasing complexity, on embedding methods will be investigated. In this
context, evaluating more complex embedding methods which have been shown to deal well with
hierarchies between concepts such as RotH [23] would be interesting. Moreover, an evaluation
on multiple datasets would allow greater confidence in regards to the transferability of the
described concepts. However, we are not aware of any suitable public datasets in the industrial
domain at this time.
Furthermore, the behaviour of the embedding methods for varying levels of noise in the data
should be investigated, since complex information models are rarely error free. Additionally,
uncertainties of operators could be encoded using soft rules.
In the patterns modelling operator knowledge presented in this work we strongly relied
on relations to represent properties of vertices and relations. These properties could also be
represented as attributes of vertices. While this would reduce the involved hierarchies it imposes
other complexities for embedding methodologies. As such the integration of attribute-based
embeddings [40, 41] could be beneficial.
In addition, the applicability of common KG completion approaches on KGs containing oper-
ator knowledge could be researched to infer relations or nodes that have not been encountered
in reality, thereby increasing the information content of the representation.
Lastly, by an integration with learning systems, as outlined by Kursuncu et al. [38] for NLP,
we could directly measure the impact of the knowledge contained in IMs on the predictive
power of learning systems.
6. Conclusion
In this paper we presented several modelling patterns for including extracted operator knowl-
edge into industrial information models, represented as knowledge graphs. These modelling
patterns can be conceived as architectural patterns and can be combined and applied depending
on the required complexity that should be expressed. Furthermore, we presented an embedding
methodology to represent this knowledge as a vector that could be used to combine learning
systems with operator knowledge. We established a metric suited to evaluate the embedding’s
capability to capture semantic relations between conditions, i. e. quality characteristics, based
on their resulting conclusions, i. e. parametrisations. In a preliminary evaluation, we have
shown that the chosen information model and the proposed embedding methodology are able to
express and capture semantic relationships between conditions that lead to similar conclusions
if they occurred in a sufficient quantity.
Acknowledgments
This work is funded by the Bavarian Ministry of Economic Affairs, Energy and Technology in
the scope of the ADELeS project.
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