Statistical analytics has been playing an important role for uncovering patterns and trends from data in smart manufacturing. However, how statistical analytics are performed is usually stored in the underlying code and sufers from transparency and re-usability, which is vital for modern industry. To this end, we propose a statistical ontology StatsOnto that models not only the concepts in statistics, but also allows encoding the procedure of statistical analytics, which is limitedly addressed in past works. We present a preliminary evaluation of StatsOnto with a Bosch use case with a user study, competence question and coverage discussion in this poster paper.
Smart manufacturing is a term generally applied to improve manufacturing operations through
system integration, linking of physical and cyber capabilities, and taking advantage of
information including leveraging the big data analysis [
However, how statistical analytics are performed is usually stored in underlying code and sufers from transparency and re-usability, which is vital for modern industry [ 6]. Semantic technologies including ontologies are beneficial for improving the transparency since they ofer a standardised way describing statistical analysis knowledge and procedure in machine processable formalisation that opens the door for many applications [7, 8], such as automated reasoning, optimisation of statistical pipelines [9, 10]. Currently there are a few studies that discuss partially statistical analytics pipeline modelling. For instance, the computer science ontology [11, 12] contains the general knowledge about statistics, but the concepts of specific statistical calculation are not involved. Statistics ontology [13, 14] enumerates the various statistical methods, but they insuficiently study the procedures of the statistical pipelines.
To this end, we propose a statistical ontology StatsOnto with the angle of procedure orientation. We discuss StatsOnto under an industrial scenario of smart manufacturing and use real-world data provided by Bosch [15]. On the one hand, StatsOnto covers statistical methods such as feature calculation (e.g., mean), sampling and filtering; on the other hand, StatsOnto also ofers a set of classes for construction of statistical analytical pipelines, including statistical pipeline, various tasks, data entities, etc. This poster paper presents a preliminary evaluation of StatsOnto in the industrial scenario with user study, competence question and discussion of knowledge and scenario coverage.
Industrial Scenario. We limit our scope in this poster paper to an industrial scenario of smart welding manufacturing at Bosch [16], to show the real-world impact as well as examples. StatsOnto aims to help the engineers at Bosch to gain insights from the data collected from the welding production, and to monitor quality of the welding operations.
Requirements. We derive the requirements for StatsOnto based on the scenario purposes and discussion with users [17, 18, 19]: R1. Procedure-Orientation: StatsOnto should be able to reflect the statistical analytics procedure, allowing to describe sequence of statistical tasks in a data pipeline. This opens the door of knowledge graph based verification, reasoning, optimisation of statistical analytical pipelines. R2. Transparency: StatsOnto should improve the transparency of the representing statistical analytics in industry among engineers. R3. Knowledge Coverage: StatsOnto should cover the knowledge and practice of the statistical analytics, such as statistical method, data structure. R4. Purpose Coverage: StatsOnto should cover the four types of task: data inspection (e.g. find the data with certain property), statistical modelling (e.g. build the distribution of the data), data denoising (e.g. detect and remove the outliers ) and data analysis (e.g. interpolation, subsampling).
Ontology Engineering Process. We broadly follow the routine of Ontology development 101 [20, 21], which is a kind of collaborative ontology engineering methodology. The whole process can be divided into the following 4 steps. Step 1: Domain Analysis, where common statistical analytics at Bosch are discussed. Common and important terms of statistical tasks are enumerated and classified. Step 2: Concepts Formalisation, where enumerated basic concepts are formalised as classes and relationships between them. Step 3: Mechanism Investigation, where the mechanism of how StatsOnto can serve as the basis in generating KGs which represent concrete statistical analystic pipelines. This step reflects the requirement of Procedure-Orientation of StatsOnto. Step 4: System Deployment, where StatsOnto will be deployed in manufacturing and user feed-backs are collected constantly for iterative processing and further improvement. Statistical Ontology is expressed in OWL 2 EL language for its expressivity and it is still polynomial for query answering [22]. It has 88 classes, 30 properties, and 484 axioms. In particular, there are three most important classes in StatsOnto (Fig. 1), StatisticalTask, StatisticalMethod and Data. StatisticalTask can be divided into two sub-classes, the AtomicStatisticalTask and StatisticalPipeline. The former models the basic and common statistical tasks, such as mean calculation task, counting task, etc., and connects to StatisticalMethod with property hasMethod. While StatisticalPipeline can be regarded as the serialization of AtomicStatisticalTask. Each individual of StatisticalMethod is a piece of script in computer language such as Python. There are also two kinds (sub-classes) of StatisticalMethod s, namely DataSelectionMethod and FeatureCalculationMethod, which correspond to the two basic steps in statistical analytics, namely determination the target data of interest and calculation of the desired feature respectively. Besides these concepts, StatsOnto also specifies some rules, which constraint the inputs or outputs of each AtomicStatisticalTask which invokes certain StatisticalMethod. For example, the following axiom specifies, that any task which has Array as input and has MeanCalculationMethod as method, has SingleValue as output: ∃hasOutput−.(Task ⊓ ∃hasInput.Array ⊓ ∃hasMethod.MeanCalculation) ⊑ SingleValue.
User Study. We organised a workshop at Bosch and collected 28 reports from experts of diferent background, such as welding engineers, data scientists, knowledge engineers. We have also collected some typical statistical analysis tasks in Bosch’s welding manufacturing (Tab 1). The users we divided into two groups; each group first perform a statistical analytical task without our method, and then answer several single-selected questions (SSQ) (Tab 1); after that, the two groups exchange their statistical tasks and do the tasks with our method, and then answer the SSQs. Fig. 2 demonstrate StatsTask2, which aims to detect the welding operations with abnormal quality indicator (Q-Value).
Transparency. After evaluation, the correctness of SSQ for the participants with the help of StatsOnto, no matter in which group, reaches 96.7%, while the correctness without StatsOnto is about 93.3%. The results show that the ontology indeed helps the users to better understand the statistical analysis pipeline, thus increase the transparency.
Case Study and Procedure Orientation. We use an example for data denoising (Fig. 2) for demonstrating the procedure orientation. Given the input of Q-Value Array, the pipeline first extract its trend by calculating the median value with sliding window, then calculates the scattering by the diference between the trend and Q-Value. The points with large scattering (large deviation from the trend) are detected as the outliers. This shows StatsOnto is capable of representing the procedure of statistical analytics.
Knowledge Coverage. We select two example CQs in SPARQL from two aspects: knowledge query (Fig. 2c), analysis procedure query (Fig. 2d). Results show that all these CQs return desired answers on KGs generated based on StatsOnto with the welding manufacturing data, demonstrating good Knowledge Coverage of StatsOnto.
Purpose Coverage. After extensive discussion in the workshop, we categorised most statistical analytical tasks in our project into the four types of purposes (R4): data inspection, statistical modelling, data denoising and data analysis, and found most of the purpose can be covered (above 80%, considered relatively suficient).
Conclusion and Outlook. This poster presents our ongoing research of statistical ontology, which is easy to understand and covers most of statistical analytics in industrial applications. In the future we will improve on the design practices and try to reuse classes and properties (e.g., from STATO [13]) for better interoperability, some reasoning properties and mechanisms of the ontology, and further improve the purpose coverage.
Acknowledgements. The work was partially supported by the H2020 projects Dome 4.0 (Grant Agreement No. 953163), OntoCommons (No. 958371), and DataCloud (No. 101016835) and the SIRIUS Centre, Norwegian Research Council project number 237898. [2] C. Naab, et al., Application of the unscented kalman filter in position estimation a case study on a robot for precise positioning, RobAutonSyst 147 (2022) 103904. [3] E. C. Bryant, et al., Statistical analysis, 1966. [4] Z. Zheng, B. Zhou, D. Zhou, et al., Executable knowledge graph for machine learning: A
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