Compensating Data Shortages in Manufacturing with Monotonicity Knowledge

Kurnatowski, Martin von; Schmid, Jochen; Link, Patrick; Zache, Rebekka; Morand, Lukas; Kraft, Torsten; Schmidt, Ingo; Schwientek, Jan; Stoll, Anke

doi:10.3390/a14120345

Cited by 9 publications

(8 citation statements)

References 50 publications

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“…Another possible strategy would be to infer the distance metric from the data itself, possibly based on certain informed assumptions [ 41 ]. Similarly, expert knowledge could be brought to bear in the training of the regression model, for example, in the form of shape constraints [ 42 – 44 ].…”

Section: Discussionmentioning

confidence: 99%

Calibrated simplex-mapping classification

Heese

Walczak²,

Bortz³

et al. 2023

PLoS ONE

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We propose a novel methodology for general multi-class classification in arbitrary feature spaces, which results in a potentially well-calibrated classifier. Calibrated classifiers are important in many applications because, in addition to the prediction of mere class labels, they also yield a confidence level for each of their predictions. In essence, the training of our classifier proceeds in two steps. In a first step, the training data is represented in a latent space whose geometry is induced by a regular (n − 1)-dimensional simplex, n being the number of classes. We design this representation in such a way that it well reflects the feature space distances of the datapoints to their own- and foreign-class neighbors. In a second step, the latent space representation of the training data is extended to the whole feature space by fitting a regression model to the transformed data. With this latent-space representation, our calibrated classifier is readily defined. We rigorously establish its core theoretical properties and benchmark its prediction and calibration properties by means of various synthetic and real-world data sets from different application domains.

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Section: Discussionmentioning

confidence: 99%

Calibrated simplex-mapping classification

Heese

Walczak²,

Bortz³

et al. 2023

PLoS ONE

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“…Basic results on the monotonicity of multilayer perceptrons were stated in [15] and [16]. The applications include nonlinear dynamic system identification and control [17,18], credit risk rating [19,20], consumer loan evaluation [21], predicting Alzheimer's disease progression [22], manufacturing [23] or breast cancer prediction [24] and its detection on mammograms [25].…”

Section: Introductionmentioning

confidence: 99%

Monotonic Fuzzy Systems With Goniometric Membership Functions

Hušek

2024

Int. J. Fuzzy Syst.

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Fuzzy logic-based systems are nowadays commonly used in nonlinear function approximation when incoming data are available. Their main advantage is that the resulting rules can be interpreted understandably. Nevertheless, when the data are noisy an overfitting may occur which leads to poor accuracy and generalization ability. Prior information about the nonlinear function may improve fuzzy system performance. In this paper the case when the function is monotonic with respect to some or all variables is considered. Sufficient conditions for the monotonicity of first-order Takagi–Sugeno fuzzy systems with raised cosine membership functions are derived. Performance of the proposed fuzzy system is tested on two benchmark datasets

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“…In the following, this approach is referred to as the SIASCOR method for brevity. While a semi-infinite optimization approach has also been pursued in von Kurna-towski et al (2021), the algorithm used here is superior to the reference-grid algorithm from von Kurnatowski et al (2021), both from a theoretical and from a practical point of view. Additionally, von Kurnatowski et al (2021) treat only a single kind of shape constraints, namely monotonicity constraints.…”

Section: Introductionmentioning

confidence: 99%

“…In spite of the small set of available measurement data, the methodology proposed here leads to a high-quality prediction model for the surface roughness of the brushed workpiece. Aside from the brushing process, the SIASCOR method can also be successfully applied to the glass-bending and press-hardening processes described in von Kurnatowski et al (2021).…”

Section: Introductionmentioning

confidence: 99%

Capturing and incorporating expert knowledge into machine learning models for quality prediction in manufacturing

et al. 2022

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Increasing digitalization enables the use of machine learning (ML) methods for analyzing and optimizing manufacturing processes. A main application of ML is the construction of quality prediction models, which can be used, among other things, for documentation purposes, as assistance systems for process operators, or for adaptive process control. The quality of such ML models typically strongly depends on the amount and the quality of data used for training. In manufacturing, the size of available datasets before start of production (SOP) is often limited. In contrast to data, expert knowledge commonly is available in manufacturing. Therefore, this study introduces a general methodology for building quality prediction models with ML methods on small datasets by integrating shape expert knowledge, that is, prior knowledge about the shape of the input–output relationship to be learned. The proposed methodology is applied to a brushing process with 125 data points for predicting the surface roughness as a function of five process variables. As opposed to conventional ML methods for small datasets, the proposed methodology produces prediction models that strictly comply with all the expert knowledge specified by the involved process specialists. In particular, the direct involvement of process experts in the training of the models leads to a very clear interpretation and, by extension, to a high acceptance of the models. While working out the shape knowledge requires some iterations in general, another clear merit of the proposed methodology is that, in contrast to most conventional ML, it involves no time-consuming and often heuristic hyperparameter tuning or model selection step.

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Compensating Data Shortages in Manufacturing with Monotonicity Knowledge

Cited by 9 publications

References 50 publications

Calibrated simplex-mapping classification

Calibrated simplex-mapping classification

Monotonic Fuzzy Systems With Goniometric Membership Functions

Capturing and incorporating expert knowledge into machine learning models for quality prediction in manufacturing

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