Probabilistic graphical models in the manufacturing of electric vehicles

Abstract

Introduction: Battery electric vehicles (BEVs) are crucial to the reduction of green­ house gas emissions in the transportation sector. The primary component of BEVs is the energy storage system, consisting of battery cells. However, its manufacturing process is intricate, characterized by numerous causal interdependencies across production steps. The limited understanding of these interdependencies contributes to high scrap rates, resulting in increased environmental, ethical, and economic costs associated with BEVs.

Methods: In order to address this challenge, this dissertation leverages the data and measurements collected by modern manufacturing facilities and production machines. Specitically, Probabilistic Graphical Models (PGMs), which can be grouped into directed and undirected models, are applied to this data to enhance the understanding of the production process, addressing the lack of knowledge. By utilizing PGMs, this research aims to uncover hidden relationships and dependencies within the manufacturing data, enabling more informed decision-making in battery cell manufacturing. In order to tackle the inherent complexity of the data, we focus on non-linear methods.

Specifically: 1. Missing Data: We address the challenge of estimating the joint distribution when parts of the data are missing, which is a common occurrence in manufacturing data that comprises sensor measurements. The proposed estimation procedure can be viewed as a learning algorithm for undirected PGMs. 2. Real-Data Application: Additionally, we apply a state-of-the-art learning procedure for directed PGMs to actual manufacturing data. 3. Boosting: Finally, we utilize the concept of boosting to learn directed PGMs from the data and investigate the theoretical and practical benefits. We account for the circumstances in manufacturing scenarios. This includes leveraging prior knowledge in various aspects.

We account for the circumstances in manufacturi11g scenarios. This includes leveraging prior knowledge in various aspects.

Results: 1. Missing Data: The proposed method effectively learns joint distributions semi­ parametrically. A simulation study shows that the estimates improve with the sample size of the data, and the inclusion of expert knowledge in the estimation process leads to a holistic improvement in the accuracy of the estimates. 2. Real-Data Application: In contrast to other applications of PGMs, we observe large local variations in the number of relationships, challenging the assumption of sparsity. The integration of expert knowledge provides more reliable estimates in real-world manufacturing data applications. 3. Boosting: We demonstrate the consistency of a boosting-based learning algorithm for directed PGMs, which is a rare statistical guarantee for such algorithms. The practical adaptation of this algorithm proves to be competitive and, in some relevant cases, even outperforms state-of-the-art methods.

The results collectively demonstrate the significance and practical applicability of PGMs in the context of manufacturing applications.

Discussion & Outlook: We critically assess the derivation of causal relationships from data collected at the steady state of the production workflow. We propose a novel point of view on causal discovery as a recommendation system for potential causal relationships in manufacturing. Additionally, we sketch the idea of an iterative procedure involving PGM learning algorithms and experiments to derive causal relationships.