Abstracts Track 2022

Nr:	1
Title:	A Method of Developing Quantile Convolutional Neural Networks for Electric Vehicle Battery Temperature Prediction Trained on Cross-domain Data
Authors:	Andreas M. Billert
Abstract:	An efficient battery thermal management system (BTMS) for electric vehicles must, on the one hand, ensure optimal battery temperature with low energy consumption and on the other hand, take into account the effects of battery aging and power derating. This can be achieved using a predictive controller instead of fixed battery cooling thresholds. Such a controller needs a battery temperature prediction for the following drive horizon for different battery cooling thresholds to choose the optimal value. Non-linearity of the underlying physical processes and uncertainty of the forecast of the driver’s behavior and the route ahead motivate the usage of Convolutional Neural Networks (CNN) for quantile predictions. In the proposed method, cross-domain data are analyzed and processed as training data for a CNN. The input of the CNN consists of data from previous road segments as well as predictions for following road segments. The output is a prediction of the change in battery temperature as quantile sequences over a prediction horizon. This is achieved by using multiple input and output channels and a custom loss layer to incorporate the quantile losses. Properties of the collected cross-domain data sets are analyzed and considered during preprocessing. Subsequently, 150 models with 50 different sets of hyperparameters are trained. They are evaluated and ranked by point- and quantile-forecast related metrics, of which the best performing model is further analyzed. Cross-domain data used in this study consists of simulation, vehicle fleet and weather data. 860 simulations provide the effect of different battery cooling thresholds. 1504 drives with 16 vehicles of a prototype fleet between March and October 2021 cover real road conditions and profiles. They are joined by humidity and solar radiation data from the German Weather Service. The step of data understanding shows the suitability of the considered data for training, validation, and testing. All data are prepared for the CNN as data points with 43 input features from the previous 5 km, 17 foresight input features from the following 20 km and the change in battery temperature as target output for the following 20 km. All input is sampled to 250 m segments. The best performing model is identified using total loss, point-forecast and quantile-related metrics. Concerning point-forecast metrics, the 0.5 quantile (median) prediction achieves a mean absolute error of 0.27 °C and an absolute difference between prediction and true value smaller than 1.1 °C in more than 90% of the segments. Concerning quantile-related metrics, the occurrence of true values within the quantile predictions shows the capability of the method to include the model’s uncertainty. For example, 47% of the true values are below the predicted median, and 93% of the true values are below the 0.99 quantile. A plausible effect of different battery cooling thresholds on predictions points out the general applicability of the model for a predictive BTMS. The results show the ability of the developed method to well predict quantiles of changes in battery temperature for different battery cooling thresholds. Possible improvements of the method such as increasing data size, using more complex architectures as well as optimizing input and prediction horizons are discussed. The main insight of this work is the applicability of the proposed method, including domain-specific data analysis, model architecture and model evaluation.

Nr:	4
Title:	Revisiting the Solvability of Systems of Partial Fuzzy Relational Equations
Authors:	Martin Štepnicka and Nhung Cao
Abstract:	Fuzzy inference systems, i.e. systems consisting, in principle, of a fuzzy rule base and an inference mechanism, have been widely investigated from different perspectives including their logical correctness. It is not surprising that the logical correctness led mostly to the questions on the preservation of modus ponens. Indeed, whenever such a system processes an input that is equivalent to one of the rule antecedents, it is natural to expect the modus ponens to be preserved and the inferred output to be identical to the respective rule consequent. This leads to the related systems of fuzzy relational equations where the antecedent and consequent fuzzy sets are known values, the inference is represented either by the direct product related to the compositional rule of inference or by the Bandler-Kohout subproduct, and the fuzzy relation that represents the fuzzy rule base is the unknown element in the equations. The most important question is whether such systems are solvable, i.e., whether there even exists a fuzzy relation that models the given fuzzy rule base in such a way that the modus ponens is preserved. The solvability of systems of fuzzy relational is a classical topic with lots of deep and inspiring results however, only recently, it has not been combined with partiality. Partiality allows dealing with partially defined truth values, which is again a classical logical topic being studied since 1920's. Indeed, in distinct situations, we cannot define the truth value for a given predicate. We may encounter e.g. missing values in databases, various N/A values in questionnaires, meaningless undefined values from predicates with undenoted terms, e.g., a statement about the french king is neither true nor false as France has no king and so, the truth-value of such a statement is simply undefined. The partial logics have been recently extended to partial fuzzy logics and consequently, the partial fuzzy set theory has been developed based on numerous extensions of partial algebras of truth values. Partial fuzzy sets then may have undefined membership degrees for some values from the given universe and the partial algebras have to extend operations from the residuated lattice in such a way that they may incorporate a dummy value representing the undefinedness. This background leads naturally to the problem of solvability of partial fuzzy relational equations, which are equations with partial fuzzy sets in the role of antecedent and consequents as well as with partial fuzzy relation as the model of the given fuzzy rule base. Such a setting led to a recent publication that uncovers the solvability and even the shape of the solutions for most of the known algebras. In this contribution, we revisit the problem and consider a specific case that allows partiality only in the input. In other words, antecedents, as well as consequents expressing the knowledge, are fully defined. Thus also the model of the fuzzy rules is one of the standard and fully defined relations. And we investigate what happens if the input differs from one of the antecedents only by a few undefined values which mimics the situation when a description of an observed object misses a few values in its feature vector. We show, that under specific conditions, we still may preserve the modified modus ponens, i.e., that the inferred output is identical with the fully defined consequent of the respective rule.