Physics-informed neural networks (PINNs) have emerged as a promising deep learning method, capable of solving forward and inverse problems governed by differential equations. Despite their recent advance, it is widely acknowledged that PINNs are difficult to train and often require a careful tuning of loss weights when data and physics loss functions are combined by scalarization of a multi-objective (MO) problem. In this paper, we aim to understand how parameters of the physical system, such as characteristic length and time scales, the computational domain, and coefficients of differential equations affect MO optimization and the optimal choice of loss weights. Through a theoretical examination of where these system parameters appear in PINN training, we find that they effectively and individually scale the loss residuals, causing imbalances in MO optimization with certain choices of system parameters. The immediate effects of this are reflected in the apparent Pareto front, which we define as the set of loss values achievable with gradient-based training and visualize accordingly. We empirically verify that loss weights can be used successfully to compensate for the scaling of system parameters, and enable the selection of an optimal solution on the apparent Pareto front that aligns well with the physically valid solution. We further demonstrate that by altering the system parameterization, the apparent Pareto front can shift and exhibit locally convex parts, resulting in a wider range of loss weights for which gradient-based training becomes successful. This work explains the effects of system parameters on MO optimization in PINNs, and highlights the utility of proposed loss weighting schemes.

The phenomenon of knock is an abnormal combustion occurring in spark-ignition (SI) engines and forms a barrier that prevents an increase in thermal efficiency while simultaneously reducing CO${}_2$ emissions. Since knocking combustion is highly stochastic, a cyclic analysis of in-cylinder pressure is necessary. In this study we propose an approach for efficient and robust detection and identification of knocking combustion in three different internal combustion engines. The proposed methodology includes a signal processing technique, called continuous wavelet transformation (CWT), which provides a simultaneous analysis of the in-cylinder pressure traces in the time and frequency domains with coefficients. These coefficients serve as input for a convolutional neural network (CNN) which extracts distinctive features and performs an image recognition task in order to distinguish between non-knock and knock. The results revealed the following: (i) The CWT delivered a stable and effective feature space with the coefficients that represents the unique time-frequency pattern of each individual in-cylinder pressure cycle; (ii) the proposed approach was superior to the state-of-the-art threshold value exceeded (TVE) method with a maximum amplitude pressure oscillation (MAPO) criterion improving the overall accuracy by 6.15 percentage points (up to 92.62%); and (iii) The CWT + CNN method does not require calibrating threshold values for different engines or operating conditions as long as enough and diverse data is used to train the neural network.

This article introduces a method for the detection of knock occurrences in an internal combustion engine (ICE) using a 1-D convolutional neural network trained on in-cylinder pressure data. The model architecture is based on expected frequency characteristics of knocking combustion. All cycles were reduced to $60^{\circ }$ CA long windows with no further processing applied to the pressure traces. The neural networks were trained exclusively on in-cylinder pressure traces from multiple conditions, with labels provided by human experts. The best-performing model architecture achieves an accuracy of above 92% on all test sets in a tenfold cross-validation when distinguishing between knocking and non-knocking cycles. In a multiclass problem where each cycle was labeled by the number of experts who rated it as knocking, 78% of cycles were labeled perfectly, while 90% of cycles were classified at most one class from ground truth. They thus considerably outperform the broadly applied maximum amplitude of pressure oscillation (MAPO) detection method, as well as references reconstructed from previous works. Our analysis indicates that the neural network learned physically meaningful features connected to engine-characteristic resonances, thus verifying the intended theory-guided data science approach. Deeper performance investigation further shows remarkable generalization ability to unseen operating points. In addition, the model proved to classify knocking cycles in unseen engines with increased accuracy of 89% after adapting to their features via training on a small number of exclusively non-knocking cycles. The algorithm takes below 1 ms to classify individual cycles, effectively making it suitable for real-time engine control.

An optimal control of the combustion process of an engine ensures lower emissions and fuel consumption plus high efficiencies. Combustion parameters such as the peak firing pressure (PFP) and the crank angle (CA) corresponding to 50% of mass fraction burned (MFB50) are essential for a closed-loop control strategy. These parameters are based on the measured in-cylinder pressure that is typically gained by intrusive pressure sensors (PSs). These are costly and their durability is uncertain. To overcome these issues, the potential of using a virtual sensor based on the vibration signals acquired by a knock sensor (KS) for control of the combustion process is investigated. The present work introduces a data-driven approach where a signal-processing technique, designated as discrete wavelet transform (DWT), will be used as the preprocessing step for extracting informative features to perform regression tasks of the selected combustion parameters with extreme gradient boosting (XGBoost) regression models. The presented methodology will be applied to data from two different spark-ignited, single cylinder gas engines. Finally, an analysis is obtained where the important features based on the model’s decisions are identified.

A deeper understanding of the physical nature of cycle-to-cycle variations (CCV) in internal combustion engines (ICE) as well as reliable simulation strategies to predict these CCV are indispensable for the development of modern highly efficient combustion engines. Since the combustion process in ICE strongly depends on the turbulent flow field in the cylinder and, for spark-ignited engines, especially around the spark plug, the prediction of CCV using computational fluid dynamics (CFD) is limited to the modeling of turbulent flows. One possible way to determine CCV is by applying large eddy simulation (LES), whose potential in this field has already been shown despite its drawback of requiring considerable computational time and resources. This paper presents a novel strategy based on unsteady Reynolds-averaged Navier–Stokes (uRANS) CFD in combination with variational autoencoders (VAEs). A VAE is trained with flow field data from presimulated cycles at a specific crank angle. Then, the VAE can be used to generate artificial flow fields that serve to initialize new CFD simulations of the combustion process. With this novel approach, a high number of individual cycles can be simulated in a fraction of the time that LES needs for the same amount of cycles. Since the VAE is trained on data from presimulated cycles, the physical information of the cycles is transferred to the generated artificial cycles.