This paper presents the simulation of the operation of an electric forklift fleet within an intralogistics scenario. For this purpose, the open source simulation tool CARLA is used; according to our knowledge this is a novel approach in the context of logistics simulation. First, CARLA is used to generate and visualize a realistic 3D outdoor warehouse scenario, incorporating a number of randomly moving forklifts. In a next step, intralogistics transport tasks, such as pick-and-place, are simulated for the forklift fleet, including shortest-path finding. Furthermore, the capability to play back localization data, previously recorded from a ''real'' forklift fleet, is demonstrated.This play back is done in the original recreated environment, thereby enabling the visualization of the forklifts movements. Finally, the energy consumption of the forklift trucks is simulated by integrating a physical battery model that generates the state of charge (SOC) of each truck as a function of load and activity. To demonstrate the wide range of possible applications for the CARLA simulation platform, we describe two use cases. The first deals with the problem of detecting regions with critically high traffic densities, the second with optimal placement of charging stations for the forklift trucks. Both use cases are calculated for an exemplary warehouse model.

Efficient parameter identification of electrochemical models is crucial for accurate monitoring and control of lithium-ion cells. This process becomes challenging when applied to complex models that rely on a considerable number of interdependent parameters that affect the output response. Gradient-based and metaheuristic optimization techniques, although previously employed for this task, are limited by their lack of robustness, high computational costs, and susceptibility to local minima. In this study, Bayesian Optimization is used for tuning the dynamic parameters of an electrochemical equivalent circuit battery model (E-ECM) for a nickel-manganese-cobalt (NMC)-graphite cell. The performance of the Bayesian Optimization is compared with baseline methods based on gradient-based and metaheuristic approaches. The robustness of the parameter optimization method is tested by performing verification using an experimental drive cycle. The results indicate that Bayesian Optimization outperforms Gradient Descent and PSO optimization techniques, achieving reductions on average testing loss by 28.8% and 5.8%, respectively. Moreover, Bayesian optimization significantly reduces the variance in testing loss by 95.8% and 72.7%, respectively.

Bayesian parameter inference is useful to improve Li-ion battery diagnostics and can help formulate battery aging models. However, it is computationally intensive and cannot be easily repeated for multiple cycles, multiple operating conditions, or multiple replicate cells. To reduce the computational cost of Bayesian calibration, numerical solvers for physics-based models can be replaced with faster surrogates. A physics-informed neural network (PINN) is developed as a surrogate for the pseudo-2D (P2D) battery model calibration. For the P2D surrogate, additional training regularization was needed as compared to the PINN single-particle model (SPM) developed in Part I. Both the PINN SPM and P2D surrogate models are exercised for parameter inference and compared to data obtained from a direct numerical solution of the governing equations. A parameter inference study highlights the ability to use these PINNs to calibrate scaling parameters for the cathode Li diffusion and the anode exchange current density. By realizing computational speed-ups of 2250x for the P2D model, as compared to using standard integrating methods, the PINN surrogates enable rapid state-of-health diagnostics. In the low-data availability scenario, the testing error was estimated to 2mV for the SPM surrogate and 10mV for the P2D surrogate which could be mitigated with additional data.

To plan and optimize energy storage demands that account for Li-ion battery aging dynamics, techniques need to be developed to diagnose battery internal states accurately and rapidly. This study seeks to reduce the computational resources needed to determine a battery's internal states by replacing physics-based Li-ion battery models -- such as the single-particle model (SPM) and the pseudo-2D (P2D) model -- with a physics-informed neural network (PINN) surrogate. The surrogate model makes high-throughput techniques, such as Bayesian calibration, tractable to determine battery internal parameters from voltage responses. This manuscript is the first of a two-part series that introduces PINN surrogates of Li-ion battery models for parameter inference (i.e., state-of-health diagnostics). In this first part, a method is presented for constructing a PINN surrogate of the SPM. A multi-fidelity hierarchical training, where several neural nets are trained with multiple physics-loss fidelities is shown to significantly improve the surrogate accuracy when only training on the governing equation residuals. The implementation is made available in a companion repository (https://github.com/NREL/pinnstripes). The techniques used to develop a PINN surrogate of the SPM are extended in Part II for the PINN surrogate for the P2D battery model, and explore the Bayesian calibration capabilities of both surrogates.

Combining machine learning with physics is a trending approach for discovering unknown dynamics, and one of the most intensively studied frameworks is the physics-informed neural network (PINN). However, PINN often fails to optimize the network due to its difficulty in concurrently minimizing multiple losses originating from the system's governing equations. This problem can be more serious when the system's states are unmeasurable, like lithium-ion batteries (LiBs). In this work, we introduce a robust method for training PINN that uses fewer loss terms and thus constructs a less complex landscape for optimization. In particular, instead of having loss terms from each differential equation, this method embeds the dynamics into a loss function that quantifies the error between observed and predicted system outputs. This is accomplished by numerically integrating the predicted states from the neural network(NN) using known dynamics and transforming them to obtain a sequence of predicted outputs. Minimizing such a loss optimizes the NN to predict states consistent with observations given the physics. Further, the system's parameters can be added to the optimization targets. To demonstrate the ability of this method to perform various modeling and control tasks, we apply it to a battery model to concurrently estimate its states and parameters.

Autonomous exploration without interruption is important in scenarios such as search and rescue and precision agriculture, where consistent presence is needed to detect events over large areas. Ergodic search already derives continuous coverage trajectories in these scenarios so that a robot spends more time in areas with high information density. However, existing literature on ergodic search does not consider the robot's energy constraints, limiting how long a robot can explore. In fact, if the robots are battery-powered, it is physically not possible to continuously explore on a single battery charge. Our paper tackles this challenge by integrating ergodic search methods with energy-aware coverage. We trade off battery usage and coverage quality, maintaining uninterrupted exploration of a given space by at least one agent. Our approach derives an abstract battery model for future state-of-charge estimation and extends canonical ergodic search to ergodic search under battery constraints. Empirical data from simulations and real-world experiments demonstrate the effectiveness of our energy-aware ergodic search, which ensures continuous and uninterrupted exploration and guarantees spatial coverage.

Model identification of battery dynamics is a central problem in energy research; many energy management systems and design processes rely on accurate battery models for efficiency optimization. The standard methodology for battery modelling is traditional design of experiments (DoE), where the battery dynamics are excited with many different current profiles and the measured outputs are used to estimate the system dynamics. However, although it is possible to obtain useful models with the traditional approach, the process is time consuming and expensive because of the need to sweep many different current-profile configurations. In the present work, a novel DoE approach is developed based on deep reinforcement learning, which alters the configuration of the experiments on the fly based on the statistics of past experiments. Instead of sticking to a library of predefined current profiles, the proposed approach modifies the current profiles dynamically by updating the output space covered by past measurements, hence only the current profiles that are informative for future experiments are applied. Simulations and real experiments are used to show that the proposed approach gives models that are as accurate as those obtained with traditional DoE but by using 85\% less resources.

The concept of integrating physics-based and data-driven approaches has become popular for modeling sustainable energy systems. However, the existing literature mainly focuses on the data-driven surrogates generated to replace physics-based models. These models often trade accuracy for speed but lack the generalisability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in the modeling of real-world dynamic systems for optimization and control purposes. In this work, we propose a novel architecture for generating model-integrated neural networks (MINN) to allow integration on the level of learning physics-based dynamics of the system. The obtained hybrid model solves an unsettled research problem in control-oriented modeling, i.e., how to obtain an optimally simplified model that is physically insightful, numerically accurate, and computationally tractable simultaneously. We apply the proposed neural network architecture to model the electrochemical dynamics of lithium-ion batteries and show that MINN is extremely data-efficient to train while being sufficiently generalizable to previously unseen input data, owing to its underlying physical invariants. The MINN battery model has an accuracy comparable to the first principle-based model in predicting both the system outputs and any locally distributed electrochemical behaviors but achieves two orders of magnitude reduction in the solution time.

In working with customers, we often hear of a desired Digital Twin use case to drive actionable insights through what-if scenario analysis. These use cases typically include operations efficiency management, fleet management, failure predictions, and maintenance planning, to name a few. To help customers navigate this space, we developed a concise definition and four-level Digital Twin leveling index consistent with our customers' applications. In a prior blog, we described the four-level index (shown in the figure below) to help customers understand their use cases and the technologies required to achieve their desired business value. In this blog, we will illustrate how the L4 Living Digital Twins can be used to model the behavior of a physical system whose inherent behavior evolves over time.

Lithium-ion batteries are powering the ongoing transportation electrification revolution. Lithium-ion batteries possess higher energy density and favourable electrochemical properties which make it a preferable energy source for electric vehicles. Precise estimation of battery parameters (Charge capacity, voltage etc) is vital to estimate the available range in an electric vehicle. Graph-based estimation techniques enable us to understand the variable dependencies underpinning them to improve estimates. In this paper we employ Graph Neural Networks for battery parameter estimation, we introduce a unique graph autoencoder time series estimation approach. Variables in battery measurements are known to have an underlying relationship with each other in a certain correlation within variables of interest. We use graph autoencoder based on a non-linear version of NOTEARS as this allowed us to perform gradient-descent in learning the structure (instead of treating it as a combinatorial optimisation problem). The proposed architecture outperforms the state-of-the-art Graph Time Series (GTS) architecture for battery parameter estimation. We call our method GAETS (Graph AutoEncoder Time Series).