Physics-based Model Research Articles

MINN: Learning the Dynamics of Differential-Algebraic Equations and Application to Battery Modeling.

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 generalizability, adaptability, and interpretability inherent in physics-based models, which are often indispensable in modeling real-world dynamic systems for optimization and control purposes. We propose a novel machine learning architecture, termed model-integrated neural networks (MINN), that can learn the physics-based dynamics of general autonomous or non-autonomous systems consisting of partial differential-algebraic equations (PDAEs). The obtained architecture systematically solves an unsettled research problem in control-oriented modeling, i.e., how to obtain optimally simplified models that are 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.

Optimizing parameter estimation in hydrological models with convolutional neural network guided dynamically dimensioned search approach

Hydrological model calibration plays a crucial role in estimating optimal parameters for accurate simulation. Estimation of parameters is inevitable in hydrological modeling due to the challenge of directly measuring them, as most parameters are conceptual descriptions of physical processes. Modellers commonly employ optimization algorithms for calibrating hydrological models. However, these algorithms often pose computational challenges, especially when dealing with complex physics-based and distributed models. To address these challenges, our study introduces a novel approach called hydroCNN+DDS. By leveraging the strengths of Convolutional Neural Networks (CNN) and the Dynamically Dimensioned Search (DDS) algorithm, hydroCNN+DDS simplifies the model calibration process in complex physics-based models. This approach enables to capture the general patterns and relationships between discharge time series and parameters without compromising the underlying physics. We use hydroCNN+DDS to estimate parameters in the highly parameterized hydrological model, Structure for Unifying Multiple Modeling Alternatives (SUMMA) using hourly observed discharge. Notably, hydroCNN quickly generates sub-optimal parameters, serving as a good initial solution for DDS. This initialization aids DDS in converging faster towards an optimal solution. One of the notable advantages of the hydroCNN+DDS approach is its potential for spatial and temporal transferability. This feature proves valuable in dynamic systems and regions with limited historical data, expanding the applicability of the methodology. Furthermore, our proposed methodology is versatile and can be applied to any simple or complex models, accommodating any variables of interest. The best practices of good model calibration are followed in our approach.

Fusing Physics-Based and Data-Driven Models for Car-Following Modeling: A Particle Filter Approach

Fusing Physics-Based and Data-Driven Models for Car-Following Modeling: A Particle Filter Approach

Bayesian continuous wavelet transform for time-varying damping identification of cables using full-field measurement

Cables serve as the primary load-bearing element in cable-stayed bridges, making their damping level critical for structural safety evaluation. Traditional operational modal analysis (OMA) faces challenges in damping identification due to result discreteness, and limited sensor deployment often leads to the loss of crucial modal information. This paper proposes a Bayesian continuous wavelet transform with Gabor wavelet (BCWT-G) method for time-varying damping identification using full-field measurement data. A computer vision technique combining the pyramid grafting network (PGNet) with neighboring frame pixel fitting (NFPF) is used to accurately capture full-field vibration data. The time-frequency domain properties of these data are then extracted and incorporated into a Bayesian probabilistic estimation framework for modal updating. The proposed method was validated through numerical simulations using a physics-based graphics model (PBGM), and actual cable testing under complex environments, demonstrating its effectiveness and robustness in identifying the time-varying dynamic characteristics of cables.

Bridging the gap: an interpretable coupled model (SWAT-ELM-SHAP) for blue-green water simulation in data-scarce basins

Blue water (BW) and green water (GW) are crucial components of the hydrological cycle, but their accurate simulation and interpretation remain challenging in data-scarce basins. We propose the SWAT-ELM-SHAP model, coupling the Soil and Water Assessment Tool (SWAT), Ensemble Learning Model (ELM), and Shapley Additive Explanations (SHAP) method. This novel approach bridges the gap between a physically-based hydrological model, a data-driven machine learning (ML) model, and a holistically-interpreted SHAP method, offering accurate blue-green water simulation and holistic result interpretation for improved water resources management in data-scarce basins. We took the transfer simulation of blue-green water from the Xiangjiang River Basin (source basin, 82,900km²) to the Zishui River Basin (target basin, 28,142km²) as a case study to test and evaluate the feasibility of the coupled model during 1991-2022. The model performance results indicate that the simulation accuracy of our new coupled model is improved in data-scarce basins. In combination with hydrological response features generated by SWAT and meteorological features as the ELM input, our model enhances the daily blue-green water simulation. The Nash-Sutcliffe Efficiency coefficient (NSE) for BW, Green water flow (GWF), and Green water storage (GWS) consistently exceeds 0.77 during the calibration period (1991-2010) and exceeds 0.8 during the testing period (2011-2022). The interpretation results of coupled model demonstrate that SHAP holistic interpretation provides good interpretability for blue-green water simulation results in data-scarce basins. In general, the SWAT-ELM-SHAP offers a referenced approach that can reliably and efficiently simulate blue-green water in data-scarce basins, but more importantly, can further our understanding of the potential causal relationships, influence mechanisms, and variation mechanisms of blue-green water under changing environmental conditions.

Use of deep learning and data augmentation by physics-based modelling for crack characterisation from multimodal ultrasonic TFM images

Use of deep learning and data augmentation by physics-based modelling for crack characterisation from multimodal ultrasonic TFM images

Predicting Long-Term Stability from Short-Term Measurement: Insights from Modeling Degradation in Perovskite Solar Cells during Voltage Scans and Impedance Spectroscopy.

A drift-diffusion model is used to investigate the effect of device degradation on current-voltage and impedance measurements of perovskite solar cells (PSCs). Modifications are made to the open-source drift-diffusion software IonMonger to model degradation via an increasing recombination rate during the course of characterization experiments. Impedance spectroscopy is shown to be a significantly more sensitive measure of degradation than current-voltage curves, reliably detecting a power conversion efficiency drop of as little as 0.06% over a 4 h measurement. Furthermore, we find that fast degradation occurring during impedance spectroscopy can induce loops lying above the axis in the Nyquist plot, the first time this experimentally observed phenomenon has been replicated in a physics-based model.

A Comprehensive Literature Review on the Resolution of Turbine Engine Performances' Inverse Problems

Abstract Turbine engine monitoring is a well-known and well-studied subject that proves to be essential for the aeronautic industry. A popular approach in engine monitoring is constructing indicators that reflect systems' health states by leveraging operational measurements (i.e., sensors' data during flights)—this is known as the engine performance's inverse problem. There exists an extensive literature on this topic, especially revolving around two well-used types of performance indicators of aircraft engines: efficiencies and air mass flow rates of engine's modules. This review aims to provide a comprehensive survey of this particular literature, which so far has not been properly organized and structured. Our first contribution is to propose a novel taxonomy of the relevant methods. In particular, we consider the role of physics-based models—an element that provides specific advantages and challenges in the context of aircraft engines monitoring—and see if each method exploits such models inside or outside the main algorithmic process (or not exploiting them at all). Our second contribution is to identify the pros and cons of each method, along with additional insights with respect to two commonly encountered challenges: under-determined scenarios and time-series data. Finally, we give some guidelines for selecting appropriate strategies in practical situations and perspectives for future works.

A Hybrid Approach Integrating Physics-Based Models and Expert-Augmented Neural Networks for Ship Fuel Consumption Prediction

Abstract The International Maritime Organization’s recent approval of the 2023 strategy on reduction of greenhouse gas emissions amplifies the pressure on stakeholders to achieve net-zero emissions in shipping by 2050. Considering the anticipated predominance of traditional single-fuel engines into the next decade, due to their high efficiency and economic benefits, the implementation of operational measures stands as the foremost effective method for mitigating emissions and reducing fuel consumption. Accurate fuel consumption prediction is crucial for informed decision-making and operational efficiency. This paper introduces an innovative hybrid model, combining an advanced physics-based model with an expert-augmented neural network, offering superior fuel consumption predictions. Expert knowledge is integrated into the neural network model to enhance its learning capabilities. Performance is validated against DNV Navigator Insight and publicly available fuel consumption reporting data, demonstrating superiority over purely data-driven and physics-based models. This hybrid approach bridges accuracy and scalability for sustainable maritime operations.

A Study of Loss Model Parameter Sensitivity in Compressor Unsteady Flow Simulations

Abstract This article presents results from a comprehensive sensitivity analysis focused on loss models used in a recently developed compressor unsteady mean line flow model for a transonic axial-centrifugal compressor. The mean line flow model treats flow through rotors and stators in their respective reference frames (rotating or stationary), and the compressor performance is determined by the kinetic energy addition and various physics-based loss models in relative frames. In this paper, we describe the modeling approach of the compressor flow model, as well as the loss models that are used to obtain a relatively good match against test data. Sensitivity studies of selected loss model parameters are presented to show the effect of individual loss model parameters on the overall compressor characteristics in the entire speed range. The effects of losses on unsteady flow transients are assessed by comparing the transient responses when a step reduction of throttle area is applied. The comparisons show that the change in loss magnitude has weak effects on transient response if the change of loss does not significantly change the system stability.

Temperature and state-dependent electrical conductivity of soft biological tissue at hyperthermic temperatures

Objective: We present a physics-based, temperature and state-dependent electrical conductivity model for soft biological tissue under thermal therapies with a quantified damage parameter that represents the state of soft biological tissue (degree of denaturation). Most existing models consider electrical conductivity to be only temperature-dependent and evaluate tissue damage during post-processing after temperature calculation. Our model allows tissue damage to be coupled into the thermal model for a more accurate description of both RF ablation and electrosurgery. Methods: We model the denaturation process with an Arrhenius-type differential equation for chemical kinetics and a modified Stogryn equation for electrical conductivity under state transition. We present experimental data from two types of heating procedures at 128 kHz to validate and showcase the capability of our model. Results: Our model is able to capture the change in electrical conductivity during heating, cooling, and reheating procedures, which distinguishes different states and shows the irreversibility of denaturation. The model also accurately captures tissue change during slow cooking at a constant temperature, highlighting a state dependence. Conclusion: By incorporating state dependence into the model for electrical properties, we are able to capture the denaturation process more accurately and distinguish different degrees of damage. Our model allows the modeling of procedures involving repeated heating or cooling, which is impossible for models without a state dependence. While being able to adapt to patient-specific needs, the model can be used to improve planning and control in future robot-assisted surgeries to reduce unnecessary damage.

Data and model synergy-driven rolling bearings remaining useful life prediction approach based on deep neural network and Wiener process

Abstract Various Remaining Useful Life (RUL) prediction methods, encompassing model-based, data-driven, and hybrid methods, have been developed and successfully applied to prognostics and health management for diverse rolling bearing. Hybrid methods that integrate the advantages of model-based and data-driven approaches have garnered significant attention. However, the effective integration of the two methods to address the randomness in rolling bearing full lifecycle processes remains a significant challenge. To overcome the challenge, this paper proposes a data and model synergy-driven RUL prediction framework that includes two data and model synergy approaches. Firstly, a convolutional stacked bidirectional long and short-term memory network with temporal attention mechanism is established to construct health index. The RUL prediction is achieved based on HI and polynomial model. Secondly, a three-phase prediction model based on the Wiener process is established by considering the evolution law of different degradation phases. Then, two synergy methods are designed. Strategy 1: HI is adopted as the observation value for online updating of physics degradation model parameters under Bayesian framework, and the RUL prediction results are obtained from the physics degradation model. Strategy 2: The RUL prediction results from the data-driven and physics-based model are weighted linearly combined to improve the overall prediction accuracy. The effectiveness of the proposed model is verified using two bearing full lifecycle datasets. The results indicate that the proposed approach can accommodate both short-term and long-term RUL predictions, outperforming state-of-the-art single models.

An automated computational framework to construct printability maps for additively manufactured metal alloys

In metal additive manufacturing (AM), processing parameters can affect the probability of macroscopic defect formation (lack-of-fusion, keyholing, balling), which can, in turn, jeopardize the final product’s integrity. A printability map classifies regions in the processing space where an alloy can be printed with or without porosity defects. However, the creation of these printability maps is resource-intensive. Previous efforts to generate printability maps have required single-track experiments on pre-alloyed powder, limiting the utilization of these printability maps for the high-throughput design of printable alloys. We address these challenges in the case of Laser Powder Bed Fusion AM (L-PBF-AM) by introducing a fully computational, predictive approach to create printability maps for arbitrary alloys. Our framework uses physics-based thermal models and a variety of defect formation criteria. We benchmark the predictive ability of the proposed framework against literature data for the following commonly printed alloys: 316 Stainless Steel, Inconel 718, Ti-6Al-4V, AF96, and Ni-5Nb. Furthermore, we deploy the framework on NiTi-based Shape Memory Alloys (SMAs) as a case study. We scrutinize the accuracy of various sets of defect criteria and use these accuracy measurements to create an uncertainty-aware probabilistic framework capable of predicting the printability maps of arbitrary alloys. This framework has the potential to guide alloy designers to potentially easy-to-print alloys, enabling the co-design of high-performing printable alloys.

A Comprehensive Review of Remaining Useful Life Estimation Approaches for Rotating Machinery

This review paper comprehensively analyzes the prognosis of rotating machines (RMs), focusing on mechanical-flaw and remaining-useful-life (RUL) estimation in industrial and renewable energy applications. It introduces common mechanical faults in rotating machinery, their causes, and their potential impacts on RM performance and longevity, particularly in wind, wave, and tidal energy systems, where reliability is crucial. The study outlines the primary procedures for RUL estimation, including data acquisition, health indicator (HI) construction, failure threshold (FT) determination, RUL estimation approaches, and evaluation metrics, through a detailed review of published work from the past six years. A detailed investigation of HI design using mechanical-signal-based, model-based, and artificial intelligence (AI)-based techniques is presented, emphasizing their relevance to condition monitoring and fault detection in offshore and hybrid renewable energy systems. The paper thoroughly explores the use of physics-based, data-driven, and hybrid models for prognosis. Additionally, the review delves into the application of advanced methods such as transfer learning and physics-informed neural networks for RUL estimation. The advantages and disadvantages of each method are discussed in detail, providing a foundation for optimizing condition-monitoring strategies. Finally, the paper identifies open challenges in prognostics of RMs and concludes with critical suggestions for future research to enhance the reliability of these technologies.

Physics-Informed Data-Driven Approaches to State of Health Prediction of Maritime Battery Systems

Battery systems are increasingly being used for powering ocean going ships, and the number of fully electric or hybrid ships relying on battery power for propulsion and maneuvering is growing. In order to ensure the safety of such electric ships, it is of paramount importance to monitor the available energy that can be stored in the batteries, and classification societies typically require that the state of health (SOH) of the batteries can be verified by independent tests – annual capacity tests. However, this paper discusses physics-informed data-driven approaches to online diagnostics for state of health monitoring of maritime battery systems based on a combination of physical knowledge, physic-based models, insights from extensive characterization tests and operational sensor data collected from the batteries during actual operation. This represents an alternative approach to the annual capacity tests for electric ships that is found to be sufficiently robust and accurate under certain conditions. Previous attempts with purely data-driven models, including both cumulative and snapshot models, semi-supervised learning and simple models based on the state of charge did not achieve the required reliability and accuracy for them to be utilized in a ship classification perspective, as presented at previous PHM conferences. However, preliminary results from the physics-informed data-driven method presented in this paper indicate that it can be relied on for independent verification of state of health as an alternative to physical tests. It has been tested on battery cells cycled in laboratory degradation tests as well as on field returns from batteries onboard ships in service. Notwithstanding, further validation and verification of the method is recommended to further build confidence in the model predictions.

Equivalence Ratio-Driven Flame Response of an Industrial Premixed Burner: Experiments and Modeling

Abstract This paper presents an analysis of the unsteady heat release rate response of premixed flames to equivalence ratio perturbations for an industrial premixed swirl-based burner. During this investigation, perfectly and technically premixed flames were acoustically forced via fuel/air mixture flow and air flow modulations, respectively, at the same operating conditions. From the resulting flame transfer functions (FTFs), measured using the multimicrophone method, the equivalence ratio driven FTF was isolated and extracted by removing the velocity driven component, i.e., the measured FTF from the perfectly premixed flame, from the technically premixed FTF with two novel extraction techniques. The results are compared with FTFs obtained directly in a previous experimental campaign where the fuel flow was acoustically forced, the resulting equivalence ratio fluctuations measured via an infrared absorption technique, and the heat release rate response to the forcing was quantified using chemiluminescence measurements. The results from both measurement approaches agreed well highlighting the validity of the techniques. Further, to understand the governing features of the equivalence ratio driven FTF, a physics-based analytical model following the G-equation approach was developed. The contributions from flame surface area, flame speed, and heat of reaction oscillations were modeled to describe the heat release rate dynamics. A limited number of physical parameters in the analytical model were anchored on one test condition, optimized and restricted to values, which were all physically reasonable, and were subsequently used for model predictions at other operating conditions. The FTF model predictions compared well with experimental data across a range of different operating conditions. Finally, the relative contributions from flame surface area, flame speed, and heat of reaction oscillations on the features of the FTFs were identified and explored.

Designing the next generation of polymers with machine learning and physics-based models

Abstract The development of next-generation polymers necessitates optimizing several key properties simultaneously, a task that is expensive and infeasible using traditional trial-and-error experimental approaches. A promising alternative is employing a combination of machine learning and physics-based tools to rapidly screen the polymer design space and provide suggestions of new polymers that meet the critical properties required for industrial applications. In this study, we introduce a comprehensive workflow that utilizes machine learning and molecular modeling approaches to design new polymers with the focus on improving five polymer properties: (1) glass transition temperature, (2) dielectric constant, (3) refractive index, (4) stress optic coefficient, and (5) linear coefficient of thermal expansion. Using a small dataset ( < 200 unique polymers), we developed quantitative structure-property relationships (QSPRs) models to accurately predict the experimental polymer properties for both homo- and co-polymer systems. We tested several ML algorithms and identified the best models for predicting these polymer properties, achieving test set R 2 greater than 0.77 across all properties. We then explored new polymers by creating a library of over ∼10 000 homopolymers using R-group enumeration tools and applied the trained QSPR models to rapidly predict the five polymer properties. The predictions of QSPR models were used to create a multi-parameter optimization score, which helped downselect the large polymer space to ∼10 promising candidates. The properties of these selected polymer candidates were subsequently validated with classical molecular dynamics simulations and density functional theory, revealing a strong correlation with the QSPR model predictions. Finally, one of the top candidates was validated by experiments, which showed good agreement against QSPR and physics-based models. Our workflow underscores the power of combining data-driven and theoretical methods in the polymer design process given a small dataset size, offering a valuable resource for experimentalists looking to leverage computer-aided strategies in materials innovation.

Investigation of hybrid modeling and its transferability in building load prediction used for district heating systems

In the district heating systems, the historical operation data of the buildings in those areas would be partially or entirely missing. The traditional data-driven model is hard to predict the ground truth results because the historical data is not available for model training. However, utilizing the physics-based methods for load calculation takes a long time to process and encounters low accuracy issues. This paper investigates several hybrid models that integrate the data-driven model and the physics-based models with different fusion methods. The physics-based models calculate envelope load and infiltration load, based on Fourier's law and the grand canonical ensemble theory, respectively. After undergoing load processing, features fusion, and residual connection, the best advanced hybrid models generate 21.35%, 16.35%, and 12.73% better prediction results compared with the data-driven model. Moreover, the advanced hybride models also perform strong transferability across all the data quantity groups. In terms of practical application, the advanced hybrid models could be deployed with effective generalization in limited data scenarios and robust transfer capabilities. The selected best model constructed by hybrid modeling displays the highest performance and saves the total training costs with strong transferability.

Physics-guided fault diagnosis method for proton exchange membrane fuel cells based on LSTM neural network

In this paper, we propose a novel hybrid method for fault diagnosis of Proton Exchange Membrane Fuel Cells (PEMFCs) based on the combination of a physics-based model and a long short-term memory (LSTM) neural network. By incorporating the physics-based model in the fault diagnosis algorithm, we can access to several process variables not directly measured through sensors but related to the state of the PEMFC stack. The model estimates are subsequently combined with signals measured on the PEMFC stack and inputted to a LSTM neural network. The performance of the physics-guided LSTM is evaluated on an extensive dataset comprising a thousand hours of operation of a PEMFC stack under dynamic load profiles, proving the enhanced capability of the proposed fault diagnosis method in capturing complex fault patterns. Furthermore, the effectiveness of the proposed method in dealing with PEMFC aging is tested by using data from the initial phase of stack operation for algorithm training and reserving the data from the aged stack operation for the testing phase. The experimental results reveal that the proposed physics-guided LSTM method allows for a significant amelioration over purely data-driven LSTM.

Physics-informed ensemble learning with residual modeling for enhanced building energy prediction

Accurate modeling of building energy use is important to support a diverse spectrum of its downstream applications, such as building energy efficiency assessment, resilience analysis, smart control, etc. As mainstream approaches of building energy modeling, physics-based modeling builds on different fidelities of physics rules yet are usually compromised in modeling accuracy due to insufficiency of physics rules to capture real-world dynamics and incomplete input information. Data-driven approaches are computationally efficient, but black box (uninterpretable) in nature. For improved modeling of building energy use, this work proposes a physics-informed ensemble learning approach in building energy prediction through residual modeling. Specifically, we first analyze the components of building energy use data. Evidence suggests that the building energy use data can be decomposed into the physics-driven part, occupant-driven part, and white noise. Second, high-fidelity physics-based building models (EnergyPlus) and low-fidelity ones (RC models) are developed to capture the physics-driven part while time series methods are explored as the residual modeling approach to capture the occupant-driven discrepancies between physics-based simulation and measured building energy use (i.e., residuals). Finally, the physics-informed ensemble learning is proposed to integrate physics-based and data-driven models for enhanced accuracy of building energy modeling. Results demonstrate 40–90% decrease of discrepancies between modeling and field observations compared to traditional physics-based modeling methods. Moreover, when the training dataset size is small, the proposed ensemble model overperforms the pure data-driven models, demonstrating its higher robustness in extrapolation scenarios. This work makes fundamental contributions to the development of convergent modeling approaches in the building modeling field.