Physics-guided Neural Network Research Articles

Physics-guided neural network for grinding temperature prediction

Creep-feed grinding is a high-efficiency, high-precision grinding process widely used in the manufacturing of aviation engines. However, the workpiece burn and other quality issues caused by high processing temperature limit the yield of grinding. Therefore, the accurate model of grinding temperature has become the key to improving processing efficiency and quality. Different from the traditional physical or data-driven models, this paper attempts to combine both perspectives based on Physics-Guided Neural Networks (PGNN) to accurately predict grinding temperature with a small number of experiments. At the level of data acquisition, real grinding experiment data was obtained and a data augmentation method had been proposed. At the level of neural network structure, optimisation processes were implemented to enhance prediction performance, and a physics-guided loss function was inserted to guide network training. The experiment results shows that PGNN had better prediction accuracy than the physical model, while also mitigating the limitations of data-driven models on small sample sets. PGNN also performed better with noisy data and predictions out of the training data range, this reveals the benefits of PGNN for small sample problems in processing scenarios.

A micromechanical scheme with nonlinear concentration functions by physics-guided neural network

The mechanical behavior of heterogeneous materials has been reported to be significantly influenced by the nonlinear properties of both the matrix and interface. However, the micromechanical homogenization methods for predicting the effective properties are challenged in nonlinear problems due to the difficulties in solving the analytical form of the concentration tensors. In this study, we develop a nonlinear micromechanical scheme for heterogeneous materials with complex interfacial behaviors, where the key component, namely nonlinear concentration functions, is determined by the devised physics-guided neural network. In particular, the nonlinear Mori–Tanaka method (NMT) implemented within this new micromechanical scheme yields accurate solutions to axisymmetric nonlinear homogenization problems considering the effects of finite deformation, loading conditions, volume fraction, etc. Furthermore, the NMT is equivalent to the linear Mori–Tanaka method in the condition of the small deformation. Notably, this neural-network-based micromechanical scheme shows good generalization for different types of nonlinear interfaces, while the corresponding approach for generating training data via the finite element method (FEM) is cost-effective. This theoretical framework introduces a novel approach to nonlinear physical modeling, namely, not by the direct regression from the dataset but by deeply embedding neural networks in physical laws.

Enhancing accuracy of surface wind sensors in wind tunnel Testing: A Physics-Guided neural network calibration approach

Irwin’s surface wind sensor is widely used in wind tunnel testing for urban and environmental aerodynamics studies. However, the conventional physics-based calibration of this sensor could result in reduced measurement accuracy in regions with low flow velocities and high turbulence intensity. To address this issue, this study proposes a novel physics-guided neural network (PGNN) calibration approach, which couples a physics-based calibration model, derived from extended Taylor series expansions of measured wind speed, with an adaptive, data-driven general regression neural network. Sensors are calibrated within the turbulent boundary layer of an empty flat plate, considering both mean and standard deviation of wind velocity measured by high-accuracy thermal anemometry. The accuracy of calibrated sensors is then assessed using a 1:400 benchmark urban model. Experimental results show significant improvement in measurement accuracy, reducing mean absolute percentage error for wind speed standard deviation from 92.3 % with the current model to 9.8 % using PGNN.

A Novel Physics-Guided Neural Network for Predicting Fatigue Life of Materials

A physics-guided neural network (PGNN) is proposed to predict the fatigue life of materials. In order to reduce the complexity of fatigue life prediction and reduce the data required for network training, the PGNN only predicts the fatigue performance parameters under a specific loading environment, and calculates the fatigue life by substituting the load into the fatigue performance parameters. The advantage of this is that the network does not need to evaluate the effect of numerical changes in the load on fatigue life. The load only needs to participate in the error verification, which reduces the dimension of the function that the neural network needs to approximate. The performance of the PGNN is verified using published data. Due to the reduction in the complexity of the problem, the PGNN can use fewer training samples to obtain more accurate fatigue life prediction results and has a certain extrapolation ability for the changes in trained loading environment parameters. The prediction process of the PGNN for fatigue life is not completely a black box, and the prediction results are helpful for scholars to further study the fatigue phenomenon.

Interpretable chiller fault diagnosis based on physics-guided neural networks

Chillers are critical for building system energy efficiency and occupant comfort. Various methods have been developed for diagnosing chiller faults, with deep learning being a common choice due to its strong end-to-end learning capability. But in the absence of physical knowledge, deep learning models cannot provide a diagnosis outcome in accordance with the mechanisms behind faults, resulting in models lacking interpretability. In this regard, this paper proposes an interpretable chiller fault diagnosis method based on physics-guided neural networks. Through a comprehensive analysis of the chiller’s working process and fault evolution, a key physical indicator related to the condenser fouling fault is derived. Then a corresponding physical inconsistency loss function is developed to construct a condenser fouling fault-oriented diagnostic model. The proposed method has been demonstrated to be effective in reducing physical inconsistency while retaining diagnostic performance. The proposed method is conducive to applying the neural network approach in real operational scenarios and can serve as a reference for future research.

A physics-guided machine learning framework for real-time dynamic wake prediction of wind turbines

Efficient and accurate prediction of the wind turbine dynamic wake is crucial for active wake control and load assessment in wind farms. This paper proposes a real-time dynamic wake prediction model for wind turbines based on a physics-guided neural network. The model can predict the instantaneous dynamic wake field under various operating conditions using only the inflow wind speed as input. The model utilizes Taylor's frozen-flow hypothesis and a steady-state wake model to convert instantaneous inflow wind speed and turbine parameters into neural network input features. A deep convolutional neural network then maps these features to desired wake field snapshots, enabling dynamic wake predictions for wind turbines. To train the model, we generated approximately 255 000 instantaneous flow field snapshots of single-turbine wakes using the large eddy simulation, covering different thrust coefficients and yaw angles. The model was trained using the supervised learning method and verified on the test set. The results indicate that the model can effectively predict the dynamic wake characteristics, including the dynamic wake meandering and the wake deflection of the yawed turbines. The model can also assess both the instantaneous wake velocity and the instantaneous wake center of a wind turbine. At a thrust coefficient of 0.75, the root mean square error for the predicted instantaneous wake velocity is around 6.53%, while the Pearson correlation coefficient for the predicted instantaneous wake center can reach 0.624. Furthermore, once the model is trained, its prediction accuracy does not decrease with the increase in the time span.

Regression transients modeling of solid rocket motor burning surfaces with physics-guided neural network

Monitoring the burning surface regression in ground static ignition tests is crucial for predicting the internal ballistic performance of solid rocket motors (SRMs). A previously proposed ultra-sparse computed tomography imaging method provides a possibility for real-time monitoring. However, sample shortages of SRMs highlights the need for monitoring accuracy, especially given the high cost associated with the design and development of SRM systems. Therefore, constructing datasets via regression simulations to compensate for SRM sample shortages is critical. To address this issue, we recommend adopting the level-set method to dynamically track the burning surface by solving partial differential equations (PDEs). The computational cost of numerical solution is prohibitive for scientific applications involving large-scale spatiotemporal domains. The physics-informed neural network (PINN) and neural operator have been used to accelerate the solution of PDE, showing satisfactory prediction performance and high computational efficiency. We designed a physics-guided network, named LS-PhyNet, that couples the potential physical mechanisms of burning surface regression into the deep learning framework. The proposed method is capable of encoding well-established traditional numerical discretization methods into the network architecture to leverage prior knowledge of underlying physics, thus providing the model with enhanced expressive power and interpretability. Experimental results prove that LS-PhyNet can better reproduce the burning surfaces obtained by numerical solution with only small data regimes, providing a new paradigm for real-time monitoring of burning surface regression transients during static ignition tests.

HOSSNet: An efficient physics-guided neural network for simulating micro-crack propagation

The Hybrid Optimization Software Suite (HOSS), which combines the finite-discrete element method (FDEM), is an advanced approach for simulating high-fidelity fracture and fragmentation processes. However, the application of pure HOSS simulation is computationally expensive. Meanwhile, machine learning methods, which have shown tremendous success in various scientific problems, are increasingly being considered as promising alternatives to physics-based models in scientific domains. Thus, the objective of this work is to develop a new data-driven methodology to accurately reconstruct micro-crack fractures in both spatial and temporal fields. We leverage physical constraints to regularize the fracture propagation in long-term reconstructions. Additionally, we introduce perceptual loss and several machine learning optimization approaches to further enhance the reconstruction performance of fracture data. We demonstrate the effectiveness of the proposed method through both extrapolation and interpolation experiments. The results confirm that the proposed method can reconstruct high-fidelity fracture data across space and time in terms of pixel-wise reconstruction error and structural similarity. Visual comparisons also yield promising results in long-term reconstruction.

Reconstructing Turbulent Flows Using Spatio-temporal Physical Dynamics

Accurate simulation of turbulent flows is of crucial importance in many branches of science and engineering. Direct numerical simulation (DNS) provides the highest fidelity means of capturing all intricate physics of turbulent transport. However, the method is computationally expensive because of the wide range of turbulence scales that must be accounted for in such simulations. Large eddy simulation (LES) provides an alternative. In such simulations, the large scales of the flow are resolved, and the effects of small scales are modelled. Reconstruction of the DNS field from the low-resolution LES is needed for a wide variety of applications. Thus the construction of super-resolution methodologies that can provide this reconstruction has become an area of active research. In this work, a new physics-guided neural network is developed for such a reconstruction. The method leverages the partial differential equation that underlies the flow dynamics in the design of spatio-temporal model architecture. A degradation-based refinement method is also developed to enforce physical constraints and to further reduce the accumulated reconstruction errors over long periods. Detailed DNS data on two turbulent flow configurations are used to assess the performance of the model.

Physics-Guided Neural Network for Load Margin Assessment of Power Systems

The power system load margin is an important index used in power system operation centers. Traditional load margin calculation involves solving a set of differential-algebraic equations where not all information is always available. Data-driven methods such as Neural Networks (NNs) have been proposed but present poor performance and lack of generalization, especially in cases other than the operating history of power systems. In this article, we propose a Physics-Guided Neural Network (PGNN) to calculate the load margin of power systems. The PGNN is regularized by an auxiliary process that aims to reconstruct the power flow equations at the stability threshold that defines the load margin. In the PGNN training stage, there are two error functions that must be minimized, one related to the empirical knowledge of the system and the other related to the physical knowledge of the system associated with the guarantee of power flow. Case studies are presented for two test power systems, IEEE 68-bus system and Brazilian interconnected power system, considering a set of operating conditions, signal noise and outliers. The results show the superior performance of PGNN over traditional NNs.

Phy-Taylor: Partially Physics-Knowledge-Enhanced Deep Neural Networks via NN Editing.

Purely data-driven deep neural networks (DNNs) applied to physical engineering systems can infer relations that violate physics laws, thus leading to unexpected consequences. To address this challenge, we propose a physics-knowledge-enhanced DNN framework called Phy-Taylor, accelerating learning-compliant representations with physics knowledge. The Phy-Taylor framework makes two key contributions; it introduces a new architectural physics-compatible neural network (PhN) and features a novel compliance mechanism, which we call physics-guided neural network (NN) editing. The PhN aims to directly capture nonlinear physical quantities, such as kinetic energy, electrical power, and aerodynamic drag force. To do so, the PhN augments NN layers with two key components: 1) monomials of the Taylor series for capturing physical quantities and 2) a suppressor for mitigating the influence of noise. The NN editing mechanism further modifies network links and activation functions consistently with physics knowledge. As an extension, we also propose a self-correcting Phy-Taylor framework for safety-critical control of autonomous systems, which introduces two additional capabilities: 1) safety relationship learning and 2) automatic output correction when safety violations occur. Through experiments, we show that Phy-Taylor features considerably fewer parameters and a remarkably accelerated training process while offering enhanced model robustness and accuracy.

Physics-guided neural network for predicting asphalt mixture rutting with balanced accuracy, stability and rationality

The prediction of rutting performance of asphalt materials poses a significant challenge due to the intricate relationships between the rutting performance and its influencing factors. Machine learning models have gained popularity to address this challenge by offering sophisticated model structures and algorithms. However, existing models often prioritize model accuracy over stability and rationality. The increasingly complicated model structure may lead to an imbalance between the data and the model, resulting in issues such as overfitting and reduced model applicability and interpretability. In this context, this study proposes a novel modeling framework to predict the rutting performance of asphalt mixture by utilizing autoencoder for feature selection and feedforward neural network for rut depth prediction. Notably, physics information of the selected variables is implemented into the neural network to achieve the appropriate balance of model accuracy, stability, and rationality. The results demonstrate that while maintaining high model accuracy, the implementation of physics information significantly enhances the model’s stability and rationality. This framework holds great potential for accurate and reliable predictions of pavement distress by leveraging the complementary strengths of data-driven machine learning and physics-based domain knowledge.

Structural Seismic Response Reconstruction Using Physics-Guided Neural Networks

Reconstruction of data loss in structural seismic responses is important for structural health monitoring to evaluate the safety of structures. A physics-guided neural network that leverages the prior knowledge was proposed for reconstructing structural seismic responses that were inaccessible to measure or missing during earthquakes. The presented methodology consisted of convolutional neural networks with dilated kernel and fully connected neural networks, which were developed to achieve a multitask learning that involved the regression task with measured labeled displacement data and the reconstruction task of seismic response without any labels. To better balance the loss gradient across different tasks, a probabilistic model was introduced to optimize the weight coefficient for each task by quantifying the task-dependent uncertainty based on Bayesian statistics. The weight coefficient for each task can be dynamically updated during the training process, thereby improving the learning efficacy and performance accuracy of the neural networks. The probabilistic model with task-dependent uncertainty was validated to outperform the equal-weighted model (i.e. equal weight for each task) in reconstructing the structural seismic responses based on numerical data, even when the relevant physical information (i.e. Bouc–Wen model) was not complete.

Improving the out-of-sample generalization ability of data-driven chiller performance models using physics-guided neural network

Modeling of the chiller performance is essential for the implementation of optimal energy-efficient control strategies in a heating, ventilation, and air conditioning (HVAC) system. Though classical data-driven chiller performance models are widely adopted in the industry, they generally suffer from poor out-of-sample generalization abilities, which refers to the model's capability to extrapolate for new data outside the range of the training dataset. In practice, however, the available chiller operation data for model development are often insufficient or collected from a few limited operating conditions, such that extrapolation is unavoidable after the model is applied for control purposes. To deal with this issue, this paper proposed a physics-guided neural network (PGNN) to model the energy performance of chillers. By adopting a new neural network architecture, modifying the loss function, and adding limited out-of-sample data, the PGNN incorporates domain knowledge into the data-driven model to achieve better out-of-sample generalization performance. Meanwhile, the convexity and monotonicity between the dependent and independent variables in the PGNN are properly addressed. The proposed PGNN is applied to model the chiller serving a high-rise building, and results show that PGNN performs much better in extrapolation than classical models and the multi-layer perceptron model. The research demonstrated the usefulness and effectiveness of the PGNN in modeling HVAC equipment.

Unsupervised fault diagnosis framework for underwater thruster system using estimated torques and multi-head convolutional autoencoder

The thruster system is one of the most critical parts of an autonomous underwater vehicle. Feedback, propeller, motor and driver faults are four common field faults of thruster systems. This paper investigates an unsupervised framework based on torques and multi-head convolutional autoencoders for the mentioned faults. The proposed method utilizes an extended state observer to estimate the motor load. The propeller torque is estimated using a physics-guided neural network. Meanwhile, the relationship between the patterns change among torques (motor load and propeller torque) and different faults are analyzed. Then, to avoid feature aliasing, two independent encoders of the multi-head convolutional autoencoder extract the pattern features between the torques automatically. Finally, faults are detected and classified based on the various patterns of the extracted torque features. The sea trial data verified the effectiveness of the scheme. The results show that the method can accurately detect and classify five specific faults: current feedback fault, speed feedback fault, propeller loss, propeller winding and open-circuit fault.

A Bayesian defect-based physics-guided neural network model for probabilistic fatigue endurance limit evaluation

Accurate fatigue assessment of material plagued by defects is of utmost importance to guarantee safety and service continuity in engineering components. This study shows how state-of-the-art semi-empirical models can be endowed with additional defect descriptors to probabilistically predict the occurrence of fatigue failures by exploiting advanced Bayesian Physics-guided Neural Network (B-PGNN) approaches. A B-PGNN is thereby developed to predict the fatigue failure probability of a sample containing defects, referred to a given fatigue endurance limit.In this framework, a robustly calibrated El Haddad’s curve is exploited as the prior physics reinforcement of the probabilistic model, i.e., prior knowledge. Following, a likelihood function is built and the B-PGNN is trained via Bayesian Inference, thus calculating the posterior of the parameters. The arbitrariness of the choice of the related architecture is circumvented through a Bayesian model selection strategy. A case-study is analysed to prove the robustness of the proposed approach. This methodology proposes an advanced practical approach to help support the probabilistic design against fatigue failure.

Inverse Design of Two-Dimensional Shape-Morphing Structures

Abstract This study proposes an inverse method for synthesizing shape-morphing structures in the lateral direction by integrating two-dimensional hexagonal unit cell with curved beams. Analytical expressions are derived to formulate the effective Young’s modulus and Poisson’s ratio for the base unit-cell as a function of its geometric parameters. The effective lateral Poisson’s ratio can be controlled by manipulating a set of geometric parameters, resulting in a dataset of over 6000 data points with Poisson’s ratio values ranging from −1.2 to 10.4. Furthermore, we utilize the established dataset to train an inverse design framework that utilizes a physics-guided neural network algorithm, and the framework can predict design parameters for a targeted shape-morphing structure. The proposed approach enables the generation of structures with tailored Poisson’s ratio ranging from −1.2 to 3.4 while ensuring flexibility and reduced stress concentration within the predicted structure. The generated shape-morphing structures’ performance is validated through numerical simulation and physical tensile testing. The finite element analysis (FEA) simulation results confirm agreement with the designed values for the shape-morphing structure, and the tensile testing results reveal the same trend in shape-morphing behavior. The proposed design automation framework demonstrates the feasibility of creating intricate and practical shape-morphing structures with high accuracy and computational efficiency.

Neural optimization machine: a neural network approach for optimization and its application in additive manufacturing with physics-guided learning.

Neural networks (NNs) are increasingly used in design to construct the objective functions and constraints, which leads to the needs of optimization of NN models with respect to design variables. A Neural Optimization Machine (NOM) is proposed for constrained single/multi-objective optimization by appropriately designing the NN architecture, activation function and loss function. The NN's built-in backpropagation algorithm conducts the optimization and is seamlessly integrated with the additive manufacturing (AM) process-property model. The NOM is tested using several numerical optimization problems. It is shown that the increase in the dimension of design variables does not increase the computational cost significantly. Next, a brief review of the physics-guided machine learning model for fatigue performance prediction of AM components is given. Finally, the NOM is applied to design processing parameters in AM to optimize the mechanical fatigue properties through the physics-guided NN under uncertainties. One novel contribution of the proposed methodology is that the constrained process optimization is integrated with physics/knowledge and the data-driven AM process-property model. Thus, a physics-compatible process design can be achieved. Another significant benefit is that the training and optimization are achieved in a unified NN model, and no separate process optimization is needed. This article is part of the theme issue 'Physics-informed machine learning and its structural integrity applications (Part 1)'.

Nano-coated composite fastener: Structure health monitoring based on magneto-mechanical effect

The heavy metallic fasteners and undetectable defects in the joining area have long posed challenges for composite structures. In this study, we propose a composite fastener that incorporates a nano-coating on the thread and embeds magnet in the shank. Based on magneto-mechanical effect, a physics-guided neural network (PGNN) is proposed to establish a correlation between magnetic density and bearing stress. For the strengthening effect of nano-coating, the bearing strength of composite joint reinforced by nano-coated composite fastener reaches 196, representing a 26.5% increase compared to the composite joint reinforced by an un-coated fastener. When all-composite joint fails, the nano-coated fastener shears off at the shank, whereas the un-coated fastener shears off at the thread. The predicted bearing stress from PGNN can reasonably quantify the real stress situation of testing joints. The maximum prediction error of the PGNN is merely 18.9 MPa, which is 51.7% lower than that of a neural network (NN) without physical guidance. Compared with the NN, the PGNN shows the abilities of reducing prediction randomness, better convergence, and higher prediction accuracy. This research presents a possible substitute for metallic fasteners to reduce the composite structure weight and monitor structure health.

Physics-Guided Neural Network Model for Aeroengine Control System Sensor Fault Diagnosis under Dynamic Conditions

Sensor health assessments are of great importance for accurately understanding the health of an aeroengine, supporting maintenance decisions, and ensuring flight safety. This study proposes an intelligent framework based on a physically guided neural network (PGNN) and convolutional neural network (CNN) to diagnose sensor faults under dynamic conditions. The strength of the approach is that it integrates information from physics-based performance models and deep learning models. In addition, it has the structure of prediction–residual–generation-fault classification that effectively decouples the interaction between sensor faults and system state changes. First, a PGNN generates the engine’s non-linear dynamic prediction output because the PGNN has the advantage of being able to handle temporal information from the long short-term memory (LSTM) network. We use a cross-physics–data fusion scheme as the prediction strategy to explore the hidden information of the physical model output and sensor measurement data. A novel loss function that considers physical discipline is also proposed to overcome the performance limitations of traditional data-driven models because of their physically inconsistent representations. Then, the predicted values of the PGNN are compared with the sensor measurements to obtain a residual signal. Finally, a convolutional neural network (CNN) is used to classify faults for residual signals and deliver diagnostic results. Furthermore, the feasibility of the proposed framework is demonstrated on an engine sensor fault dataset. The experimental results show that the proposed method outperforms the pure data-driven approach, with the predicted RMSE being reduced from 1.6731 to 0.9897 and the diagnostic accuracy reaching 95.9048%, thereby confirming its superior performance.