Gaussian Process Regression Model Research Articles

Coupling Global Parameters and Local Flow Optimization of a Pulsed Ejector for Proton Exchange Membrane Fuel Cells

Proton exchange membrane fuel cells (PEMFCs), as an important utilization of hydrogen energy, contribute to the sustainable development of global energy. Pulsed ejectors have a high potential for improving the hydrogen utilization of PEMFCs in the full operating range by circulating unconsumed hydrogen. In this study, a pulsed ejector applied to a 120 kW fuel cell was designed, and the flow characteristics were analysed using computational fluid dynamics (CFD). Based on the data from the CFD model, the global optimization of the ejector was carried out using the Gaussian process regression (GPR) surrogate model and the grey wolf optimization (GWO) algorithm. The local structure was then further optimized using an adjoint method coupling streamlining modification that takes into account the local flow characteristics. The CFD results showed that, under a fixed structure, increasing the pressure difference between the secondary flow and the ejector outlet would promote boundary layer separation, shorten the shockwave chain length, change the effective flow area of the secondary flow, and lower the entrainment ratio (ER). The analytical results from the GPR model indicated significant interactions among the structural parameters. The globally optimized ejector using GPR and GWO improved the hydrogen entrainment ratio from 1.42 to 3.12 at the design point. Furthermore, the results of streamlining local optimization show that the entrainment ratio increased by 1.67% at the design point and increased by up to 3.99% over the full operating range compared to the optimized ejector by global optimization.

Prediction of mechanical properties of LPBF built part based on process monitoring and Gaussian process regression

As a highly promising technology in additive manufacturing, the laser powder bed fusion has only limited application due to its low reproducibility. In this study, the image information of the 316L specimen after laser scanning and powder paving of each layer was acquired by a complementary metal–oxide–semiconductor industrial camera. The important features were selected, extracted and quantificated by analyzing the tensile test results. Finally, combined with the laser power, the quantified features were as input of a Gaussian process regression model based on optimization algorithm of grid search to predict the tensile strength of 316L specimen. The results show that the quantized image features have a significant improvement on the regression effect, and the coefficient of determination (R 2) is improved from 63% to 90.57% compared to using only the laser power as input.

Prediction and optimisation of gasoline quality in petroleum refining: The use of machine learning model as a surrogate in optimisation framework

Prediction and optimisation of gasoline quality in petroleum refining: The use of machine learning model as a surrogate in optimisation framework

Effect of Human Head Shape on the Risk of Traumatic Brain Injury: A Gaussian Process Regression-based Machine Learning Approach.

Computational head injury models are promising tools for understanding and predicting traumatic brain injuries. However, most available head injury models are "average" models that employ a single set of head geometry (e.g., 50th-percentile U.S. male) without considering variability in these parameters across the human population. A significant variability of head shapes exists in U.S. Army soldiers, evident from the Anthropometric Survey of U.S. Army Personnel (ANSUR II). The objective of this study is to elucidate the effects of head shape on the predicted risk of traumatic brain injury from computational head injury models. Magnetic resonance imaging scans of 25 human subjects are collected. These images are registered to the standard MNI152 brain atlas, and the resulting transformation matrix components (called head shape parameters) are used to quantify head shapes of the subjects. A generative machine learning model is used to generate 25 additional head shape parameter datasets to augment our database. Head injury models are developed for these head shapes, and a rapid injurious head rotation event is simulated to obtain several brain injury predictor variables (BIPVs): Peak cumulative maximum principal strain (CMPS), average CMPS, and the volume fraction of brain exceeding an injurious CMPS threshold. A Gaussian process regression model is trained between head shape parameters and BIPVs, which is then used to study the relative sensitivity of the various BIPVs on individual head shape parameters. We distinguish head shape parameters into 2 types: Scaling components ${T_{xx}}$, ${T_{yy}}$, and ${T_{zz}}$ that capture the breadth, length, and height of the head, respectively, and shearing components (${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$) that capture the relative skewness of the head shape. An overall positive correlation is evident between scaling components and BIPVs. Notably, a very high, positive correlation is seen between the BIPVs and the head volume. As an example, a 57% increase in peak CMPS was noted between the smallest and the largest investigated head volume parameters. The variation in shearing components ${T_{xy}},{T_{xz}},{T_{yx}},{T_{yz}},{T_{zx}}$, and ${T_{zy}}$ on average does not cause notable changes in the BIPVs. From the Gaussian process regression model, all 3 BIPVs showed an increasing trend with each of the 3 scaling components, but the BIPVs are found to be most sensitive to the height dimension of the head. From the Sobol sensitivity analysis, the ${T_{zz}}$ scaling parameter contributes nearly 60% to the total variance in peak and average CMPS; ${T_{yy}}$ contributes approximately 20%, whereas ${T_{xx}}$ contributes less than 5%. The remaining contribution is from the 6 shearing components. Unlike peak and average CMPS, the VF-CMPS BIPV is associated with relatively evenly distributed Sobol indices across the 3 scaling parameters. Furthermore, the contribution of shearing components on the total variance in this case is negligible. Head shape has a considerable influence on the injury predictions of computational head injury models. Available "average" head injury models based on a 50th-percentile U.S. male are likely associated with considerable uncertainty. In general, larger head sizes correspond to greater BIPV magnitudes, which point to potentially a greater injury risk under rapid neck rotation for people with larger heads.

Enabling efficient regional seismic fragility assessment of multi‐component bridge portfolios through Gaussian process regression and active learning

AbstractRegional seismic fragility assessment of bridge portfolios must address the embedded uncertainties and variations stemming from both the earthquake hazard and bridge attributes (e.g., geometry, material, design detail). To achieve bridge‐specific fragility assessment, multivariate probabilistic seismic demand models (PSDM) have recently been developed that use both the ground motion intensity measure and bridge parameters as inputs. However, explicitly utilizing bridge parameters as inputs requires numerous nonlinear response history analyses (NRHAs). In this situation, the associated computational cost increases exponentially for high‐fidelity bridge models with complex component connectivity and sophisticated material constitutive laws. Moreover, it remains unclear how many analyses are sufficient for the response data and the resulting demand model to cover the entire solution space without overfitting. To deal with these issues, this study integrates Gaussian process regression (GPR) and active learning (AL) into a multistep workflow to achieve efficient regional seismic fragility assessment of bridge portfolios. The GPR relaxes the probability distribution assumptions made in typical cloud analysis‐based PSDMs to enable heteroskedastic nonparametric seismic demand modeling. The AL leverages the varying standard deviation to select the least but most representative bridge‐model‐ground‐motion sample pairs to conduct NRHA with much‐improved efficiency. Both independent and correlated multi‐output GPRs are proposed to deal with bridge portfolios with seismic demand correlations among multiple components (column, bearing, shear key, abutment, unseating, and joint seal). Considering a single benchmark highway bridge class in California as the case study, the AL‐GPR framework and the associated component‐level fragility results are investigated in terms of their efficiency, accuracy, and robustness. The fragility results show that 70 AL‐selected samples would enable the GPR to derive bridge‐specific fragility models comparable to the ones using the multiple stripes analysis approach with 1950 ground motions considered for each individual bridge. The AL‐GPR model also successfully captures the physics of how bridge span length, deck area, column slenderness, and steel reinforcement ratio would change the damage state exceedance probabilities of different bridge components. The efficiency of AL stems from the fact that, with the multi‐output independent GPR, a stable and reliable fragility model can be achieved using 50 AL‐selected samples compared to at least 270 randomly chosen samples. The proposed methodology advances the state of the art in enabling more efficient and reliable regional seismic fragility assessment of multi‐component bridge portfolios.

Non-oscillatory fracture mode partition for interface crack under mixed-mode loading

The oscillatory crack-tip field in the classical interface fracture mechanics solution often leads to complications in identifying the mode mixity in bimaterial interface fracture problems. In this paper, a non-singular series solution for the continuum problem of a crack on the cohesive-spring interface under mixed-mode loading is presented and compared to the classical oscillatory solution. A Gaussian process regression model was also developed to enable quick evaluation of the phase angle for interface delamination characterization by using mixed-mode bending fracture test.

Machine-Learning-Based Kinetic-Free Hybrid Gray-Box Model to Predict Sulfuric-Acid-Catalyzed Esterification Reaction.

The sulfuric-acid-catalyzed esterification reaction of 2-butanol and propionic anhydride is a vital industrial process. In this paper, several experiments are conducted via reaction calorimetry to validate that both sulfuric and propionic acids have discernible catalytic effects on the reaction. This finding complicates the accurate description of the reaction kinetics through traditional methods. So this paper turns to a kinetic-free black-box model, Gaussian process regression (GPR) model via 24 experiments, as a more adaptable approach. Besides, the best GPR model is combined with traditional heat balance model to generate a hybrid gray-box model, which can give complete knowledge of reaction process. The hybrid gray-box model finally achieves maximum root-mean-square error (RMSE) of 0.0069 for conversion, 0.6535 for temperature, and 10.6087 for heat flow rate, underscoring its pretty good predictive ability.

A physical simulation-machine learning model for optimal process schemes in laser-based directed energy deposition process

The major challenge faced is the definition of optimal process variables for rich quality of fabricated parts in laser-based directed energy deposition (DED-LB) processes. However, predicting the optimal process scheme using machine learning models is still challenging owing to the need for a large amount of training experimental data with high costs in DED-LB. In view of this, a physical simulation (PS)-machine learning (ML) model using a relatively small accurate data set of 31 simulation data for optimal process schemes is proposed in DED-LB process in this study. Firstly, a powder-scale high precision phenomenon model incorporating the mass transfer, phase transformations and heat transfer and using Lagrangian particle model to add mass is developed to depict the DED-LB process. Then, a Gaussian process regression (GPR) agent model is established to rapidly and accurately predict the geometry and dilution rate of deposition tracks under different manufacturing parameters based on the high precision simulation results. Finally, a PS-ML model for process parameter optimization is developed using the particle swarm algorithm (PSO), and the optimized parameters are experimentally validated. The results show that the developed powder-scale model and GPR model results are consistent with the Inconel 718 alloy experimental results. The proposed PS-ML model can increase the accuracy of the ML models even with a small simulation data set. None of PS-ML model optimization results has a relative error of more than 3% to the experimental results, and the dilution rate is reduced by up to 61.66% compared to the experimental design parameters without optimization. The proposed physical simulation-machine learning model in this study enables inexpensive and accurate optimization of DED-LB process parameters.

A novel decoupled approach combining invertible cross-entropy method with Gaussian process modeling for reliability-based design and topology optimization

Design optimization considering the presence of uncertainties in parameters poses an extremely challenging problem. The source of difficulties comes with reliability-based formulations, where addressing the probabilistic problem exhausts the large computing efforts for failure estimations of the structure violating limit-state functions (LSFs). This paper proposes a novel decoupled approach for effectively solving reliability-based design optimization (RBDO) problems, namely an invertible cross-entropy (iCE) method advantageously combined with a Gaussian process regression (GPR) model, termed as iCE-GPR. The GPR model is applied to approximate the spectrum of LSFs under random parameters. Furthermore, to enhance the accurate prediction of the system failure probability, an active learning process is applied to systematically refine the GPR model by adding new learning points in the region with the largest uncertainty and high-reliability sensitivity through the maximization of an expected feasibility function (EFF). Based on the updated GPR model, the failure probability is estimated by a cost-effective cross-entropy (CE) method without any calls to the actual performance function. To perform the decoupling optimization process with the reliability analysis, the novel iCE, based on the CE method, is developed to update the most probable point (MPP) assigned for the next deterministic optimization process in determining the new optimal design. The method iteratively performs the deterministic optimization process based on the MPP underpinning LSFs sequentially updated by the active learning process. The proposed iCE-GPR method fast-converges the optimal design and significantly alleviates computational burdens associated with reliability analyses. The proposed method is also applied to solve a reliability-based topology optimization (RBTO) problem. Four numerical examples for both the RBDO and RBTO problems are provided to illustrate efficiency and robustness of the proposed iCE-GPR method.

A Gaussian process approach for rapid evaluation of skin tension

Skin tension plays a pivotal role in clinical settings, it affects scarring, wound healing and skin necrosis. Despite its importance, there is no widely accepted method for assessing in vivo skin tension or its natural pre-stretch. This study aims to utilise modern machine learning (ML) methods to develop a model that uses non-invasive measurements of surface wave speed to predict clinically useful skin properties such as stress and natural pre-stretch. A large dataset consisting of simulated wave propagation experiments was created using a simplified two-dimensional finite element (FE) model. Using this dataset, a sensitivity analysis was performed, highlighting the effect of the material parameters and material model on the Rayleigh and supersonic shear wave speeds. Then, a Gaussian process regression model was trained to solve the ill-posed inverse problem of predicting stress and pre-stretch of skin using measurements of surface wave speed. This model had good predictive performance (R2 = 0.9570) and it was possible to interpolate simplified parametric equations to calculate the stress and pre-stretch. To demonstrate that wave speed measurements could be obtained cheaply and easily, a simple experiment was devised to obtain wave speed measurements from synthetic skin at different values of pre-stretch. These experimental wave speeds agree well with the FE simulations, and a model trained solely on the FE data provided accurate predictions of synthetic skin stiffness. Both the simulated and experimental results provide further evidence that elastic wave measurements coupled with ML models are a viable non-invasive method to determine in vivo skin tension. Statement of significanceTo prevent unfavourable patient outcomes from reconstructive surgery, it is necessary to determine relevant subject-specific skin properties. For example, during a skin graft, it is necessary to estimate the pre-stretch of the skin to account for shrinkage upon excision. Existing methods are invasive or rely on the experience of the clinician. Our work aims to present an innovative framework to non-invasively determine in vivo material properties using the speed of a surface wave travelling through the skin. Our findings have implications for the planning of surgical procedures and provides further motivation for the use of elastic wave measurements to determine in vivo material properties.

Surrogate modeling with non-stationary-noise based Gaussian process regression and K-Fold ANN for systems featuring uneven sensitivity distribution

In the realm of aircraft design, there is a prevalent need for surrogate modeling techniques capable of efficiently and accurately modeling objects with high evaluation costs and uneven sensitivity distributions, such as those encountered in the nonlinear buckling of thin-walled structures and aerodynamics at transonic speeds. However, the non-stationary Gaussian Process Regression (GPR) model requires extensive hyperparameters or judicious assumptions, limiting its applications in such tasks, and the commonly used K-Fold methodology suffers from inherent instability. Addressing these issues, this paper proposes an active learning method for surrogate modeling in systems featuring uneven sensitivity distribution, integrating non-stationary-noise GPR and K-Fold Artificial Neural Network (ANN) methodology, namely NSN-GPR-KF. Instead of relying on a non-stationary kernel function, the algorithm regards noise as a non-stationary factor within a stationary GPR framework, with noise levels estimated via the K-Fold ANN methodology, allowing GPR to efficiently adapt to non-stationary systems while avoiding the aforementioned requirements for non-stationary GPR. Case validations, performed on two test functions with pronounced uneven spatial sensitivity, demonstrate that NSN-GPR-KF outperforms commonly used stationary GPR and pure K-Fold methodology. It synthesizes the exploration capabilities of GPR with the exploitation proficiency of the K-Fold methodology, achieving comparable global accuracy with reduced sample sizes—up to 26% and 22% less than the other two algorithms, respectively. The algorithm was successfully applied to predict the buckling load of thin-walled pipe beams, demonstrating accelerated convergence and approximately 25% greater accuracy compared to pure K-Fold model. These results suggest that NSN-GPR-KF can serve as an efficient and precise modeling tool for engineering tasks with high evaluation costs and complex sensitivity distributions.

Adaptive switching and routing protocol design and optimization in internet of things based on probabilistic models

Through smart cities, Intelligent Transportation Systems (ITS), the agricultural sector, and wearable devices, the Internet of Things (IoT) has revolutionized several human interests. Through the development of new cluster tasks, the Decision-Making System (DMS) of Cluster Heads (CHs), and improving the accuracy of traffic prediction and reliability of transportation, the present study intends to improve the energy depletion of IoT devices. The paper explores the subject of data flow optimization using Fuzzy Assisted Cuckoo Search Optimization (FACSO), traffic flow using Gaussian Process Regression (GPR), and CH prediction using the Stochastic Optimization Algorithm (SOA). Optimizing network lifetime while minimizing Energy Consumption (EC) is feasible through the practical application of the SOA, GPR, and FACSO models. Increasing End-to-End Delay (EED), Network Throughput (NT), and energy efficiency can be rendered feasible through a real-time DMS regarding routing employing a novel approach referred to as FACSO. This approach has enhanced the efficacy and reliability of Wireless Sensor Networks (WSN). With up to 500 nodes and an EC of 0.3451 J, the experiment's findings demonstrate that a proposed SOA-FACSO model achieves superior EED.

USING MACHINE LEARNING TO PREDICT THE MECHANICAL PROPERTIES OF PET FIBER-REINFORCED CONCRETE

Fiber-reinforced concrete enhances structural integrity by improving post-cracking behavior and ductility, yet traditional fibers can be costly and have a significant environmental impact. Recently, polyethylene terephthalate (PET) fiber, derived from recycled plastic bottles, has been used as a reinforcing material in concrete to enhance its mechanical properties. Utilizing advanced machine learning algorithms, this research analyzes a comprehensive dataset collected from existing literature on the mechanical properties of PET fiber-reinforced concrete (PFRC), including concrete density, water-to-binder ratio, fine and coarse aggregates, and fiber parameters such as volume fraction and aspect ratio of PET fibers. Through the application of Polynomial Regression, Exponential Gaussian Process Regression (GPR), and Cubic Support Vector Machine (SVM) models, the study effectively predicts PFRC’s mechanical behavior, showcasing high R² values indicating the models’ predictive strength: 0.93 for compressive, 0.92 for flexural, and 0.92 for tensile properties. This investigation highlights the exceptional accuracy of Exponential GPR and Cubic SVM models in capturing complex, non-linear relationships within the material, demonstrating machine learning’s capability to advance the sustainable development of construction materials. This study provides significant insights into optimizing the use of recycled fibers for concrete reinforcement.

Adaptive Design of Experiments to Fit Surrogate Gaussian Process Regression Models Allows Fast Sensitivity Analysis of the Input Waveform for Patient-Specific 3D CFD Models of Liver Radioembolization

Background and objectivePatient-specific 3D computational fluid dynamics (CFD) models are increasingly being used to understand and predict transarterial radioembolization procedures used for hepatocellular carcinoma treatment. While sensitivity analyses of these CFD models can help to determine the most impactful input parameters, such analyses are computationally costly. Therefore, we aim to use surrogate modelling to allow relatively cheap sensitivity analysis. As an example, we compute Sobol's sensitivity indices for three input waveform shape parameters. MethodsWe extracted three characteristic shape parameters from our input mass flow rate waveform (peak systolic mass flow rate, heart rate, systolic duration) and defined our 3D input parameter space by varying these parameters within 75%-125% of their nominal values. To fit our surrogate model with a minimal number of costly CFD simulations, we developed an adaptive design of experiments (ADOE) algorithm. The ADOE uses 100 Latin hypercube sampled points in 3D input space to define the initial design of experiments (DOE). Subsequently, we re-sample input space with 10,000 Latin Hypercube sampled points and cheaply estimate the outputs using the surrogate model. In each of 27 equivolume bins which divide our input space, we determine the most uncertain prediction of the 10,000 points, compute the true outputs using CFD, and add these points to the DOE. For each ADOE iteration, we calculate Sobol's sensitivity indices, and we continue to add batches of 27 samples to the DOE until the Sobol indices have stabilized. ResultsWe tested our ADOE algorithm on the Ishigami function and showed that we can reliably obtain Sobol's indices with an absolute error <0.1. Applying ADOE to our waveform sensitivity problem, we found that the first-order sensitivity indices were 0.0550, 0.0191 and 0.407 for the peak systolic mass flow rate, heart rate, and the systolic duration, respectively. ConclusionsAlthough the current study was an illustrative case, the ADOE allows reliable sensitivity analysis with a limited number of complex model evaluations, and performs well even when the optimal DOE size is a priori unknown. This enables us to identify the highest-impact input parameters of our model, and other novel, costly models in the future.

Prediction of key quality attributes in Salvia miltiorrhiza standard decoction using a Gaussian process regression model.

Nonstationary, nonlinear mass transfer in traditional Chinese medicine (TCM) extraction poses challenges to correlating process characteristics with quality parameters, particularly in defining clear parameter ranges for the process. The aim of the study was to provide a solution for quality consistency analysis in TCM preparation processes. Salvia miltiorrhiza was taken as an example for 15 batches of standard decoction. Using aqueous extract, alcoholic extract, and the content of salvianolic acid B as herb material key quality attributes, multiple nonlinear regression, Gaussian process regression, and artificial neural network models were employed to predict the key quality attributes including the paste yield, the content of salvianolic acid B, and the transfer rate. The evaluation criteria were root mean square error, mean absolute percentage error, and R2. The Gaussian process regression model had the best prediction effect on the paste yield, the content of salvianolic acid B, and the transfer rate, with R2 being 0.918, 0.934, and 0.919, respectively. Utilizing Gaussian process regression model confidence intervals, along with Shewhart control and intervals optimized through process capability index analysis, the quality control range of the standard decoction was determined as follows: paste yield, 25.14%-33.19%; salvianolic acid B content, 2.62%-4.78%; and transfer rate, 56.88%-64.80%. This study combined the preparation process of standard decoction with the Gaussian process regression model, accurately predicted the key quality attributes, and determined the quality parameter range by using process analysis tools, providing a new idea for the quality consistency standard of TCMprocesses.

Post-earthquake building damage assessment: A multi-period inspection routing approach for Gaussian process regression

In the wake of seismic events, prompt and accurate building damage assessment is crucial to inform post-disaster interventions and recovery efforts. This paper advances a novel multi-period planning strategy for post-earthquake building inspections, conceptualizing the task as a multi-period orienteering problem (MPOP). In this framework, each building selected for inspection hosts a specific reward indicating its informative value for damage assessment. The objective is to design inspection routes that maximize damage information acquisition while adhering to time constraints. After data collection, we utilize a Gaussian process regression (GPR) model to estimate the damage in uninspected buildings. To validate our approach, we conduct an earthquake simulation with realistic building information from San Francisco. The experimental outcomes reveal that our multi-period damage assessment framework maintains robust performance across diverse scenarios and consistently surpasses conventional period-by-period inspection strategies, yielding enhanced damage information acquisition and greater precision in damage estimation. This outcome underscores the effectiveness of our proposed method in strengthening post-earthquake damage assessment and improving recovery planning.

The Enhanced Adsorption Capacity of Ziziphus jujuba Stones Modified with Ortho-Phosphoric Acid for Organic Dye Removal: A Gaussian Process Regression Approach

Here, the chemical modification of Ziziphus jujuba stones (ZJS) treated with ortho-phosphoric acid (ZJS-H3PO4) is investigated to enhance its adsorption properties for organic dyes. The physicochemical properties of ZJS-H3PO4 reveal increased porosity (87.29%), slightly higher bulk density (0.034 g mL−1), and enhanced acidity (31.42 m eq g g−1) compared to untreated ZJS. XRF analysis confirms the successful incorporation of orthophosphoric acid during treatment due to a significant increase in phosphorus content. The maximum adsorption capacity of methylene blue on ZJS-H3PO4 is found to be 179.83 mg g−1, demonstrating its efficacy as a potential adsorbent for organic dyes. These findings suggest that modifying ZJS with orthophosphoric acid could be a promising strategy to enhance its adsorption performance in various environmental applications. Furthermore, Gaussian process regression (GPR) is employed to model MB adsorption by ZJS-H3PO4. Optimization of the GPR model involves evaluating different kernel functions and meticulously adjusting parameters to maximize its ability to capture complex relationships in the data. The obtained GPR model demonstrates remarkable performance with high correlation coefficients (R) and low root mean square errors (RMSEs) across all study phases. Model validation is performed through residual analysis, confirming its effectiveness and accuracy in predicting MB adsorption. Finally, a user-friendly interface is developed to facilitate the usage of the GPR model in future applications, representing a significant advancement in environmental process modeling and ecosystem management.

Development of an Emulator for Radiation Physics Simulator Using Stochastic Variational Gaussian Process Model

This paper describes an emulator that uses a Stochastic Variational Gaussian process (SVGP) regression model to parameterize radiation in a numerical weather prediction (NWP) model that meteorologically models the Earth's weather system. The computation of radiative processes is very large, accounting for most of the total NWP model computation. Statistical emulators are surrogate models that represent simulators and can overcome the computational limitations of very complex simulators such as radiative processes. Recently, artificial neural network-based radiative transfer emulators have been developed, and in this study, a statistical model, GP, is used to develop a radiative transfer emulator. The GP model has the advantage of calculating the uncertainty of the prediction along with the prediction, so the uncertainty of the prediction can be utilized appropriately. However, the computational complexity of the conventional GP model is very high, making it difficult to apply to large data. To solve this problem, an approximate approach, the SVGP model, was utilized. To further reduce the dimensionality of the input variables, we used a combined neural network and SVGP model. As a result, the SVGP-based radiative physics emulator improved its accuracy by about 20% compared to the artificial neural network emulator. However, the computation speed was about 3 to 9 times slower than the neural network emulator, but it was faster than the computation speed of the NWP model. This suggests that statistical emulators can be used to replace NWP model simulators.

Complementing Drawability Assessment of Deep-Drawn Components With Surrogate-Based Global Sensitivity Analysis

Abstract In the early-stage development of sheet metal parts, key design properties of new structures must be specified. As these decisions are made under significant uncertainty regarding drawing configuration changes, they sometimes result in the development of new parts that, at a later design stage, will not be drawable. As a result, there is a need to increase the certainty of experience-driven drawing configuration decisions. Complementing this process with a global sensitivity analysis (GSA) can provide insight into the impact of various changes in drawing configurations on drawability, unveiling cost-effective strategies to ensure the drawability of new parts. However, when quantitative global sensitivity approaches, such as Sobol's method, are utilized, the computational requirements for obtaining Sobol indices can become prohibitive even for small application problems. To circumvent computational limitations, we evaluate the applicability of different surrogate models engaged in computing global design variable sensitivities for the drawability assessment of a deep-drawn component. Here, we show in an exemplary application problem, that both a standard Gaussian process regression (GPR) model and an ensemble model can provide commendable results at a fraction of the computational cost. We compare our surrogate models to existing approaches in the field. Furthermore, by comparing drawability measures we show that the error introduced by the surrogate models is of the same order of magnitude as that from the choice of drawability measure. In consequence, our surrogate models can improve the cost-effective development of a component in the early design phase.

Machine learning-powered estimation of malachite green photocatalytic degradation with NML-BiFeO3 composites

This study explores the potential of photocatalytic degradation using novel NML-BiFeO3 (noble metal-incorporated bismuth ferrite) compounds for eliminating malachite green (MG) dye from wastewater. The effectiveness of various Gaussian process regression (GPR) models in predicting MG degradation is investigated. Four GPR models (Matern, Exponential, Squared Exponential, and Rational Quadratic) were employed to analyze a dataset of 1200 observations encompassing various experimental conditions. The models have considered ten input variables, including catalyst properties, solution characteristics, and operational parameters. The Exponential kernel-based GPR model achieved the best performance, with a near-perfect R2 value of 1.0, indicating exceptional accuracy in predicting MG degradation. Sensitivity analysis revealed process time as the most critical factor influencing MG degradation, followed by pore volume, catalyst loading, light intensity, catalyst type, pH, anion type, surface area, and humic acid concentration. This highlights the complex interplay between these factors in the degradation process. The reliability of the models was confirmed by outlier detection using William’s plot, demonstrating a minimal number of outliers (66–71 data points depending on the model). This indicates the robustness of the data utilized for model development. This study suggests that NML-BiFeO3 composites hold promise for wastewater treatment and that GPR models, particularly Matern-GPR, offer a powerful tool for predicting MG degradation. Identifying fundamental catalyst properties can expedite the application of NML-BiFeO3, leading to optimized wastewater treatment processes. Overall, this study provides valuable insights into using NML-BiFeO3 compounds and machine learning for efficient MG removal from wastewater.