Gaussian Process Regression Model Research Articles

Impact of Solder Voids on IGBT Thermal Behavior: A Multi-Methodological Approach

This study investigates the thermal behavior of Insulated Gate Bipolar Transistors (IGBTs) with a focus on the influence of solder voids within the device. Utilizing a combination of Finite Element Method (FEM) simulations, X-ray imaging, and SEM-EDX analysis, we accurately modeled the internal structure of IGBTs to assess the impact of void characteristics on thermal resistance. The findings reveal that the presence and characteristics of solder voids—particularly their size, number, and distribution—significantly affect the thermal resistance of IGBT devices. Experimental measurements validate the FEM model’s accuracy, confirming that voids disrupt the heat flow path, which can lead to increased thermal resistance and potential device failure. Five regression models, including Gaussian process regression (GPR) and neural networks, were employed to predict the thermal resistance based on void characteristics, with the GPR models demonstrating superior performance. The optimal GPR RQ model consistently provided accurate predictions with an RMSE of 0.0050 and R2 of 0.9728. Using the void percentage as the only input parameter for the regression models significantly impacted the prediction accuracy, showing the importance of the void extraction method. This study shows the necessity of minimizing solder voids and offers a robust methodological framework for a better prediction of the reliability of IGBTs.

Energy loss and efficiency investigations of a dual clutch transmission based on adaptive experiment and analytical simulation

Energy transfer improvement and energy consumption reduction are getting more crucial in the automotive sector. As one of the essential elements directly influencing energy transfer in the powertrain system, transmission losses have been widely analyzed with both simulation and experimental approaches. For a better characterization of individual losses, this paper investigates and compares most of the available analytical models for further system implementation. Regarding laboratory experiments, an adaptive sampling strategy is presented and analyzed for various operating conditions. Compared to the traditional factorial design, the applied Gaussian Process Regression (GPR) delivers both estimations and their predictive variances in the entire experiment process. Besides, new measurement candidates can be determined with the prior information from GPR model. The analytical simulation and adaptive measurement are employed to investigate a seven-speed transmission. With both approaches, a detailed discussion about total transmission losses and individual loss mechanisms are performed under various operating conditions.

Gaussian process regression with levy flight optimization: Advanced AR66 adsorption studies

The coal fly ash (CFA), which is the residue generated by coal-fired power plants, was converted into a valuable zeolite material known as zeolite P (ZNa-P) through thermal and acid pretreatments followed by microwave radiation. Various analytical techniques were utilized to analyze the resulting zeolite, including X-ray diffraction, scanning electron microscopy, Fourier transform infrared spectroscopy, thermogravimetric analysis, BET analysis, and zeta potential measurement. The efficiency of ZNa-P in eliminating anionic dyes from aqueous solutions was exhibited by successfully removing acid red dye 66 (AR66) from a solution composed of water. To optimize the removal process, Central Composite Design (CCD) was applied to investigate the impact of four main parameters: solution pH, initial dye concentration, adsorbent mass, and contact time. The generated CCD database was modeled using Gaussian process regression (GPR) with the Lévy flight distribution (LFD) optimization algorithm. The GPR model was then used to determine optimal conditions for maximum AR66 absorption (3405.3 mg/g), with a pH of 2, initial dye concentration of 1000 mg/L, adsorbent mass of 0.2 g/L, and contact time of 11 minutes. Furthermore, the GPR model exhibited significantly lower error (32.58 mg/g) in predicting the experimental values compared to the CCD model (204.92 mg/g), highlighting the efficiency and superiority of the GPR model in this study.

Integrated form-position measurement of large-aperture transparent elements based on stereoscopic phase measuring deflectometry

In the field of ultra-precision manufacturing and measurement, sub-aperture stitching is a widely employed technique for the measurement of complex optical components. Those influencing factors like system errors and numerical bias introduce notable stitching errors in the overlapped areas between sub-apertures, consequently degrading measurement accuracy. In addition, the surfaces forms, refractive indices, and positions are difficult to be specified simultaneously. In this paper, an integrated measurement method based on the stereo deflectometry is proposed, which can measure the surface form, refractive index, and relative position of large-aperture transparent components together. This method utilizes a Gaussian process regression model to decouple and predict the refractive index and relative positions of the upper and lower surfaces. Then, a robust sub-aperture stitching technique with an adaptive distance function is employed to correct the positioning errors of sub-apertures. The feasibility and effectiveness of this method are demonstrated. The final stitched surface results exhibit a measurement error of 320 nm and a thickness deviation of 28 μm.

Experimental validation of data-driven reactive control strategy for wave energy converters: A Gaussian process regression approach

Wave energy is a renewable energy source that can generate electricity without emitting carbon dioxide using wave energy converters (WECs). WECs face several challenges, such as effectively harnessing wave energy, ensuring operational safety, and implementing cost-saving measures. In this study, a data-driven reactive control strategy for WECs using Gaussian process regression is experimentally validated. The control strategy aimed to maximize energy absorption while satisfying physical constraints without a WEC dynamic model. In this study, the Gaussian process regression model represents a WEC dynamic model using an approximation function based on the input/output data. Experimental validation results confirmed that the proposed data-driven reactive control strategy effectively controlled the WEC and improved its performance using the Gaussian model. Moreover, performance was improved under different wave conditions compared to those used during training. The control strategy can be useful in situations where conventional methods cannot realize ideal control parameters, such as when substantial model errors exist or the WEC dynamic model changes over time. The data-driven approach that uses Gaussian process regression reduces learning costs compared to other machine-learning methods. It also has stable control performance because it is independent of the training dataset. The potential of data-driven approaches for optimizing WEC control strategies was highlighted.

A data-driven multi-objective optimization approach for enhanced methanol yield and exergy loss minimization in direct hydrogenation of CO[formula omitted]

The stability and control of process industries have historically faced obstacles due to inherent uncertainties in their operations. This work focuses on leveraging machine learning models as a surrogate to facilitate real-time optimization of operating conditions of the direct hydrogenation of CO2 to enhance methanol production while minimizing exergy losses. Numerous studies have explored steady-state exergy analysis and the impact of various process conditions on methanol production. However, there is a notable absence of research investigating the influence of exergy destruction on methanol production under dynamic conditions. Initially, a commercial software Aspen HYSYS was utilized to design, model, and simulate the methanol synthesis plant. Exergy analysis was conducted to quantify the process exergy losses, exergy efficiency, and potential areas for improvement. The process model transitioned to a dynamic mode by incorporating ±5% uncertainty into critical operating conditions, i.e., temperature, pressure, and molar flow rate, simulating real-world variability and resulting in a dataset of 370 samples. Two machine learning models; the Gaussian process regression (GPR) and artificial neural network (ANN) model were developed using the data samples to predict the process exergy losses and molar flow rate of methanol produced. To enhance the predictive capabilities of these deployed models, Bayesian optimization was employed for hyperparameter tuning. The developed models were employed as surrogates in multi-objective genetic algorithm (MOGA) environments with the aim of maximizing the production of methanol with minimum exergy losses under uncertainty. The optimized process conditions, derived from MOGA-based methods, underwent cross-validation using the Aspen model. This analysis revealed that the methanol synthesis plant exhibited an exergy loss of 2425 kW, an exergy efficiency of 97.78%, and an improvement potential of 53.74 kW. The GPR and ANN models demonstrated high correlation coefficients (R2) of 0.9928 and 0.9375, and root mean square error (RMSE) values of 38.93 and 1.122, respectively. Incorporating these machine learning models as surrogates within the optimization frameworks notably outperformed the base case, achieving maximum methanol production while minimizing exergy losses in the process.

Utilizing undisturbed soil sampling approach to predict elastic modulus of cohesive soils: a Gaussian process regression model

Utilizing undisturbed soil sampling approach to predict elastic modulus of cohesive soils: a Gaussian process regression model

Bayesian dynamic modelling for probabilistic prediction of pavement condition

Significant funds have been allocated to maintain road networks each year in developed countries. Performance prediction is crucial for pavement management systems to adjust working plans and budget allocation. As a Bayesian nonparametric method, Gaussian process regression (GPR) is powerful in predicting nonlinear time series and quantifying uncertainty. However, it remains computationally intensive and fails to adapt to the time-varying characteristics. To address such issues, a dynamic GPR model is proposed for probabilistic prediction of the International Roughness Index (IRI) for flexible pavements. A moving window strategy is developed to substantially shrink the size of training data, which effectively alleviates computational cost and thus leads to a dynamic GPR. A genetic algorithm is then adopted to determine the optimal window size by considering the trade-off between computational efficiency and accuracy. A dataset acquired from Long-Term Pavement Performance (LTPP) is used to demonstrate the feasibility of the dynamic GPR. Its performance is compared to traditional GPR as well as dynamic and static Bayesian linear regression (BLR) models. The comparison results indicate that the proposed dynamic GPR can increase the accuracy by 0.86, 1.52, and 2.27 times for dynamic BLR, static GPR, and static BLR, respectively. It exhibits the best results in terms of accuracy and uncertainty metrics due to its nonlinear modelling and time-varying ability.

Machine learning assisted improved desalination pilot system design and experimentation for the circular economy

Desalination is among the most feasible solutions to supply sustainable and clean drinking water in water scarcity areas. In this regard, Multi-Effect Desalination (MED) systems are particularly preferred for harsh feeds (high temperature and salinity) because of their robust mode of operation for water production. However, maintaining the efficient operation of the MED systems is challenging because of the large system design and variables' interdependencies that are sensitive to the distillate production. Therefore, this research leverages the power of machine learning and optimization to estimate the optimal operating conditions for the maximum distillate production from the MED system. In the first step, detailed experimentation is conducted for distillate production against hot water temperature (HWT) varying from 38 to 70 °C, and feed water temperature (FWT) is changed from 34 to 42 °C. Whereas, the feed flow rate (FFR) is investigated to be varied nearly from 3.6 to 8.7 LPM in the three stages, i.e., FFR-S1, FFR-S2 and FFR-S3. The compiled dataset is used to make the process models of the MED system by three ML-based algorithms, i.e., Artificial Neural Network (ANN), Support Vector Machine (SVM), and Gaussian Process Regression (GPR) under rigorous hyperparameters optimization. GPR exhibited superior predictive performance than those of ANN and SVM on R2 value of 0.99 and RMSE of 0.026 LPM. Monte Carlo technique-based variable significance analysis revealed that the HWT has the highest effect on distillate production with a percentage significance of 95.6 %. Then Genetic Algorithm is used to maximize the distillate production with the GPR model embedded in the optimization problem. The GPR-GA driven maximum distillate production is estimated on HWT = 70 ± 0.5 °C, FWT = 40 ± 2.5 °C, FFR-S1 = 6 ± 2.6 LPM, FFR-S2 = 7 ± 1 LPM and FFR-S3 = 7 ± 1. The ML-GA-based system analysis and optimization of the MED system can boost the distillate production that promotes operation excellence and circular economy from the desalination sector.

Integrating MODFLOW and machine learning for detecting optimum groundwater abstraction considering sustainable drawdown and climate changes

Detecting optimum groundwater abstraction is a challenging objective. This study proposes a new approach for identifying the optimum pumping rates by integrating MODFLOW with machine learning (ML). The adopted strategy has been applied to the Oligocene and Eocene aquifers in the western desert of Minia, Egypt. MODFLOW-2005 model has been utilized to simulate various management scenarios, including current and expected climate scenarios of two Representative Concentration Pathways (RCPs): RCP 4.5 and RCP 8.5. The steady-state and transient MODFLOW models were calibrated using the groundwater levels of 37 observation wells with a coefficient of correlation (R2) of 0.986 and 0.988, respectively. The developed model has been run for 80 years, from 2020 to 2100. The results of MODFLOW demonstrated a drawdown in the groundwater level in the two aquifers, about 40, 41, and 42 m, owing to current climate conditions and scenarios of RCP 4.5 and RCP 8.5, respectively, in 2100. Generated data based on the calibrated model has been used to develop the ML models. ML models have been applied to predict the pumping rates using the well coordinates, aquifer type, evapotranspiration, the operating period in days, and drawdown as inputs. For this purpose, four ML models, Gaussian Process Regression (GPR), Support Vector Regression (SVR), Tree, and Artificial Neural Network (ANN)) were developed and evaluated. All ML models demonstrated an effective performance during the training and validation processes, particularly the GPR model, which has the best ability to predict the pumping rates with a correlation coefficient, RMSE, and Mean Absolute Error (MAE) equal to 1.0, 6.53, and 8.04, respectively. Therefore, the GPR model has been utilized to identify the optimum pumping rates. The findings of the GPR model revealed that the optimum abstraction of the Oligocene aquifer is 602266, 625329, and 635061 m3/day, while the Eocene aquifer’s optimal groundwater abstraction is 10229801, 1027906, and 102936 m3/day, considering the current climate, RCP 4.5, and RCP8.5, respectively. Anticipated findings are supposed to be instrumental for decision-makers, offering valuable insights into sustainable groundwater management. The novel integration methodology promotes the efficient use of groundwater, contributing to achieving sustainable development goals (SDGs).

Towards autonomous learning and optimisation in textile production: data-driven simulation approach for optimiser validation

AbstractThe textile industry is a traditional industry branch that remains highly relevant in Europe. The industry is under pressure to remain profitable in this high-wage region. As one promising approach, data-driven methods can be used for process optimisation in order to reduce waste, increase profitability and relieve mental burden on staff members. However, approaches from research rarely get adopted into practice. We identify the high dimensionality of textile production processes leading to high model uncertainty as well as an incomplete problem formulation as the two main problems. We argue that some form of an autonomous learning agent can address this challenge, when it safely explores advantageous, unknown new settings by interacting with the process. Our main goal is to facilitate the adoption of promising research into practical applications. The main contributions of this paper include the derivation and formulation of a probabilistic optimisation problem for high-dimensional, stationary production processes. We also create a highly adaptable simulation of the textile carded nonwovens production process in Python that implements the optimisation problem. Economic and technical behavior of the process is approximated using both Gaussian Process Regression (GPR) models trained with industrial data as well as physics-motivated explicit models. This ’simulation first’-approach makes the development of autonomous learning agents for practical applications feasible because it allows for cheap testing and validation before physical trials. Future work will include the comparison of the performance of different agent approaches.

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.

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

AbstractHardware‐based sensing frameworks such as cooperative fuel research engines are conventionally used to monitor research octane number (RON) in the petroleum refining industry. Machine learning techniques are employed to predict the RON of integrated naphtha reforming and isomerisation processes. A dynamic Aspen HYSYS model was used to generate data by introducing artificial uncertainties in the range of ±5% in process conditions, such as temperature, flow rates, etc. The generated data was used to train support vector machines (SVM), Gaussian process regression (GPR), artificial neural networks (ANN), regression trees (RT), and ensemble trees (ET). Hyperparameter tuning was performed to enhance the prediction capabilities of GPR, ANN, SVM, ET and RT models. Performance analysis of the models indicates that GPR, ANN, and SVM with R2 values of 0.99, 0.978, and 0.979 and RMSE values of 0.108, 0.262, and 0.258, respectively performed better than the remaining models and had the prediction capability to capture the RON dependence on predictor variables. ET and RT had an R2 value of 0.94 and 0.89, respectively. The GPR model was used as a surrogate model for fitness function evaluations in two optimisation frameworks based on genetic algorithm and particle swarm method. Optimal parameter values found by the optimisation methodology increased the RON value by 3.52%. The proposed methodology of surrogate‐based optimisation will provide a platform for plant‐level implementation to realise the concept of industry 4.0 in the refinery.

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.

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.

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.

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.