Kriging Model Research Articles

An active learning reliability method combining population Monte Carlo and Kriging model for small failure probability

This study investigates the analysis of small failure probability problems and proposes the AK-PMC method, which combines the Population Monte Carlo (PMC) method with an active learning Kriging model (AK). The PMC method, as a variant of importance sampling, iteratively improving the quality of particles by reweighting them and updating the proposal distributions. In AK-PMC, Kriging model and PMC collaborate with each other. In each iteration, PMC draws potential importance samples according to the prediction information of Kriging model and Kriging is updated by choosing an optimal training point among the importance samples of PMC. After several iterations, the importance samples of PMC will cover the important failure regions and the Kriging model will accurately predict the limit state surface. To avoid the waste of training points, the relative error of failure probability estimated by PMC is derived by considering the prediction information of Kriging model. Three numerical examples and one practical engineering example are investigated to verify the performance of the proposed method.

Investigation and Optimization of Wave Suppression Baffles in Automobile Integrated Water Tanks

The risk of liquid agitation in pump-driven tanks within integrated tanks has significantly escalated due to the growing demands for tank integration in new-energy vehicles. In order to solve the problem of liquid sloshing in integrated tanks, this paper presents the design of a baffle structure aimed at reducing waves in integrated water tanks. The numerical simulation method of combining the level-set function with the volume of fluid (CLSVOF) has been employed, significantly enhancing the accuracy of numerical calculations related to a two-phase flow field inside an integrated tank. A comparison was made by analyzing different factors, notably baffle length (L), baffle depth (H), and baffle angle (θ), to investigate their influences in suppressing liquid agitation within the integrated water tank. Numerical computations were conducted utilizing design points acquired by the Latin hypercube sampling technique. The Kriging approximation modelling method was employed to hold down computing time. The Pareto solution was obtained by means of the non-dominated sorting genetic algorithm II, while the optimal solution set was evaluated and ranked using the multi-criteria decision-making algorithm (MCDM). The results show that increasing the baffle depth within a certain range can effectively suppress the wave height in the tank. When the baffle depth is increased to a certain value, the effect on wave-height suppression in the water tank is limited. When the baffle length and angle of the baffle exceed a certain value, it will also have the effect of suppressing the wave height in the tank. After comparing various factors of the baffle, it was ultimately found that the wave suppression effect is maximal when the length of the baffle is 13 millimeters, the depth of the baffle is 49 millimeters, and the angle of the baffle is -20 degrees. The main contribution of this study is the proposed wave-suppressing baffle structure, which provides new insights for the future structural design of integrated water tanks.

An efficient surrogate model for system reliability with multiple failure modes

AbstractThe failure modes of complex systems are often highly dependent. Aiming at the reliability analysis of engineering systems with multiple failure modes, an efficient surrogate model for system reliability with multiple failure modes is proposed, namely, the Copula Adaptive Kriging surrogate model (CAKSM). First, the initial Kriging model is established based on the initial samples. In order to select more effective added samples to update the Kriging model, a new learning function, namely, Copula Unites with Expected Improvement Function (CUEIF), is established. The function can make a reasonable sample selection by considering the failure correlation. Then, based on the optimal Copula function, the reliability data of each failure mode are coupled and analyzed. In order to adapt to various computing scales, regularization is introduced to improve the prediction speed of the surrogate model, and the probability density function of each performance function is obtained by introducing nonparametric kernel density estimation. Finally, the effectiveness of the CAKSM method and the learning function CUEIF is verified through four examples.

Hydrodynamic model-driven evolutionary algorithm-based operation optimization of an experimental drainage pumping station

ABSTRACT The effective operation of pumping stations plays a crucial role in urban flood management. However, challenges persist in optimizing pumping station operations, including inaccuracies in characterizing flood propagation and the high computational costs associated with optimization. This study introduces a novel optimization approach for pumping station operation that integrates a hydrodynamic model with evolutionary algorithms, leveraging data-driven technology. The method iteratively computes operation rules using the adaptive particle swarm optimization (APSO) algorithm to identify optimal solutions. The hydrodynamic model accurately simulates flood propagation and provides hydraulic parameters for the objective function and constraints of the APSO algorithm. With the predictive capability of the Kriging model, the optimization enhances efficiency by reducing the frequency of calls to the hydrodynamic model. A study case of a flood management digital twin experimental platform was then taken for the application. Compared to initial operation rules, the objective function value of the proposed method is reduced by 28.7, 32.5, and 25%, respectively, under varying magnitudes of unsteady flood inflows, demonstrating high performances in both flood mitigation and operation cost control. Moreover, the method only requires 70 calls to the hydrodynamic model to formulate the decision operation rule.

Development of electromagnetic pollution maps utilizing Gaussian process spatial models

The rapid proliferation of wireless technologies in everyday environments demands the quick and precise estimation of electromagnetic field distribution. This distribution is commonly depicted through the electric field strength across various geographical areas. The objective of this research is to determine the most effective geospatial model for generating a national-level electric field strength map within the 30 MHz–6 GHz frequency range. To achieve this, we employed five different methodologies for constructing the electric field strength map. Four of these methodologies are based on Gaussian process regression, while the fifth utilizes the classical weighted-average method of the nearest neighbor. Our study focused on a country with a total area of 9251 km2, using a dataset comprising 3621 measurements. The findings reveal that Gaussian process spatial models, also known as Kriging models, generally outperform other methods when applied to spatial data. However, it was observed that, after excluding some outlier data points, the performance of the classical nearest neighbor models becomes comparable to that of the Gaussian process models. This indicates the potential for both approaches to be effective, depending on the data quality and the presence of outliers.

A hybrid sparrow optimization Kriging model and its application in geological modeling

With the proposal of intelligent mines, the demand for drilling is increasing daily. Therefore, it is particularly crucial to gather more geological data by interpolation of limited drilling data for subsequent three-dimensional geological modeling. In this paper, a hybrid sparrow optimization Kriging model (HSSA), in which chaos theory and Levy flight are integrated into the initial population update algorithm of the sparrow algorithm and the location update algorithm of the entrants, is proposed. Next, the golden sine optimization algorithm is introduced into the reconnaissance and early warning mechanism of the sparrow algorithm to further improve the accuracy and local escape ability. By the correlation optimization of the original sparrow algorithm, the speed and accuracy of swarm intelligence optimization are further improved. In addition, the model solves the parameters of the variation function of the ordinary Kriging interpolation and reduces the generation error of the formation data interpolation. The results of relevant experiments show that the hybrid sparrow optimization Kriging model improves the accuracy and convergence speed compared with other swarm intelligence algorithms and that the accuracy of this model is improved by 8.4% compared with the original Kriging interpolation algorithm. Based on the hybrid sparrow optimization Kriging model, we propose a three-dimensional stratigraphic model for the Yangchangwan Coal Mine, which provides further support for mining operations and three-dimensional stratigraphic research in this area. The accuracy and applicability of the hybrid sparrow optimization Kriging model are further explained using a case study with the stratigraphic model data in the Yangchangwan Coal Mine. HSSA with significant potential for applications in industries such as coal mining and geological exploration. In these fields, the efficient acquisition, processing, and modeling of stratigraphic data are critical for enhancing geological interpretation and optimizing operational workflows.

Applied machine learning: Performance prediction of heat pipe with mesh wick

This study presents an investigation of a heat pipe with a mesh wick, utilizing machine learning (ML) techniques. The model including radial basis function interpolation (RBF), Kriging model (KRG), and the k-nearest neighborhood model (K-NN) were studied and compared. A set of training and validating populations were classified using a k-means clustering technique. The design variable included the geometric shape of heat pipe such as its diameter, the properties and percentage used of working fluid, and the temperature at the evaporator. The prediction case study included the heat transfer rate (q), and total difference temperature between evaporator and condenser section (ΔT). The prediction results found that the ΔT gave the most accurate indicator while the q is passable to applied. The Kriging model proved to be the most accurate, achieving an RMSE of 0.9896 and R2 of 0.9149 for heat transfer rate prediction, and an RMSE of 0.1902 and R2 of 0.9398 for total temperature difference prediction with 90 % training data. The second-best accuracy was achieved by the RBF model, with the linear, thin plate, and cubic spline kernels performing reasonably well.

Life cycle assessment of metal powder production: a Bayesian stochastic Kriging model-based autonomous estimation

Metal powder contributes to the environmental burdens of additive manufacturing (AM) substantially. Current life cycle assessments (LCAs) of metal powders present considerable variations of lifecycle environmental inventory due to process divergence, spatial heterogeneity, or temporal fluctuation. Most importantly, the amounts of LCA studies on metal powder are limited and primarily confined to partial material types. To this end, based on the data surveyed from a metal powder supplier, this study conducted an LCA of titanium and nickel alloy produced by electrode-inducted and vacuum-inducted melting gas atomization, respectively. Given that energy consumption dominates the environmental burden of powder production and is influenced by metal materials’ physical properties, we proposed a Bayesian stochastic Kriging model to estimate the energy consumption during the gas atomization process. This model considered the inherent uncertainties of training data and adaptively updated the parameters of interest when new environmental data on gas atomization were available. With the predicted energy use information of specific powder, the corresponding lifecycle environmental impacts can be further autonomously estimated in conjunction with the other surveyed powder production stages. Results indicated the environmental impact of titanium alloy powder is slightly higher than that of nickel alloy powder and their lifecycle carbon emissions are around 20 kg CO2 equivalency. The proposed Bayesian stochastic Kriging model showed more accurate predictions of energy consumption compared with conventional Kriging and stochastic Kriging models. This study enables data imputation of energy consumption during gas atomization given the physical properties and producing technique of powder materials.

Association between residential noise exposure and burnout among healthcare workers in Taiwan: a cross-sectional study

Few studies have explored the association between residential noise exposure and burnout. In this study, we investigated the association between residential noise exposure and burnout prevalence among 5416 health-care workers in Taiwan from 2012 to 2017. Burnout was evaluated using the Mandarin version of the Copenhagen Burnout Inventory by considering both continuous and binary measures. We applied ordinary Kriging models to calculate the annual average residential noise exposure at an individual level. Multivariable linear regression models and logistic regression models were employed. Restricted cubic splines were used to explore dose–response relationships. The median age of the health-care workers was 31.5 years. In the multivariable linear regression models, exposure to residential noise (per 1 dBA) was associated with increases in personal burnout and work-related burnout scores by 1.59 ± 0.25 and 1.38 ± 0.20, respectively. In the multivariable logistic regression models, the adjusted odds ratios were 1.24 (95% confidence interval [CI]: 1.16, 1.32) for personal burnout and 1.19 (95% CI: 1.13, 1.26) for work-related burnout per 1-dBA increase in residential noise exposure. Linear dose–response associations of burnout with residential noise level were detected. Our findings suggest that exposure to residential noise may increase the risk of burnout among health-care workers.

PLIC-FSR-SYS: System reliability analysis based on parallel learning of influential components with filtered sample region

In practical engineering, system reliability analysis is highly concerned since many structures or products have multiple failure modes. Accordingly, this paper develops an innovative method for system reliability analysis by parallel learning of influential component limit-state functions with filtered sample region (PLIC-FSR-SYS) based on Kriging modeling. Different from the traditional adaptive learning methods that train only one component in each iteration when constructing the surrogate of the composite limit-state function, a new strategy is explored to adaptively identify several important components in one iteration so as to train them simultaneously. In the meanwhile, a filtering formula is explored to determine the fatal region so that the unimportant samples can be removed to further accelerate the training process. Based on the join forces of parallel learning of influential components and avoiding the training at unimportant samples, PLIC-FSR-SYS can achieve a fairly efficient system reliability analysis with multiple failure modes. Finally, four different case studies, including an engineering application to the ultra-voltage on-load tap-changer, are conducted to prove the effectiveness of the proposed method. The results indicate that compared to traditional adaptive learning methods, the proposed method makes a significant efficiency improvement for system reliability analysis with multiple failure modes.

A grey incidence-based algorithm for optimization of accelerated degradation test

PurposeThe purpose of this paper is to optimize the degradation test for products subject to multiple types of inherent stresses and external random shocks. The mechanism that shows how the variables to be optimized influence the considered multiple objectives is also aimed to be explored by using the grey incidence analysis (GIA) model.Design/methodology/approachThe Gamma process is employed to model the influences of different types of stresses and external random shocks. The GIA model is introduced to transfer multiple considered objectives as a comprehensive degree of grey incidence. The particle swarm optimization is integrated to search the globally optimal value of the characteristic variables to be optimized.FindingsThe acceleration of tested stresses and external random shocks both make the engineering systems become more vulnerable to the inherent degradation. And, the Kriging model can provide guidance of searching the optimal values of test characteristic variables and mitigate the computation burden. The grey incidence model can make the optimization focused and improve the optimality of objective values.Originality/valueThe proposed method can effectively overcome the drawbacks brought by the limitation of test data and can specify the dependence strength between the inherent degradation and external random shock. The computation cost and accuracy of optimization can be simultaneously ensured by the proposed model.

Fatigue strength reliability assessment of turbofan blades subjected to intake disturbances based on the improved kriging model

This paper aims to develop an efficient and precise reliability analysis method to enhance the numerical prediction accuracy for complex structures. Kriging, an implicit surrogate model, used to address highly nonlinear and complex problems. In this study, genetic algorithms (GA) are utilized to optimize the parameters of the Kriging model, which is then integrated with a distributed collaborative strategy to introduce the Genetic Algorithm Optimized Distributed Collaborative Kriging Model (DCGAK). Using the CFM56-fan blade as a case study, the impact of intake disturbances at the engine inlet is evaluated to assess the fatigue strength reliability of the blade. Comparison with different mathematical models demonstrates that the prediction accuracy of DCGAK closely aligns with the Monte Carlo sampling results, suggesting promising prospects for its application in numerical prediction and reliability analysis. This approach enriches the current methods for structural reliability analysis of complex mechanical systems.

Structural Performance Analysis and Optimization of Small Diesel Engine Exhaust Muffler

In recent years, the optimization of diesel engine exhaust mufflers has predominantly targeted acoustic performance, while the impact on engine power performance has often been overlooked. Therefore, this paper proposes a parallel perforated tube expansion muffler and conducts a numerical analysis of its acoustic and aerodynamic performance using the finite element method. Then, a Kriging model is established based on the Design of Experiments to reveal the impact of different parameter couplings on muffler performance. With transmission loss (TL) and pressure loss (PL) as the optimization objectives, a multi-objective optimization study is carried out using the competitive multi-objective particle swarm optimization (CMOPSO). The optimization results indicate that this method can simplify the optimization model and improve optimization efficiency. After CMOPSO calculation, the average TL of the muffler increased from 27.3 dB to 31.6 dB, and the PL decreased from 1087 Pa to 953 Pa, which reduced the exhaust noise and improved the fuel economy of the engine, thus enhancing the overall performance of the muffler. This work provides a reference and guidance for the optimal design of mufflers for small agricultural diesel engines.

A new active learning surrogate model for time- and space-dependent system reliability analysis

This study introduces a novel method for time- and space-dependent system reliability analysis, integrating an active learning surrogate model with an innovative parallel updating strategy. A global Kriging model is developed to represent the signs of random samples using efficient global optimization. From a Bayesian perspective, the prediction probabilities of random sample signs within the time-space domain are calculated, and the sample with the lowest prediction probability is chosen to update the global Kriging model. The system extremum for each sample in the time-space domain is determined, and the corresponding random variables, time-space coordinates, and failure modes are selected. To further decrease iteration times, a parallel updating strategy that considers both the predicted probability and the correlation among candidate samples is proposed. Additionally, a new stopping criterion is introduced to balance accuracy and efficiency, terminating the updating process appropriately. The method's accuracy and efficiency are validated through three examples.

Improving acoustic absorption modeling of additively manufactured microperforated panels through kriging-based approaches

Microperforated panels (MPPs) have emerged as good acoustic absorbers, with the Maa model being commonly utilized for predicting their acoustic absorption and impedance. However, discrepancies arise when applying this model to MPPs fabricated through additive manufacturing. Additive manufacturing offers design flexibility, but it challenges traditional acoustic models by not achieving ideal geometric characteristics. For instance, non-circular perforations resulting from the additive manufacturing, deviate from the perfect circular shape assumed in the Maa model. This non-ideal geometry poses challenges in predicting MPP acoustic absorption, particularly at lower frequencies and in wideband scenarios. Microscopic examinations reveal microporosity within panel solids, adding complexities not usually accounted for by models assuming a solid structure around perforations. This study investigates the observed disparity between Maa model predictions and experimental results due to manufacturing defects, microporosity within the MPPs and panel vibration. We address these challenges by introducing Kriging, a spatial interpolation technique, to refine the absorption model. The Kriging model demonstrates remarkable agreement with experimental data, offering a more accurate representation of the acoustic performance of additively manufactured MPPs. The proposed methodology not only contributes to advancing the understanding of acoustic absorption in MPPs but is also promising for optimizing their performance in real-world applications.

Thermal Fault-Tolerant Asymmetric Dual-Winding Motors in Integrated Electric Braking System for Autonomous Vehicles

A conventional dual-winding (DW) motor has two internal windings consisting of a master part and a slave part, each connected to a different electronic control unit (ECU) to realize a redundant system. However, existing DW motors have a problem related to heat generation in both the healthy mode and the faulty mode of the motor operation. In the healthy mode, unexpected overloads can cause both windings to burn out simultaneously due to equal heat distribution. If the current sensor fails to measure correctly, the motor may exceed the designed current density of 4.7 [Arms/mm2] under air-cooling conditions, further increasing burnout risk. External factors such as excessive load cycles or extreme heat conditions can further exacerbate this issue. In the faulty mode, the motor requires double the current to generate maximum torque, leading to rapid temperature increases and a high risk of overheating. To address these challenges, this paper proposes the design of a thermal fault-tolerant asymmetric dual-winding (ADW) motor, which improves heat management in both healthy and faulty modes for autonomous vehicles. A lumped-parameter thermal network (LPTN) with a piecewise stator-housing model (PSMs) was employed to evaluate the coil temperature during faulty operation. An optimal design approach, incorporating kriging modeling, Design of Experiments (DOE), and a genetic algorithm (GA), was also utilized. The results confirm that the proposed ADW motor design effectively reduces the risk of simultaneous burnout in the healthy mode and overheating in the faulty mode, offering a robust solution for autonomous vehicle applications.

Noise-Aware Active Learning to Develop High-Temperature Shape Memory Alloys with Large Latent Heat.

Shape memory alloys (SMAs) with large latent heat absorbed/released during phase transformation at elevated temperatures benefit their potential application on thermal energy storage (TES) in high temperature environment like power plants, etc. The desired alloys can be designed quickly by searching the vast component space of doped NiTi-based SMAs via data-driven method, while be challenging with the noisy experimental data. A noise-aware active learning strategy is proposed to accelerate the design of SMAs with large latent heat at elevated phase transformation temperatures based on noisy data. The optimal noise level is estimated by minimizing the model error with incorporation of a range of noise levels as noise hyper-parameters into the noise-aware Kriging model. The employment of this strategy leads to the discovery of the alloy with latent heat of -36.08 J g-1, 9.2% larger than the best value (-33.04 J g-1) in the original training dataset within another four experiments. Additionally, the alloy represents high austenite finish temperature (481.71°C) and relatively small hysteresis. This promotes the latent heat TES application of SMAs in high temperature circumstance. It is expected that the noise-aware approach can be convenient for the accelerated materials design via the data-driven method with noisydata.

Quantified active learning Kriging model for structural reliability analysis

A quantified active learning Kriging-based (qAK) methodology for structural reliability analysis is presented. The proposed approach is based on an updated probability density function (PDF), which is dominant in the vicinity of the limit-state surface. This PDF is created using weights based on an improved learning function called the most probable misclassification function. This function is used as a metric for efficiently updating the Kriging model, as it symmetrically quantifies the uncertainty of candidate points in terms of the model’s accuracy. The proposed approach accurately approximates the points that lie on the limit-state surface. Moreover, a probabilistic-based stopping criterion is proposed. The new support points are selected using the weighted K-means algorithm and the sample from the updated PDF. Thus, the method does not require solving an optimization problem or using a sampling algorithm. The proposed qAK methods are more reliable and robust than previous implementations of the Kriging method for structural reliability assessment. The proposed approach is presented within the framework of standard reliability methods, i.e., the Monte Carlo and the Subset Simulation methods. The efficiency of the proposed qAK methods is demonstrated with the aid of six case studies.

Assessing soil fungal diversity under different sampling schemes in conjunction with remote sensing technologies in a subtropical forest

Fungi, serving as real-time bioindicators to environmental changes and stressors, are crucial for effective forest conservation and management practices under ongoing global change. However, the large-scale assessment of soil fungi still encounters challenges in striking a balance between the extensive sampling costs and the limited accuracy of minimal sampling. In this study, we analyzed 1,606 soil samples collected from 625 quadrats (20 m × 20 m) within a 25-ha subtropical forest dynamic plot in East China. Our primary objective was to explore the impact of different sampling schemes, in conjunction with remote sensing (RS) technologies, on the interpolation of soil fungal diversity using Ordinary Kriging (OK) and Co-kriging (CoK) models. Our findings suggested that a sampling scheme including points at 0 m (the base points) and 8 m within each quadrat, totaling to 26 points/ha, would be a sufficient scheme. This scheme with OK model yielded comparable results to those of more intensive schemes (at 0, 2, 5 and 8 m), but required the fewest sampling points. Upon incorporating each RS variable separately into the CoK models, including two vegetation indices (normalized difference vegetation index and transformed chlorophyll absorption ratio index 2), three terrain attributes (Elevation, Aspect and Slope), and the synthesis of these RS variables, the accuracy of the predicted results was further improved for each sampling scheme. By leveraging high-precision soil DNA sequencing in conjunction with cost-effective RS technologies, this study proposes a rapid and affordable approach for monitoring soil fungal diversity on a large scale. This will facilitate data collection for understanding responses of forest soil fungi to ongoing global change.

A novel directional simulation method for estimating failure possibility

Failure possibility plays a crucial role in assessing the safety level of structures under fuzzy uncertainty. However, the traditional fuzzy simulation method suffers from computational inefficiency as it requires a large number of samples for accurate estimation. To address this issue, a directional simulation method is proposed to improve the efficiency of estimating failure possibility. The directional simulation method reformulates the failure possibility estimation into two key steps: the generation of direction samples and the estimation of conditional failure possibility under each direction sample in the polar coordinate system of the standard fuzzy space. To ensure direction uniformity, these direction samples are generated by adopting a good lattice point set based on stratified sampling on the unit hypercube. The conditional failure possibility under each direction sample is estimated by solving the minimum root of a nonlinear equation. The proposed method effectively reduces the dimensionality of the fuzzy input and greatly improves the computational efficiency. To further enhance efficiency, an adaptive Kriging model is embedded into the directional simulation method to reduce the number of performance function evaluations. Four examples are performed to illustrate the accuracy and efficiency of the proposed method. The results highlight the superiority of the directional simulation method over the traditional fuzzy simulation method, offering substantial improvements in computational efficiency while maintaining high estimation accuracy.