Sobol Sequence Research Articles

Adaptive Data-Driven Deep-Learning Surrogate Model for Frontal Polymerization in Dicyclopentadiene.

Frontal polymerization (FP) is a self-sustaining curing process that enables rapid and energy-efficient manufacturing of thermoset polymers and composites. Computational methods conventionally used to simulate the FP process are time-consuming, and repeating simulations are required for sensitivity analysis, uncertainty quantification, or optimization of the manufacturing process. In this work, we develop an adaptive surrogate deep-learning model for FP of dicyclopentadiene (DCPD), which predicts the evolution of temperature and degree of cure orders of magnitude faster than the finite-element method (FEM). The adaptive algorithm provides a strategy to select training samples efficiently and save computational costs by reducing the redundancy of FEM-based training samples. The adaptive algorithm calculates the residual error of the FP governing equations using automatic differentiation of the deep neural network. A probability density function expressed in terms of the residual error is used to select training samples from the Sobol sequence space. The temperature and degree of cure evolution of each training sample are obtained by a 2D FEM simulation. The adaptive method is more efficient and has a better prediction accuracy than the random sampling method. With the well-trained surrogate neural network, the FP characteristics (front speed, shape, and temperature) can be extracted quickly from the predicted temperature and degree-of-cure fields.

Derivative-Variance Hybrid Global Sensitivity Measure with Optimal Sampling Method Selection

This paper proposes a derivative-variance hybrid global sensitivity measure with optimal sampling method selection. The proposed sensitivity measure is as computationally efficient as the derivative-based global sensitivity measure, which also serves as the conservative estimation of the corresponding variance-based global sensitivity measure. Moreover, the optimal sampling method for the proposed sensitivity measure is studied. In search of the optimal sampling method, we investigated the performances of six widely used sampling methods, namely Monte Carlo sampling, Latin hypercube sampling, stratified sampling, Latinized stratified sampling, and quasi-Monte Carlo sampling using the Sobol and Halton sequences. In addition, the proposed sensitivity measure is validated through its application to a rural bridge.

Development of an Artificial Intelligence Model to Predict Combustion Properties, With a Focus on Auto-Ignition Delay

Abstract Hydrogen-compatible gas turbines are one way to decarbonize electricity production. However, burning and handling hydrogen is not trivial because of its high reactivity and tendency to detonate. Mandatory safety parameters, such as auto-ignition delay times, can be estimated thanks to predictive detailed kinetic models, but with significant calculation times that limit coupling with fluid mechanic codes. An auto-ignition prediction tool was developed based on an artificial intelligence (AI) model for fast computations and an implementation into an explosion model. A dataset of ignition delay times (IDTs) was generated automatically using a recent detailed kinetic model from National University of Galway (NUIG) selected from the literature. Generated data cover a wide operating range and different compositions of fuels. Clustering problems in sample points were avoided by a quasi-random Sobol sequence, which covers uniformly the entire input parameter space. The different algorithms were trained, cross-validated, and tested using a database of more than 70,000 ignitions cases of natural gas/hydrogen blends calculated with the full kinetic model by using a common split of 70/30 for training, testing. The AI model shows a high degree of robustness. For both the training and testing datasets, the average value of the correlation coefficient was above 99.91%, and the mean absolute error (MAE) and the mean square error (MSE) were around 0.03 and lower than 0.04, respectively. Tests showed the robustness of the AI model outside the ranges of pressure, temperature, and equivalence ratio of the dataset. A deterioration is, however, observed with increasing amounts of large alkanes in the natural gas.

Probabilistic evaluation of dynamic positioning operability with a Quasi-Monte Carlo approach

During the design phase of an offshore unit, estimating the station-keeping capabilities of the dynamic positioning (DP) system is mandatory. This means, in conventional offshore applications, to determine the maximum sustainable wind speed as a function of the encounter heading, which the unit may counteract by employing the onboard actuators or mooring lines only. Besides the deterministic estimation of DP capability, it is possible to assess the operability of the DP system following a non-deterministic probabilistic process by employing the site-specific joint wind-wave distributions to model the environment. In such a case, the operability results from a Monte Carlo integration process. Here it is proposed to enhance the applicability of the probabilistic analysis of DP operability, investigating the application of a Quasi-Monte Carlo method. In this sense, the procedure uses quasi-random samplings following a Sobol sequence instead of employing random samples of the joint distributions. In this paper, the Quasi-Monte Carlo process is tested and compared on a reference ship, highlighting the improvements to the established probabilistic DP prediction concerning the number of calculations needed to estimate operability. The significant reduction of computational time makes the newly implemented method suitable for the early design stage applications.

IPSAL: Implementation of the module to generate the Sobol sequence and indices

Sensitivity and uncertainty analysis hold significant importance across a range of applications, spanning from industrial problems to climate change, financial risk assessment, as well as mathematical and computational models. These analyses involve identifying influential input parameters in models to comprehend their impact on the output. Sensitivity analysis can be performed locally, examining parameter effects at a fixed value, or globally, evaluating the model across a range of parameter values. The Sobol method stands as a robust approach for global sensitivity analysis, employing a Sobol sequence to create samples more uniformly within the input parameter space, thus enabling efficient exploration of model inputs. This paper aims to introduce a computational implementation in Scilab to generate the Sobol sequence for utilization in sensitivity analysis through the Sobol method. A test case was applied to generate Sobol sequences and discuss the obtained results.

High-throughput determination of grain size distributions by EBSD with low-discrepancy sampling.

Because microstructure plays an important role in the mechanical properties of structural materials, developing the capability to quantify microstructures rapidly is important to enabling high-throughput screening of structural materials. Electron backscatter diffraction (EBSD) is a common method for studying microstructures and extracting information such as grain size distributions (GSDs), but is not particularly fast and thus could be a bottleneck in high-throughput systems. One approach to accelerating EBSD is to reduce the number of points that must be scanned. In this work, we describe an iterative method for reducing the number of scan points needed to measure GSDs using incremental low-discrepancy sampling, including on-the-fly grain size calculations and a convergence test for the resulting GSD based on the Kolmogorov-Smirnov test. We demonstrate this method on five real EBSD maps collected from magnesium AZ31B specimens and compare the effectiveness of sampling according to two different low discrepancy sequences, the Sobol and R2 sequences, and random sampling. We find that R2 sampling is able to produce GSDs that are statistically very similar to the GSDs of the full density grids using, on average, only 52% of the total scan points. For EBSD maps that contained monodisperse GSDs and over 1000 grains, R2 sampling only required an average of 39% of the total EBSDpoints.

Research on line loss analysis and intelligent diagnosis of abnormal causes in distribution networks: artificial intelligence based method.

The primary source of energy losses in distribution networks (DNs) is rooted in line losses, which is crucial to conduct a thorough and reasonable examination of any unusual sources of line losses to guarantee the power supply in a timely and safe manner. In recent studies, identifying and analyzing abnormal line losses in DNs has been a widely and challenging research subject. This article investigates a key technology for the line loss analyses of DNs and intelligent diagnosis of abnormal causes by implementing artificial intelligence (AI), resulting in several prominent results. The proposed algorithm optimizes the parameters of the support vector machine (SVM) and suggests an intelligent diagnosis algorithm called the Improved Sparrow Search Algorithm and Support Vector Machine (ISSA-SVM). The ISSA-SVM algorithm is trained to calculate the data anomalies of line losses when changing loads and exhibiting exceptional performance to identify abnormal line losses. The accuracy of abnormality identification employing the ISSA-SVM algorithm reaches an impressive 98%, surpassing the performances of other available algorithms. Moreover, the practical performance of the proposed approach for analyzing large volumes of abnormal line loss data daily in DNs is also noteworthy. The ISSA-SVM accurately identifies the root causes of abnormal line losses and lowers the error in calculating abnormal line loss data. By combining different types of power operation data and creating a multidimensional feature traceability model, the study successfully determines the factors contributing to abnormal line losses. The relationship between transformers and voltage among various lines is determined by using the Pearson correlation, which provides valuable insights into the relationship between these variables and line losses. The algorithm's reliability and its potential to be applied to real-world scenarios bring an opportunity to improve the efficiency and safety of power supply systems. The ISSA that incorporates advanced techniques such as the Sobol sequence, golden sine algorithm, and Gaussian difference mutation appears to be a promising tool.

Kernel extreme learning with harmonized bat algorithm for prediction of pyrene toxicity in rats.

Polycyclic aromatic hydrocarbons (PAHs) are organic pollutants and manufactured substances conferring toxicity to human health. The present study investigated whether pyrene, a type of PAH, harms rats. Our research provides an effective feature selection strategy for the animal dataset from Wenzhou Medical University's Experimental Animal Center to thoroughly examine the impacts of PAH toxicity on rat features. Initially, we devised a high-performance optimization method (SCBA) and added the Sobol sequence, vertical crossover and horizontal crossover mechanisms to the bat algorithm (BA). The SCBA-KELM model, which combines SCBA with the kernel extreme learning machine model (KELM), has excellent accuracy and high stability for selecting features. Benchmark function tests are then used in this research to verify the overall optimization performance of SCBA. In this paper, the feature selection performance of SCBA-KELM is verified using various comparative experiments. According to the results, the features of the genes PXR, CAR, CYP2B1/2 and CYP1A1/2 have the most impact on rats. The SCBA-KELM model's classification performance for the gene dataset was 100%, and the model's precision value for the public dataset was around 96%, as determined by the classification index. In conclusion, the model utilized in this research is anticipated to be a reliable and valuable approach for toxicological classification and assessment.

A reliability evaluation method for complex systems based on the editable GSPN and adaptive Monte Carlo simulation

AbstractThis paper presents an innovative EGSPN (Editable Generalized Stochastic Petri Net) model, optimizing the size of GSPN (Generalized Stochastic Petri Net) while preserving its core benefits. Specifically, the EGSPN introduces a transition termed “editable transition,” which allows for the establishment of any dynamic logic, thereby circumventing the intricacies associated with the EGSPN model structure. A Monte Carlo (MC) simulation technique is put forth for EGSPN analysis, enhanced by the integration of Sobol sequences with a Bayesian optimizer. This MC simulation approach, unbounded by any specific distribution constraints, exhibits accelerated convergence rates. To address the issue of preset sampling size, an adaptive sampling strategy rooted in confidence intervals has been proposed. By real‐time computation of margin of errors under varying confidence levels, simulations can be halted prior to reaching the preset sampling size. This method strikes a balance between reduced simulation time and maintained accuracy. The applicability and efficacy of the proposed method are further elucidated through a numerical example of a flight control system.

Multistep short-term wind power forecasting model based on secondary decomposition, the kernel principal component analysis, an enhanced arithmetic optimization algorithm, and error correction

Wind power forecasting can effectively improve the energy utilization efficiency of a power system and ensure its stable operation. In this study, a novel hybrid multistep prediction model, including the complete ensemble empirical mode decomposition with adaptive noise (CEEMDAN), variational mode decomposition (VMD), the kernel principal component analysis (KPCA), an enhanced arithmetic optimization algorithm (ENAOA), a bidirectional long short-term memory (BILSTM) neural network, and error correction, was designed for short-term wind power forecasting. First, the collected original wind power data were decomposed into multiple intrinsic mode functions (IMFs) through a secondary decomposition composed of the CEEMDAN and VMD, which eliminated the interactions between different components to achieve denoising. Second, the KPCA was adopted to reduce the dimensionality of the multiple IMFs by extracting the principal components, effectively reducing the complexity of the multidimensional IMF data and improving the forecasting efficiency of the proposed prediction model. Subsequently, an ENAOA was proposed based on the Sobol sequence, adaptive T-distribution, and random walk strategy to optimize the BILSTM parameters. Finally, multiple preprocessed components were predicted by the optimized BILSTM, after which error correction was performed to obtain the final prediction results, which could further reduce the forecast error of the designed prediction model. Based on two sets of data collected from a wind farm in northwest China, the simulation results of 1-step, 4-step, 7-step, and 10-step forecasting revealed that compared with other incomplete models, the various algorithms adopted in the hybrid forecasting model reduced the prediction errors to different degrees, significantly enhanced the wind power prediction performance, and validated the effectiveness and feasibility of the proposed model.

Research on Reactive Power Optimization Based on Hybrid Osprey Optimization Algorithm

This paper presents an improved osprey optimization algorithm (IOOA) to solve the problems of slow convergence and local optimality. First, the osprey population is initialized based on the Sobol sequence to increase the initial population’s diversity. Second, the step factor, based on Weibull distribution, is introduced in the osprey position updating process to balance the explorative and developmental ability of the algorithm. Lastly, a disturbance based on the Firefly Algorithm is introduced to adjust the position of the osprey to enhance its ability to jump out of the local optimal. By mixing three improvement strategies, the performance of the original algorithm has been comprehensively improved. We compared multiple algorithms on a suite of CEC2017 test functions and performed Wilcoxon statistical tests to verify the validity of the proposed IOOA method. The experimental results show that the proposed IOOA has a faster convergence speed, a more robust ability to jump out of the local optimal, and higher robustness. In addition, we also applied IOOA to the reactive power optimization problem of IEEE33 and IEEE69 node, and the active power network loss was reduced by 48.7% and 42.1%, after IOOA optimization, respectively, which verifies the feasibility and effectiveness of IOOA in solving practical problems.

Efficient Quality Diversity Optimization of 3D Buildings through 2D Pre-optimization.

Quality diversity algorithms can be used to efficiently create a diverse set of solutions to inform engineers' intuition. But quality diversity is not efficient in very expensive problems, needing 100.000s of evaluations. Even with the assistance of surrogate models, quality diversity needs 100s or even 1000s of evaluations, which can make it use infeasible. In this study we try to tackle this problem by using a pre-optimization strategy on a lower-dimensional optimization problem and then map the solutions to a higher-dimensional case. For a use case to design buildings that minimize wind nuisance, we show that we can predict flow features around 3D buildings from 2D flow features around building footprints. For a diverse set of building designs, by sampling the space of 2D footprints with a quality diversity algorithm, a predictive model can be trained that is more accurate than when trained on a set of footprints that were selected with a space-filling algorithm like the Sobol sequence. Simulating only 16 buildings in 3D, a set of 1024 building designs with low predicted wind nuisance is created. We show that we can produce better machine learning models by producing training data with quality diversity instead of using common sampling techniques. The method can bootstrap generative design in a computationally expensive 3D domain and allow engineers to sweep the design space, understanding wind nuisance in early design phases.

Enhanced Harris hawks optimization-based fuzzy k-nearest neighbor algorithm for diagnosis of Alzheimer's disease

In order to stop deterioration and give patients with Alzheimer's disease (AD) early therapy, it is crucial to correctly diagnose AD and its early stage, mild cognitive impairment (MCI). A framework for diagnosing AD is presented in this paper, which includes magnetic resonance imaging (MRI) image preprocessing, feature extraction, and the Fuzzy k-nearest neighbor algorithm (FKNN) model. In particular, the framework's novelty lies in the use of an improved Harris Hawks Optimization (HHO) algorithm named SSFSHHO, which integrates the Sobol sequence and Stochastic Fractal Search (SFS) mechanisms for optimizing the parameters of FKNN. The HHO method improves the quality of the initial population overall by incorporating the Sobol sequence, and the SFS mechanism increases the algorithm's capacity to get out of the local optimum solution. Comparisons with other classical meta-heuristic algorithms, state-of-the-art HHO variants in low and high dimensions, and enhanced meta-heuristic algorithms on 30 typical IEEE CEC2014 benchmark test problems show that the overall performance of SSFSHHO is significantly better than other comparative algorithms. Moreover, the created framework based on the SSFSHHO-FKNN model is employed to classify AD and MCI using MRI scans from the ADNI dataset, achieving high classification performance for 6 representative cases. Experimental findings indicate that the proposed algorithm performs better than a number of high-performance optimization algorithms and classical machine learning algorithms, thus offering a promising approach for AD classification. Additionally, the proposed strategy can successfully identify relevant features and enhance classification performance for AD diagnosis.

Model updating of rotor system based on the adaptive Gaussian process model using unbalance response

For predicting the dynamic responses of rotor system with high accuracy, an adaptive Gaussian process model-based model updating method for rotor system using the unbalance responses is proposed. To utilize the data from multiple sensors, multi-channel data fusion is adopted to construct the objective function of the model updating. The fusion feature is the mean of the cumulative distribution function of the response errors of each channel. The Gaussian process model is used to describe the mapping relationship between the selected parameters and fusion features. An adaptive sampling strategy is developed to reduce the computation cost of repeated finite element calculation. Based on Sobol sequence sampling, new sampling parameters are added near the sample parameter with a larger error in the predicted value. The performance of the proposed method is validated by a gas-generator rotor and a dual-disks rotor. Results show that the unbalance responses of the updated model show good agreement with the exact responses and measured responses. The maximum error of the support parameters for the gas-generator rotor is 3.56%. For the dual-disks rotor, the discrepancies of the first three modal frequencies between the updated model and the measured model are below 1%, 2.5% and 5%. The proposed method is effective for model updating of the rotor system.

Global sensitivity analysis of complex moduli of carbon fiber reinforced polymer

AbstractGlobal sensitivity analysis of complex moduli of carbon fiber reinforced polymer (CFRP) is performed by using variance‐based sensitivity analysis. Twelve material properties of matrix and fiber are selected as input arguments, including fiber volume fraction, three matrix properties, and eight carbon fiber properties. Ten thousand samples are generated with Sobol sequence. Based on the correspondence principle, six complex moduli of unidirectional CFRP, and two complex moduli of quasi‐isotropic laminate, orthogonal laminate, and symmetric laminate with different fiber angles are predicted using the generalized method of cells and classical laminate theory. The sensitivity indexes of all input arguments are calculated. The results show that the loss factors of CFRP are mainly affected by the matrix loss factor and fiber axial loss factor, and slightly affected by the fiber transverse loss factor.Highlights Sensitivity analysis reveals key factors influencing CFRP complex moduli. Impact of fiber and matrix properties on CFRP damping revealed. Insights for high‐damping and high‐stiffness CFRP development. Enhanced understanding of energy absorption mechanisms. Uncovering the dominant role of matrix and fiber axial properties in damping.

Learning the random variables in Monte Carlo simulations with stochastic gradient descent: Machine learning for parametric PDEs and financial derivative pricing

AbstractIn financial engineering, prices of financial products are computed approximately many times each trading day with (slightly) different parameters in each calculation. In many financial models such prices can be approximated by means of Monte Carlo (MC) simulations. To obtain a good approximation the MC sample size usually needs to be considerably large resulting in a long computing time to obtain a single approximation. A natural deep learning approach to reduce the computation time when new prices need to be calculated as quickly as possible would be to train an artificial neural network (ANN) to learn the function which maps parameters of the model and of the financial product to the price of the financial product. However, empirically it turns out that this approach leads to approximations with unacceptably high errors, in particular when the error is measured in the ‐norm, and it seems that ANNs are not capable to closely approximate prices of financial products in dependence on the model and product parameters in real life applications. This is not entirely surprising given the high‐dimensional nature of the problem and the fact that it has recently been proved for a large class of algorithms, including the deep learning approach outlined above, that such methods are in general not capable to overcome the curse of dimensionality for such approximation problems in the ‐norm. In this article we introduce a new numerical approximation strategy for parametric approximation problems including the parametric financial pricing problems described above and we illustrate by means of several numerical experiments that the introduced approximation strategy achieves a very high accuracy for a variety of high‐dimensional parametric approximation problems, even in the ‐norm. A central aspect of the approximation strategy proposed in this article is to combine MC algorithms with machine learning techniques to, roughly speaking, learn the random variables (LRV) in MC simulations. In other words, we employ stochastic gradient descent (SGD) optimization methods not to train parameters of standard ANNs but instead to learn random variables appearing in MC approximations. In that sense, the proposed LRV strategy has strong links to Quasi‐Monte Carlo (QMC) methods as well as to the field of algorithm learning. Our numerical simulations strongly indicate that the LRV strategy might indeed be capable to overcome the curse of dimensionality in the ‐norm in several cases where the standard deep learning approach has been proven not to be able to do so. This is not a contradiction to the established lower bounds mentioned above because this new LRV strategy is outside of the class of algorithms for which lower bounds have been established in the scientific literature. The proposed LRV strategy is of general nature and not only restricted to the parametric financial pricing problems described above, but applicable to a large class of approximation problems. In this article we numerically test the LRV strategy in the case of the pricing of European call options in the Black‐Scholes model with one underlying asset, in the case of the pricing of European worst‐of basket put options in the Black‐Scholes model with three underlying assets, in the case of the pricing of European average put options in the Black‐Scholes model with three underlying assets and knock‐in barriers, as well as in the case of stochastic Lorentz equations. For these examples the LRV strategy produces highly convincing numerical results when compared with standard MC simulations, QMC simulations using Sobol sequences, SGD‐trained shallow ANNs, and SGD‐trained deep ANNs.

Bearing Fault-Detection Method Based on Improved Grey Wolf Algorithm to Optimize Parameters of Multistable Stochastic Resonance.

In an effort to overcome the problem that the traditional stochastic resonance system cannot adjust the structural parameters adaptively in bearing fault-signal detection, this article proposes an adaptive-parameter bearing fault-detection method. First of all, the four strategies of Sobol sequence initialization, exponential convergence factor, adaptive position update, and Cauchy-Gaussian hybrid variation are used to improve the basic grey wolf optimization algorithm, which effectively improves the optimization performance of the algorithm. Then, based on the multistable stochastic resonance model, the structure parameters of the multistable stochastic resonance are optimized through improving the grey wolf algorithm, so as to enhance the fault signal and realize the effective detection of the bearing fault signal. Finally, the proposed bearing fault-detection method is used to analyze and diagnose two open-source bearing data sets, and comparative experiments are conducted with the optimization results of other improved algorithms. Meanwhile, the method proposed in this paper is used to diagnose the fault of the bearing in the lifting device of a single-crystal furnace. The experimental results show that the fault frequency of the inner ring of the first bearing data set diagnosed using the proposed method was 158 Hz, and the fault frequency of the outer ring of the second bearing data set diagnosed using the proposed method was 162 Hz. The fault-diagnosis results of the two bearings were equal to the results derived from the theory. Compared with the optimization results of other improved algorithms, the proposed method has a faster convergence speed and a higher output signal-to-noise ratio. At the same time, the fault frequency of the bearing of the lifting device of the single-crystal furnace was effectively diagnosed as 35 Hz, and the bearing fault signal was effectively detected.

Improved multi-objective grasshopper optimization algorithm and application in capacity configuration of urban rail hybrid energy storage systems

Aiming at addressing problems of poor diversity and ergodicity of initial population, slow convergence speed, and susceptibility to local optima in conventional multi-objective grasshopper optimization algorithm (MOGOA), an improved MOGOA is proposed in this paper. The proposed algorithm is based on Sobol sequence, adaptive social force, cosine parameter c, as well as Levy flight mechanism (SACLMOGOA), where Sobol sequence is adopted to initialize the population, thereby improving the diversity and ergodicity of the initial population. The adaptive social force is proposed to enhance the global exploration ability in the early stage of iteration and the local development ability in the late stage of iteration. A cosine type parameter c is used to ensure sufficient exploration time and rapid convergence of the algorithm during position update process and Levy flight is used to guide some grasshoppers to mutate, enhancing the ability to escape from the local optima and improving the performance and efficiency of the algorithm. The proposed algorithm is tested with ZDT and DTLZ series benchmark test functions to validate its effectiveness, and it is also compared with conventional MOGOA, multi-objective particle swarm optimization, multi-objective gray Wolf, and multi-objective jellyfish algorithms. The simulation results demonstrate that the proposed algorithm outperforms other algorithms in terms of inverse generational distance (IGD), spread (SP), maximum spread (MS), run time and Wilcoxon rank sum test. Furthermore, the proposed algorithm is successfully applied to the capacity configuration of the urban rail hybrid energy storage systems (HESS) of Changsha Metro Line 1 in China, reducing the traction network voltage fluctuations by 3.3 % and 2.2 % compared to no HESS capacity configuration optimization, and by 14 % and 5.7 % compared to no HESS during train starting and breaking, respectively. While achieving the goal of energy-saving and voltage stabilization, the cost of the hybrid energy storage systems is minimized as well. All of these have demonstrated SACLMOGOA is an effective tool for solving complex multi-objective optimization problems in engineering.

Method study on failure probability and uncertainty analysis of stress corrosion cracking in fixed parts of PWR

To estimate the failure probability of stress corrosion cracking (SCC) in the fixed parts of pressurized water reactors (PWR), an approach based on the Paris model was developed and its uncertainty analysis was performed as well. In the study of SCC failure, the uncertainty of fracture toughness was translated into integral form to improve calculation efficiency. Moreover, uncertainty parameters such as crack size and Paris model coefficients were studied in the uncertainty analysis. On this basis, the thermowell of the pressurizer of PWR as an example was analyzed in this study. The Monte Carlo (MC) method and polynomial chaos expansion (PCE) approach were used to calculate the mean value, relative uncertainty, upper limit of tolerance interval of failure probability, and sensitivity coefficient of input parameter to compare the advantages and disadvantages of these methods. According to the results, compared with the other method, 300 sets of sampling with Latin Hypercube sampling (LHS) and Sobol sequences can converge the mean, and 300 sets of sampling with Halton sequence and Hammersley sequence can converge the relative uncertainty. When LHS with the 4th order Wilks' formula and Halton sequence with the 1st order Wilks' formula to compute the upper limit of tolerance interval, the accuracy and cost of the computation can be balanced. According to the results of the sensitivity analysis, crack aspect ratio is the most sensitive parameter. PCE surrogate model can accurately calculate the mean, relative uncertainty, the upper limit of tolerance interval and sensitivity coefficient, thereby reducing the computational cost.

An enhanced grey wolf optimizer boosted machine learning prediction model for patient-flow prediction

Large and medium-sized general hospitals have adopted artificial intelligence big data systems to optimize the management of medical resources to improve the quality of hospital outpatient services and decrease patient wait times in recent years as a result of the development of medical information technology and the rise of big medical data. However, owing to the impact of several elements, including the physical environment, patient, and physician behaviours, the real optimum treatment effect does not meet expectations. In order to promote orderly patient access, this work provides a patient-flow prediction model that takes into account shifting dynamics and objective rules of patient-flow to handle this issue and forecast patients' medical requirements. First, we propose a high-performance optimization method (SRXGWO) and integrate the Sobol sequence, Cauchy random replacement strategy, and directional mutation mechanism into the grey wolf optimization (GWO) algorithm. The patient-flow prediction model (SRXGWO-SVR) is then proposed using SRXGWO to optimize the parameters of support vector regression (SVR). Twelve high-performance algorithms are examined in the benchmark function experiments' ablation and peer algorithm comparison tests, which are intended to validate SRXGWO's optimization performance. In order to forecast independently in the patient-flow prediction trials, the data set is split into training and test sets. The findings demonstrated that SRXGWO-SVR outperformed the other seven peer models in terms of prediction accuracy and error. As a result, SRXGWO-SVR is anticipated to be a reliable and efficient patient-flow forecast system that may help hospitals manage medical resources as effectively as possible.