A sample-efficient deep learning method for multivariate uncertainty qualification of acoustic–vibration interaction problems

This study presents an efficient Monte Carlo simulation method to solve multivariate uncertainty problems in structural dynamic systems. The full model is obtained by the adaptive time-step material point method, and the multivariate surrogate model is built and analyzed for uncertainty by the adaptive sparse polynomial chaos expansion. The cubic spline interpolation method serves as a bridge between the original full model and the multivariate surrogate model, which improves the sampling efficiency of Monte Carlo simulation. Numerical results show that the proposed algorithm can significantly improve the efficiency and accuracy of uncertainty analysis.

The detection process of partial discharge (PD) ultra-high frequency (UHF) signal is easily affected by white noise and periodic narrowband noise, which hinder the fault diagnosis of high-voltage electrical appliances. In order to extract PD UHF signal and suppress noise effectively, this paper provides a new method to detect PD UHF signal by EDSSV and low rank RBF neural network. Firstly, the singular value decomposition (SVD) is performed on the mixed noises of PD signal. Secondly, the peak index of energy difference spectrum of singular value (EDSSV) is selected as optimal singular value threshold, and then the periodic narrowband noise is eliminated by reconstructing the effective rank order. Finally, radial basis function (RBF) neural network is used to approximate the denoised PD signal, and Gaussian window filter is used to extract the PD signal. To verify the performance of the proposed method, we compared it with other three algorithms in simulation and field detection, including adaptive singular value decomposition (ASVD), singular value decomposition based on S-transform and MTFM (S-SVD) and EMD-WT algorithms. Particularly, four evaluation indices are designed for the detection data, which consider both the noise suppression and feature preservation. The results demonstrate the validity of the proposed method with higher signal-to-noise ratio and less waveform distortion.

Construction of radial basis function neural networks (RBFN) involves selection of radial basis function centroid, radius (width or scale), and number of radial basis function (RBF) units in the hidden layer. The K-means clustering algorithm is frequently used for selection of centroids and radii. However, with the K-means clustering algorithm, the number of RBF units is usually arbitrarily selected, which may lead to suboptimal performance of the neural network model. Besides, class membership and the related probability distribution are not considered. Linear averaging (L-A) was devised for selection of centroids and radii for the RBFs and computing the number of RBF units. The proposed method considers the class membership and localized probability density distribution of each class in the training sets. The parameters related to the network construction were investigated. The network was trained with the QuickProp algorithm (QP) or Singular Value Decomposition (SVD) algorithm and evaluated with the poly(chlorobiphenyl) (PCB) mass spectra and an Italian olive oil reference data set. The prediction accuracy of PCB data sets was better than 94%, and the prediction accuracy with Italian olive oil data sets achieved 100% with RMSEP as low as 2.4 × 10-3. The training times were usually about a second on a personal computer. The performance of neural networks constructed from the linear-averaging method was observed to be better than that with the K-means algorithm with these data sets.

این مطالعه به منظور بررسی پیش بینی شاخص های عملکرد تولیدی در مرغان تخم گذار با استفاده از شبکه های عصبی مصنوعی و رگرسیون غیرخطی چندگانه انجام شد. بررسی بر روی اطلاعات چهار دوره متوالی پرورش در یک واحد پرورش مرغ تخم گذار صورت گرفت. روش های داده-کاوی شامل رگرسیون خطی و غیر خطی، شبکه عصبی پرسپترون سه لایه، شبکه عصبی پرسپترون چهار لایه و شبکه عصبی با تابع پایه ای شعاعی بود. در این مدل ها از متغیرهای سن گله، میزان خوراک مصرفی و فصل تولید به عنوان متغیر پیشگو و شاخص های عملکرد تولیدی شامل درصد تخم-گذاری، وزن توده ای تخم مرغ تولیدی و ضریب تبدیل غذایی به عنوان متغیر پاسخ استفاده شد. نتایج نهایی رگرسیون های خطی نشان داد که برای تمامی متغیرهای وابسته مورد مطالعه متغیر مستقل سن گله معنی دار می باشد. بنابراین رگرسیون غیر خطی شاخص های عملکرد تولیدی در مقابل سن برای مقایسه با شبکه های عصبی مختلف مورد بررسی قرار گرفت و برای مقایسه کلیه مدل ها از ضریب تعیین (R2) و میانگین قدر مطلق خطا (MAE) استفاده شد. نتایج نشان داد بین شبکه های عصبی مصنوعی مختلف مورد مطالعه، شبکه با تابع پایه ای شعاعی بهتر از سایر مدل های در پیش‌بینی شاخص های عملکرد تولیدی مرغان تخم گذار عمل می کند.

This study explores a hybrid method to enhance the efficiency of Monte Carlo simulations for European option pricing by incorporating neural network models. Traditional Monte Carlo Methods require high computational costs when dealing with high-dimensional financial derivatives due to the increased demand for simulation paths to achieve prediction accuracy. By integrating a feedforward neural network, this research aims to predict future price paths based on intermediate simulations, effectively reducing the number of paths while maintaining pricing accuracy. The proposed model employs residual block, regularization, early stopping, and other techniques to capture the nonlinear relationships between price paths and payoffs. Based on the trained model, the number of simulation paths required is successfully reduced from 10,000 to around 4,000 5,000 without significantly reducing prediction accuracy while achieving a balance in computation costs. The method exhibits stable predictive performance and computational efficiency, providing a potential solution for reducing the overhead of pricing complex financial derivatives. Future work could explore more advanced neural network architectures and hybrid with other techniques to further improve performance and efficiency.

PurposePrompted by the reliability and robustness of the previously proposed method of non-destructive measurement of thermal conductivity (TC) for anisotropic materials, the enhanced approach is presented in this study. The main improvement lies in the substitution of the analytic solution of direct problem solver with a numerical one. This solver, used during the inverse procedure that fits measurement data into simulated ones, is proposed to be a numerical one (finite volume method). Moreover, the purpose of this study is to show the applicability of the reduce order model for retrieving thermal conductivity of solid body.Design/methodology/approachIn the proposed methodology, both the laser heat source and temperature measurements are performed on the same side of the sample material, which is the main difference with respect to the classic Parker flash method. To speed up the computational time, the full numerical model used in the course of inverse solution is replaced by the proper orthogonal decomposition (POD)-radial basis function (RBF) reduced order model, which is fast and accurate.FindingsThe TCs measured using the proposed methodology are in good agreement with the well established (but destructive) measurement methods. The advantage of the proposed approach lies in the optimal approximation properties of the POD approximation basis used in reduced order model, as well as in its regularization properties.Practical implicationsThe proposed technique has high application potential in the design of novel apparatus for non-destructive measurement of TCs for both isotropic and anisotropic materials.Originality/valueThis is the first time when the POD-RBF reduced order model is used in the procedure of non-destructive TC measurement for anisotropic bodies.

A hybrid projection/data-driven reduced order model for the Navier-Stokes equations with nonlinear filtering stabilization

Aiming at the problem of human behavior recognition, this paper proposes a human behavior classification algorithm based on radial basis function (BP) neural network. The singular value decomposition (SVD) and principal component analysis (PCA) are used for feature extraction, and the linear discriminant analysis (LDA) is used for feature transformation to make it easier to distinguish between various categories. Finally, BP neural network classifier is used to recognize human behavior. The experimental results show that compared with the nearest neighbor classification and k-nearest neighbor classification (kNN), the proposed algorithm has a higher recognition rate. The result of BP neural network classifier is the best, it can fit the boundary of each category well.

This article proposes a method for building reduced-order models (ROMs) to address the issue of long solving time in traditional ANSYS finite element models, which can provide fast simulation results based on different loading conditions. Firstly, an orthogonal experiment is designed to obtain simulation results from the ANSYS model as training data. Secondly, the singular value decomposition (SVD) is combined with neural network regression to establish the reduced-order model. Then, the ROM generator software is built based on MATLAB. Finally, a stress reduced-order model of a specific finite element model is constructed, and the accuracy and efficiency of the proposed method are verified by comparing the simulation results with the results calculated by the reduced-order model, which can improve the solving efficiency while ensuring the accuracy of the solution.

In this paper, a novel radial basis function (RBF) neural network is proposed and applied successively for online stable identification and control of nonlinear discrete-time systems. The proposed RBF network has one hidden layer neural network (NN) with its all parameters being adaptable. The RBF network parameters are optimized by gradient descent method with stable learning rate whose stable convergence behavior is proved by Lyapunov stability approach. The aim of construction of the proposed RBF network is to combine power of the networks which have different mapping abilities. These networks are auto-regressive exogenous input model, nonlinear static NN model and nonlinear dynamic NN model. In simulations, the proposed network is applied for the direct inverse control of one benchmark nonlinear functioned system and Van de Vusse reaction in a CSTR discrete system even there exist large disturbances. From simulations, it is seen that the RBF network with stable learning rate identifies and controls nonlinear systems accurately.

Fault diagnosis for wireless sensor is very important to ensure signal acquisition precision. Radial basis function (RBF) neural network has strong classification ability. However, the selection of the connection weights, the hidden centers and the widths has an important influence on the classification performance of the RBF neural network in the learning process of RBF neural network. Thus, ant colony optimization is employ to gain the parameters of radial basis function neural network. Therefore, a novel method for fault diagnosis of wireless sensor based on RBF neural network and ant colony optimization is presented. The results of computational experiments show that ACO- RBF neural network has a great higher than RBF neural network.

With large-scale wind farms integrated into power systems, the computational requirements for reliability evaluation of composite power systems are increasing. This paper introduces a new concept of dynamic orthogonal list, which is a form of multiple failure retrievals to avoid repeatedly calling the optimal power flow (OPF) program in the stage of state evaluation. An existing algorithm of cross-entropy (CE) method was developed to deal with the rare events in sampling. The major contribution of CE is to achieve convergence faster and reduce the number of samples, thus shortening the consuming time in the stage of sampling. This paper proposes a fast reliability evaluation process which combines the CE method with dynamic orthogonal list (CE-DOL), comprehensively improving the computational efficiency of Monte Carlo simulation (MCS). The proposed method is tested on a modified IEEE-RTS 79 system. In addition, for comparison purposes, the efficiencies of MCS, CE, and CE-DOL are estimated in the cases of different system adequacies. It is shown that, in range of certain reliability level, the proposed method is much more efficient compared with the CE method. Finally, the applicability of different methods is analyzed under different system reliability levels.

A pressure deconvolution technique based on ridge regression with existing convolution features was explored and reinterpreted to frame a new optimization problem structure. We found a way to split the feature matrix into a deconvolution part and a smoothing part that handle each effect independently. The deconvolution part is comprised of a convolution matrix (Toeplitz matrix) for discrete-time convolution while the smoothing part is composed of a basis function of the impulse response. Hence, this formulation preserves linearity (a superposition of pressure solution) and the kernel for nonlinear mapping (e.g., polynomial kernel, radial basis function kernel, etc.) is effective only on the smoothing part (a basis function of impulse response). Importantly, the key idea of existing convolution feature is the modelling of the impulse response with a linear combination of a basis functions.For single-well pressure behavior, ridge regression often struggles with high-frequency measurements that contain multistage responses. An impulse response might share similar functional characteristics, for example wellbore storage and pseudosteady state are both linear responses but there is only one linear basis function in the ridge regression which cannot describe them both. In traditional well test interpretation, the engineer is typically focused on certain parts of the impulse response on a log-scale, to identify reservoir behavior (e.g., early-time for wellbore storage, transient-time for infinite acting radial flow, late-time for boundary effect, etc.). Analogously, a basis function could be formed from multiple pressure responses in each log-interval (inherent from a solution of the diffusion equation) then bridged together with a constraint on function value and its derivative at each interval boundary. This is the basic principle of spline regression that has more flexibility in terms of function expression. In addition, it also subsumes ridge regression with Laplacian regularization.For multiwell pressure behavior, additional basis functions are included to handle interference responses. Typically, the exponential integral is approximated with a logarithm function for single-well pressure response which is also one of the basis functions in previous convolution features. Nonetheless, interference pressure response is more subtle and its solution could not be easily approximated, which previously resulted in a poor fitting using earlier methods. By inspection of the convergent series of the exponential integral, its higher-order terms are associated with 1/tm that can be easily included as a basis function to enhance the capability of the model and capture the detail of the interference test that is essential for multiwell problems. A full extension to multiwell problems is also presented with the additional derivative constraint for the impulse response and symmetry constraint. Finally, we can quantify the sensitivity of the deconvolution process using singular value decomposition (SVD) and Monte Carlo simulation (MCS). Using singular value decomposition, we could reveal the orthogonal basis of the feature matrix and its corresponding singular value that helped us identify the effectiveness of the basis functions as well as their susceptibility to noise of certain pattern. Nevertheless, singular value decomposition is only suitable for noisy pressure measurement problems without inequality constraint. Thus, Monte Carlo simulation is required for full quantification of noisy measurements in both pressure and flow rate. We can observe a propagation of error in measurement to a band in pressure prediction and pressure derivative of the impulse response.This study developed a more robust method for deconvolution of pressure measurements. In addition, the mathematical insights obtained in the study allow for a more general understanding of how the deconvolution problem can be deconstructed into its relevant parts – likely allowing for expanded capability of deconvolution algorithms in industrial practice.

To improve the accuracy of tracking unmanned vehicles on known trajectories, two optimised model predictive control (MPC) trajectory tracking control systems are designed based on the adaptive compensation and robust control of a radial basis function (RBF) neural network. Based on the traditional MPC trajectory tracking controller and the local approximation characteristics of the RBF neural network, the proposed RBF compensation–MPC control system is designed to compensate for the inaccuracy in the MPC prediction model arising from modelling errors. The results show that this method can achieve a root mean square error of less than 0.3703 m for the lateral position. Subsequently, to suppress the error generated by the RBF neural network and reduce the degree of vehicle sideslip, the error is considered to be external interference, and the anti-interference characteristic of the RBF robust control is incorporated into the RBF robust-MPC control system. Following the re-optimisation of the RBF robust control, the root mean square error of the lateral position is set within 0.2352 m. The results of a MATLAB/Carsim joint simulation show that using the RBF robust control can improve the tracking accuracy of the traditional MPC controller compared with RBF compensation control, while simultaneously improving the driving stability of the vehicle.

The medical digital twin is emerging as a viable opportunity to provide patient-specific information useful for treatment, prevention and surgical planning. A bottleneck toward its effective use when computational fluid dynamics (CFD) techniques and tools are adopted for the high fidelity prediction of blood flow, is the significant computing cost required. Reduced order models (ROM) looks to be a promising solution for facing the aforementioned limit. In fact, once ROM data processing is accomplished, the consumption stage can be performed outside the computer-aided engineering software adopted for simulation and, in addition, it could be also implemented on interactive software visualization interfaces that are commonly employed in the medical context. In this paper we demonstrate the soundness of such a concept by numerically investigating the effect of the bulge shape for the ascending thoracic aorta aneurysm case. Radial basis functions (RBF) based mesh morphing enables the implementation of a parametric shape, which is used to build up the ROM framework and data. The final result is an inspection tool capable to visualize, interactively and almost in real-time, the effect of shape parameters on the entire flow field. The approach is first verified considering a morphing action representing the progression from an average healthy patient to an average aneurismatic one (Capellini et al. in Proceedings VII Meeting Italian Chapter of the European Society of Biomechanics (ESB-ITA 2017), 2017; Capellini et al. in J. Biomech. Eng. 140(11):111007-1–111007-10, 2018). Then, a set of shape parameters, suitable to consistently represent a widespread number of possible bulge configurations, are defined and accordingly generated. The concept is showcased taking into account the steady flow field at systolic peak conditions, using ANSYS®Fluent®and its ROM environment for CFD and ROM calculations respectively, and the RBF MorphTM software for shape parametrization.