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This paper proposes a novel approach for broadband acoustic shape sensitivity analysis based on the direct differentiation approach. Since the system matrices of the boundary element method (BEM) for the analysis of acoustic state and acoustic sensitivity have frequency dependence, repeated calculations are needed at different frequencies. This is very time-consuming, especially for sensitivity calculations used in shape optimization design. The Taylor series expansion of the Hankel function is carried out to separate the frequency-dependent and frequency-independent terms in the acoustic shape sensitivity boundary integral equation to construct a frequency-independent system matrix. In addition, due to the formation of asymmetric full-coefficient matrices in acoustic shape sensitivity equations based on the BEM, repeatedly solving system equations is also extremely time-consuming at broadband frequencies for large scale issues. The second-order Arnoldi approach was employed to create a reduced-order model that maintains the key features of the initial full-order model. The strong singular and supersingular integrals within the sensitivity equations can be calculated directly utilizing the singularity elimination technique. Finally, several numerical examples confirm the accuracy and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

In this article, an innovative method is proposed for broadband topology optimization of sound‐absorbing materials adhering to the surface of a sound barrier structure. Helmholtz equation for the acoustic problems is solved using the boundary element method, while sensitivities of the objective function with respect to a large number of design variables are calculated via a sensitivity analysis method originated from the adjoint variable method (AVM), and the optimal solution is obtained by the method of moving asymptotes (MMA). Since the traditional single‐frequency topology optimization is frequency dependent, that is, the optimal solution at a certain frequency may not be optimal at other frequencies, broadband topology optimization of sound‐absorbing materials is conducted in this work. To address the problem of tremendous computational cost due to repetitive calculations at each discrete frequency point during broadband optimization, Taylor expansion of the Hankel function is performed to decouple the frequency dependent and independent terms in the BEM equations. For large‐scale problems, a reduced‐order model that retains the essential structures and key properties of the original model is built using the second‐order Arnoldi (SOAR) method. The accuracy and feasibility of the proposed algorithms are finally validated via some two‐dimensional numerical examples. [ABSTRACT FROM AUTHOR]

• The generalized n th order perturbation boundary integral equation is derived for wave propagation problems. • The isogeometric BEM base on n th order perturbation boundary integral equation is proposed. • A new formula for tackling the singularity in n th order derivative boundary integral equation is presented. • Fast multipole method is adapted to the n th order derivative boundary integral equation. This paper proposes a novel generalized n th order perturbation isogeometric fast multipole boundary element method for time harmonic wave propagation in infinite domains. The non-uniform rational B-splines are employed to construct structural geometries and discretize boundary integral equations. The randomness of wave number for incident plane wave is considered as the source of system uncertainty. The generalized n th order perturbation method is employed to model the physical field depending on the input random variable. The n th order derivatives of field functions and kernel functions in the boundary integral equations are derived by generalized n th order Taylor series expansions with a small perturbation parameter. The subtraction of singularity technique is used to evaluate the singular integrals and the fast multipole method is applied to accelerate the solution. The Monte Carlo simulations are conducted in numerical examples to demonstrate the validity and correctness of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The paper introduces a novel method for simulating acoustic–shell interaction subject to seabed reflection. The vibration of thin-shell structure is analyzed using the finite element method (FEM) with Kirchhoff–Love shell elements. Exterior acoustic fields associated with seabed reflection is simulated by the boundary element method (BEM) with half-space fundamental solutions. Then the FEM and BEM are coupled to simulate interaction between acoustics wave and shell vibration in the context of isogeometric analysis. Finally, fast multipole method is formulated for the coupled system to accelerate computation and reduce memory storage. Numerical examples are provided to demonstrate the accuracy of the algorithm. • Analyzing acoustic–shell interaction by considering seabed reflection. • Coupling FEM and BEM based on half-space fundamental solutions. • Accelerating acoustic computation with fast multipole methods. [ABSTRACT FROM AUTHOR]

This study proposes an optimization approach to maximize the transmission loss (TL) of a muffler by optimizing the thickness of the embedded porous layer. The objective function, i.e. the TL value, is computed by the four-pole parameters based on the boundary element analysis, and the thicknesses assigned to the discretized elements are naturally chosen as the design variables, resulting in a continuous optimization problem. The sound-absorbing property of the porous layer is simulated using the local admittance boundary condition in the boundary element method (BEM) to link the objective function with the design variable. An efficient sensitivity analysis is developed on the basis of the adjoint variable method and the BEM. Finally, the method of moving asymptotes is applied to solve the optimization problem with the assistance of sensitivity information. As the design variable only affects the (local) admittance value, resulting in a diagonal admittance matrix, and the coefficient matrices of the boundary element analysis will not be influenced by the design variables, we can regard the overall optimization as highly efficient. Moreover, the proposed and previously developed (density-based) optimization approaches are compared. Results show high similarities in the optimization results, thus validating the presented optimization approach. The numerical results also indicate the frequency-dependency of the optimized design. The frequency-averaged TL in the frequency band of interest is selected as the objective function to achieve a multi-frequency optimization. [ABSTRACT FROM AUTHOR]

This paper presents a model order reduction method to accelerate broadband topology optimization of structural-acoustic interaction systems by coupling Finite Element Methods and Boundary Element Methods. The finite element method is used for simulating thin-shell vibration and the boundary element method for exterior acoustic fields. Moreover, the finite element and boundary element methods are implemented in the context of isogeometric analysis, whereby the geometric accuracy and high order continuity of Kirchhoff-Love shells can be guaranteed and meantime no meshing is necessary. The topology optimization method takes continuous material interpolation functions in the density and bulk modulus, and adopts adjoint variable methods for sensitivity analysis. The reduced order model is constructed based on second-order Arnoldi algorithm combined with Taylor's expansions which eliminate the frequency dependence of the system matrices. Numerical results show that the proposed algorithm can significantly improve the efficiency of broadband topology optimization analysis. • Broadband topology optimization of 3D structural-acoustic interaction with reduced order isogeometric FEM/BEM. • Model order reduction is conducted for topology optimization of structural-acoustic interaction by coupling FEM/BEM. • The isogeometric analysis is applied to the topology optimization framework with reduced order FEM/BEM. [ABSTRACT FROM AUTHOR]

This research contributes to the topology optimization of acoustic–structure interaction problems with infinite acoustic domain by focusing on two issues, namely, the variation of the acoustic–structure interface and free-floating elements. To handle the variation of the coupling interface, we divide the analyzed domain into the bounded and unbounded domains by using a virtual surface. For the bounded domain where the coupling interface may appear, we model it with the mixed displacement–pressure (u/p) finite element method (mixed FEM). Then, the boundary element method (BEM) is utilized to model the non-reflecting boundary conditions on the truncated surface. The mixed FEM enables the explicit representation of the acoustic–solid interface in the optimized domain to be circumvented. By spatial variation of the mass density, shear and bulk moduli in the mixed FEM, the topology optimization procedure can be easily implemented similar to standard density approaches. With regard to the free–floating elements, we establish a connected component filter to delete these useless elements. This treatment avoids unreasonable but possibly optimized results. The proposed method is verified by several optimization examples. [ABSTRACT FROM AUTHOR]

A novel boundary element method based on subdivision surfaces is applied to simulate wave scattering problems governed by the Helmholtz equation. The Loop subdivision scheme widely used in the CAD (computer aided design) field is applied to represent the geometric model and approximate physical field variables. The novelty of this work is that it is the first time to apply the fast multipole method for subdivision surface boundary element method to accelerate the solution of the system of equations. It is demonstrated that the subdivision surfaces boundary element method based on the Loop subdivision scheme performs well in terms of accuracy, and automatically provides multiresolution subdivision hierarchy models to meet the requirements of different precision. This approach is then applied to several real-world applications to illustrate the potential for integrated engineering analysis. [ABSTRACT FROM AUTHOR]

A shape optimization approach based on isogeometric wideband fast multipole boundary element method (IGA WFMBEM) in 2D acoustics is developed in this study. The key treatment is shape sensitivity analysis by using the adjoint variable method under isogeometric analysis (IGA) conditions. A set of efficient parameters of the wideband fast multipole method has been identified for IGA boundary element method. Shape optimization is performed by applying the method of moving asymptotes. IGA WFMBEM is validated through an acoustic scattering example. The proposed optimization approach is tested on a sound barrier and two multiple structures to demonstrate its potential for engineering problems. [ABSTRACT FROM AUTHOR]

In this work, we develop an optimization approach to optimize the distribution of porous material layer inside cavity. The optimization seeks to improve the absorbing effects of the porous material, decreasing the noise level at regions of interest or increasing the sound energy dissipated by the porous material. To achieve the preset optimization aim, two different objective functions are accordingly defined. The acoustic absorption characteristics of porous materials are numerically described using the Delany–Bazley–Miki empirical model and modeled by the admittance boundary conditions in the boundary element analysis. Based on the solid isotropic material with penalization method, an admittance interpolation scheme is established between the element admittance and artificial element density. This transforms the discrete optimization into a continuous optimization problem, which can be solved by a gradient solver with the sensitivity information. As a key treatment in this study, we develop a fast sensitivity analysis approach based on an adjoint variable method and the fast multipole method to calculate the sensitivities of the objective function with respect to a large number of design variables. Finally, we validate the proposed optimization approach through a cabin example. [ABSTRACT FROM AUTHOR]

This paper formulates a model order reduction method for electromagnetic boundary element analysis and extends it to computer-aided design integrated shape optimization of multi-frequency electromagnetic scattering problems. Firstly, a series expansion technique is adopted to decouple frequency-dependent terms from the integrands in boundary element formulation, and the second-order Arnoldi procedure is utilized to reduce the order of original systems. Secondly, to ensure geometric exactness and avoid re-meshing during shape optimization, the isogeometric boundary element method is employed, which uses the Non-Uniform Rational B-splines to represent the geometry and to discretize boundary integral equations. Lastly, we employ the Grey Wolf Optimization-Artificial Neural Network as a surrogate model for shape optimization in multi-frequency electromagnetic scattering problems, with the radar cross section as the objective function. Several examples are provided to demonstrate the accuracy and efficiency of the proposed algorithm. • An effective model order reduction scheme for boundary element analysis of electromagnetics. • Series expansions for frequency decoupling of IGABEM for electromagnetic scattering. • Neural network enhanced by Grey wolf algorithm for CAD-integrated electromagnetic shape optimization. [ABSTRACT FROM AUTHOR]

Summary: This paper presents an efficient topology optimization procedure for exterior acoustic‐structure interaction problems, in which the coupled systems are formulated by the boundary element method (BEM) and the finite element method (FEM). So far, the topology optimization based on the coupled FEM‐BEM still faces several issues needed to be addressed, especially the efficient design sensitivity analysis for the coupled systems. In this work, we contribute to these issues in two main aspects. Firstly, the adjoint variable method (AVM) formulations are derived for sensitivity analysis of arbitrary objective function, and the feedback coupling between the structural and acoustic domains are taken into consideration in the sensitivity analysis. Secondly, in addition to the application of fast multipole method (FMM) in the acoustic BEM response analysis, the FMM is now updated to adapt to the arising different multiplications in the AVM equations. These accelerations save considerable computing time and memory. Numerical tests show that the developed approach permits its application to large‐scale problems. Finally, some basic observations for the optimized designs are drawn from the numerical investigations. [ABSTRACT FROM AUTHOR]

In this paper, an isogeometric dual reciprocity boundary element method (IG-DRBEM) is proposed for the time-domain acoustic wave problem in 3D infinite domain. The fundamental solution of the potential problem is used to establish the boundary-domain integral equation, which avoids the problem of solving the coefficient matrix repeatedly at different times. On the one hand, in order to maintain the dimensionality reduction advantages of the boundary element method, the classical dual reciprocity method is used to transform the domain integral into a boundary integral. On the other hand, for purpose of satisfying the boundary conditions at infinite distance accurately, a reliable integral convergence criterion is established by adopting the approximate variation coefficient. Furthermore, the effects of different approximation functions, variation coefficients, time steps, number of interior points and elements on the results are discussed in detail by several typical examples. Numerical results show that the proposed method has high accuracy and good stability even when analyzing geometrically complex dolphin models. • IGABEM for solving acoustic wave in time domain is proposed for the first time. • The coefficient matrix formed by the boundary integral equation only requires to be calculated once. • The adaptive expansion basis function satisfying the integral regularization condition is proposed. • The multi-patch dolphin model is solved and a stable solution is obtained. [ABSTRACT FROM AUTHOR]

A topology optimization approach based on the boundary element method (BEM) and the optimality criteria (OC) method is proposed for the optimal design of sound absorbing material distribution within sound barrier structures. The acoustical effect of the absorbing material is simplified as the acoustical impedance boundary condition. Based on the solid isotropic material with penalization (SIMP) method, a topology optimization model is established by selecting the densities of absorbing material elements as design variables, volumes of absorbing material as constraints, and the minimization of sound pressure at reference surface as design objective. A smoothed Heaviside-like function is proposed to help the SIMP method to obtain a clear 0-1 distribution. The BEM is applied for acoustic analysis and the sensitivities with respect to design variables are obtained by the direct differentiation method. The Burton-Miller formulation is used to overcome the fictitious eigen-frequency problem for exterior boundary-value problems. A relaxed form of OC is used for solving the optimization problem to find the optimal absorbing material distribution. Numerical tests are provided to illustrate the application of the optimization procedure for 2D sound barriers. Results show that the optimal distribution of the sound absorbing material is strongly frequency dependent, and performing an optimization in a frequency band is generally needed. [ABSTRACT FROM AUTHOR]

Full interaction between structural and fluid domains must be considered for light structures immersed in heavy fluid (e.g. thin steel shells in water). The structural-acoustic design sensitivity analysis provides information on the effect of the design variable on acoustic performance, which makes it a key step for noise control and structural-acoustic optimization. This study uses the finite element method (FEM) to model the structure domain, while the fast multipole boundary element method (BEM) is applied to the exterior acoustic domain. An adjoint operator approach is developed to calculate the sensitivity of the radiated sound power with respect to the design variables, which can be any structural or fluid parameter (e.g. fluid or structural density, Poisson's ratio, Young's modulus, and geometric measures). Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm. [ABSTRACT FROM AUTHOR]

The complete interaction between the structural domain and the acoustic domain needs to be considered in many engineering problems, especially for the acoustic analysis concerning thin structures immersed in water. This study employs the finite element method to model the structural parts and the fast multipole boundary element method to model the exterior acoustic domain. Discontinuous higher-order boundary elements are developed for the acoustic domain to achieve higher accuracy in the coupling analysis. Structural-acoustic design sensitivity analysis can provide insights into the effects of design variables on radiated acoustic performance and thus is important to the structural-acoustic design and optimization processes. This study is the first to formulate equations for sound power sensitivity on structural surfaces based on an adjoint operator approach and equations for sound power sensitivity on arbitrary closed surfaces around the radiator based on the direct differentiation approach. The design variables include fluid density, structural density, Poisson's ratio, Young's modulus, and structural shape/size. A numerical example is presented to demonstrate the accuracy and validity of the proposed algorithm. Different types of coupled continuous and discontinuous boundary elements with finite elements are used for the numerical solution, and the performances of the different types of finite element/continuous and discontinuous boundary element coupling are presented and compared in detail. Copyright © 2016 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

Abstract: A coupling algorithm based on the finite element method (FEM) and the wideband fast multipole boundary element method (wideband FMBEM) is proposed for acoustic fluid–structure interaction simulation and structural–acoustic design sensitivity analysis by using the direct differentiation method. The wideband fast multipole method (FMM), which is developed by combining the original FMM and the diagonal form FMM, is used to accelerate the calculation of the matrix–vector products in boundary element analysis. The iterative solver generalized minimal residual method is applied to accelerate the calculation of the solution to the linear system of equations. The FEM/wideband FMBEM algorithm makes it possible to predict the effects of arbitrarily shaped vibrating structures on the sound field numerically. Numerical examples are presented to demonstrate the validity and efficiency of the proposed algorithm. [Copyright &y& Elsevier]

We propose an efficient Monte Carlo simulation method to address the multivariate uncertainties in acoustic–vibration interaction systems. The deep neural network acts as a general surrogate model to enhance the sampling efficiency of Monte Carlo Simulation. Singular Value Decomposition - Radial Basis Functions (SVD-RBF) acts as a bridge between the original full model and the neural network, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The snapshots of full order models are obtained with isogeometric analysis, in which we couple two numerical schemes for vibro–acoustic interaction problems: the isogeometric finite element method for simulating vibration of Kirchhoff–Love shells and isogeometric boundary element method for exterior acoustic waves. Numerical results show that the proposed algorithm can significantly improve the efficiency of uncertainty analysis. • A novel surrogate based method is proposed to accelerate multivariate stochastic analysis. • The acoustic–vibration coupling problem is solved with IGA FEM/BEM methods. • The SVD-RBF method is used to accelerate training of neutral network. [ABSTRACT FROM AUTHOR]

This paper presents a wideband fast multipole boundary element method (FMBEM) for two dimensional acoustic design sensitivity analysis based on the direct differentiation method. The wideband fast multipole method (FMM) formed by combining the original FMM and the diagonal form FMM is used to accelerate the matrix-vector products in the boundary element analysis. The Burton-Miller formulation is used to overcome the fictitious frequency problem when using a single Helmholtz boundary integral equation for exterior boundary-value problems. The strongly singular and hypersingular integrals in the sensitivity equations can be evaluated explicitly and directly by using the piecewise constant discretization. The iterative solver GMRES is applied to accelerate the solution of the linear system of equations. A set of optimal parameters for the wideband FMBEM design sensitivity analysis are obtained by observing the performances of the wideband FMM algorithm in terms of computing time and memory usage. Numerical examples are presented to demonstrate the efficiency and validity of the proposed algorithm. [ABSTRACT FROM AUTHOR]

Based on isogeometric boundary element method (IGA BEM) and piecewise constant level set (PCLS) method, a new topology optimization approach is proposed to design the distribution of sound absorbing materials (SAMs) on structural surfaces. First, an efficient IGA BEM is developed with the combination of multipatch discretization and parallel CPU design. A complex submarine model comprising multiple non-uniform rational B-spline surfaces is built for engineering optimization design. Second, the PCLS method is applied to represent the multiple SAM domains without gray elements, and the sensitivities of the objective function with respect to PCLS functions are obtained using the adjoint variable method. Finally, the optimization algorithm based on PCLS method is improved by a novel penalty coefficient formulation and ordered volume constraints. The improved optimization algorithm can realize the control of multimaterial volume fractions and make the objective function steadily converge for different volume structures without the need to change any parameters. The accuracy, efficiency, and applicability of the proposed approach in engineering are demonstrated by several numerical examples. [ABSTRACT FROM AUTHOR]

• Bloch eigenvalue problems in phononic structures are formulated using isogeometric boundary element method. • Bloch boundary condition is directly specified to the control points of the boundary of unit cell. • Nonlinear eigenvalue problems are solved using a contour integral projection method with Gerschgorin disk theory. • Models designed by using both Computer-Aided Design software and graphic software are computed. In this paper, a computational methodology for the band structure analysis of 2D acoustic phononic structures based on the isogeometric boundary element method(IGABEM) is studied. IGABEM not only improves the accuracy of numerical model, but also retains the geometric accuracy and makes the pre-processing procedure relatively simpler for models designed through using computer-aided design(CAD) softwares. B-splines, which are widely employed in computer graphics and CAD industry, are used as basis functions for 2D phononic unit cells. The Bloch periodic boundary condition is directly specified to the control points on the virtual boundary of a unit cell. The Bloch eigenvalue problems derived with IGABEM show strong nonlinear features resulted from the adoption of fundamental solutions. To overcome the nonlinearity, a contour integral projection method with Gerschgorin disk theory-based eigenspace identification is introduced to the extraction of the Bloch eigenvalues for the description of dispersion curves. Numerical examples with models from different CAD softwares are investigated to demonstrate the accuracy and effectiveness of the proposed method. [ABSTRACT FROM AUTHOR]

This paper presents an acoustic topology optimization approach using isogeometric boundary element methods based on subdivision surfaces to optimize the distribution of sound adsorption materials adhering to structural surfaces. The geometries are constructed from triangular control meshes through Loop subdivision scheme, and the associated Box-spline functions that generate limit smooth subdivision surfaces are employed to discretize the acoustic boundary integral equations. The effect of sound-absorbing materials on the acoustic response is characterized by acoustic impedance boundary conditions. The optimization problem is formulated in the framework of Solid Isotropic Material with Penalization methods and the sound absorption coefficients on elements are selected as design variables. The potential of the proposed topology optimization approach for engineering prototyping is illustrated by numerical examples. • Isogeometric boundary element method is applied to exterior acoustic analysis. • Subdivision surfaces are used in both CAD and numerical analysis. • The sound absorbing material distribution is optimized. • Burton-Miller method is adopted to prevent instabilities. • Adjoint variable method is employed for sensitivity analysis. [ABSTRACT FROM AUTHOR]

This study proposes a deep learning framework to perform uncertainty quantification of vibro-acoustic coupling problems for robot manta rays. First, Loop subdivision surfaces are used to build the geometric models of robot manta rays. Next, by incorporating the geometric modelling basis functions for numerical simulation, we couple isogeometric finite element and boundary element methods to calculate the sound pressure in the exterior domain of the structure, which generates initial samples for surrogate modelling. Then, deep neural networks are trained as surrogate models with multi-dimensional random inputs to expand the dataset for uncertainty quantification. Finally, the SDE-Net is employed to use the expanded data to quantify uncertainties of system responses caused by geometric and material parameters. Numerical experiments are given to demonstrate the accuracy and effectiveness of the present method. • A deep neural network framework is designed to accelerate uncertainty quantification. • The IGA FEM/BEM is applied to solve acoustic-vibration coupling problems. • SDE-Net is used to calculate aleatoric and epistemic uncertainty simultaneously. [ABSTRACT FROM AUTHOR]

• IG-DRBEM for solving time-domain infinite domain sound field reconstruction problem. • Non-iterative time-domain acoustic holography method. • POD-RBF prediction of time-domain sound pressure for large-scale structures. In this paper, a novel non-iterative reconstruction method of time-domain sound pressure and rapid prediction scheme of large-scale sound field are proposed respectively based on the isogeometric dual reciprocity boundary element method (IG-DRBEM) and proper orthogonal decomposition - radial basis functions (POD-RBF). By establishing the non-iterative inversion theory in the meaning of least squares, infinite domain acoustic holography is achieved with a small number of measured sound pressure information. Furthermore, the POD-RBF network is adopted to predict large-scale sound pressure. The presented work further expands the scope of application of IG-DRBEM, and gives full play to its advantage of not having to calculate the coefficient matrix repeatedly when analyzing the sound field at different moments. Moreover, in order to satisfy the integral regularization conditions, a suitable convergence condition about variation coefficients is investigated. Numerical results show that the proposed method has high accuracy and good stability even when the sound pressure of complex airship model is predicted with large-scale freedom. [ABSTRACT FROM AUTHOR]

• 1 A reduced-order model is directly constructed from the POD-RBF to prediction crack propagation path. • 2 An efficient POD-RBF operation for stochastic analysis with multiple variables is proposed. • 3 An improved polygon mesh remeshing algorithm is used for crack propagation simulation. An efficient Monte Carlo simulation (MCS) method that analyses the influences of multivariate uncertain parameters on the response of cracked structures is proposed. The scaled boundary finite element method (SBFEM) is used to solve the static and dynamic crack propagation problems and obtain a full-order snapshot model. The combination of a proper orthogonal decomposition with model order reduction and a radial basis function is used to achieve accelerated stochastic analysis based on MC simulations. The proper orthogonal decomposition-radial basis function (POD-RBF) method is more difficult to use directly for multivariate problems. Thus, we proposed an efficient operation suitable for multiple input variables. In crack propagation simulations, an optimized polygon meshing algorithm is used. Numerical results show that the proposed method can stochastically analyse multidimensional input variables and effectively obtain the responses of cracked structures, which verifies the effectiveness of the POD-RBF method. [ABSTRACT FROM AUTHOR]

• The multi-patch IG-DRBEM based on the PIM for non-Fourier transient heat transfer in FGMs is proposed. • The application scope of IG-DRBEM is extended to random uncertainty analysis for the first time. • The hyperbolic truncated adaptive sparse PCE uncertainty quantification framework based on IGABEM is constructed. In this paper, the precise integration multi-patch isogeometric dual reciprocity boundary element method (IG-DRBEM) of the non-Fourier transient heat transfer problem in functionally graded materials (FGMs) is proposed, and the stochastic analysis of multidimensional material uncertainty by hyperbolic truncated adaptive sparse polynomial chaos expansion (PCE) is established based on the determine theory. Up to now, most research results of the isogeometric analysis boundary element method (IGABEM) in transient heat transfer problems are based on Fourier's law. The main reason is the higher-order derivative term with respect to time in the non-Fourier heat transfer control equation leads to additional domain integrals in the boundary-domain integral equation. The dual reciprocity method (DRM) can transform the domain integral to the boundary conveniently and maintain the dimension reduction advantage of the BEM. The introduction of the precise integration method (PIM) can improve the stability and accuracy of the time-domain solution. In the random analysis based on IG-DRBEM, a sparse PCE strategy with hyperbolic truncation is constructed to overcome the dimensional disaster difficulty of traditional PCE. Through the proposed adaptive iterative process, a relatively small number of PCE terms are retained compared with the full PCE on the premise of meeting the error estimation requirements. The presented method is verified to have good accuracy and high efficiency by the complex model similar to actual engineering, which further expands the application extent of IG-DRBEM. [ABSTRACT FROM AUTHOR]

• A reduced-order model is directly constructed from the POD-RBF. • A novel surrogate method is proposed to accelerate stochastic analysis by combining the POD-RBF and DNN. • The POD-RBF is used as a bridge between SBFEM and DNN to rapidly implement predictions of large-scale and multi-dimensional input variable response functions. An efficient Monte Carlo (MC) simulation method is proposed to address multivariate uncertainties in the dynamic fracture analysis of cracked structures. Deep neural networks (DNN) based on model order reduction are special surrogate models for enhancing the sampling efficiency of MC simulation. Proper orthogonal decomposition-radial basis functions (POD-RBF) bridge the original full model and the DNN, enabling the training datasets of the neural network to be evaluated rapidly from a reduced-order model. The full-order model snapshot of the cracked structure is obtained using the scaled boundary finite element method (SBFEM). We innovatively tackle multidimensional uncertainties, including individual crack lengths, material parameters, and their combinations. Numerical examples show that the POD-RBF-DNN-MC surrogate model benefits from the uncertainty analysis of large scale and multidimensional random input variables. The method is simpler than full-order sampling and eliminates the scale problem of POD-RBF. In addition, the POD-RBF-DNN-MC surrogate model is more efficient than full-order MC, POD-RBF-MC only, and DNN-MC only, with respect to accelerating the stochastic response analysis based on MC. Finally, we validate the proposed algorithm and show that it significantly improves the efficiency of uncertainty analysis. [ABSTRACT FROM AUTHOR]