Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal ro...Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.展开更多
Based on wavelet packet decomposition （WPD） algorithm and Teager energy operator （TEO）, a novel gearbox fault detection and diagnosis method is proposed. Its process is expatiated after the principles of WPD and T...Based on wavelet packet decomposition （WPD） algorithm and Teager energy operator （TEO）, a novel gearbox fault detection and diagnosis method is proposed. Its process is expatiated after the principles of WPD and TEO modulation are introduced respectively. The preprocessed sigaaal is interpolated with the cubic spline function, then expanded over the selected basis wavelets. Grouping its wavelet packet components of the signal based on the minimum entropy criterion, the interpolated signal can be decomposed into its dominant components with nearly distinct fault frequency contents. To extract the demodulation information of each dominant component, TEO is used. The performance of the proposed method is assessed by means of several tests on vibration signals collected from the gearbox mounted on a heavy truck. It is proved that hybrid WPD-TEO method is effective and robust for detecting and diagnosing localized gearbox faults.展开更多
Based on grow tree composite model, Finite Field Wavelet Grow Tree (FW-GT) was proposed in this paper. FW-GT is a novel framework to be used in data encryption enhancing data security. It is implemented by replacement...Based on grow tree composite model, Finite Field Wavelet Grow Tree (FW-GT) was proposed in this paper. FW-GT is a novel framework to be used in data encryption enhancing data security. It is implemented by replacement operator and wavelet operator. Forward integration and inverse decomposition of FW-GT are performed by replacement, inverse wavelets and its corresponding replacement, wavelet transforms. Replacement operator joined nonlinear factor, wavelet operator completed data transformation between lower dimensional space and higher dimensional space. FW-GT security relies on the difficulty of solving nonlinear equations over finite fields. By using FW-GT, high security of data could be obtained at the cost of low computational complexity. It proved FW-GT algorithm’s correctness in this paper. The experimental result and theory analysis shows the excellent performance of the algorithm.展开更多
A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite...A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.展开更多
Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system...Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system identification, the leastsquares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.展开更多
In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator ...In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.展开更多
By rewriting the projection operator P<sub>0</sub> in wavelets in another formula,we obtain a characterization of dim J<sub>V</sub><sub>0</sub>（x）where V<sub>0</sub> i...By rewriting the projection operator P<sub>0</sub> in wavelets in another formula,we obtain a characterization of dim J<sub>V</sub><sub>0</sub>（x）where V<sub>0</sub> is a Γ-shift-invariant subspace of L<sup>2</sup>（R<sup>n</sup>）derived from a dual wavelet basis and prove that there does not exist a wavelet function ψ ∈ L<sup>2</sup>（R）such that （?）has compact support and ∪<sub>k</sub>∈ZZ（supp■+4πk）=R up to a zero subset of R.展开更多
The continuous wavelet transform(CWT)is one of the crucial damage identification tools in the vibration-based damage assessment.Because of the vanishing moment property,the CWT method is capable of featuring damage si...The continuous wavelet transform(CWT)is one of the crucial damage identification tools in the vibration-based damage assessment.Because of the vanishing moment property,the CWT method is capable of featuring damage singularity in the higher scales,and separating the global trends and noise progressively.In the classical investigations about this issue,the localization property of the CWT is usually deemed as the most critical point.The abundant information provided by the scale-domain information and the corresponding effectiveness are,however,neglected to some extent.Ultimately,this neglect restricts the sufficient application of the CWT method in damage localization,especially in noisy conditions.In order to address this problem,the wavelet correlation operator is introduced into the CWT damage detection method as a post-processing.By means of the correlations among different scales,the proposed operator suppresses noise,cancels global trends,and intensifies the damage features for various mode shapes.The proposed method is demonstrated numerically with emphasis on characterizing damage in noisy environments,where the wavelet scale Teager-Kaiser energy operator is taken as the benchmark method for comparison.Experimental validations are conducted based on the benchmark data from composite beam specimens measured by a scanning laser vibrometer.Numerical and experimental validations/comparisons present that the introduction of wavelet correlation operator is effective for damage localization in noisy conditions.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.42005003 and 41475094)。
文摘Nonlinear science is a fundamental area of physics research that investigates complex dynamical systems which are often characterized by high sensitivity and nonlinear behaviors.Numerical simulations play a pivotal role in nonlinear science,serving as a critical tool for revealing the underlying principles governing these systems.In addition,they play a crucial role in accelerating progress across various fields,such as climate modeling,weather forecasting,and fluid dynamics.However,their high computational cost limits their application in high-precision or long-duration simulations.In this study,we propose a novel data-driven approach for simulating complex physical systems,particularly turbulent phenomena.Specifically,we develop an efficient surrogate model based on the wavelet neural operator(WNO).Experimental results demonstrate that the enhanced WNO model can accurately simulate small-scale turbulent flows while using lower computational costs.In simulations of complex physical fields,the improved WNO model outperforms established deep learning models,such as U-Net,Res Net,and the Fourier neural operator(FNO),in terms of accuracy.Notably,the improved WNO model exhibits exceptional generalization capabilities,maintaining stable performance across a wide range of initial conditions and high-resolution scenarios without retraining.This study highlights the significant potential of the enhanced WNO model for simulating complex physical systems,providing strong evidence to support the development of more efficient,scalable,and high-precision simulation techniques.
基金This project is supported by National Natural Science Foundation of China (No.50605065)Natural Science Foundation Project of CQ CSTC (No.2007BB2142)
文摘Based on wavelet packet decomposition （WPD） algorithm and Teager energy operator （TEO）, a novel gearbox fault detection and diagnosis method is proposed. Its process is expatiated after the principles of WPD and TEO modulation are introduced respectively. The preprocessed sigaaal is interpolated with the cubic spline function, then expanded over the selected basis wavelets. Grouping its wavelet packet components of the signal based on the minimum entropy criterion, the interpolated signal can be decomposed into its dominant components with nearly distinct fault frequency contents. To extract the demodulation information of each dominant component, TEO is used. The performance of the proposed method is assessed by means of several tests on vibration signals collected from the gearbox mounted on a heavy truck. It is proved that hybrid WPD-TEO method is effective and robust for detecting and diagnosing localized gearbox faults.
文摘Based on grow tree composite model, Finite Field Wavelet Grow Tree (FW-GT) was proposed in this paper. FW-GT is a novel framework to be used in data encryption enhancing data security. It is implemented by replacement operator and wavelet operator. Forward integration and inverse decomposition of FW-GT are performed by replacement, inverse wavelets and its corresponding replacement, wavelet transforms. Replacement operator joined nonlinear factor, wavelet operator completed data transformation between lower dimensional space and higher dimensional space. FW-GT security relies on the difficulty of solving nonlinear equations over finite fields. By using FW-GT, high security of data could be obtained at the cost of low computational complexity. It proved FW-GT algorithm’s correctness in this paper. The experimental result and theory analysis shows the excellent performance of the algorithm.
文摘A new numerical technique based on the wavelet derivative operator is presented as an alternative to BPM to study the integrated optical waveguide. The wavelet derivative operator is used instead of FFT/IFFT or finite difference to calculate the derivatives of the transverse variable in the Helmholtz equation. Results of numerically simulating the injected field at z =0 are exhibited with Gaussian distribution in transverse direction propagating through the two dimensional waveguides (with linear and/or nonlinear refractive index) , which are similar to those in the related publications. Consequently it is efficient and needs not absorbing boundary by introducing the interpolation operator during calculating the wavelet derivative operator. The iterative process needs fewer steps to be stable. Also, when the light wave meets the changes of mediums, the wavelet derivative operator has the adaptive property to adjust those changes at the boundaries.
基金Project supported by the National Natural Science Foundation of China(Grant No.61271395)the Natural Science Foundation of Jiangsu Province,China(Grant No.BK20161513)
文摘Because of the fractional order derivatives, the identification of the fractional order system（FOS） is more complex than that of an integral order system（IOS）. In order to avoid high time consumption in the system identification, the leastsquares method is used to find other parameters by fixing the fractional derivative order. Hereafter, the optimal parameters of a system will be found by varying the derivative order in an interval. In addition, the operational matrix of the fractional order integration combined with the multi-resolution nature of a wavelet is used to accelerate the FOS identification, which is achieved by discarding wavelet coefficients of high-frequency components of input and output signals. In the end, the identifications of some known fractional order systems and an elastic torsion system are used to verify the proposed method.
文摘In this paper, we show the construction of orthogonal wavelet basis on the interval [0, 1],using compactly supportted Daubechies function. Forwardly, we suggest a kind of method to deal with the differential operator in view of numerical analysis and derive the appoximation algorithm of wavelet ba-sis and differential operator, which affects on the basis, to functions belonging to L2 [0, 1 ]. Numerical computation indicate the stability and effectiveness of the algorithm.
文摘By rewriting the projection operator P<sub>0</sub> in wavelets in another formula,we obtain a characterization of dim J<sub>V</sub><sub>0</sub>（x）where V<sub>0</sub> is a Γ-shift-invariant subspace of L<sup>2</sup>（R<sup>n</sup>）derived from a dual wavelet basis and prove that there does not exist a wavelet function ψ ∈ L<sup>2</sup>（R）such that （?）has compact support and ∪<sub>k</sub>∈ZZ（supp■+4πk）=R up to a zero subset of R.
基金the National Natural Science Foundation of China(Grant Nos.51405369&51335006)the National Key Basic Research Program of China(Grant No.2015CB057400)+3 种基金the National Natural Science Foundation of Shaanxi Province(Grant No.2016JQ5049)the Young Talent fund of University Association for Science and Technology in Shaanxi of China(Grant No.20170502)the open foundation of Zhejiang Provincial Key Laboratory of Laser Processing Robot/Key Laboratory of Laser Precision Processing&Detection(Grant No.lzsy-11)and the Fundamental Research Funds for the Central Universities(Grant No.xjj2014107)
文摘The continuous wavelet transform(CWT)is one of the crucial damage identification tools in the vibration-based damage assessment.Because of the vanishing moment property,the CWT method is capable of featuring damage singularity in the higher scales,and separating the global trends and noise progressively.In the classical investigations about this issue,the localization property of the CWT is usually deemed as the most critical point.The abundant information provided by the scale-domain information and the corresponding effectiveness are,however,neglected to some extent.Ultimately,this neglect restricts the sufficient application of the CWT method in damage localization,especially in noisy conditions.In order to address this problem,the wavelet correlation operator is introduced into the CWT damage detection method as a post-processing.By means of the correlations among different scales,the proposed operator suppresses noise,cancels global trends,and intensifies the damage features for various mode shapes.The proposed method is demonstrated numerically with emphasis on characterizing damage in noisy environments,where the wavelet scale Teager-Kaiser energy operator is taken as the benchmark method for comparison.Experimental validations are conducted based on the benchmark data from composite beam specimens measured by a scanning laser vibrometer.Numerical and experimental validations/comparisons present that the introduction of wavelet correlation operator is effective for damage localization in noisy conditions.
