CN117421561A - Turbulence denoising method and system based on parameter optimization VMD (virtual machine direction detector) combined wavelet - Google Patents
Turbulence denoising method and system based on parameter optimization VMD (virtual machine direction detector) combined wavelet Download PDFInfo
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Abstract
Description
技术领域Technical field
本发明属于海洋湍流去噪技术领域,特别涉及一种基于参数优化VMD联合小波的湍流去噪方法及系统。The invention belongs to the technical field of ocean turbulence denoising, and in particular relates to a turbulence denoising method and system based on parameter optimized VMD combined wavelet.
背景技术Background technique
海洋湍流是海洋环流中的复杂流动现象,其在海洋环境中的分布和演化对于理解海洋循环、潮汐、混合等过程至关重要。海洋湍流是一种非线性的复杂流体运动。在海洋环境中,海洋湍流的方向和流速变化较大且具有随机性。因此,需要不断优化设计更科学、精密的湍流观测仪器进行海洋湍流数据获取。由于海洋湍流的多尺度过程和海洋环流的复杂运动,仅依靠单点观测无法满足对湍流相互作用的分析研究。Ocean turbulence is a complex flow phenomenon in ocean circulation. Its distribution and evolution in the ocean environment are crucial to understanding ocean circulation, tides, mixing and other processes. Ocean turbulence is a nonlinear complex fluid motion. In the marine environment, the direction and velocity of ocean turbulence vary greatly and are random. Therefore, it is necessary to continuously optimize and design more scientific and precise turbulence observation instruments to obtain ocean turbulence data. Due to the multi-scale process of ocean turbulence and the complex motion of ocean circulation, analysis and research on turbulent interactions cannot be satisfied by relying solely on single-point observations.
通过使用多点位、高分辨率的时空同步观测,可以更好地分析湍流的演变过程。为了满足在小尺度范围内进行三维立体、多维同步观测的研究需求,采用矩阵式剖面湍流观测系统进行海洋湍流数据采集,实现了对全海深湍流混合的水平时空同步立体化观测,有助于湍流多尺度耦合研究,为实现海洋时空多维度测量提供了一种新的观测方式。By using multi-point, high-resolution spatio-temporal simultaneous observations, the evolution of turbulence can be better analyzed. In order to meet the research needs for three-dimensional and multi-dimensional synchronous observation in a small scale, a matrix profile turbulence observation system is used to collect ocean turbulence data, which realizes horizontal space-time synchronous three-dimensional observation of turbulent mixing in the whole sea depth, which is helpful to The study of multi-scale coupling of turbulence provides a new observation method for achieving multi-dimensional measurements of ocean space and time.
然而,由于海洋环境复杂性和测量条件的限制,矩阵式剖面湍流观测平台时刻处在各种海洋背景噪声之中,湍流剪切信号不可避免地受到噪声的污染,这使得信号处理和分析更加困难。因此,通过检测复杂海洋背景下的噪声污染,尽量消除噪声对观测数据的干扰,是保障观测平台稳定性和提高湍流观测数据有效性的重要途径。湍流剪切信号的噪声污染具有频带多样性,对此,目前常用的去噪方法有模态分解去噪和小波变换去噪等。However, due to the complexity of the marine environment and limitations of measurement conditions, the matrix profile turbulence observation platform is always surrounded by various ocean background noises, and the turbulence shear signals are inevitably contaminated by noise, which makes signal processing and analysis more difficult. . Therefore, detecting noise pollution in complex ocean backgrounds and minimizing the interference of noise on observation data is an important way to ensure the stability of the observation platform and improve the effectiveness of turbulence observation data. The noise pollution of turbulent shear signals has frequency band diversity. For this, currently commonly used denoising methods include mode decomposition denoising and wavelet transform denoising.
在传统的分解方法中,经验模态分解(EMD)可以递归地将含噪原始信号分解为固定数目的模态函数(IMF)分量,但各IMF分量之间存在较多的模态混叠以及产生虚假分量,对去噪效果产生较大的影响。变分模态分解(VMD)基于完全非递归分解,可以将含噪原始信号分解成一系列IMF分量,并计算每个IMF分量的中心频率,能有效地解决EMD中模态混叠的现象,但其存在惩罚因子α和IMF分量分解层数K需人工依据经验确定的缺陷。Among traditional decomposition methods, empirical mode decomposition (EMD) can recursively decompose the noisy original signal into a fixed number of modal function (IMF) components, but there are many modal aliasing and Produces false components, which has a greater impact on the denoising effect. Variational mode decomposition (VMD) is based on completely non-recursive decomposition. It can decompose the noisy original signal into a series of IMF components and calculate the center frequency of each IMF component. It can effectively solve the phenomenon of modal aliasing in EMD. However, It has the disadvantage that the penalty factor α and the number of IMF component decomposition layers K need to be determined manually based on experience.
发明内容Contents of the invention
本发明的目的在于提出一种基于参数优化VMD联合小波的湍流去噪方法,该方法可消除湍流剪切信号中的噪声干扰,从而提高海洋湍流数据的准确性。The purpose of this invention is to propose a turbulence denoising method based on parameter-optimized VMD combined wavelet, which can eliminate noise interference in turbulent shear signals, thereby improving the accuracy of ocean turbulence data.
本发明为了实现上述目的,采用如下技术方案:In order to achieve the above objects, the present invention adopts the following technical solutions:
一种基于参数优化VMD联合小波的湍流去噪方法,包括如下步骤:A turbulence denoising method based on parameter optimized VMD joint wavelet, including the following steps:
步骤1. 通过NGO算法对VMD方法的参数进行寻优,根据得到的最优参数[α,K]对测量的原始湍流剪切信号x(t)进行变分模态分解,计算各模态分量uK(t)与原始湍流剪切信号x(t)的相关系数M,判断各模态分量uK(t)中的有效分量um(t)和噪声分量uK-m(t);Step 1. Use the NGO algorithm to optimize the parameters of the VMD method, perform variational mode decomposition on the measured original turbulent shear signal x(t) based on the obtained optimal parameters [α, K], and calculate each modal component. The correlation coefficient M between u K (t) and the original turbulence shear signal x (t) is used to determine the effective component u m (t) and noise component u Km (t) in each modal component u K (t);
步骤2. 将得到的噪声分量uK-m(t)剔除,并利用小波阈值法对有效分量um(t)进行去噪,得到去噪后的湍流有效分量ym(t);Step 2. Eliminate the obtained noise component u Km (t), and use the wavelet threshold method to denoise the effective component u m (t), and obtain the denoised turbulence effective component y m (t);
步骤3. 将湍流有效分量ym(t)进行数据重构,得到去噪后的剪切信号s(t)。Step 3. Reconstruct the data of the effective turbulence component y m (t) to obtain the denoised shear signal s(t).
此外,在上述基于参数优化VMD联合小波的湍流去噪方法的基础上,本发明还提出了一种与之相对应的基于参数优化VMD联合小波的湍流去噪系统,其采用如下技术方案:In addition, based on the above turbulence denoising method based on parameter optimized VMD joint wavelet, the present invention also proposes a corresponding turbulence denoising system based on parameter optimized VMD joint wavelet, which adopts the following technical solution:
一种基于参数优化VMD联合小波的湍流去噪系统,包括:A turbulence denoising system based on parameter optimized VMD combined wavelet, including:
分解模块,用于通过NGO算法对VMD方法的参数进行寻优,根据得到的最优参数[α,K]对测量的原始湍流剪切信号x(t)进行变分模态分解,计算各模态分量uK(t)与原始湍流剪切信号x(t)的相关系数M,判断各模态分量uK(t)中的有效分量um(t)和噪声分量uK-m(t);The decomposition module is used to optimize the parameters of the VMD method through the NGO algorithm. According to the obtained optimal parameters [α, K], the measured original turbulence shear signal x(t) is subjected to variational mode decomposition, and each mode is calculated. The correlation coefficient M between the state component u K (t) and the original turbulence shear signal x (t) is used to determine the effective component u m (t) and the noise component u Km (t) in each modal component u K (t);
小波阈值去噪模块,用于将得到的噪声分量uK-m(t)剔除,并利用小波阈值法对有效分量um(t)进行去噪,得到去噪后的湍流有效分量ym(t);The wavelet threshold denoising module is used to eliminate the obtained noise component u Km (t), and use the wavelet threshold method to denoise the effective component u m (t), and obtain the denoised turbulence effective component y m (t) ;
以及数据重构模块,用于将湍流有效分量ym(t)进行数据重构,得到去噪后的剪切信号s(t)。and a data reconstruction module, which is used to reconstruct the data of the effective turbulence component y m (t) to obtain the denoised shear signal s(t).
此外,在基于参数优化VMD联合小波的湍流去噪方法的基础上,本发明还提出了一种用于实现基于参数优化VMD联合小波的湍流去噪方法的计算机设备。In addition, based on the turbulence denoising method based on parameter optimized VMD joint wavelet, the present invention also proposes a computer device for implementing the turbulence denoising method based on parameter optimized VMD joint wavelet.
该计算机设备包括存储器和处理器,存储器中存储有可执行代码,处理器执行所述可执行代码时,用于实现上面述及的基于参数优化VMD联合小波的湍流去噪方法的步骤。The computer device includes a memory and a processor, and executable code is stored in the memory. When the processor executes the executable code, it is used to implement the above-mentioned steps of the turbulence denoising method based on parameter-optimized VMD joint wavelet.
此外,在基于参数优化VMD联合小波的湍流去噪方法的基础上,本发明还提出了一种用于实现基于参数优化VMD联合小波的湍流去噪方法的计算机可读存储介质。In addition, based on the turbulence denoising method based on parameter-optimized VMD joint wavelet, the present invention also proposes a computer-readable storage medium for implementing the turbulence denoising method based on parameter-optimized VMD joint wavelet.
该计算机可读存储介质,其上存储有程序,当该程序被处理器执行时,用于实现上面述及的基于参数优化VMD联合小波的湍流去噪方法的步骤。The computer-readable storage medium has a program stored thereon, and when the program is executed by the processor, it is used to implement the above-mentioned steps of the turbulence denoising method based on parameter-optimized VMD joint wavelet.
本发明具有如下优点:The invention has the following advantages:
如上所述,本发明述及了一种基于参数优化VMD联合小波的湍流去噪方法,该方法采用多模态分解去噪策略,依托NGO算法对变分模态分解的惩罚参数α和分解参数K进行寻优,联合小波阈值方法消除频带内噪声污染,对现有去噪技术进行改进,可消除湍流剪切信号中的噪声干扰,从而提高海洋湍流数据的准确性,以便于对湍流信号的进一步分析研究。本发明方法适用于复杂的海洋环境,能够实现海洋水文信息观测的精细化、立体化、同步化。As mentioned above, the present invention describes a turbulence denoising method based on parameter optimized VMD combined wavelet. This method adopts a multi-modal decomposition denoising strategy and relies on the NGO algorithm to determine the penalty parameter α and decomposition parameters of variational mode decomposition. K is optimized, combined with the wavelet threshold method to eliminate noise pollution in the frequency band, and the existing denoising technology is improved to eliminate the noise interference in the turbulence shear signal, thereby improving the accuracy of ocean turbulence data and facilitating the analysis of turbulence signals. Further analysis and research. The method of the invention is suitable for complex marine environments and can achieve refinement, three-dimensionality and synchronization of marine hydrological information observation.
附图说明Description of the drawings
图1为本发明实施例中基于参数优化VMD联合小波的湍流去噪方法的流程图。Figure 1 is a flow chart of the turbulence denoising method based on parameter optimized VMD combined wavelet in the embodiment of the present invention.
图2为仿真信号与经过本发明方法去噪处理后的结果对比图;其中,(a)为原始含噪信号示意,(b)为NGO-VMD联合小波去噪示意。Figure 2 is a comparison chart between the simulated signal and the result after denoising by the method of the present invention; (a) is a schematic of the original noisy signal, and (b) is a schematic of NGO-VMD joint wavelet denoising.
图3为本发明实施例中湍流剪切信号去噪对比图。Figure 3 is a comparison chart of turbulent shear signal denoising in the embodiment of the present invention.
图4为本发明实施例中湍流信号去噪对比谱图。Figure 4 is a comparative spectrum chart of turbulence signal denoising in the embodiment of the present invention.
图5为本发明实施例中湍流耗散率去噪对比图。Figure 5 is a comparison chart of turbulence dissipation rate denoising in the embodiment of the present invention.
具体实施方式Detailed ways
下面结合附图以及具体实施方式对本发明作进一步详细说明:The present invention will be further described in detail below in conjunction with the accompanying drawings and specific embodiments:
实施例1Example 1
本实施例述及了一种基于参数优化VMD联合小波的湍流去噪方法,该方法通过矩阵式剖面湍流仪采集得到原始剪切信号,初始化NGO算法的参数,设定最小化包络熵为适应度值,获取最小包络熵对应的α和K值作为VMD算法的最优参数,使用最优参数的VMD算法对原始湍流剪切信号进行模态分解,并根据各模态分量与原始湍流剪切信号的相关系数去除噪声分量,保留有效分量,完成首次去噪,之后对保留的有效分量进行小波阈值去噪,实现二次去噪,对去噪后的各分量进行信号重构,获取较为纯净的湍流剪切信号。This embodiment describes a turbulence denoising method based on parameter optimized VMD combined wavelet. This method collects the original shear signal through a matrix profile turbulence meter, initializes the parameters of the NGO algorithm, and sets the minimum envelope entropy to adapt degree value, obtain the α and K values corresponding to the minimum envelope entropy as the optimal parameters of the VMD algorithm, use the VMD algorithm with optimal parameters to perform modal decomposition of the original turbulence shear signal, and compare each modal component with the original turbulence shear signal. Cut the correlation coefficient of the signal to remove the noise component, retain the effective components, and complete the first denoising. Then, perform wavelet threshold denoising on the retained effective components to achieve the second denoising. Reconstruct the signal for each component after denoising, and obtain a more accurate signal. Pure turbulent shear signal.
北方苍鹰算法(Northern Goshawk Optimization,NGO)是于2021年提出的一种种群智能优化算法,具有收敛速度快,稳定性好的特点。选用该算法对VMD的参数进行寻优,筛选出最合适的惩罚因子α和分解层数K作为VMD的最优参数。为提高湍流数据的去噪效果,将NGO-VMD方法联合小波阈值法进行二次去噪,可得到更为精确的湍流剪切信号。The Northern Goshawk Optimization (NGO) is a population intelligent optimization algorithm proposed in 2021. It has the characteristics of fast convergence speed and good stability. This algorithm is used to optimize the parameters of VMD, and the most appropriate penalty factor α and decomposition layer number K are selected as the optimal parameters of VMD. In order to improve the denoising effect of turbulence data, the NGO-VMD method is combined with the wavelet threshold method for secondary denoising, which can obtain a more accurate turbulence shear signal.
如图1所示,本实施例中基于参数优化VMD联合小波的湍流去噪方法,包括如下步骤:As shown in Figure 1, the turbulence denoising method based on parameter optimized VMD joint wavelet in this embodiment includes the following steps:
步骤1. 通过NGO算法对VMD方法的参数进行寻优,根据得到的最优参数[α,K]对测量的原始湍流剪切信号x(t)进行变分模态分解,计算各模态分量uK(t)与原始湍流剪切信号x(t)的相关系数M,判断各模态分量uK(t)中的有效分量um(t)和噪声分量uK-m(t)。Step 1. Use the NGO algorithm to optimize the parameters of the VMD method, perform variational mode decomposition on the measured original turbulent shear signal x(t) based on the obtained optimal parameters [α, K], and calculate each modal component. The correlation coefficient M between u K (t) and the original turbulence shear signal x (t) determines the effective component u m (t) and the noise component u Km (t) in each modal component u K (t).
通过矩阵式剖面湍流观测仪采集海洋环境中的湍流信息,得到原始湍流剪切信号x(t)。The turbulence information in the marine environment is collected through the matrix profile turbulence observer, and the original turbulence shear signal x(t) is obtained.
通过NGO算法对VMD方法的参数进行寻优,以最小化包络熵EPmin作为适应度函数,经全局搜索和局部搜索获取最小包络熵值对应的VMD最优参数[α0,K0]。The parameters of the VMD method are optimized through the NGO algorithm, and the minimum envelope entropy E Pmin is used as the fitness function. The optimal VMD parameters [α 0 , K 0 ] corresponding to the minimum envelope entropy value are obtained through global search and local search. .
具体的,以最小化包络熵作为适应度函数,长度为q的湍流信号x(j)的包络熵定义为:Specifically, taking the minimum envelope entropy as the fitness function, the envelope entropy of the turbulence signal x(j) with length q is defined as:
; ;
; ;
其中,ω(j)是信号x(j)经Hilbert解调后得到的包络信号, pj是ω(j)的归一化形式,EP是依据信息熵计算规则得到,依据EP衡量VMD的分解效果。Among them, ω(j) is the envelope signal obtained after Hilbert demodulation of signal x(j), p j is the normalized form of ω(j), E P is obtained according to the information entropy calculation rule, and is measured according to E P The decomposition effect of VMD.
湍流信号经过VMD方法分解后,若某分量中包含的噪声较多,则该分量的稀疏性弱,包络熵较大;反之,若某分量中包含的噪声较少,则包络熵较小。After the turbulence signal is decomposed by the VMD method, if a certain component contains more noise, the sparsity of the component is weak and the envelope entropy is larger; conversely, if a certain component contains less noise, the envelope entropy is smaller .
在参数组合α和K中,选择K个分量中的最小包络熵作为局部极小熵EPmin,与该最小包络熵值对应的分量包含较多的纯净湍流信息;将局部极小熵值作为搜索过程的适应度函数,寻找最佳分量对应的参数组合[α0,K0],完成参数优化过程。In the parameter combination α and K, the minimum envelope entropy among the K components is selected as the local minimum entropy E Pmin . The component corresponding to the minimum envelope entropy value contains more pure turbulence information; the local minimum entropy value is As the fitness function of the search process, find the parameter combination [α 0 , K 0 ] corresponding to the best component to complete the parameter optimization process.
利用NGO算法对VMD的惩罚参数α和分解参数K寻优的具体计算过程如下:The specific calculation process of using the NGO algorithm to optimize the penalty parameter α and decomposition parameter K of VMD is as follows:
步骤1.1. 初始化种群。Step 1.1. Initialize the population.
在NGO算法中,种群矩阵X为:In the NGO algorithm, the population matrix X is:
。 .
式中,Xi 为编号为i北方苍鹰的位置,N为种群数量,m为求解的维度,取值为2,为编号为i的北方苍鹰在第j维的位置,j取1或2。In the formula , is the position of the northern goshawk numbered i in the jth dimension, j is 1 or 2.
计算过程分为搜寻阶段和狩猎阶段。The calculation process is divided into search phase and hunting phase.
步骤1.2. 搜寻阶段过程如下:Step 1.2. The search phase process is as follows:
; ;
; ;
; ;
式中,k为[1,N]范围内的随机整数;为编号为i的北方苍鹰在第j维的更新位 置;Fi为目标函数值,即最小化包络熵;为更新后的包络熵值;Pi为编号为i的猎物位 置,FPi为猎物对应的目标函数值;r为 0~1 之间的随机数,I的值为1或2,用于更新北方苍鹰 的位置,表示编号为i北方苍鹰更新后的位置。搜寻阶段通过全局搜索不断更新VMD优 化参数以获取最优参数范围,每次更新位置时计算湍流信号VMD分解的包络熵EP来优化VMD 参数。 In the formula, k is a random integer in the range of [1, N]; is the updated position of the northern goshawk numbered i in the jth dimension; F i is the objective function value, which is to minimize the envelope entropy; is the updated envelope entropy value; Pi is the position of the prey numbered i, F Pi is the objective function value corresponding to the prey; r is a random number between 0 and 1, and the value of I is 1 or 2, used for Update northern goshawk location, Indicates the updated position of northern goshawk number i. In the search stage, the VMD optimization parameters are continuously updated through global search to obtain the optimal parameter range. Each time the position is updated, the envelope entropy E P of the VMD decomposition of the turbulence signal is calculated to optimize the VMD parameters.
步骤1.3. 狩猎阶段,对空间进行局部搜索以确定最优解。Step 1.3. In the hunting phase, a local search is performed on the space to determine the optimal solution.
; ;
; ;
。 .
式中,为狩猎阶段编号为i的北方苍鹰在第j维的新位置;R为区域半径;t为 当前迭代次数;T为最大迭代次数;为更新后的目标函数值。 In the formula, is the new position of the northern goshawk numbered i in the hunting stage in the jth dimension; R is the radius of the area; t is the current number of iterations; T is the maximum number of iterations; is the updated objective function value.
根据全局搜索与局部搜索相结合更新所有VMD参数后,此时确定了所有目标函数EP以及当前最优解[α,K],然后NGO算法进入下一次迭代,种群成员根据搜寻和狩猎阶段继续更新,直到完成最后一次迭代,整个迭代过程中获得的最小包络熵EPmin对应的最优解[α0,K0]作为湍流剪切信号进行VMD分解的最佳参数。NGO算法中的各个参数设置如下:After updating all VMD parameters based on the combination of global search and local search, all objective functions E P and the current optimal solution [α, K] are determined at this time. Then the NGO algorithm enters the next iteration, and the population members continue according to the search and hunting stages. Updated until the last iteration is completed, the optimal solution [α 0 , K 0 ] corresponding to the minimum envelope entropy E Pmin obtained during the entire iteration process is used as the best parameter for VMD decomposition of the turbulent shear signal. The various parameters in the NGO algorithm are set as follows:
搜索过程中,设定最小分解层数Kmin=2,最大分解层数Kmax=12;最小惩罚因子αmin=0,最大惩罚因子αmax=8000,种群数量N为10,最大迭代次数T为30。During the search process, set the minimum number of decomposition layers K min =2, the maximum number of decomposition layers K max =12; the minimum penalty factor α min =0, the maximum penalty factor α max =8000, the population number N as 10, and the maximum number of iterations T is 30.
以最小包络熵值EPmin为适应度函数,对湍流信号进行VMD分解,通过每次代入不同组合的α和K对EP进行计算,再相互比较更新当前最小包络熵值,当迭代次数达到最大迭代值时,保存全局最小包络熵EPmin以及其对应的参数组合α和K,最终确定惩罚参数α为879,分解参数K为9,作为湍流信号VMD变换的相应参数值,即完成VMD的优化过程。Using the minimum envelope entropy value E Pmin as the fitness function, perform VMD decomposition of the turbulence signal, calculate E P by substituting different combinations of α and K each time, and then compare with each other to update the current minimum envelope entropy value. When the number of iterations When the maximum iteration value is reached, the global minimum envelope entropy E Pmin and its corresponding parameter combination α and K are saved. The penalty parameter α is finally determined to be 879 and the decomposition parameter K is 9, which are used as the corresponding parameter values of the VMD transformation of the turbulence signal, that is, it is completed. Optimization process of VMD.
将寻优得到的参数α和K作为VMD的最优参数,对湍流信号进行分解得到 K个IMF分量uK(t);为了确定各IMF分量uK(t)与原始湍流剪切信号x(t)之间的相关性,引入皮尔逊相关系数,设定相关系数大于或等于Ω为有效IMF分量,0<Ω<1;定义公式如下:Using the optimized parameters α and K as the optimal parameters of VMD, the turbulence signal is decomposed to obtain K IMF components u K (t); in order to determine the relationship between each IMF component u K (t) and the original turbulence shear signal x ( t), introduce the Pearson correlation coefficient, and set the correlation coefficient to be greater than or equal to Ω as the effective IMF component, 0<Ω<1; the definition formula is as follows:
。 .
式中,表示原始湍流剪切信号x(t),为原始湍流剪切信号x(t)的均值,表 示VMD分解得到的模态分量,为模态分量的均值;在本实施例中,Ω例如取值为0.5。 In the formula, represents the original turbulent shear signal x(t), is the mean value of the original turbulent shear signal x(t), Represents the modal components obtained by VMD decomposition, is the mean value of the modal components; in this embodiment, Ω takes a value of 0.5, for example.
剔除相关系数小于0.5的IMF分量uK-m(t),保留相关系数大于或等于0.5的IMF分量um(t),其中,m为湍流有效分量个数,完成湍流信号的初步降噪过程。IMF components u Km (t) with correlation coefficients less than 0.5 are eliminated, and IMF components u m (t) with correlation coefficients greater than or equal to 0.5 are retained, where m is the number of effective turbulence components, completing the preliminary noise reduction process of turbulence signals.
步骤2. 将得到的噪声分量uK-m(t)剔除,并利用小波阈值法对有效分量um(t)进行去噪,得到去噪后的湍流有效分量ym(t)。Step 2. Eliminate the obtained noise component u Km (t), and use the wavelet threshold method to denoise the effective component u m (t), and obtain the denoised effective turbulence component y m (t).
步骤2.1. 对保留的湍流有效分量um(t)进行小波阈值去噪,计算步骤如下:Step 2.1. Perform wavelet threshold denoising on the retained turbulence effective component u m (t). The calculation steps are as follows:
小波阈值去噪法是一种基于小波变换的理论和方法,通过对信号在小波域中的系数进行阈值处理来实现去除噪声的目的。The wavelet threshold denoising method is a theory and method based on wavelet transform, which achieves the purpose of removing noise by thresholding the coefficients of the signal in the wavelet domain.
步骤2.1.1. 确定合适的小波基函数,对湍流有效分量进行小波分解,得到小波系数。Step 2.1.1. Determine the appropriate wavelet basis function, perform wavelet decomposition on the effective component of turbulence, and obtain the wavelet coefficients.
。 .
式中,aβ(n)为近似系数,bβ(n)为细节系数, h为低通滤波器系数,g为高通滤波器系数,β为分解层数,n表示采样点个数,k=1,2,...,n-1。In the formula, a β (n) is the approximate coefficient, b β (n) is the detail coefficient, h is the low-pass filter coefficient, g is the high-pass filter coefficient, β is the number of decomposition layers, n represents the number of sampling points, k =1,2,...,n-1.
步骤2.1.2. 选择合适的阈值函数对小波系数进行阈值处理,阈值函数如下:Step 2.1.2. Select an appropriate threshold function to perform threshold processing on the wavelet coefficients. The threshold function is as follows:
。 .
式中,U为湍流信号去噪后小波系数,w为湍流信号去噪前小波系数,λ为小波阈值。In the formula, U is the wavelet coefficient after denoising the turbulence signal, w is the wavelet coefficient before denoising the turbulence signal, and λ is the wavelet threshold.
步骤2.1.3. 利用去噪后小波系数进行信号重构,得到重构后湍流有效分量,即为小波去噪后湍流信号;重构公式为:Step 2.1.3. Use the denoised wavelet coefficients to reconstruct the signal to obtain the reconstructed turbulence effective component, which is the wavelet denoised turbulence signal; the reconstruction formula is:
。 .
其中,表示小波去噪后湍流信号,表示近似系数,表示细节系数。 in, represents the turbulence signal after wavelet denoising, represents the approximate coefficient, Represents the detail coefficient.
步骤2.2. 小波基选取db5小波,分解层数界定为4层,对有效IMF分量进行降噪处理,得到二次去噪后的有效IMF分量ym(t)。Step 2.2. The db5 wavelet is selected as the wavelet base, and the number of decomposition layers is defined as 4 layers. The effective IMF component is denoised to obtain the effective IMF component y m (t) after secondary denoising.
步骤3. 将湍流有效分量ym(t)进行数据重构,得到更为精确的去噪后的剪切信号s(t),公式如下:Step 3. Reconstruct the data of the effective turbulence component y m (t) to obtain a more accurate denoised shear signal s(t). The formula is as follows:
。 .
将去噪后的湍流信号s(t)与未去噪信号x(t)进行谱对比与耗散率对比,验证去噪精度。Compare the spectrum and dissipation rate of the denoised turbulence signal s(t) and the non-denoised signal x(t) to verify the denoising accuracy.
图2示出了本发明的仿真信号以及利用本发明所提NGO-VMD联合小波去噪对比图。其中,图2 中的(a)为原始含噪信号示意,图2 中的(b)为NGO-VMD联合小波去噪示意。Figure 2 shows a comparison diagram of the simulated signal of the present invention and the use of NGO-VMD joint wavelet denoising proposed by the present invention. Among them, (a) in Figure 2 is a schematic of the original noisy signal, and (b) in Figure 2 is a schematic of NGO-VMD joint wavelet denoising.
在进行湍流信号处理之前,本发明使用了NGO-VMD联合小波去噪,对模拟仿真加噪信号进行了去噪对比,并计算了三个去噪指标:信噪比(SNR)、均方根误差(RMSE)以及与纯净原始信号的互相关系数(cc)。通过计算发现,去噪后信号的信噪比为:24.5441;均方根误差为:0.1676;互相关系数为:0.9966。从图2的对比结果以及三个去噪指标可知,本发明所提NGO-VMD联合小波去噪的效果较好,因此,本发明方法能够用于湍流信号去噪。Before performing turbulence signal processing, the present invention uses NGO-VMD joint wavelet denoising, conducts denoising comparison on the simulated noise signal, and calculates three denoising indicators: signal-to-noise ratio (SNR), root mean square error (RMSE) and cross-correlation coefficient (cc) with the pure original signal. Through calculation, it is found that the signal-to-noise ratio of the denoised signal is: 24.5441; the root mean square error is: 0.1676; and the cross-correlation coefficient is: 0.9966. From the comparison results in Figure 2 and the three denoising indicators, it can be seen that the NGO-VMD joint wavelet denoising effect proposed by the present invention is better. Therefore, the method of the present invention can be used for turbulence signal denoising.
图3示出了本发明的湍流剪切信号去噪对比图。将原始湍流剪切信号与本发明方法去噪后剪切信号进行对比分析,净化后的时间序列也保留了湍流序列的间歇性和级联性质。原始湍流剪切信号的波动明显大于去噪信号。去噪信号的时间序列也呈现了原始时间序列的属性,原始剪切数据和重建的剪切谱之间的一致性较好。Figure 3 shows a comparison diagram of turbulent shear signal denoising according to the present invention. Comparative analysis of the original turbulence shear signal and the shear signal after denoising by the method of the present invention shows that the purified time series also retains the intermittency and cascade properties of the turbulence sequence. The fluctuations of the original turbulent shear signal are significantly larger than those of the denoised signal. The time series of the denoised signal also exhibits the properties of the original time series, and the consistency between the original shear data and the reconstructed shear spectrum is good.
图4示出了本发明的湍流信号去噪对比谱图。将原始湍流剪切信号与本发明方法去噪后剪切信号进行对比分析,并与标准Nasmyth谱进行拟合分析。根据对比结果与拟合情况分析可得,采用本发明去噪方法处理形成的剪切波数谱在截止波数(图中竖虚线)之前与标准Nasmyth谱拟合度更高,能够有效提高湍流信号的信噪比,确保了在复杂海洋环境获取的湍流数据更为精确。Figure 4 shows the turbulence signal denoising comparison spectrum of the present invention. The original turbulent shear signal and the shear signal after denoising by the method of the present invention are compared and analyzed, and the fitting analysis is performed with the standard Nasmyth spectrum. According to the comparison results and fitting analysis, it can be seen that the shear wave number spectrum formed by the denoising method of the present invention has a higher fitting degree to the standard Nasmyth spectrum before the cut-off wave number (vertical dotted line in the figure), which can effectively improve the accuracy of the turbulence signal. The signal-to-noise ratio ensures more accurate turbulence data acquired in complex ocean environments.
图5示出了本发明的湍流耗散率去噪对比图。将原始湍流耗散率与本发明方法去噪后湍流耗散率进行对比分析可知,经本发明提供的新的去噪方法处理后的湍流耗散率的波动较原始耗散率更小,且整体量级更趋近于标准的MicroRider耗散率(约为10-9 W kg-1),证明本发明所提的去噪方法能实现准确的湍流信号去噪,使去噪数据更贴近于纯净海洋湍流数据,为后续研究湍流空间特征分布以及动力学演化规律提供了可靠的数据保障。Figure 5 shows a comparison chart of turbulence dissipation rate denoising according to the present invention. Comparative analysis of the original turbulence dissipation rate and the turbulence dissipation rate after denoising by the method of the present invention shows that the fluctuation of the turbulence dissipation rate after processing by the new denoising method provided by the present invention is smaller than the original dissipation rate, and The overall magnitude is closer to the standard MicroRider dissipation rate (about 10 -9 W kg -1 ), which proves that the denoising method proposed in the present invention can achieve accurate turbulence signal denoising and make the denoised data closer to Pure ocean turbulence data provides reliable data guarantee for subsequent research on the spatial distribution of turbulence characteristics and dynamic evolution rules.
综上,本发明所提基于参数优化VMD联合小波的湍流去噪方法,能够直观地获取信号在变分模态分解中的最优参数,实现对原始湍流剪切信号的精确模态分解,有效地将有用信号和噪声信号从混合信号中分离出来,同时还保留了信号的原有特征,采取小波阈值的方法进行二次去噪,确保了湍流数据更为精确,降低了复杂海洋环境对湍流观测数据的影响,对于研究海洋湍流的复杂时空演化、相互关系以及作为模型验证的依据具有重要意义。In summary, the turbulence denoising method based on parameter optimized VMD combined with wavelet proposed by the present invention can intuitively obtain the optimal parameters of the signal in the variational mode decomposition, achieve accurate mode decomposition of the original turbulence shear signal, and effectively The useful signal and noise signal are separated from the mixed signal, while retaining the original characteristics of the signal. The wavelet threshold method is used for secondary denoising, ensuring that the turbulence data is more accurate and reducing the impact of the complex ocean environment on turbulence. The influence of observation data is of great significance for studying the complex spatiotemporal evolution and interrelationships of ocean turbulence and as a basis for model verification.
本发明所提基于参数优化VMD联合小波的湍流去噪方法,在推动海洋信号测量仪器的进一步优化的同时,为深入挖掘复杂海洋演化过程的动力学机理提供精确数据支撑。The turbulence denoising method based on parameter optimized VMD combined with wavelet proposed by the present invention not only promotes the further optimization of ocean signal measurement instruments, but also provides accurate data support for in-depth exploration of the dynamic mechanism of complex ocean evolution processes.
实施例2Example 2
本实施例2述及了一种基于参数优化VMD联合小波的湍流去噪系统,该系统与上述实施例1述及的基于参数优化VMD联合小波的湍流去噪方法基于相同发明构思。This embodiment 2 describes a turbulence denoising system based on parameter-optimized VMD joint wavelet. This system is based on the same inventive concept as the turbulence denoising method based on parameter-optimized VMD joint wavelet described in the above-mentioned embodiment 1.
具体的,基于参数优化VMD联合小波的湍流去噪系统,包括:Specifically, the turbulence denoising system based on parameter optimized VMD combined wavelet includes:
分解模块,用于通过NGO算法对VMD方法的参数进行寻优,根据得到的最优参数[α,K]对测量的原始湍流剪切信号x(t)进行变分模态分解,计算各模态分量uK(t)与原始湍流剪切信号x(t)的相关系数M,判断各模态分量uK(t)中的有效分量um(t)和噪声分量uK-m(t);The decomposition module is used to optimize the parameters of the VMD method through the NGO algorithm. According to the obtained optimal parameters [α, K], the measured original turbulence shear signal x(t) is subjected to variational mode decomposition, and each mode is calculated. The correlation coefficient M between the state component u K (t) and the original turbulence shear signal x (t) is used to determine the effective component u m (t) and the noise component u Km (t) in each modal component u K (t);
小波阈值去噪模块,用于将得到的噪声分量uK-m(t)剔除,并利用小波阈值法对有效分量um(t)进行去噪,得到去噪后的湍流有效分量ym(t);The wavelet threshold denoising module is used to eliminate the obtained noise component u Km (t), and use the wavelet threshold method to denoise the effective component u m (t), and obtain the denoised turbulence effective component y m (t) ;
以及数据重构模块,用于将湍流有效分量ym(t)进行数据重构,得到去噪后的剪切信号s(t)。and a data reconstruction module, which is used to reconstruct the data of the effective turbulence component y m (t) to obtain the denoised shear signal s(t).
需要说明的是,基于参数优化VMD联合小波的湍流去噪系统中,各个功能模块的功能和作用的实现过程具体详见上述实施例1中方法中对应步骤的实现过程,在此不再赘述。It should be noted that in the turbulence denoising system based on parameter optimized VMD joint wavelet, the implementation process of the functions and functions of each functional module is detailed in the implementation process of the corresponding steps in the method in the above-mentioned Embodiment 1, which will not be described again here.
实施例3Example 3
本实施例3述及了一种计算机设备,该计算机设备用于实现上述实施例1中述及的基于参数优化VMD联合小波的湍流去噪方法。This embodiment 3 describes a computer device, which is used to implement the turbulence denoising method based on parameter-optimized VMD combined wavelet described in the above-mentioned embodiment 1.
具体的,该计算机设备包括存储器和一个或多个处理器。在存储器中存储有可执行代码,当处理器执行可执行代码时,用于实现基于参数优化VMD联合小波的湍流去噪方法的步骤。Specifically, the computer device includes a memory and one or more processors. The executable code is stored in the memory, and when the processor executes the executable code, it is used to implement the steps of the turbulence denoising method based on parameter-optimized VMD joint wavelet.
本实施例中计算机设备为任意具备数据数据处理能力的设备或装置,此处不再赘述。In this embodiment, the computer device is any device or device with data processing capabilities, which will not be described again here.
实施例4Example 4
本实施例4述及了一种计算机可读存储介质,该计算机可读存储介质用于实现上述实施例1中述及的基于参数优化VMD联合小波的湍流去噪方法。This embodiment 4 describes a computer-readable storage medium, which is used to implement the turbulence denoising method based on parameter-optimized VMD combined wavelet described in the above-mentioned embodiment 1.
具体的,本实施例4中的计算机可读存储介质,其上存储有程序,该程序被处理器执行时,用于实现上述基于参数优化VMD联合小波的湍流去噪方法的步骤。Specifically, the computer-readable storage medium in Embodiment 4 has a program stored thereon, and when the program is executed by the processor, it is used to implement the above steps of the turbulence denoising method based on parameter-optimized VMD joint wavelet.
该计算机可读存储介质可以是任意具备数据处理能力的设备或装置的内部存储单元,例如硬盘或内存,也可以是任意具备数据处理能力的设备的外部存储设备,例如设备上配备的插接式硬盘、智能存储卡(Smart Media Card,SMC)、SD卡、闪存卡(Flash Card)等。The computer-readable storage medium can be an internal storage unit of any device or device with data processing capabilities, such as a hard disk or a memory, or it can be an external storage device of any device or device with data processing capabilities, such as a plug-in device equipped with the device. Hard disk, Smart Media Card (SMC), SD card, Flash Card, etc.
当然,以上说明仅仅为本发明的较佳实施例,本发明并不限于列举上述实施例,应当说明的是,任何熟悉本领域的技术人员在本说明书的教导下,所做出的所有等同替代、明显变形形式,均落在本说明书的实质范围之内,理应受到本发明的保护。Of course, the above descriptions are only preferred embodiments of the present invention. The present invention is not limited to the above-mentioned embodiments. It should be noted that all equivalent substitutions made by any person familiar with the art under the teaching of this specification , obvious deformation forms, all fall within the essential scope of this specification, and should be protected by the present invention.
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