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基于本征正交分解的湍流去噪

卢垚 刘欢 吴加学

卢垚,刘欢,吴加学. 基于本征正交分解的湍流去噪[J]. 海洋学报,2022,44(x):1–13 doi: 10.12284/hyxb2022089
引用本文: 卢垚,刘欢,吴加学. 基于本征正交分解的湍流去噪[J]. 海洋学报,2022,44(x):1–13 doi: 10.12284/hyxb2022089
Lu Yao,Liu Huan,Wu Jiaxue. Turbulence denoising based on Proper Orthogonal Decomposition[J]. Haiyang Xuebao,2022, 44(x):1–13 doi: 10.12284/hyxb2022089
Citation: Lu Yao,Liu Huan,Wu Jiaxue. Turbulence denoising based on Proper Orthogonal Decomposition[J]. Haiyang Xuebao,2022, 44(x):1–13 doi: 10.12284/hyxb2022089

基于本征正交分解的湍流去噪

doi: 10.12284/hyxb2022089
基金项目: 国家自然科学基金联合基金(U1901209);国家自然科学基金面上项目(41676082);南方海洋科学与工程广东省实验室(珠海)创新团队建设项目(311021004)
详细信息
    作者简介:

    卢垚(1996-),男,主要从事海洋湍流混合与物质输移研究。E-mail:luyao27@mail2.sysu.edu.cn

    通讯作者:

    刘欢(1980-),男,副教授,主要从事河口动力学研究。E-mail:liuhuan8@mail.sysu.edu.cn

Turbulence denoising based on Proper Orthogonal Decomposition

  • 摘要: 在近岸河口湍流研究中,实测的湍流资料往往容易受到噪声的影响,导致湍流特征量的估算出现偏差。本征正交分解是一种将流场在能量上进行分解再重构的方法,基于该方法,结合数值实验和野外实测资料,对包含噪声的湍流数据进行了去噪处理。结果表明:(1)本征正交分解能有效去除湍流中的噪声。在进行信号重构时,应将保留能量的百分比与湍流能量占比保持一致。去噪的效果与噪声占比有关,噪声占比越高,去噪效果越明显。(2)在实测资料中,憩流时刻的噪声占比要显著大于非憩流时刻,水平方向的噪声占比要大于垂直方向。经过本征正交分解去噪后,各湍流特征量的估算更加合理。
  • 图  1  脉动速度特征时间序列(a),概率分布(b),能谱(c)

    Fig.  1  Properties of fluctuation velocity time series (a), probability distribution (b), energy spectrum (c)

    图  2  不同湍流能量占比90%(a),80%(b),70%(c),60%(d) 下MSE随保留能量的变化曲线

    Fig.  2  Relationship between MSE and remaining energy at different ratio of turbulent energy 90% (a), 80% (b), 70% (c), 60% (d)

    图  3  不同湍流能量占比去噪前后垂直方向能谱对比60%(a),70%(b),80%(c),90%(d)

    Fig.  3  Comparison of energy spectrum in vertical direction before and after denoising at different ratio of turbulent energy 60% (a), 70% (b), 80% (c), 90% (d)

    图  4  座底四脚架观测平台照片

    Fig.  4  Photograph of a bottom-mounted four legged frame

    图  5  野外观测各要素的时间序列深度和平均流速(a); uvw方向的噪声占比(b)

    图中阴影表示憩流时刻

    Fig.  5  Time series of each features from field observation depth and average velocity (a); the proportion of the noise in u, v, and w directions (b)

    The shadow indicates slack tide

    图  6  平均流速与平均噪声占比关系

    Fig.  6  The relationship between average velocity and proportion of average noise

    图  7  各方向脉动流速能谱曲线(a)u方向;(b)v方向;(c)w方向

    灰色实线为单组(300 s)的能谱,黑色实线为非憩流时刻系综平均能谱,黑色虚线为憩流时刻系综平均能谱

    Fig.  7  Energy spectrum of fluctuation velocity in different direction (a)u direction, (b)v direction, (c)w direction

    The gray solid line is the energy spectrum of a single group (300 s), the black solid line is the ensemble average energy spectrum of non-slack tide, and the black dotted line is the ensemble average energy spectrum of slack tide

    图  8  去噪前后各方向脉动流速系综平均能谱

    a. 憩流u方向;b. 憩流v方向;c. 憩流w方向;d. 非憩流u方向;e. 非憩流v方向;f. 非憩流w方向;黑色点线和红色点线分别为憩流时刻和非憩流时刻满足准各向同性比(R)的区间(在5.2.2节中讨论)

    Fig.  8  Ensemble average energy spectrum of fluctuation velocity in different direction before and after denoising

    a. u direction at slack; b v direction at slack; c. w direction at slack; d. u direction at non-slack; e. v direction at non-slack; f. w direction at non-slack. The black dotted line and red dotted line are the intervals that satisfy the quasi isotropic ratio of slack tide and non-slack tide respectively (discussed in 5.2.2)

    图  9  去噪前后湍流特征量时间序列

    a. 雷诺应力;b. 湍动能;c. 湍动能耗散率

    Fig.  9  Time series of turbulence properties before and after denoising

    a. Reynolds stress; b. turbulent kinetic energy; c. turbulent dissipation rate

    图  10  去噪前后雷诺应力的时间序列

    Fig.  10  Time series of Reynolds stress before and after denoising

    图  11  去噪前后的湍流能量平衡关系(a)u方向;(b)w方向;

    Fig.  11  Turbulent energy balance before and after denoising (a) u direction, (b) w direction

    图  12  去噪前后R随频率的变化曲线

    黑色和红色垂直虚线分别为憩流和非憩流时刻去噪前后开始偏离0.8~2(阴影区间)的频率

    Fig.  12  Variation of R as a function of frequency before and after denoising

    The black and red vertical dashed lines indicate the frequency range before and after denoising at the slack tide and the non-slack tide that deviate from 0.8 ~ 2 (the shadow interval)

    表  1  脉动速度统计量

    Tab.  1  Fluctuation velocity statistics

    统计量脉动速度/(m·s–1
    纵向(u侧向(v垂向(w
    标准差/(m·s–10.3640.3380.287
    偏态–0.0240.0500.003
    峰度2.8983.0822.990
    下载: 导出CSV

    表  2  去噪前后湍流统计量对比(湍流能量占比70%,保留能量70%)

    Tab.  2  Comparison of turbulent statistics before and after denoising (70% of turbulent energy, 70% of remaining energy)

    统计量原始脉动速度/(m·s−1加入噪声后脉动速度/(m·s−1去噪后脉动速度/(m·s−1
    纵向(x侧向(y垂向(z纵向(x侧向(y垂向(z纵向(x侧向(y垂向(z
    标准差/m·s−10.3640.3380.2870.4380.4070.3430.3670.3410.289
    偏态–0.0240.0500.0030.0190.036–0.0100.0530.071–0.003
    峰度2.8983.0822.9902.9903.0743.0153.0163.0743.103
    下载: 导出CSV
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  • 收稿日期:  2021-09-09
  • 修回日期:  2021-12-28
  • 网络出版日期:  2022-03-25

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