CN115251947A - A method for removing EMG noise in ECG signal based on singular value decomposition - Google Patents
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Abstract
Translated fromChinese
Description
Translated fromChinese技术领域technical field
本发明涉及心电信号降噪技术领域，具体为一种基于奇异值分解的心电信号中肌电噪声去除方法。The invention relates to the technical field of electrocardiographic signal noise reduction, in particular to a method for removing myoelectric noise in electrocardiographic signals based on singular value decomposition.
背景技术Background technique
目前心血管疾病的已经成为威胁我国居民的最严重疾病之一，心血管疾病的预防和监测成为不可忽视的问题，心电信号作为人体最直接生理信号，能够反应心脏健康状况，但心电信号容易受到各种噪声的干扰，包括基线漂移、市电干扰、肌电噪声，其中肌电噪声主要是人体肌肉微小运动产生，其频域范围与心电信号频域重叠，无法采用基于频域分割的滤波器去除，肌电噪声的去除已经成为心电信号滤波的难点。At present, cardiovascular disease has become one of the most serious diseases threatening the residents of our country. The prevention and monitoring of cardiovascular disease has become a problem that cannot be ignored. As the most direct physiological signal of the human body, the ECG signal can reflect the health of the heart, but the ECG signal It is susceptible to interference from various noises, including baseline drift, mains interference, and electromyographic noise. Among them, electromyographic noise is mainly generated by the tiny movements of human muscles, and its frequency domain overlaps with the frequency domain of the ECG signal, so frequency-based segmentation cannot be used The removal of the filter and the removal of EMG noise have become the difficulty of ECG signal filtering.
目前肌电噪声去除方法主要采用带通滤波器、小波变换阈值法等方法，带通滤波器主要基于傅里叶变换的频域滤波,其具有计算简单的优点、但无法去除肌电噪声和心电信号频域重叠部分；小波变换是一种新的变换分析方法，它继承和发展了短时傅里叶变换局部化的思想，同时克服了窗口大小不随频率变换的缺点，能对时间(空间)局部化分析，小波阈值法就是利用小波变换将心电信号分解为不同层次的细节系数与相似系数，然后对系数采用软硬阈值方法去除噪声，最后采用小波逆变换对子带信号重构得到干净心电信号，小波变换能够突出信号的特征，但阈值的选择较为困难，阈值过大，则会造成信号的失真和过度降噪，阈值选择过小，噪声去除不完成。At present, EMG noise removal methods mainly use band-pass filter, wavelet transform threshold method and other methods. The band-pass filter is mainly based on Fourier transform frequency domain filtering, which has the advantage of simple calculation, but it cannot remove EMG noise and heart rate. The overlapping part of the frequency domain of electrical signals; wavelet transform is a new transformation analysis method, which inherits and develops the idea of short-time Fourier transform localization, and overcomes the disadvantage that the window size does not change with frequency, and can analyze time (space) ) localization analysis, the wavelet threshold method is to use wavelet transform to decompose the ECG signal into detail coefficients and similarity coefficients at different levels, and then use soft and hard threshold methods to remove noise for the coefficients, and finally use wavelet inverse transform to reconstruct sub-band signals to obtain For clean ECG signals, wavelet transform can highlight the characteristics of the signal, but the selection of the threshold is more difficult. If the threshold is too large, it will cause signal distortion and excessive noise reduction. If the threshold is too small, the noise removal will not be completed.
现有方法都只适用于心电信号中不含或者包含少量肌电噪声，带通滤波器和小波变换阈值法只能去除微弱的肌电噪声，对于运动场景，心电信号中包含大量肌电噪声，降噪效果较弱，无法适用于较大信噪比情况；同时现有方法未考虑心电信号本身具有的准周期性质，即人体心脏跳动的规律性，带通滤波器使用噪声和信号频率不同进行滤波，但肌电噪声和心电信号频域具有重叠部分，小波变换考虑将信号分解为子带信号，然后使用阈值法去除，但子带信号中肌电噪声无法衡量。The existing methods are only suitable for ECG signals that do not contain or contain a small amount of myoelectric noise. The band-pass filter and wavelet transform threshold method can only remove weak myoelectric noise. For sports scenes, the ECG signal contains a large amount of myoelectric noise. Noise, the noise reduction effect is weak, and cannot be applied to the situation with a large signal-to-noise ratio; at the same time, the existing methods do not consider the quasi-periodic nature of the ECG signal itself, that is, the regularity of the human heart beating, and the band-pass filter uses noise and signal Different frequencies are used for filtering, but the EMG noise and the ECG signal have overlapping parts in the frequency domain. The wavelet transform considers decomposing the signal into sub-band signals, and then uses the threshold method to remove them, but the EMG noise in the sub-band signals cannot be measured.
发明内容Contents of the invention
(一)解决的技术问题(1) Solved technical problems
针对现有技术的不足，本发明提供了一种基于奇异值分解的心电信号中肌电噪声去除方法，本发明方法能够利用心电信号的准周期性质，构造轨迹矩阵，然后使用奇异值分解提取主要波形特征，提高了滤波前后心电信号的相关性和输出信噪比，减少了均方根误差，实现不同噪声层次下肌电噪声的有效去除。Aiming at the deficiencies of the prior art, the present invention provides a method for removing myoelectric noise in electrocardiographic signals based on singular value decomposition. The method of the present invention can utilize the quasi-periodic nature of electrocardiographic signals to construct a trajectory matrix, and then use singular value decomposition Extract the main waveform features, improve the correlation of the ECG signal before and after filtering and the output signal-to-noise ratio, reduce the root mean square error, and realize the effective removal of EMG noise under different noise levels.
(二)技术方案(2) Technical solutions
为实现以上目的，本发明通过以下技术方案予以实现：一种基于奇异值分解的心电信号中肌电噪声去除方法，具体包括以下步骤：In order to achieve the above object, the present invention is achieved through the following technical solutions: a method for removing myoelectric noise in electrocardiographic signals based on singular value decomposition, specifically comprising the following steps:
S1、合成噪声心电信号：合成噪声信号主要用于验证算法的有效性以及评价降噪效果，使用干净心电信号和肌电噪声在不同放大系数上叠加合成污染程度不同的模拟噪声信号；S1. Synthetic noise ECG signal: The synthetic noise signal is mainly used to verify the effectiveness of the algorithm and evaluate the noise reduction effect. The clean ECG signal and EMG noise are superimposed on different amplification factors to synthesize analog noise signals with different pollution levels;
S2、寻找心电信号QRS波：寻找心电信号QRS波提取心电信号主要特征，心电信号包含P波、T波、QRS波等，其中QRS波具有最大的幅值和能量，是心电信号分析中必不可少的步骤；S2. Find the QRS wave of the ECG signal: Find the QRS wave of the ECG signal to extract the main features of the ECG signal. An essential step in signal analysis;
S3、计算相邻R波间隔：计算相邻R波间隔根据已有R波位置计算RR间隔(两个相邻R波间隔)，得到不同长度RR波间隔，RR波数组如下RR＝[R1R2,R2R3,R3R4,…Rn-1Rn]；S3. Calculate the adjacent R-wave interval: Calculate the adjacent R-wave interval and calculate the RR interval (two adjacent R-wave intervals) according to the existing R-wave position to obtain RR-wave intervals of different lengths. The RR wave array is as follows RR=[R1 R2 ,R2 R3 ,R3 R4 ,...Rn-1 Rn ];
S4、分割心拍：分割心拍将心电信号切分成以R波为中心的不同片段，具体思想如下，根据上一步得到的RR间隔数组得出与左侧R峰间隔RlR，右侧R峰间隔RRr，最大心拍间隔RRmax，向被选取R峰左侧取0.5RlR,向R峰右侧取0.5RRr长度作为一个完整心拍，此时分割得到的心拍长度不相等，左右同时填充0至0.5RRmax，心拍总长度统一为RRmax+1；S4. Segment heart beat: Segment the heart beat to divide the ECG signal into different segments centered on the R wave. The specific idea is as follows. According to the RR interval array obtained in the previous step, the distance between the R peak on the left and the R peak on the right is Rl R. Interval RRr , the maximum heartbeat interval RRmax , take 0.5Rl R to the left of the selected R peak, and take 0.5RRr length to the right of the R peak as a complete heartbeat. At this time, the length of the heartbeat obtained by segmentation is not equal. Fill in 0 to 0.5RRmax , and the total length of the beat is uniformly RRmax +1;
S5、构造轨迹矩阵：构造周期轨迹矩阵将前面处理的一系列心拍序列叠加构成二维轨迹矩阵，其中A轨迹矩阵的公式为：S5. Construct trajectory matrix: Construct periodic trajectory matrix and superimpose a series of previously processed heart beat sequences to form a two-dimensional trajectory matrix, wherein the formula of A trajectory matrix is:
S6、奇异值分解：奇异值分解将二维矩阵分解成相互成交的特征值和特征向量，奇异值分解是一种矩阵分解方法，其定义为：A＝UΣVT,U、V为矩阵A分割后的左右奇异矩阵，Σ除主对角线以上元素全为0，主对角线元素称为奇异值，奇异值从大到小排列，最大奇异值代表信号主要成分；S6. Singular value decomposition: Singular value decomposition decomposes a two-dimensional matrix into eigenvalues and eigenvectors that interact with each other. Singular value decomposition is a matrix decomposition method, which is defined as: A=UΣVT , U and V are matrix A divisions After the left and right singular matrix, the elements above the main diagonal of Σ are all 0, and the elements of the main diagonal are called singular values. The singular values are arranged from large to small, and the largest singular value represents the main component of the signal;
S7、选取奇异值：重构心电信号时，选取最大奇异值作为干净信号，其他奇异值作为噪声置0，然后重构出二维信号矩阵，最后将矩阵中每一行取出还原出干净ECG信号；S7. Select singular values: when reconstructing ECG signals, select the largest singular value as a clean signal, and set other singular values as noise to 0, then reconstruct a two-dimensional signal matrix, and finally extract each row in the matrix to restore a clean ECG signal ;
S8、心电信号还原：将二维矩阵还原成已滤波的干净信号。S8. ECG signal restoration: restore the two-dimensional matrix to a filtered clean signal.
优选的，所述步骤S3中数组中R1R2表示第一个R峰和第二个R峰之间间隔。Preferably, R1 R2 in the array in step S3 represents the interval between the first R peak and the second R peak.
优选的，所述步骤S5中S1为第一个R峰所在位置，Z为最大RR间隔的一半长度作为基准长度，矩阵中每一行代表一个分割完成后的心拍，一条心电信号由n个心拍组成，其中每个心拍的R位置Sn是严格对齐的。Preferably, in the step S5, S1 is the position of thefirst R peak, Z is half the length of the maximum RR interval as the reference length, each row in the matrix represents a heartbeat after the segmentation is completed, and an electrocardiographic signal consists of n heartbeats composition, where the R position Sn of each beat is strictly aligned.
优选的，所述步骤S7中重构出的二维信号矩阵公式为：A′＝u1σ1v1，其中A′为重构的信号矩阵，σ1为最大奇异值，u1，v1分别为奇异值所对应的奇异向量。Preferably, the formula of the two-dimensional signal matrix reconstructed in step S7 is: A'=u1 σ1 v1 , where A' is the reconstructed signal matrix, σ1 is the largest singular value, u1 , v1 are the singular vectors corresponding to the singular values.
(三)有益效果(3) Beneficial effects
本发明提供了一种基于奇异值分解的心电信号中肌电噪声去除方法。具备以下有益效果：The invention provides a method for removing myoelectric noise in electrocardiographic signals based on singular value decomposition. Has the following beneficial effects:
(1)、该基于奇异值分解的心电信号中肌电噪声去除方法，相比于传统降噪方法，本方法在心电信号被噪声污染严重时具有强大降噪效果，其输出信噪比、噪声提升都比小波变换阈值法、带通滤波器高，代表更强降噪能力，同时均方根误差比传统方法小，说明其失真较小。(1), the EMG noise removal method based on singular value decomposition, compared with the traditional noise reduction method, this method has a strong noise reduction effect when the ECG signal is seriously polluted by noise, and its output signal-to-noise ratio, The noise enhancement is higher than the wavelet transform threshold method and the band-pass filter, representing a stronger noise reduction capability, and the root mean square error is smaller than the traditional method, indicating that its distortion is small.
(2)、该基于奇异值分解的心电信号中肌电噪声去除方法，相较于传统噪声去除方案，本方法考虑了心电信号本身固有的周期性质，即心电信号中QRS波为主要特征，具有周期性，与人体心跳相对应，奇异值分解能够提取矩阵的主要成分，同时心拍分割方法充分考虑了每个心拍间隔长度的不同，避免心拍固定长度分割造成QRS波错位。(2) Compared with the traditional noise removal scheme, the EMG noise removal method based on singular value decomposition in this method takes into account the inherent periodic nature of the ECG signal itself, that is, the QRS wave in the ECG signal is the main The feature is periodic and corresponds to the heartbeat of the human body. The singular value decomposition can extract the main components of the matrix. At the same time, the heart beat segmentation method fully considers the difference in the interval length of each heart beat to avoid the QRS wave misalignment caused by the fixed length segmentation of the heart beat.
附图说明Description of drawings
图1为本发明肌电噪声去除方法流程图；Fig. 1 is the flow chart of myoelectric noise removal method of the present invention;
图2为本发明心拍分割方法原理图；Fig. 2 is the schematic diagram of heart beat segmentation method of the present invention;
图3为本发明与已有方法在肌电噪声去除上对比图；Fig. 3 is a comparison diagram between the present invention and existing methods on the removal of myoelectric noise;
图4为本发明不同输入信噪比下的降噪评价图。Fig. 4 is a noise reduction evaluation diagram under different input signal-to-noise ratios according to the present invention.
具体实施方式Detailed ways
下面将结合本发明实施例中的附图，对本发明实施例中的技术方案进行清楚、完整地描述，显然，所描述的实施例仅仅是本发明一部分实施例，而不是全部的实施例。基于本发明中的实施例，本领域普通技术人员在没有做出创造性劳动前提下所获得的所有其他实施例，都属于本发明保护的范围。The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only some, not all, embodiments of the present invention. Based on the embodiments of the present invention, all other embodiments obtained by persons of ordinary skill in the art without making creative efforts belong to the protection scope of the present invention.
请参阅图1-4，本发明实施例提供一种技术方案：一种基于奇异值分解的心电信号中肌电噪声去除方法，用于ECG降噪，具体包括以下步骤：Please refer to FIGS. 1-4. Embodiments of the present invention provide a technical solution: a method for removing myoelectric noise in ECG signals based on singular value decomposition, which is used for ECG noise reduction, and specifically includes the following steps:
S1、合成包含肌电噪声(EMG)的ECG信号：(1)使用python从MIT-BIH噪声压力数据库读取肌电噪声信号MA，MIT-BIH噪声压力数据库采集了肌电噪声，市电干扰，基线漂移，是降噪算法测试的金标准，MIT-BIH心律不齐数据库包含常见心律不齐节拍心房早搏、心室早搏、传导阻滞等节律，本实施例使用这两个数据库验证本发明效果，从MIT-BIH心律不齐数据库读取101号干净心电信号；S1. Synthesizing ECG signals containing electromyographic noise (EMG): (1) using python to read the electromyographic noise signal MA from the MIT-BIH noise stress database, the MIT-BIH noise stress database collected electromyographic noise, mains interference, Baseline drift is the gold standard for noise reduction algorithm testing. The MIT-BIH arrhythmia database contains rhythms such as atrial premature beats, ventricular premature beats, and conduction block. This example uses these two databases to verify the effect of the present invention. Read the clean ECG signal No. 101 from the MIT-BIH arrhythmia database;
(2)根据噪声叠加原理，ECGstimulate＝ECGclear+σEMG，ECGstimulat为合成混合信号，σ为噪声叠加比例，EMG为肌电噪声MA，选取干净信号长度为2500个数据点，选择对应肌电噪声数据为2500点数据，分别输入2dB，4dB，8dB，16dB噪声，不同信噪比根据σ值不同计算。(2) According to the principle of noise superposition, ECGstimulate = ECGclear + σEMG, ECGstimulate is a synthetic mixed signal, σ is the noise superposition ratio, EMG is the EMG noise MA, the length of the clean signal is selected as 2500 data points, and the corresponding EMG The noise data is 2500 points of data, input 2dB, 4dB, 8dB, 16dB noise respectively, different signal-to-noise ratios are calculated according to different σ values.
S2、QRS波寻找，主要从ECG信号中寻找QRS波，QRS波为心电信号中最明显峰值，目前通用峰值寻找算法如pan-Tompks算法，wavlet算法等，本发明选取pan-Tompks算法，提取心电信号中R波，得到R波对应位置，提取对应的R波位置数组为[154,407,561,923,1195,1468,1736,1996,2246]，包含9个心拍R波位置。S2, QRS wave search, mainly search for QRS wave from ECG signal, QRS wave is the most obvious peak value in electrocardiogram signal, general peak search algorithm such as pan-Tompks algorithm, wavlet algorithm etc. at present, the present invention selects pan-Tompks algorithm, extracts The R wave in the ECG signal is obtained to obtain the corresponding position of the R wave, and the corresponding R wave position array is extracted as [154, 407, 561, 923, 1195, 1468, 1736, 1996, 2246], including 9 cardiac beat R wave positions.
S3、计算相邻RR波间隔，构造RR间隔数组，根据获得R波位置数据，计算RR波间隔(ECG中相邻R波峰距离)，RR间隔数组为[253,154,362,272,273,268,260,250]，从数组中可以发现，最大RR间隔为362。S3. Calculate the interval between adjacent RR waves and construct an array of RR intervals. Calculate the interval of RR waves (the distance between adjacent R peaks in the ECG) according to the obtained R wave position data. The array of RR intervals is [253,154,362,272,273,268,260,250]. It can be found from the array that The RR interval is 362.
S4、心拍分割，如图2所示，红色心拍为待分割心拍，这里选取第二个心拍具体描述，其中左侧距离L1w为253，右侧距离L2为154，根据分割方法，左侧取0.5*L1长度121，右侧取0.5*L2长度77，分同时将左右填充至最大长度一半及181，此时心拍总长度为363，对所有心拍分割填充，得到一系列等长心拍。S4. Heart beat segmentation, as shown in Figure 2, the red heart beat is the heart beat to be divided. Here, the second heart beat is selected for specific description, wherein the left distance L1w is 253, and the right distance L2 is 154. According to the segmentation method, the left side is 0.5 *L1 length is 121, the right side is 0.5*L2 length is 77, and the left and right are filled to half of the maximum length and 181 at the same time. At this time, the total length of the heartbeat is 363, and all heartbeats are divided and filled to obtain a series of equal-length heartbeats.
S5、构造轨迹矩阵，使用python中numpy高性能库函数矩阵存储心拍，矩阵的每一行为一个单独的心拍，如图3所示为矩阵前三行数据图。S5. Construct a trajectory matrix, use the numpy high-performance library function matrix in python to store heartbeats, and each row of the matrix is a separate heartbeat, as shown in Figure 3 for the first three rows of data in the matrix.
S6、奇异值分解轨迹矩阵，提取心电信号主要波形特征，奇异值分解采用python的numpy库中np.linalg.svd(traix)函数，numpy()是python专为科学计算开发计算库，包含矩阵分解、矩阵奇异值分解、矩阵QR分解等，本实施例中采用numpy库函数实现奇异值分解。S6. Singular value decomposition trajectory matrix, extracting the main waveform features of ECG signals, singular value decomposition using the np.linalg.svd(traix) function in python's numpy library, numpy() is a computing library specially developed for scientific computing in python, including matrices Decomposition, matrix singular value decomposition, matrix QR decomposition, etc., adopt numpy library function to realize singular value decomposition in this embodiment.
S7、选取最大奇异值作为心电信号特征，重构信号矩阵，奇异值分解得到的奇异值为[14.95642755、2.32091189、1.63704141、1.12070935、0.83488297、0.52250907、0.40032248、0.33921127、0.18226298]，可以看出第一个奇异值占据主要成分，选取14.95作为心电信号中干净信号特征，其他奇异值置为0，重构二维轨迹矩阵。S7. Select the largest singular value as the feature of the ECG signal, reconstruct the signal matrix, and the singular value obtained by singular value decomposition is [14.95642755, 2.32091189, 1.63704141, 1.12070935, 0.83488297, 0.52250907, 0.40032248, 0.33921127, 0.1828], it can be seen that the first 22629 The first singular value occupies the main component, and 14.95 is selected as the clean signal feature in the ECG signal, and the other singular values are set to 0, and the two-dimensional trajectory matrix is reconstructed.
S8、将二维的信号矩阵还原成滤波的干净信号，还原的心电信号中已经去除了肌电噪声，如图3所示，含噪信号包含4db噪声信号，可以看出心电信号被噪声严重污染，使用奇异值分解后的信号基本不含肌电噪声，小波变换阈值法滤波后信号已经严重失真，带通滤波器基本没有降噪效果，为了量化本发明的提升与改善，使用输出信噪比、百分比均方根误差、相关系数、均方根误差评价算法，图4为本发明与带通滤波器、小波变换阈值法在0dB，4dB，8dB，12dB，16dB不同输入信噪比下其对应输出信噪比、百分比均方根误差、相关系数、均方根误差值(输入信噪比越小、肌电噪声含量越高)，从图4a中可以看出，在高肌电噪声污染情况下(0dB，4dB)，本发明方法具有输出信噪比7.1dB，比小波变换和带通滤波器具有更好噪声去除能力，随着噪声含量逐渐减少，本发明依旧保持较高输出信噪比；从图4b，c中可以看出，在不同噪声层次，本发明方法误差都比小波变换、带通滤波器值小，说明信号失真程度小；从图4d中，在高肌电噪声噪声污染下(0dB输入信噪比)，本发明方法滤波后信号和干净信号依然保持94％相关性，小波变换和带通滤波器在0dB输入信噪比下，相关性低于80％，信号严重失真。S8. Restore the two-dimensional signal matrix into a filtered clean signal. Myoelectric noise has been removed from the restored ECG signal. As shown in Figure 3, the noisy signal contains 4db noise signal. It can be seen that the ECG signal is noised Severely polluted, the signal after using singular value decomposition does not contain myoelectric noise substantially, the signal after wavelet transform threshold method filtering has been seriously distorted, and the bandpass filter has basically no noise reduction effect, in order to quantify the promotion and improvement of the present invention, use the output signal Noise ratio, percentage root mean square error, correlation coefficient, root mean square error evaluation algorithm, Fig. 4 is that the present invention and band-pass filter, wavelet transform threshold value method are under 0dB, 4dB, 8dB, 12dB, under 16dB different input signal-to-noise ratios It corresponds to the output signal-to-noise ratio, percentage root mean square error, correlation coefficient, and root mean square error value (the smaller the input signal-to-noise ratio, the higher the myoelectric noise content). Under the pollution situation (0dB, 4dB), the inventive method has output signal-to-noise ratio 7.1dB, has better noise removal ability than wavelet transform and band-pass filter, along with noise content gradually reduces, the present invention still maintains higher output signal Noise ratio; As can be seen from Fig. 4b and c, at different noise levels, the error of the method of the present invention is smaller than the value of wavelet transform and band-pass filter, indicating that the degree of signal distortion is small; from Fig. 4d, at high myoelectric noise Under the noise pollution (0dB input signal-to-noise ratio), the signal after the method filtering of the present invention and clean signal still keep 94% correlation, and wavelet transform and band-pass filter are under 0dB input signal-to-noise ratio, and correlation is lower than 80%, and signal Seriously distorted.
同时本说明书中未作详细描述的内容均属于本领域技术人员公知的现有技术。At the same time, the content not described in detail in this specification belongs to the prior art known to those skilled in the art.
需要说明的是，在本文中，诸如第一和第二等之类的关系术语仅仅用来将一个实体或者操作与另一个实体或操作区分开来，而不一定要求或者暗示这些实体或操作之间存在任何这种实际的关系或者顺序。而且，术语“包括”、“包含”或者其任何其他变体意在涵盖非排他性的包含，从而使得包括一系列要素的过程、方法、物品或者设备不仅包括那些要素，而且还包括没有明确列出的其他要素，或者是还包括为这种过程、方法、物品或者设备所固有的要素。It should be noted that in this article, relational terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply that there is a relationship between these entities or operations. There is no such actual relationship or order between them. Furthermore, the term "comprises", "comprises" or any other variation thereof is intended to cover a non-exclusive inclusion such that a process, method, article or apparatus comprising a set of elements includes not only those elements, but also includes elements not expressly listed. other elements of or also include elements inherent in such a process, method, article, or device.
尽管已经示出和描述了本发明的实施例，对于本领域的普通技术人员而言，可以理解在不脱离本发明的原理和精神的情况下可以对这些实施例进行多种变化、修改、替换和变型，本发明的范围由所附权利要求及其等同物限定。Although the embodiments of the present invention have been shown and described, those skilled in the art can understand that various changes, modifications and substitutions can be made to these embodiments without departing from the principle and spirit of the present invention. and modifications, the scope of the invention is defined by the appended claims and their equivalents.
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