A full data segmentation method and system for multi-scale analysis of sea-air time series

Abstract

The present invention belongs to the technical field of ocean and atmosphere time series analysis, and discloses a full data segmentation method and system for multi-scale analysis of ocean and atmosphere time series. The method calculates the statistics of data in each time window until the window slides to a position where its right end is larger than the center position of the original time series; calculates the statistics of ocean and atmosphere time series at different time points as representative points until the window slides to a position where its left end is smaller than the center position of the original time series; calculates the statistics of the time period of the original ocean and atmosphere time series at N / 2 as the representative point; and obtains the multi-scale statistics of the ocean and atmosphere time series that depend on time in different time periods and different time scales. The segmentation method of the present invention makes full use of all the data of the original time series, and the statistics storage matrix can be determined in advance as a suitable size, and its maximum sparsity is 50%, which not only effectively utilizes the data, but also improves the storage and calculation efficiency of the statistics.

Description

Technical Field

[0001] The present invention belongs to the technical field of ocean and atmosphere time series analysis, and in particular relates to a full data segmentation method and system for multi-scale analysis of ocean and atmosphere time series. Background Art

[0002] Time-dependent multi-scale features are important methods for studying time series, such as the coherence spectrum and coherence spectrum of two time series in wavelet analysis, time-dependent intrinsic correlation (TDIC), calculation of multi-scale entropy (MSE: multi-scale entropy) of a single time series, multi-scale detrended fluctuation analysis (MSDFA: multi-scale detrended fluctuation analysis), nonlinearity (DN: degree of nonlinearity), etc. In addition, many data analysis methods such as window Fourier transform, power spectrum analysis, window sliding average, etc., also require the time series to be segmented and calculated.

[0003] The traditional method gives a window length and starts from the left end of the time series and slides the window unidirectionally to the right to calculate the physical quantity. When the window slides to the end of the original time series, the last window usually cannot meet the length of a window. At this time, there are three ways to deal with this part of the data: (1) discard this part of the data. This will cause a waste of the end data, and from a time perspective, this part of the data is the most recent and has more reference value for the current or near future; (2) directly use the remaining data as a window width for calculation. The disadvantage is that the sampling points may not be enough to meet the statistical conditions, and the confidence level is difficult to guarantee. In addition, the method for determining the representative point of the time period in this window is different from that of the previous window. If it is a multi-scale analysis, the position of the representative point of the last window at each scale must be re-determined. (3) Use 0 to fill the window length for calculation. Later, this part of the result can be interpolated and truncated as needed. This processing method is the most commonly used. For example, in the current wavelet analysis method, the data statistics at different time scales are calculated by filling 0. The selection of the representative point and the data sampling size of the last window are the same as those of the previous window. It can maintain the stability of the window length division, but its disadvantage is that it introduces new errors at the endpoints. The part outside the influence cone of wavelet analysis is the result of zero-filling calculation, which is generally not accepted in analysis.

[0004] In the calculation of traditional multi-scale analysis methods, there are three variables: window width, window sliding step (or overlapping length of adjacent windows), and time scale (or its increasing step). The time scale (corresponding to the window width) is determined according to the window width and the window sliding step. For different time scales, the representative points determined by the sliding window may be different from the representative points of the previous or subsequent windows, which requires expanding the size of the statistical storage matrix or performing interpolation approximation processing. The continuous wavelet analysis method is to slide the window point by point, which makes the scale of the statistical storage matrix in the time dimension close to the length of the original time series, so the length of the time series will greatly affect the storage matrix and calculation time of the statistics.

[0005] Through the above analysis, the problems and defects of the existing technology are: in the analysis of ocean and atmospheric time series data, the endpoint effect caused by the processing of the end data of the original time series and the storage matrix caused by the uncertainty of the position of the representative points of the multi-scale window are huge or sparse, which reduces the efficiency of data information storage and calculation. Summary of the invention

[0006] In order to overcome the problems existing in the related art, the disclosed embodiment of the present invention provides a full data segmentation method and system for multi-scale analysis of sea-air time series, and specifically relates to a full data segmentation method for multi-scale analysis of sea-air time series. It also relates to an efficient method for window grid segmentation and calculation in multi-scale analysis of computational time series. The purpose of the present invention is to solve the problems of endpoint effect caused by the processing of the end data of the original time series and the huge or sparse storage matrix caused by the uncertainty of the position of the multi-scale window representative point in the current such methods.

[0007] The technical solution is as follows: A full data segmentation method for multi-scale analysis of sea-air time series, comprising:

[0008] S101, given length is The basic window width is determined based on the time series, and the window is slid from the left end of the time series in the direction of time growth. The window sliding step is set to half of the basic window width, and the statistics of the data in each time window are calculated step by step until the window slides to the right end of the window, which is larger than the center position of the original time series.

[0009] S102, sliding the window from the right end of the time series in the opposite direction of time increase with the basic window width and the window sliding step, and gradually calculating the statistics of the ocean and atmosphere time series at different time points as representative points, until the window slides to a position where the left end of the window is smaller than the center of the original time series;

[0010] S103, calculate the original time series of ocean and atmosphere is the statistic of the time period representing the point;

[0011] S104, setting the time scale to the basic window width The above sliding window and statistical calculation process is repeated at different time scales to obtain time-dependent multi-scale statistics of ocean and atmosphere time series at different time periods and time scales.

[0012] In step S101, the basic window width is , the window sliding step size is , No. The representative points of a window are: , the window slides to its right end larger than the center position of the original time series: .

[0013] In step S101, the two time series are respectively: , the total length of both is ; Basic window number for:

[0014]

[0015] In the formula, is the length of the original time series, To round, To find the minimum value.

[0016] In step S101, according to the length of the original time series and the size of the matrix storing the statistics Determine the window sliding step size , the expression is:

[0017]

[0018] Before the calculation begins, determine the size of the statistics storage matrix:

[0019] Number of basic windows × number of time scales = .

[0020] In step S101, a window is slid down on a given time scale to calculate the statistics of two time periods, including the correlation coefficient of two time series, or the entropy and nonlinearity of a single time series; wherein, the time series samples in the window are slid in the direction of time growth until the right end time point is greater than the midpoint of the total time series, and then stop. At this time, if the window continues to slide to the right, according to the window sliding step, the representative point of the window will be on the right side of the midpoint of the total time series.

[0021] In step S102, the window width and window sliding step , starting from the right end of the time series, sliding in the opposite direction of time increase, gradually calculate the statistics of the ocean and atmosphere time series at different time points as representative points; among them, from right to left, sliding in the opposite direction of time growth until the left end time point is less than the midpoint of the total time series At this time, if the window continues to slide to the left, according to the window sliding step, the representative point of the window will be on the left side of the midpoint of the total time series.

[0022] In step S101 and step S102, sliding the window from the right end of the data to the left and sliding the window from the left end of the data to the right are performed in parallel.

[0023] In step S103, for a given time scale, after steps S101 and S102 are completed, the statistics of the time series with the midpoint of the entire time series as the representative point are calculated, that is, the window , calculate the statistics of the time series within this window period.

[0024] In step S104, the above sliding window and calculating statistics process is repeated at different time scales to obtain time-dependent multi-scale statistics of the ocean and atmosphere time series at different time periods and different time scales, including:

[0025] When the window is a basic window , window width , window sliding step , then The representative points of the time period within the window are:

[0026]

[0027] For any , the corresponding time scale is: , the window sliding step size is , so the first The representative points of a window are:

[0028]

[0029] Comparing formula (3) and formula (4), when hour, Pick , thereby traversing the representative points of the basic window; when hour, are positive integers and form a continuous set of natural numbers, Depend on To express, that is, The representative points of each time scale all fall into the representative point set of the basic window and are its continuous subset.

[0030] Another object of the present invention is to provide a full data segmentation system for multi-scale analysis of sea-air time series, the system implements the full data segmentation method for multi-scale analysis of sea-air time series, and the system comprises:

[0031] The statistical calculation module of the data in each time window is used to calculate the statistical value of the given length. The basic window width is determined based on the time series, and the window is slid from the left end of the time series in the direction of time growth. The window sliding step is set to half of the basic window width, and the statistics of the data in each time window are calculated step by step until the window slides to the right end larger than the center position of the original time series;

[0032] The representative point statistics calculation module is used to slide the window from the right end of the time series to the opposite direction of time increase with the basic window width and window sliding step, and gradually calculate the statistics of the ocean and atmosphere time series at different time points as representative points until the window slides to a position where its left end is smaller than the center of the original time series;

[0033] The module for calculating the statistics of representative time periods is used to calculate the original time series of ocean and atmosphere. is the statistic of the time period representing the point;

[0034] Multi-scale statistics acquisition module, used to set the time scale to the basic window width The above sliding window and statistical calculation process is repeated at different time scales to obtain time-dependent multi-scale statistics of ocean and atmosphere time series at different time periods and time scales.

[0035] In combination with all the above technical solutions, the beneficial effects of the present invention are as follows: Time series (original time series), determine the basic window width (the length of data when the time scale is the smallest) , starting from the left end of the time series, the window is slid in the direction of time growth, and the window sliding step is set to half the basic window width (i.e. ), No. The representative point of a window is (The median of the data segment in the time window). The statistics of the data in each time window are calculated step by step (such as the correlation coefficient of two time series, the nonlinearity of a single time series, etc.) until the window slides to the right end larger than the center position of the original time series. ; Based on the basic window width and window sliding step , sliding the window from the right end of the time series in the opposite direction of time increase, gradually calculating the statistics of the ocean and atmosphere time series at different time points as representative points, until the window slides to its left end smaller than the center position of the original time series; calculating the original time series of the ocean and atmosphere at The statistics of the time period of the representative point; set the time scale (window width of the time series) to the basic window width times (i.e. , is the length of the original time series), repeating the above sliding window and calculating statistics process at different time scales. In this way, we obtain time-dependent multi-scale statistics of ocean and atmospheric time series at different time periods (representative points) and different time scales (window widths). The traditional sliding window method slides the window in one direction on the time series, which is easy to cause data redundancy (the length of the data at the end of the original time series is less than one window width); and the window sliding step and the increase in time scale are unrelated, resulting in uncertainty in the final redundant data length; for different time scales (corresponding to different window widths), the representative point of the window data segment will also change, resulting in the statistical storage matrix being too large and sparse. The dissection method of the present invention makes full use of all the data of the original time series, and the statistical storage matrix can be determined in advance as a suitable size, with a maximum sparsity of 50%, which not only effectively utilizes the data, but also improves the storage and calculation efficiency of statistics.

[0036] The present invention introduces basic window units, simplifies the difficulty of multi-scale analysis algorithms, saves algorithm storage space, can significantly improve computing efficiency, save money in commercial computing, and is more suitable for big data computing. Traditional methods choose between discarding some data and introducing endpoint effects, while this method uses a sliding window from both ends of the data to the middle, which not only fully utilizes the data but also avoids introducing endpoint effects. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] The accompanying drawings herein are incorporated in and constitute a part of the specification, illustrate embodiments consistent with the present disclosure, and together with the description, serve to explain the principles of the present disclosure;

[0038] Figure 1 It is a flow chart of a full data segmentation method for multi-scale analysis of sea-air time series provided by an embodiment of the present invention;

[0039] Figure 2 It is a schematic diagram of a conventional window partitioning method provided by an embodiment of the present invention;

[0040] Figure 3 It is a schematic diagram of window segmentation of a full data segmentation method for multi-scale analysis of sea-air time series provided by an embodiment of the present invention;

[0041] Figure 4 is a flow chart of a traditional method provided by an embodiment of the present invention;

[0042] Figure 5This is a process principle of a full data dissection method for multi-scale analysis of sea-air time series provided by an embodiment of the present invention;

[0043] Figure 6 It is a data graph used in a calculation example of a full data dissection method for multi-scale analysis of sea-air time series provided in an embodiment of the present invention;

[0044] Figure 7 It is a multi-scale correlation coefficient diagram of Nino12 and Nino34 time series dependent on time calculated by a full data partitioning method for multi-scale analysis of sea-air time series of the present invention;

[0045] Figure 8 The time-dependent multi-scale correlation coefficient diagram of the Nino12 and Nino34 time series calculated by the traditional method;

[0046] Fig. 9 This is an example diagram of calculating a single time series using the method of the present invention;

[0047] Fig.10 This is an example diagram of the traditional method for calculating a single time series. DETAILED DESCRIPTION

[0048] In order to make the above-mentioned objects, features and advantages of the present invention more obvious and easy to understand, the specific embodiments of the present invention are described in detail below in conjunction with the accompanying drawings. In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention can be implemented in many other ways different from those described herein, and those skilled in the art can make similar improvements without violating the connotation of the present invention, so the present invention is not limited by the specific implementation disclosed below.

[0049] The embodiment of the present invention provides a full data segmentation method and system for multi-scale analysis of sea-air time series. In the multi-scale analysis problem of time series, the window (time scale) is divided from both ends of the data to the middle, which makes full use of the data and avoids the endpoint effect. The three variables of window width, overlapping window width, and scale increase step length in the traditional method are replaced by a single variable of basic window width, which greatly simplifies the algorithm and the matrix space required by the algorithm. The innovation of this method is:

[0050] The present invention first gives the basic window number , so that the length of the original time series can be Determine the basic window width (the length of the data when the time scale is the smallest) ; Take the window sliding step size as the basic window width ,Right now ; The time scale is based on the basic window width This greatly reduces the complexity of calculating the window representative point and the window length, and can reduce the sparsity of the storage matrix of the statistical calculation results, thereby improving the storage and calculation efficiency.

[0051] Embodiment 1, as Figure 1 As shown, a full data segmentation method for multi-scale analysis of sea-air time series provided by an embodiment of the present invention comprises the following steps:

[0052] S101, given length is The basic window width is determined based on the time series, and the window is slid from the left end of the time series in the direction of time growth. The window sliding step is set to half of the basic window width, and the statistics of the data in each time window are calculated step by step until the window slides to the right end of the window, which is larger than the center position of the original time series.

[0053] Length is The time series is the original time series, and the basic window width is determined, that is, the data length when the time scale is the smallest. , No. The representative point of a window is is the median of the time window data segment, and the center position is ;

[0054] S102, sliding the window from the right end of the time series in the opposite direction of time increase with the basic window width and the window sliding step, and gradually calculating the statistics of the ocean and atmosphere time series at different time points as representative points, until the window slides to a position where the left end of the window is smaller than the center of the original time series;

[0055] The basic window width is , the window sliding step size is ;

[0056] S103, calculate the original time series of ocean and atmosphere is the statistic of the time period representing the point;

[0057] S104, setting the time scale to the basic window width Repeat the above sliding window and statistical calculation process at different time scales to obtain time-dependent multi-scale statistics of ocean and atmosphere time series at different time periods and time scales.

[0058] Set the time scale to the basic window width times, that is .

[0059] For example, in step S101, the basic window width is determined based on the length of the ocean and atmosphere time series and the calculation requirements. Suppose the two time series are , the total length of both is From the perspective of the size of the statistics storage matrix and the resolution of the contour graph, when the number of basic windows is 200, the calculation time and image output time are both fast, and the image resolution is clear enough, so 200 is set as the upper limit of the basic window. Insufficient, the number of samples in each basic window is too small, and the obtained statistics (such as correlation coefficient, etc.) are difficult to pass the confidence test. Set to:

[0060]

[0061] In the formula, is the length of the original time series, To round, To find the minimum value.

[0062] if , the amount of data is large, Taking the upper limit of 200 can ensure that the calculation time of the statistics is controllable, the storage matrix of the statistics is controllable, and the matrix has sufficient resolution when displayed as a graphic. ,but , but it can still ensure that the number of samples in each basic window is not less than 30, which can meet the basic confidence test of the statistic.

[0063] In step S101, the length of the original time series can be and the size of the matrix storing the statistics Sure :

[0064]

[0065] Furthermore, when the window slides, the window sliding step is half of the basic window width, that is, . So The representative point of a sampling window (the median of that period of time) is (Median of the window data).

[0066] Therefore, the size of the statistics storage matrix can be determined before the calculation begins:

[0067] Number of basic windows × number of time scales =

[0068] In step S101, a window is slid down at a given time scale (window width) to calculate the statistics of two time periods, such as the correlation coefficient of two time series, or the entropy and nonlinearity of a single time series. The time series samples in the window are slid down in the direction of time growth until the right end time point is greater than the midpoint of the total time series. At this time, if the window is continued to slide to the right, according to the window sliding step (half of the basic window width, i.e. ), the representative point of the window will be to the right of the midpoint of the total time series. According to the following steps, the calculation will be repeated.

[0069] Exemplarily, in step S102, the same window width as step S101 is used. and window sliding step , starting from the right end of the time series, sliding in the opposite direction of time increase, and gradually calculating the statistics of the ocean and atmosphere time series at different time points as representative points. When the traditional one-way rightward sliding window causes the end of the original time series to be less than a window width, or the remaining data is discarded, causing the latest data to be unable to participate in the calculation; or the window length is supplemented with 0, introducing new errors at the endpoint; or the statistics are directly calculated with insufficient data, reducing the confidence of this part of the data. In addition, when the time scale increases, the representative point of the new window needs to be re-determined in the traditional method. This method can effectively avoid the above problems by sliding the window from the left and right ends.

[0070] Exemplarily, in step S102, a window is slid down to calculate the statistics within a time period at a given time scale (window width), and the window is slid in the opposite direction of time growth (from right to left) until the left end time point is less than the midpoint of the total time series. At this point, if you continue to slide the window to the left, according to the window sliding step (half of the basic window width, that is, ), the representative point of the window (the median of the time period) will be on the left side of the midpoint of the total time series. According to step S101, the calculation will be repeated.

[0071] For example, in step S103, for a given time scale (window width), after steps S101 and S102 are completed, the statistics of the time series with the midpoint of the entire time series as the representative point are additionally calculated, that is, the window width is taken. , calculate the statistics of the time series within this window period. This step is to ensure that steps S101 and S102 will not cause window sliding jumps near the midpoint of the entire time series.

[0072] Exemplarily, in step S104, the time scale (window width) is increased in units of the basic window width 2r, while the window sliding step is maintained at r. This ensures that under different time scales (window widths), the representative points of each time period fall on the representative points of the basic window, so that the size of the matrix storing the statistics can be determined before the calculation begins, avoiding the computational complexity caused by the expansion of the matrix dimension and the resulting sparsity of the matrix.

[0073] Specifically include:

[0074] , that is, when the window is a basic window, the window width , window sliding step , then The representative point (median) of the time period within a window (only the window sliding to the right is considered, the window sliding to the left can be obtained according to symmetry) is:

[0075]

[0076] For any , the corresponding time scale is: , the window sliding step size is , so the first The representative points of a window are:

[0077]

[0078] Comparing formula (3) and formula (4), when hour, Pick , thereby traversing the representative points of the basic window; when hour, are positive integers and form a continuous set of natural numbers, Depend on To express, that is, The representative points of each time scale all fall into the representative point set of the basic window and are its continuous subset. This result allows the size of the storage matrix of the statistic to be determined before the calculation begins, which is , which can avoid the computational complexity caused by excessive matrix space opening and the sparsity of effective matrix elements.

[0079] Exemplarily, the sliding windows in two directions of step S101 and step S102 may be performed in parallel and simultaneously, thereby improving calculation efficiency.

[0080] Exemplarily, in the above calculation process, the three variables of basic window width, window sliding step and time scale increase step are represented by one variable, namely window sliding step, which simplifies the calculation process.

[0081] It can be seen from the above embodiments that the traditional one-way rightward sliding window will cause the data at the end of the original time series that is less than a window width to be discarded, resulting in the waste of the latest data; or directly calculating statistics with data that is less than the window length, the confidence level is difficult to guarantee, and the representative point of the time period needs to be re-determined on different time scales; or the window length is supplemented with 0, resulting in the introduction of new errors at the endpoint (endpoint effect). This method slides the window from the left and right ends of the original time series to the center, which can effectively avoid the above problems in traditional methods.

[0082] Traditional multi-scale analysis methods require three variables in calculation: window width, window sliding step (or overlapping length of adjacent windows), and time scale (or its increasing step). Moreover, the positions of window representative points calculated at different time scales are not related, which makes it difficult to set the statistical storage matrix. This method combines the above three variables with the window sliding step. The complexity of calculating the representative point of the window and the window length is reduced, and the statistical calculation results can be stored in a predetermined size. , is the length of the original time series) and the sparsity is 50%.

[0083] This method can fully utilize the original time series sampling points while maintaining a good resolution of the statistical calculation results, eliminate endpoint effects, reduce the use of variables in the calculation, reduce the size of the statistical storage matrix, and improve calculation efficiency.

[0084] Embodiment 2, the embodiment of the present invention provides a full data dissection system for multi-scale analysis of sea-air time series, the system comprising:

[0085] The statistical calculation module of the data in each time window is used to determine the basic window width for a given time series of length N, slide the window from the left end of the time series in the direction of time growth, and set the window sliding step to half of the basic window width. The statistics of the data in each time window are calculated step by step until the window slides to a position where its right end is larger than the center of the original time series;

[0086] The representative point statistics calculation module is used to slide the window from the right end of the time series to the opposite direction of time increase with the basic window width and window sliding step, and gradually calculate the statistics of the ocean and atmosphere time series at different time points as representative points until the window slides to a position where its left end is smaller than the center of the original time series;

[0087] The representative point time period statistics calculation module is used to calculate the statistics of the original time series of ocean and atmosphere in the time period with N / 2 as the representative point;

[0088] The multi-scale statistics acquisition module is used to set the time scale to n times the basic window width, repeat the above sliding window and calculating statistics process at different time scales, and obtain the time-dependent multi-scale statistics of the ocean and atmosphere time series at different time periods and different time scales.

[0089] To further illustrate the effects of the embodiments of the present invention, the following experiment was conducted.

[0090] Figure 2 It is a traditional window partitioning scheme. Figure 3 This is the window partitioning scheme of the present invention. The horizontal axis is time (the center position of the representative point), and each line segment represents a window; the vertical axis represents the time scale (i.e., the window width), and the length of each line segment represents a different time scale. The gray triangle in the figure is the value range of the window representative point, which is also the effective storage range of the statistical matrix (equivalent to the range of the influence cone in wavelet analysis). Figure 2 In the figure, the solid box indicates the window width , the horizontal and vertical filled boxes represent the window sliding step length , the filled box with slashes indicates the increase in time scale When the time scale is fixed, The time scale The representative point of the window (median) The location of Sure:

[0091]

[0092] Among them, when the time scale hour, Not necessarily included When the window slides from left to right (the dotted arrow below the horizontal axis), data redundancy will occur at the end of the original time series, which will lead to problems such as endpoint effect or discarding of end data. Figure 3 In the figure, the horizontal and vertical filled boxes indicate the window sliding step length. , the solid box in the horizontal axis direction represents the basic window width (equal to ), the solid box on the ordinate represents the increase in time scale (also equal to ). At this time, The time scale The representative point of the window (median) The location is determined only by To determine:

[0093]

[0094] When the time scale hour, Included in The window moves from the left and right sides to the center of the original time series ( All sampling points of the original time series will be completely included in a window, without redundant data and without the need to supplement.

[0095] Figure 4 It is the traditional method. Figure 5 This is the method of the present invention. The minimum window width of the traditional method Overlap length with adjacent windows Take a smaller value ( For different time scales, the position of the window representative point cannot be determined in advance, so the statistics storage matrix The size is usually of the same order of magnitude as the square of the original time length. The window slides in one direction (step a6), so the redundant data at the end of the original time series needs special processing (various processing methods are described above, not given in this flow chart). The method of the present invention first determines the size of the statistics storage matrix (step b1), because it is much smaller than the square of the original time series length, so the space required for statistics storage is reduced; and this method links the basic window width, the window sliding step, and the time scale increase step, so the number of judgments and cycles required in the calculation is also reduced, which speeds up the calculation.

[0096] Figure 6 The data used in the calculation example of the full data segmentation method for multi-scale analysis of sea-air time series provided in the embodiment of the present invention are Nino12 and Nino34 indexes for a total of 1380 months from January 1900 to December 2014. The data comes from the website of the Physical Science Laboratory of the National Oceanic and Atmospheric Administration of the United States.

[0097] In the present invention, the amount of data is small. , so the basic window width will be fixed to 30 sampling points in the calculation. , the storage matrix size is 92×46.

[0098] Figure 7 It is a multi-scale correlation coefficient diagram of Nino12 and Nino34 time series dependent on time calculated by a full data dissection method for multi-scale analysis of sea-air time series in the present invention, Figure 8 The time-dependent multi-scale correlation coefficients of the Nino12 and Nino34 time series calculated by traditional methods.

[0099] The horizontal axis is time (the position of the representative point), and the vertical axis is the window width (i.e., the time scale). As the time scale increases, the number of windows decreases, and the position of the representative point tends to the center of the original time series, so the calculation result is effectively stored as a matrix size ( ), that is, the sparsity is 50%, which is reflected in the figure as an isosceles triangle. The color scale represents the linear correlation coefficient of Nino12 and Nino34. For the convenience of comparison, the traditional method here is different from the present invention only in the window sliding method (sliding to the right, discarding the redundant data at the end), and other methods such as window width, window sliding step, time scale increase step, etc. are all adopted by the present invention. Figure 8 The two circles in the figure indicate the main differences between the two methods. Due to the one-way sliding of the window in the traditional method, the redundant data at the end of the original time series is discarded. Generally speaking, the length of the discarded data on the right side of the traditional method changes with the increase of the time scale. Figure 8 The middle triangle (representing the valid data portion of the storage matrix) will appear jagged. In this example, due to the regularity of the matrix (the matrix size and the position of the representative points adopt the method of the present invention), the result of the traditional method also only has rough points at the top of the triangle.

[0100] Fig. 9 and Fig.10 The following are examples of comparing the calculation of a single time series using the method of the present invention and the traditional method. The data used is Figure 6 The Nino12 time series in the statistic is the degree of nonlinearity that depends on time. For the sake of comparison, the traditional method here only differs from the present invention in the window sliding method (sliding to the right and discarding redundant data). Other aspects such as window width, window sliding step, and time scale increase step are all adopted by the present invention. Since the window of the traditional method slides in one direction, the redundant data at the end of the original time series is discarded. Generally speaking, the length of the discarded data at the right end of the original time series in the traditional method changes with the increase of the time scale, so Fig.10 The middle triangle (representing the valid data part of the storage matrix) will appear jagged. In this example, due to the regularity of the matrix (the matrix size and the position of the representative points adopt the method of the present invention), the calculation results given by the traditional method ( Fig.10 ) and no non-smooth points appear, but the triangular matrix of the storage statistics composed of the representative points is biased to the left compared with the result of the method of the present invention. This is because the redundant data at the end of the original time series is discarded.

[0101] The above description is only a preferred specific implementation manner of the present invention, but the protection scope of the present invention is not limited thereto. Any modifications, equivalent substitutions and improvements made by any technician familiar with the technical field within the technical scope disclosed by the present invention and within the spirit and principles of the present invention should be covered within the protection scope of the present invention.

Claims

1. A full data dissection method for multi-scale analysis of sea-air time series, characterized in that: The method includes: S101, given a time series of length N, determine the basic window width, start sliding the window from the left end of the time series in the direction of time growth, set the window sliding step to half the basic window width, and gradually calculate the statistics of the data in each time window until the window slides to the right end of the window larger than the center position of the original time series; S102, sliding the window from the right end of the time series in the opposite direction of time increase with the basic window width and the window sliding step, and gradually calculating the statistics of the ocean and atmosphere time series at different time points as representative points, until the window slides to a position where the left end of the window is smaller than the center of the original time series; S103, calculating the statistics of the original time series of ocean and atmosphere in the time period with N / 2 as the representative point; S104, setting the time scale to n times the basic window width, repeating the above sliding window and calculating statistics at different time scales, and obtaining time-dependent multi-scale statistics of ocean and atmosphere time series at different time periods and different time scales; In step S101, the basic window width is 2r, the window sliding step is r, the representative point of the i-th window is: i·r+1 / 2, and the window slides to its right end larger than the center position of the original time series: i·r+1 / 2≤N / 2<(i+1)r+1 / 2; In step S101, assume that two time series are: X(i), i=1, 2...N, Y(i), i=1, 2...N, and the total length of both is N; the number of basic windows N w for: N w =min[int(N / 30),200](1) In the formula, N is the length of the original time series, int() is for rounding, and min[] is for finding the minimum value; In step S103, for a given time scale, after steps S101 and S102 are completed, the statistics of the time series with the midpoint of the entire time series as the representative point are additionally calculated, that is, the window [int(N / 2-r), int(N / 2+r)] is taken to calculate the statistics of the time series within this window period.

2. The full data segmentation method for multi-scale analysis of air-sea time series according to claim 1 is characterized in that: In step S101, according to the length N of the original time series and the number N of basic windows w Determine the window sliding step length r, the expression is: r=int(N / N w ) (2) Before the calculation begins, the size of the matrix storing the statistics is determined as: Number of basic windows × number of time scales = N w ×2N w .

3. The full data segmentation method for multi-scale analysis of sea-air time series according to claim 1 is characterized in that: In step S101, a window is slid down on a given time scale to calculate the statistics of two time periods, including the correlation coefficient of two time series, or the entropy and nonlinearity of a single time series; wherein, the time series samples in the window are slid in the direction of time growth until the right end time point is greater than the midpoint of the total time series, and then stop. At this time, if the window continues to slide to the right, according to the window sliding step, the representative point of the window will be on the right side of the midpoint of the total time series.

4. The full data segmentation method for multi-scale analysis of sea-air time series according to claim 1 is characterized in that: In step S102, with a window width of 2r and a window sliding step length of r, starting from the right end of the time series, sliding in the opposite direction of time increase, and gradually calculating the statistics of the ocean and atmosphere time series at different time points as representative points; wherein, from right to left, sliding the window in the opposite direction of time increase until the left end time point is less than N / 2 of the midpoint of the total time series stops; at this time, if the window continues to slide to the left, according to the window sliding step length, the representative point of the window will be on the left side of the midpoint of the total time series.

5. The full data segmentation method for multi-scale analysis of sea-air time series according to claim 1 is characterized in that: In step S101 and step S102, sliding the window from the right end of the data to the left and sliding the window from the left end of the data to the right are performed in parallel.

6. The full data segmentation method for multi-scale analysis of sea-air time series according to claim 1 is characterized in that: In step S104, the above sliding window and calculating statistics process is repeated at different time scales to obtain time-dependent multi-scale statistics of the ocean and atmosphere time series at different time periods and different time scales, including: When the window is a basic window, j=1, the window width is 2r, and the window sliding step is r, then the representative point of the time period in the nth window is: p(1,n)=n·r+1 / 2(3) For any j>1, the corresponding time scale is: 2r+2(j-1)r=2j·r, and the window sliding step is r, so the representative point of the mth window is: Comparing formula (3) and formula (4), when j=1, m is n, thereby traversing the representative points of the basic window; when j>1, j+m-1>m is a positive integer and forms a continuous natural number subset, j+m-1 is represented by n, that is, the representative points of the jth time scale all fall in the representative point set of the basic window and are its continuous subset.

7. A full data dissection system for multi-scale analysis of sea-air time series, characterized in that: The system implements the full data segmentation method for multi-scale analysis of sea-air time series according to any one of claims 1 to 6, and the system comprises: The statistical calculation module of the data in each time window is used to determine the basic window width for a given time series of length N, slide the window from the left end of the time series in the direction of time growth, and set the window sliding step to half of the basic window width. The statistics of the data in each time window are calculated step by step until the window slides to the right end of the window larger than the center position of the original time series; The representative point statistics calculation module is used to slide the window from the right end of the time series to the opposite direction of time increase with the basic window width and window sliding step, and gradually calculate the statistics of the ocean and atmosphere time series at different time points as representative points until the window slides to the left end of the window smaller than the center position of the original time series; The representative point time period statistics calculation module is used to calculate the statistics of the original time series of ocean and atmosphere in the time period with N / 2 as the representative point; The multi-scale statistics acquisition module is used to set the time scale to n times the basic window width, repeat the above sliding window and calculating statistics process at different time scales, and obtain the time-dependent multi-scale statistics of the ocean and atmosphere time series at different time periods and different time scales.

Images