A method for obtaining the length of a sliding observation window based on data analysis

Abstract

This invention discloses a method for obtaining the length of a sliding observation window based on data analysis. The method includes: connecting a sensor signal to a data acquisition and storage system via a transmission channel and a process channel to obtain a signal time series; performing a Fast Fourier Transform (FFT) on the time series to obtain a frequency domain sequence; calculating the contribution rate of each amplitude value to the entire signal; selecting the frequency signal with the greatest influence and reconstructing the time domain signal through an Inverse Fourier Transform (IFT); evaluating the difference between the reconstructed signal and the original time domain signal; and selecting more frequency components until the inversely transformed time domain signal meets the requirements of an effective threshold. The least common multiple of the frequencies of the final reconstructed signal is used as the window length. This invention is applicable to determining the length of the observation window when the process is complex or the mechanism is unclear. It relies solely on time series data to determine the observation window length, eliminating the need for mechanistic knowledge of process variables, thus significantly reducing the professional knowledge required of personnel. Furthermore, it can utilize existing data acquisition systems in industrial systems without requiring additional hardware, thereby greatly reducing costs.

Description

Technical Field

[0001] This invention belongs to the field of process monitoring in industrial systems, specifically involving the problem of determining the length of the observation window in a time series. In particular, when the mechanism is unclear, this method can obtain a suitable observation window length simply by observing the data sequence, thereby realizing the selection of the observation window in complex systems or when the mechanism is unclear. Background Technology

[0002] In industrial processes, data is typically presented as time series. Time series data plays a crucial role in industrial process monitoring, especially online monitoring. To meet online monitoring requirements, time series data are typically obtained through observation windows or sliding observation windows. Observation windows that are too small cannot fully reflect the patterns in the time series, while those that are too large require more time, failing to meet the requirement for speed. Current practices rely on repeated trials based on the physical meaning of the data. However, because industrial process time series are inherently complex due to the influence of process operating patterns and the operating environment, and because the mechanisms of some industrial processes, such as microbial metabolism, are not yet fully understood, obtaining an observation window is time-consuming, laborious, and difficult to be accurate. Therefore, finding an observation window that directly reflects the characteristics of the original signal from the time series data has significant application value for industrial process monitoring.

[0003] Since frequency domain signals have significant physical meaning and are more stable than time domain signals, and frequency domain signals can be combined in different ways to form arbitrary time domain signals, considering that most of the useful signals in industrial signals are concentrated in the low frequency band, while the high frequency band usually means noise signals, the length of the sliding window only needs to be able to cover the useful signals. Conversely, if we know the frequency of the useful signals, we can determine the length of the sliding window based on these frequencies.

[0004] Based on the above ideas, this invention converts the time-domain signal into a frequency-domain signal, filters out high-frequency noise, and reconstructs the time series. While meeting the accuracy requirements, the sliding window length is determined by the frequency characteristics of the equivalent frequency-domain signal. Thus, the sliding window length for different time series can be obtained simply through data analysis. Summary of the Invention

[0005] The technical problem to be solved by this invention is to ensure that the information of the time series is not lost by using only the observed time series without relying on the physical meaning and process information of the data itself, through frequency band decomposition and signal reconstruction, and then to calculate the appropriate observation window length by using the information of the included frequency bands.

[0006] The technical solution adopted in this invention is:

[0007] Step 1: Connect the sensor signal to the data acquisition and storage system via the transmission channel and process channel to obtain a signal time series with a time length of T. k is the sampling time;

[0008] Step 2: Perform time series analysis on the time series and perform a fast Fourier transform according to formula (1).

[0009] (1)

[0010] In the formula, ; obtain frequency domain sequence Let its amplitude be ;

[0011] Step 3: Calculate the contribution rate of each amplitude value to the entire signal. , (2)

[0012] Based on the calculation results Sort by size;

[0013] Step 4: Select the frequency signals with the greatest influence to reconstruct the time-domain signal. First, select the two largest frequency signals. Corresponding , so that the rest , get new ,Will Convert to time domain signal via inverse Fourier transform The transformation formula is shown in equation (3).

[0014] (3)

[0015] Step 5: Obtain the original time series and transformed time series The resulting error time series ,Right now

[0016] (4)

[0017] In the formula, Sampling time, This represents the number of samples in the time series.

[0018] Step Six: Evaluate the magnitude of the difference between it and the original time-domain signal, using the root mean square error. In form, and ,Right now

[0019] (5)

[0020] (6)

[0021] (7)

[0022] Set threshold ,when Less than the effective threshold This indicates that the selected frequency can contain information from the original signal, and the approximation is valid if the calculated frequency is within acceptable limits. Greater than the effective threshold This indicates that the selected frequency cannot contain the information of the original signal, and more frequency components need to be selected. ;

[0023] Step 7: Repeat steps 2 through 6 until the time-domain signal obtained by inverse transformation satisfies the following conditions. Until the effective threshold requirement is met, that is: ;

[0024] Step 8: Use the least common multiple of the frequencies of the final reconstructed signals as the window length, assuming the corresponding periods of the included frequency signals are as follows. Then the length of the sliding window is

[0025] (8)

[0026] In the formula, It represents the least common multiple.

[0027] The present invention provides a method for obtaining the observation window length using time series information. Compared with the prior art, the advantages of the present invention are as follows:

[0028] This method is suitable for determining the length of the observation window when the process or mechanism is unclear. This method, which is based on data analysis to obtain the length of the sliding observation window, has a good theoretical basis and convenient operation, thus avoiding the time-consuming, laborious and inaccurate empirical methods.

[0029] This method can determine the observation window length based solely on time series data, without requiring knowledge of the mechanisms of process variables, thus greatly reducing the professional knowledge required of staff.

[0030] This method can utilize existing data acquisition systems in industrial systems without requiring additional hardware, thus significantly reducing costs. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of the structure of a method for obtaining the length of a sliding observation window based on data analysis according to the present invention;

[0032] Figure 2This is a flowchart of a method for obtaining the length of a sliding observation window based on data analysis according to the present invention;

[0033] Figure 3 The test signal consists of three sets of frequencies according to the present invention;

[0034] Figure 4 This is the frequency domain waveform after the fast Fourier transform of this invention;

[0035] Figure 5 This is the signal spectrum under the new sampling window length of the present invention;

[0036] Figure 6 It is the original signal and frequency components of the complex time-domain signal of this invention;

[0037] Figure 7 This refers to signal comparison under the new sampling window of the present invention. Implementation

[0038] The following describes in detail a method for obtaining the length of a sliding observation window based on data analysis according to the present invention, with reference to embodiments and accompanying drawings.

[0039] like Figure 1 As shown, this invention discloses a method for obtaining the length of a sliding observation window based on data analysis, used for observation window acquisition in industrial process monitoring. The method includes: acquiring industrial process data to be analyzed using sensors; a signal transmission channel; a process channel converting analog signals into digital signals; a data acquisition and storage unit acquiring time-series data; performing time-series analysis on the time-series data; and finally obtaining the observation window for the time-series data. The observation window result is periodically fed back to the time-series analysis to prevent characteristic changes caused by shifts in the industrial process operating point, which would necessitate adjustments to the observation window. Here, sensors correspond to variables with actual physical meaning, including but not limited to temperature, flow rate, and pressure; the signal transmission channel includes both physical channels composed of communication cables and signal lines, as well as wireless channels; the process channel refers to the physical unit that converts analog quantities into digital quantities; data acquisition and storage refers to a unit with a microprocessor capable of reading and storing digital quantities; and time-series analysis refers to... Figure 2 The software generated by the flowchart shown can be embedded into existing monitoring software in industrial systems, or it can run independently in a simulation environment.

[0040] Operating steps

[0041] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The specific embodiments described are only for explanation and illustration of the present invention and are not intended to limit the present invention.

[0042] Step 1: Connect the sensor signal to the data acquisition and storage system via the transmission channel and process channel to obtain a signal time series with a time length of T, where k is the sampling time.

[0043] Step 2: Perform time series analysis on the time series and perform a fast Fourier transform according to formula (1).

[0044] (1)

[0045] In the formula ; Obtain the frequency domain sequence Let its amplitude be ;

[0046] Step 3: Calculate the contribution rate of each amplitude value to the entire signal. ,Right now (2)

[0047] Based on the calculation results Sort by size;

[0048] Step 4: Select the frequency signals with the greatest influence to reconstruct the time-domain signal. First, select the two largest frequency signals. Corresponding , so that the rest , get new ,Will Convert to time domain signal via inverse Fourier transform The transformation formula is shown in equation (3).

[0049] (3)

[0050] Step 5: Obtain the original time series and transformed time series The resulting error time series ,Right now

[0051] (4)

[0052] In the formula, Sampling time, This represents the number of samples in the time series.

[0053] Step Six: Evaluate the magnitude of the difference between it and the original time-domain signal, using the root mean square error. In form, and ,Right now

[0054] (5)

[0055] (6)

[0056] (7)

[0057] Set threshold ,when Less than the effective threshold This indicates that the selected frequency can contain information from the original signal, and the approximation is valid if the calculated frequency is within acceptable limits. Greater than the effective threshold This indicates that the selected frequency cannot contain the information of the original signal, and more frequency components need to be selected. ;

[0058] Step 7: Repeat steps 2 through 6 until the time-domain signal obtained by inverse transformation satisfies the following conditions. Until the effective threshold requirement is met, that is: ;

[0059] Step 8: Use the least common multiple of the frequencies of the final reconstructed signals as the window length, assuming the corresponding periods of the included frequency signals are as follows. Then the length of the sliding window is

[0060] (8)

[0061] In the formula, It represents the least common multiple.

[0062] The simulation verification is given below.

[0063] A series of time series were constructed by adding periodic functions with fixed frequencies to verify the accuracy of the window length selection. Since the actual signal can be obtained as a periodic signal of different frequencies through Fourier decomposition, the artificially set frequency will not affect the reliability of the method.

[0064] (1) Simple time-domain signal composed of three sets of frequency signals

[0065] Three sets of frequency signals were superimposed to form a time-domain signal with a length of 20,000, which was used as the test signal. Figure 3 As shown.

[0066] The sampling frequency is 10kHz. First, it is transformed to obtain a signal of length 10000 through a Fast Fourier Transform. To ensure consistency with the number of discrete-time signals, zeros are added to supplement the signal. The resulting waveform is shown below. Figure 4 As shown.

[0067] from Figure 4As can be seen, there are three frequencies in the signal: 50Hz, 93Hz, and 136Hz. The two frequency components with larger amplitudes, 50Hz and 136Hz, are selected to recover the original signal. The resulting new time-domain signal is not much different from the original signal. Therefore, the least common multiple of these two frequencies, 3400, is selected as the observation window length.

[0068] A 3400-byte segment was randomly selected from the time series signal, and the sampled signal was processed. The result is as follows. Figure 5 As shown, its spectrum basically retains the main frequency components of the original signal and can reflect the main characteristics of the original signal.

[0069] (2) Complex time-domain signals composed of multiple frequency signals

[0070] The given signal consists of 10 frequency components with frequencies of 50Hz, 72Hz, 93Hz, 119Hz, 140Hz, 181Hz, 157Hz, 98Hz, 131Hz, and 119Hz, and corresponding amplitudes of 2, 0.2, 1.5, 1, 0.15, 0.8, 0.35, 1.2, 0.6, and 0.3, respectively. The corresponding time-domain signal and frequency components are shown below. Figure 6 As shown, selecting the five main frequency components ensures minimal difference from the original signal. The sampling frequency for the selected observation window length is calculated based on these five frequency components. The observation window length is then determined according to this sampling period. Randomly selected window length data is compared with the signal within the sampling window after inverse Fourier transform, as shown below. Figure 7 As shown, the reconstructed signal has a good consistency with the original signal.

Claims

1. A method for obtaining the length of a sliding observation window based on data analysis, characterized in that, The method for obtaining the length of the sliding observation window includes: Step 1: Connect the sensor signal to the data acquisition and storage system via the transmission channel and process channel to obtain a signal time series with a time length of T. k is the sampling time; Step 2: For this time series For time series analysis, perform a Fast Fourier Transform using the following formula. In the formula, ; obtain frequency domain sequence Let its amplitude be ; Step 3: Calculate the contribution rate of each amplitude value to the entire signal. According to the following formula Based on the calculation results Sort by size; Step 4: Select the frequency signals with the greatest influence to reconstruct the time-domain signal. First, select the two largest ones. Corresponding , so that the rest , get new ,Will Convert to time domain signal via inverse Fourier transform Its transformation formula is as follows: ; Step 5: Obtain the original time series and transformed time series The resulting error time series According to the following formula In the formula, Sampling time, This represents the number of samples in the time series. Step Six: Evaluate the magnitude of the difference between it and the original time-domain signal, using the root mean square error. , and The formula is as follows: ; ; Set threshold ,when Less than the effective threshold This indicates that the selected frequency can contain information from the original signal, and the approximation is valid if the calculated frequency is within acceptable limits. Greater than the effective threshold This indicates that the selected frequency cannot contain the information of the original signal, and more frequency components need to be selected. ; Step 7: Repeat steps 2 through 6 until the time-domain signal obtained by inverse transformation satisfies the following conditions. Until the effective threshold requirement is met, that is: ; Step 8: Use the least common multiple of the frequencies of the final reconstructed signals as the window length, assuming the corresponding periods of the included frequency signals are as follows. Then the length of the sliding window is In the formula, It represents the least common multiple.

2. The method for obtaining the length of a sliding observation window according to claim 1, characterized in that, The signal time series mentioned in step 1 It is formed by connecting sensor signals to the data acquisition and storage system through the transmission channel and process channel.

3. The method for obtaining the length of the sliding observation window according to claim 1, characterized in that, In step 3, the contribution rate of each amplitude value to the entire signal is calculated based on the results. Sort by size.

4. The method for obtaining the length of the sliding observation window according to claim 1, characterized in that, Step 4 involves selecting the frequency signal with the greatest influence to reconstruct the time-domain signal.

5. The method for obtaining the length of a sliding observation window according to claim 1, characterized in that, The error time series mentioned in step 5 From the original time series and transformed time series Formed.

6. The method for obtaining the length of a sliding observation window according to claim 1, characterized in that, Step 6 involves evaluating the difference between the signal and the original time-domain signal, using the root mean square (RMS) and... and .

7. The method for obtaining the length of a sliding observation window according to claim 1, characterized in that, In step 8, the least common multiple of the frequencies of the signals ultimately participating in the reconstruction is used as the window length.

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