CN117892055B - Water temperature data calculation method based on curve fitting and Nyquist theorem - Google Patents
Water temperature data calculation method based on curve fitting and Nyquist theorem Download PDFInfo
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Abstract
The invention discloses a water temperature data calculation method based on curve fitting and Nyquist theorem, which comprises the following steps: s1, acquiring original measured water temperature data and performing data outlier processing on the original measured water temperature data to obtain measured water temperature data; s2, performing curve fitting on the measured water temperature data by adopting a trigonometric function to obtain fitted measured water temperature data; s3, resampling the fitted actually measured water temperature data by using a Nyquist sampling method to obtain water temperature data of which the water temperature data of a minute scale is reduced to be water temperature data of an hour scale; according to the method, the original water temperature data is subjected to data preprocessing, so that the accuracy of actually measured water temperature data is improved; by adopting a triangle curve fitting and Nyquist sampling method, the rapid and flexible resampling of water temperature data is realized, the requirements on data and calculation force are low, and the calculation efficiency is improved; and the fitting effect and the sampling effect are evaluated by using root mean square error and correlation coefficient, so that the accuracy and reliability of the measured water temperature data are improved.
Description
Technical Field
The invention relates to the technical field of water temperature data processing, in particular to a water temperature data calculation method based on curve fitting and Nyquist theorem.
Background
The existing water temperature resampling method mainly comprises an averaging method, a time sequence analysis method, a machine learning method, a deep learning method and the like. The averaging method is too coarse, and is not enough for consideration of data change in a short time range, and machine learning and deep learning require a large amount of training data, and have high requirements on calculation force and data amount. Therefore, the existing water temperature resampling method is too coarse, has high requirements on data and calculation force, increases the calculation cost and reduces the calculation efficiency.
Disclosure of Invention
Aiming at the defects in the prior art, the invention provides a water temperature data calculation method based on curve fitting and Nyquist theorem, and rapid and flexible resampling of water temperature data is realized by introducing a triangular curve fitting and Nyquist sampling method.
In order to achieve the aim of the invention, the invention adopts the following technical scheme:
a water temperature data calculation method based on curve fitting and Nyquist theorem comprises the following steps:
S1, acquiring original measured water temperature data and performing data outlier processing on the original measured water temperature data to obtain measured water temperature data;
s2, performing curve fitting on the measured water temperature data by adopting a trigonometric function to obtain fitted measured water temperature data;
And S3, resampling the fitted actually measured water temperature data by using a Nyquist sampling method to obtain water temperature data of which the water temperature data of a minute scale is reduced to be the water temperature data of an hour scale.
Further, the step S1 specifically includes:
S11, setting a measurement time interval, and acquiring measured water temperature data in a set time period to obtain original measured water temperature data;
and S12, carrying out data interpolation and replacement on the missing value and the abnormal value of the original measured water temperature data by adopting a cubic spline interpolation method, and then carrying out data combination to obtain the measured water temperature data.
Further, step S2 specifically includes:
s21, defining the date, amplitude, center point and width of a trigonometric function curve to obtain a trigonometric fitting function;
S22, setting an initial value of amplitude as a maximum temperature value, setting an initial value of a central point as an average value of time, setting an initial value of width as a time interval from a start time to an end time according to the trigonometric fitting function and the measured water temperature data, and performing trigonometric function curve fitting by adopting a nonlinear least square method to obtain the fitted measured water temperature data.
Further, the fitting effect of the fitted measured water temperature data and the measured water temperature data is judged by adopting the root mean square error and the correlation coefficient, and if the root mean square error is smaller and the correlation coefficient is larger, the fitting effect is better.
Further, the root mean square error is calculated as:
Wherein MSE represents root mean square error, n represents data amount, y i represents the ith measured water temperature value of measured water temperature data, And the ith fitting water temperature value of the fitted measured water temperature data is represented.
Further, the calculation formula of the correlation coefficient is:
Wherein R 2 represents a correlation coefficient, n represents a data amount, y i represents an ith measured water temperature value of measured water temperature data, An i-th fitting water temperature value representing the fitted measured water temperature data,Mean value of measured water temperature data is shown.
Further, the step S3 specifically includes:
s31, calculating the Nyquist frequency according to the fitted actually measured water temperature data;
s32, resampling the fitted actually measured water temperature data at the nyquist frequency according to the nyquist frequency, and obtaining water temperature data for reducing the water temperature data of the minute scale to the water temperature data of the hour scale.
The invention has the following beneficial effects:
According to the water temperature data calculation method based on curve fitting and Nyquist theorem, data preprocessing is performed on original actually measured water temperature data, and accuracy of the actually measured water temperature data is improved; secondly, a triangle curve fitting and Nyquist sampling method is adopted to realize rapid and flexible resampling of measured water temperature data, so that the requirements on data and calculation force are low, and the calculation efficiency is improved; and finally, the fitting effect and the sampling effect are evaluated by using root mean square error and correlation coefficient, so that the accuracy and reliability of the measured water temperature data are improved.
Drawings
FIG. 1 is a flow chart of a method for calculating water temperature data based on curve fitting and Nyquist theorem;
FIG. 2 is a schematic diagram of a partial measured water temperature data change curve;
FIG. 3 is a graph showing a comparison of a partial fitted measured water temperature data and a measured water temperature data change curve;
Fig. 4 is a schematic diagram of an hour-scale water temperature data change curve obtained by resampling the fitted measured water temperature data by a nyquist sampling method.
Detailed Description
The following description of the embodiments of the present invention is provided to facilitate understanding of the present invention by those skilled in the art, but it should be understood that the present invention is not limited to the scope of the embodiments, and all the inventions which make use of the inventive concept are protected by the spirit and scope of the present invention as defined and defined in the appended claims to those skilled in the art.
As shown in fig. 1, a method for calculating water temperature data based on curve fitting and nyquist theorem includes the following steps S1-S3:
s1, acquiring original measured water temperature data and performing data outlier processing on the original measured water temperature data to obtain measured water temperature data.
In this example, measured water temperature data from day 10, month 15, 2023 to day 11, month 15, 2023 was used as raw measured water temperature data, and measurement was performed every 5 minutes during this period. The preprocessing of the original measured water temperature data mainly comprises the processing of abnormal values and missing values, in the embodiment, the processing of the abnormal values and the missing values is performed by adopting a cubic spline interpolation method, and all the data are combined to obtain a combined measured water temperature data graph. Wherein, partial measured water temperature data are shown in table 1:
Table 1 partial actual measured water temperature data table
| Sequence number | Time of | Water temperature value |
| 0 | 2023-10-15 23:55:04 | 14.91 |
| 1 | 2023-10-15 23:50:04 | 14.92 |
| 2 | 2023-10-15 23:45:05 | 14.93 |
| 3 | 2023-10-15 23:40:05 | 14.94 |
| 4 | 2023-10-15 23:35:04 | 14.95 |
| 5 | 2023-10-15 23:30:04 | 14.96 |
| 6 | 2023-10-15 23:25:04 | 14.98 |
| 7 | 2023-10-15 23:20:05 | 14.99 |
| 8 | 2023-10-15 23:15:04 | 14.99 |
| 9 | 2023-10-15 23:10:05 | 15.01 |
Specifically, step S1 specifically includes S11-S12:
s11, setting a measurement time interval, and acquiring measured water temperature data in a set time period to obtain original measured water temperature data.
And S12, carrying out data interpolation and replacement on the missing value and the abnormal value of the original measured water temperature data by adopting a cubic spline interpolation method, and then carrying out data combination to obtain the measured water temperature data.
S2, performing curve fitting on the measured water temperature data by adopting a trigonometric function to obtain the fitted measured water temperature data.
As shown in fig. 2, fig. 2 is a schematic diagram of a partial measured water temperature data change curve. In fig. 2, the abscissa indicates time and the ordinate indicates measured water temperature. The change of some measured water temperature data is shown in fig. 2, and it can be seen from fig. 2 that the measured water temperature data has a periodicity similar to a trigonometric function on a certain time scale.
In this embodiment, data fitting is performed on the measured water temperature data. Because the actually measured water temperature data has periodicity similar to a trigonometric function on a certain time scale, the invention adopts the trigonometric function to fit a water temperature curve, and adopts a nonlinear least square method to solve parameters such as amplitude, frequency, phase and the like of the fitted curve. The specific fitting process comprises the following steps: defining a trigonometric fit function, namely defining the date, amplitude, center point and width of a trigonometric function curve, wherein the center point is the position of the peak value of the trigonometric function curve on the x-axis (namely time in the embodiment), and the width is the width of the trigonometric function curve, so that the distance between the peak and the trough can be influenced; then, calculating a trigonometric fitting function by utilizing a curve_fit function of scipy, firstly setting an initial value of amplitude, namely setting the initial value as a maximum temperature value, setting an initial value of a central point, namely setting the initial value as an average value of time, setting an initial value of width, namely setting the time interval from a starting date to an ending date, inputting measured water temperature data into the fitting function, and performing trigonometric function curve fitting by utilizing a nonlinear least square method to obtain the fitted measured water temperature data. The measured water temperature data after partial fitting obtained by trigonometric curve fitting calculation are shown in table 2:
table 2 measured water temperature data table after partial fitting
As shown in fig. 3, fig. 3 is a schematic diagram showing a comparison of the measured water temperature data after the partial fitting and the measured water temperature data change curve. In fig. 3, the abscissa indicates time, the ordinate indicates water temperature, the broken line indicates a fitted curve, and the solid line indicates an actual measurement value. In the embodiment, original discrete water temperature data is converted into continuous values expressed by functional relations through triangular curve fitting, and a foundation is laid for sampling in the subsequent step.
Specifically, step S2 specifically includes S21-S22:
and S21, defining the date, amplitude, center point and width of the trigonometric function curve to obtain a trigonometric fitting function.
S22, setting an initial value of amplitude as a maximum temperature value, setting an initial value of a central point as an average value of time, setting an initial value of width as a time interval from a start time to an end time according to the trigonometric fitting function and the measured water temperature data, and performing trigonometric function curve fitting by adopting a nonlinear least square method to obtain the fitted measured water temperature data.
In this embodiment, the accuracy of the trigonometric curve fitting needs to calculate indexes such as fitting error and correlation coefficient to evaluate the accuracy and reliability of the fitting. In this embodiment, the fitting error is measured by using a root Mean Square Error (MSE), which is a measure of the average square error between the measured water temperature value and the fitted water temperature value, and therefore, when the root mean square error is smaller, the better the fitting effect is indicated; in addition, the larger the correlation coefficient (R 2) is, the better the fitting effect is.
Specifically, the fitting effect of the fitted measured water temperature data and the measured water temperature data is judged by adopting the root mean square error and the correlation coefficient, and if the root mean square error is smaller and the correlation coefficient is larger, the fitting effect is better.
Specifically, the root mean square error is calculated as:
Wherein MSE represents root mean square error, n represents data amount, y i represents the ith measured water temperature value of measured water temperature data, And the ith fitting water temperature value of the fitted measured water temperature data is represented.
Specifically, the calculation formula of the correlation coefficient is:
Wherein R 2 represents a correlation coefficient, n represents a data amount, y i represents an ith measured water temperature value of measured water temperature data, An i-th fitting water temperature value representing the fitted measured water temperature data,Mean value of measured water temperature data is shown.
In this embodiment, the calculated root Mean Square Error (MSE) is 0.00581263, and the calculated correlation coefficient (R 2) is 0.95808921, and it can be seen that the root mean square error is smaller and the correlation coefficient is larger, so that the fitting effect is better.
And S3, resampling the fitted actually measured water temperature data by using a Nyquist sampling method to obtain water temperature data of which the water temperature data of a minute scale is reduced to be the water temperature data of an hour scale.
In this embodiment, there are two simple rules for nyquist sampling, the highest frequency component of the first acquisition must be less than half the sampling rate, and the second must be equally spaced. Therefore, the Nyquist sampling method is utilized to resample the fitted actually measured water temperature data to obtain water temperature data with a minute scale reduced to water temperature data with an hour scale, so as to obtain water temperature data with better sampling effect. The water temperature data of the partial hour scale obtained by resampling the fitted measured water temperature data by the nyquist sampling method is shown in table 3:
table 3 partial hour scale water temperature data table
As shown in fig. 4, fig. 4 is a schematic diagram of an hour-scale water temperature data change curve obtained after resampling the fitted measured water temperature data by the nyquist sampling method. In fig. 4, the abscissa indicates time, the ordinate indicates water temperature, and the solid line with diamond points indicates resampled data (data resampled at1 hour intervals). It can be found from fig. 4 that, after resampling the fitted measured water temperature data by using the nyquist sampling method, complete water temperature data with good sampling effect and hour scale can be obtained.
Specifically, step S3 specifically includes S31-S32:
s31, calculating the Nyquist frequency according to the fitted water temperature data.
S32, resampling the fitted water temperature data at the nyquist frequency according to the nyquist frequency, and obtaining water temperature data for reducing the water temperature data of the minute scale to the water temperature data of the hour scale.
For sampling effect evaluation, the main evaluation index is reconstruction error, and the smaller the reconstruction error is, the more accurate the sampling and restoring process is. Therefore, in this embodiment, the reconstruction error is quantified by the root mean square error and the correlation coefficient between the measured water temperature data and the fitted measured water temperature data, and the sampling effect is better as the root mean square error is smaller. In this embodiment, the root Mean Square Error (MSE) is 0.00410242 and the correlation coefficient (R 2) is 0.97019832. It can be seen that the root mean square error is smaller, and the correlation coefficient is larger, so that the sampling effect is better.
According to the water temperature data calculation method based on curve fitting and Nyquist theorem, data preprocessing is performed on original water temperature data, and accuracy of actually measured water temperature data is improved; secondly, a triangular curve fitting and Nyquist sampling method is adopted to realize rapid and flexible resampling of water temperature data, so that the requirements on data and calculation force are low, and the calculation efficiency is improved; and finally, the fitting effect and the sampling effect are evaluated by using root mean square error and correlation coefficient, so that the accuracy and reliability of the measured water temperature data are improved.
The principles and embodiments of the present invention have been described in detail with reference to specific examples, which are provided to facilitate understanding of the method and core ideas of the present invention; meanwhile, as those skilled in the art will have variations in the specific embodiments and application scope in accordance with the ideas of the present invention, the present description should not be construed as limiting the present invention in view of the above.
Those of ordinary skill in the art will recognize that the embodiments described herein are for the purpose of aiding the reader in understanding the principles of the present invention and should be understood that the scope of the invention is not limited to such specific statements and embodiments. Those of ordinary skill in the art can make various other specific modifications and combinations from the teachings of the present disclosure without departing from the spirit thereof, and such modifications and combinations remain within the scope of the present disclosure.
Claims (3)
1. The water temperature data calculation method based on curve fitting and Nyquist theorem is characterized by comprising the following steps of:
S1, acquiring original measured water temperature data and performing data outlier processing on the original measured water temperature data to obtain measured water temperature data;
s2, performing curve fitting on the measured water temperature data by adopting a trigonometric function to obtain fitted measured water temperature data;
the step S2 specifically includes:
s21, defining the date, amplitude, center point and width of a trigonometric function curve to obtain a trigonometric fitting function;
S22, setting an initial value of amplitude as a maximum temperature value, setting an initial value of a central point as an average value of time, setting an initial value of width as a time interval from a start time to an end time according to a trigonometric fitting function and measured water temperature data, and performing trigonometric function curve fitting by adopting a nonlinear least square method to obtain the fitted measured water temperature data;
the fitting effect of the fitted measured water temperature data and the measured water temperature data is judged by adopting the root mean square error and the correlation coefficient, and if the root mean square error is smaller and the correlation coefficient is larger, the fitting effect is better;
The calculation formula of the root mean square error is as follows:
Wherein MSE represents root mean square error, n represents data amount, y i represents the ith measured water temperature value of measured water temperature data, An ith fitting water temperature value representing the fitted measured water temperature data;
the calculation formula of the correlation coefficient is as follows:
Wherein R 2 represents a correlation coefficient, n represents a data amount, y i represents an ith measured water temperature value of measured water temperature data, An i-th fitting water temperature value representing the fitted measured water temperature data,Mean value of measured water temperature data is shown;
And S3, resampling the fitted actually measured water temperature data by using a Nyquist sampling method to obtain water temperature data of which the water temperature data of a minute scale is reduced to be the water temperature data of an hour scale.
2. The method for calculating water temperature data based on curve fitting and nyquist theorem according to claim 1, wherein step S1 specifically comprises:
S11, setting a measurement time interval, and acquiring measured water temperature data in a set time period to obtain original measured water temperature data;
and S12, carrying out data interpolation and replacement on the missing value and the abnormal value of the original measured water temperature data by adopting a cubic spline interpolation method, and then carrying out data combination to obtain the measured water temperature data.
3. The method for calculating water temperature data based on curve fitting and nyquist theorem according to claim 1, wherein step S3 specifically comprises:
s31, calculating the Nyquist frequency according to the fitted actually measured water temperature data;
s32, resampling the fitted actually measured water temperature data at the nyquist frequency according to the nyquist frequency, and obtaining water temperature data for reducing the water temperature data of the minute scale to the water temperature data of the hour scale.
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