A method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics.

Abstract

This invention belongs to the field of water quality monitoring and data analysis technology, and is a method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics. The method includes: constructing an initial factor set; calculating the minimum MIC (micronizable value) of dissolved oxygen and each influencing factor in the initial factor set; setting a target MIC value; selecting several factors with MIC values ​​greater than the target MIC value to form a second factor set; calculating the cross-wavelet power spectrum, cross-wavelet phase spectrum, and cross-wavelet coherence condensation spectrum of dissolved oxygen and each influencing factor in the second factor set; plotting the cross-wavelet power spectrum and phase spectrum to determine whether there is a significant correlation between dissolved oxygen and each influencing factor; quantifying the influence of each parameter on dissolved oxygen content using principal component analysis, and identifying and outputting the key factors of dissolved oxygen. This invention can comprehensively analyze the correlation between dissolved oxygen and influencing factors, and effectively identify the key factors affecting dissolved oxygen in rivers.

Description

Technical Field

[0001] This invention belongs to the field of water quality monitoring and data analysis, specifically involving a method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics. Background Technology

[0002] Dissolved oxygen in water is essential for the survival of aquatic organisms. Sufficient dissolved oxygen is a necessary condition for their survival and a key indicator of the overall health of aquatic ecosystems. However, dissolved oxygen concentration is influenced by various factors, such as water temperature, water quality, and light intensity. These factors may exhibit complex nonlinear relationships and time-varying characteristics, making accurate identification of key factors affecting dissolved oxygen challenging. The response of dissolved oxygen concentration to changes in these influencing factors has a certain time lag. To effectively manage and protect the aquatic ecological environment, a thorough analysis of the correlation between dissolved oxygen and its influencing factors is necessary. Traditional correlation analysis methods are often limited to linear relationships and struggle to reveal the signal characteristics in the time and frequency domains. Therefore, a method is needed that can comprehensively analyze the nonlinear relationships between dissolved oxygen and its influencing factors, revealing signal characteristics in the time and frequency domains, and identifying key factors affecting river dissolved oxygen. Summary of the Invention

[0003] To address the technical problems existing in the prior art, this invention proposes a method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics. This method can handle the nonlinear relationship between dissolved oxygen and its influencing factors, analyze the correlation between the two in the time and frequency domain, comprehensively analyze the correlation between dissolved oxygen and influencing factors, and effectively identify key factors affecting dissolved oxygen in rivers.

[0004] The objective of this invention can be achieved by adopting the following technical solutions:

[0005] A method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics, the method comprising:

[0006] S1. Select multiple factors affecting dissolved oxygen in rivers to construct an initial factor set, and use the maximum information coefficient (MIC) method to calculate the MIC values ​​of dissolved oxygen and each factor in the initial factor set.

[0007] S2. Set the target value of MIC, filter several factors whose MIC value is greater than the target value of MIC, and arrange the several influencing factors in descending order of MIC value to form a second factor set.

[0008] S3. Calculate the cross-wavelet power spectrum, cross-wavelet phase spectrum, and cross-wavelet coherent condensation spectrum of dissolved oxygen and each influencing factor of the second factor set using cross-wavelet transform (XWT).

[0009] S4. Based on the calculated cross wavelet power spectrum, cross wavelet phase spectrum and cross wavelet coherence coefficient, draw the cross wavelet power spectrum and phase spectrum. Based on the wavelet power spectrum and phase spectrum, determine the influencing factors that are significantly correlated with dissolved oxygen at different scales and frequencies.

[0010] S5. Quantify the influence of each factor that is significantly correlated with dissolved oxygen on dissolved oxygen using principal component analysis. Identify the key factors affecting dissolved oxygen based on the degree of influence and output the key factors affecting dissolved oxygen.

[0011] Specifically, step S1 includes the following steps:

[0012] S11. Select multiple factors affecting dissolved oxygen in rivers from meteorological, hydrological and water quality indicators to form an initial factor set. Use the initial factor set as the independent variable X and dissolved oxygen concentration as the dependent variable Y to construct dataset D.

[0013] S12. Grid the scatter plot of dataset D according to the X-axis and Y-axis to obtain grid G. Calculate the mutual information of dataset D on grid G ​​with different probability distributions and take the maximum mutual information to obtain the maximum mutual information value of different probability distributions.

[0014] S13. Normalize the maximum mutual information values ​​of different probability distributions to obtain the MIC values ​​between each influencing factor and dissolved oxygen.

[0015] Specifically, step S2 includes the following steps:

[0016] Set the target MIC value to 0.3, select several influencing factors with MIC values ​​≥ 0.3, arrange the influencing factors in descending order of MIC value, and form a second factor set.

[0017] Specifically, step S3 includes the following steps:

[0018] S31. Perform continuous wavelet transform on the time series of the influence factors and the time series of dissolved oxygen in the second factor set respectively to obtain the continuous wavelet transform results of the time series of influence factors and the time series of dissolved oxygen. Calculate the cross wavelet power spectrum based on the continuous wavelet transform results.

[0019] S32. Based on the continuous wavelet transform results of the influence factor time series and the dissolved oxygen time series, calculate the cross wavelet phase spectrum of the influence factor time series and the dissolved oxygen time series.

[0020] S33. Based on the continuous wavelet transform results and the cross wavelet power spectrum, calculate the cross wavelet coherence coefficients of the influence factor time series and the dissolved oxygen time series.

[0021] Specifically, step S4 includes the following steps:

[0022] S41. Draw a cross-wavelet power spectrum based on the calculated cross-wavelet power spectrum, and analyze the interaction strength between dissolved oxygen and each influencing factor at different time and frequency scales based on the cross-wavelet power spectrum to obtain the analysis results of the cross-wavelet power spectrum.

[0023] S42. Based on the calculated cross-wavelet phase spectrum and cross-wavelet coherence coefficient, plot the cross-wavelet phase spectrum. Analyze the time-frequency correlation between dissolved oxygen and each influencing factor based on the wavelet coherence coefficient values ​​shown in the cross-wavelet phase spectrum. Analyze the positive and negative correlation between dissolved oxygen and each influencing factor in the time-frequency domain based on the phase relationship shown in the cross-wavelet phase spectrum to obtain the analysis results of the cross-wavelet phase spectrum.

[0024] S43. Based on the analysis results of the cross-wavelet power spectrum and the cross-wavelet phase spectrum, analyze the correlation and changes between dissolved oxygen and influencing factors at different scales and frequencies. High-frequency scale reflects the short-term changes in correlation, and low-frequency scale reflects the long-term changes in correlation, thus obtaining the influencing factors that are significantly correlated with dissolved oxygen at different scales and frequencies.

[0025] Specifically, step S41 includes the following steps: plotting the cross wavelet power spectrum in the form of a two-dimensional image to obtain a cross wavelet power spectrum diagram, with time as the horizontal axis and scale or frequency as the vertical axis, and the color depth representing the magnitude of the cross wavelet power; the darker the color, the greater the cross wavelet power, indicating a stronger correlation between the two variables at that time and scale.

[0026] Specifically, step S42 includes the following steps: plotting the wavelet coherence in the form of a two-dimensional image based on the calculated cross-wavelet phase spectrum and cross-wavelet coherence coefficients to obtain a cross-wavelet phase spectrum. With time as the horizontal axis and scale or frequency as the vertical axis, the color depth represents the magnitude of wavelet coherence. The darker the color, the greater the wavelet coherence, indicating a stronger linear correlation between the two variables at that time and scale. Using color or arrows to represent phase differences reveals the leading or lagging relationship between the two variables. The direction of the arrow indicates whether one variable leads or lags the other, and the angle of the arrow indicates the magnitude of the phase difference.

[0027] Specifically, step S5 includes the following steps:

[0028] S51. Form a significant factor set by combining the influencing factors that are significantly correlated with dissolved oxygen, standardize the data of the significant factor set and construct a variable matrix;

[0029] S52. Calculate the covariance matrix of the variable matrix, calculate the eigenvalues ​​of the covariance matrix, and calculate the corresponding eigenvectors based on the eigenvalues.

[0030] S53. Several principal components are calculated based on the eigenvectors and variable matrices;

[0031] S54. Calculate the contribution rate of each principal component and the cumulative contribution rate, set a preset range for the cumulative contribution rate, select p principal components that make the cumulative contribution rate within the preset range, and obtain the key influencing factors that ultimately affect dissolved oxygen based on the p principal components.

[0032] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0033] This invention provides a method for identifying key dissolved oxygen (DO) factors based on nonlinear and time-varying characteristics. By combining the maximum information coefficient (MIC) method and cross-wavelet transform to analyze the correlation between DO and environmental influencing factors, the MIC method is used to calculate the minimum information coefficient (MIC) values ​​of DO and each influencing factor in the initial factor set. These MIC values ​​capture the nonlinear relationships between variables, overcoming the shortcomings of traditional linear analysis methods and revealing the complex nonlinear relationship between DO and environmental influencing factors, thus improving the accuracy of correlation analysis. The cross-wavelet transform analysis in the time-frequency domain captures the correlation between time series at different time periods and frequencies, identifying the dynamic relationship between DO and environmental factors over time, distinguishing between short-term disturbances and long-term trends. Principal component analysis quantifies the influence of each significantly correlated factor on DO, identifying key factors affecting DO based on their influence levels, effectively identifying key factors influencing DO concentration, and providing more granular analysis results. Attached Figure Description

[0034] To more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the drawings used in the description of the embodiments or the prior art will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on the structures shown in these drawings without creative effort.

[0035] Figure 1 This is a flowchart of the method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics in an embodiment of the present invention.

[0036] Figure 2 This is a graph showing the comparison of dissolved oxygen and water temperature data over time in an embodiment of the present invention.

[0037] Figure 3This is a schematic diagram showing the results of dissolved oxygen concentration and the maximum information coefficient (MIC) values ​​between various factors in an embodiment of the present invention.

[0038] Figure 4 This is the wavelet power spectrum of dissolved oxygen and water temperature in an embodiment of the present invention;

[0039] Figure 5 This is the wavelet phase spectrum of dissolved oxygen and water temperature in an embodiment of the present invention. Detailed Implementation

[0040] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Obviously, the described embodiments are only some embodiments of the present invention, not all embodiments, and the implementation of the present invention is not limited thereto. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Example 1:

[0042] like Figure 1 As shown, the method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics according to the present invention includes the following steps:

[0043] S1. Select multiple factors affecting dissolved oxygen in rivers to construct an initial factor set, and use the maximum information coefficient method to calculate the MIC value of dissolved oxygen and each factor in the initial factor set.

[0044] Specifically, the maximum information coefficient (MIC) method is a statistical method for measuring the correlation between variables. By dynamically dividing the grid, it calculates the maximum mutual information value of the variables at different resolutions. The maximum mutual information value is the MIC value, which is used to describe the nonlinear relationship between dissolved oxygen and different influencing factors. However, it is difficult to characterize the mutual relationship and localization characteristics between different signals in the time and frequency domains.

[0045] S11. Select multiple influencing factors of river dissolved oxygen from meteorological, hydrological, and water quality indicators to form an initial factor set. Use the initial factor set as the independent variable X and dissolved oxygen concentration as the dependent variable Y to construct a dataset D(X,Y). Let the initial factor set be... .

[0046] In this embodiment, meteorological, hydrological, and water quality data are used as independent variables. To comprehensively analyze the influencing factors of river dissolved oxygen, 20 influencing factors are selected from meteorological, hydrological, and water quality indicators to form an initial factor set. Meteorological indicators include precipitation, air temperature, water vapor pressure, sea level pressure, 2-minute average wind speed, 2-minute average wind direction, relative humidity, and horizontal visibility. Hydrological indicators include water temperature, conductivity, pH, water level, flow rate, flow velocity, and turbidity. Water quality indicators include total nitrogen, ammonia nitrogen, total phosphorus, permanganate index, and dissolved oxygen from 25 days prior. Let the initial factor set be... Let dissolved oxygen concentration be Y. Since the independent variable indicators are different, their dimensions and time intervals are also different. Therefore, it is necessary to preprocess the data related to the independent variable indicators, smooth the data, eliminate noise, fill missing values ​​in the data through interpolation, and standardize the data to eliminate the influence of dimensions. In this embodiment, a river basin in a certain province is selected as the experimental area. A dataset D(X,Y) is constructed based on the 2018-2020 data from five long-term meteorological stations and hydrological and water quality monitoring stations in the river basin of that province. Specifically, it includes meteorological data and hydrological and water quality data. The meteorological station data includes precipitation, air temperature, water vapor pressure, sea level pressure, 2-minute average wind speed, 2-minute average wind direction, relative humidity, and horizontal visibility; the hydrological data includes water temperature, conductivity, pH, water level, flow rate, flow velocity, and turbidity; the water quality data includes total nitrogen, ammonia nitrogen, total phosphorus, permanganate index, and dissolved oxygen 25 days prior.

[0047] like Figure 2 The figure shows a comparison of dissolved oxygen (DO) and water temperature data over time. It illustrates the relationship between DO concentration and water temperature changes over time, with the horizontal axis representing the time series, the primary vertical axis representing dissolved oxygen concentration (mg / L), and the secondary vertical axis representing water temperature. By comparing the changes in both, it is generally observed that an increase in water temperature leads to a decrease in dissolved oxygen.

[0048] In this embodiment, the independent variable X and dependent variable Y in the dataset D(X,Y) are standardized to eliminate the influence of variable dimensions and make them have the same scale. The calculation formula is as follows:

[0049] ;

[0050] in: These are the standardized values ​​of the independent variables, representing the standardized value of the j-th factor on day i. These are the original data values, representing the observation value of the j-th factor on day i. It is the mean of the j-th variable; It is the standard deviation of the j-th variable.

[0051] With water temperature, DO25 Taking 5 days of monitoring data as an example, dataset D is formed. After standardization, dataset D is used to obtain data matrix Z. Dataset D and matrix Z are as follows:

[0052] D ;

[0053] ;

[0054] S12. Grid the scatter plot of dataset D(X,Y) according to the X and Y axes, using x rows and y columns. x x y Given a grid G, calculate the mutual information of the dataset D(X,Y)D on the grid G ​​for different probability distributions and take the maximum mutual information to obtain the maximum mutual information value for different probability distributions.

[0055] The scatter plot of the finite dataset D(X,Y) is gridded along the X and Y axes with x rows and y columns to obtain xx. y The grid G, using The distribution (probability density) of dataset D on grid G ​​can be obtained from the proportion of points falling into grid G ​​in dataset D. Different grid partitioning methods will yield different results. Probability distribution, calculating different The mutual information of probability distributions is calculated using the following formula:

[0056] ;

[0057] In the formula: I(X,Y) is the mutual information of variables X and Y; P(x,y) is the joint density function of variables X and Y; P(x) and P(y) are the marginal density functions of X and Y, respectively. Mutual information represents a useful information metric in information theory, indicating the amount of information contained in one random variable about another. It can also be understood as the reduction of the uncertainty of one random variable due to the certainty of one random variable.

[0058] To obtain the maximum mutual information for different probability distributions, we take the maximum mutual information value:

[0059] ;

[0060] In the formula: To be based on xx y The maximum mutual information value of the grid G.

[0061] S13. Normalize the maximum mutual information values ​​on grids of different sizes G to obtain the MIC values ​​between each influencing factor and dissolved oxygen.

[0062] To facilitate comparison and analysis between data of different units or magnitudes, the maximum information value is normalized:

[0063] ;

[0064] In the formula: This is the maximum mutual information value after normalization.

[0065] Different xx y The value obtained by dividing the grid The maximum value is the maximum information coefficient (MIC) between variables X and Y. The MIC values ​​are all within (0, 1), where 1 indicates perfect correlation and 0 indicates independence.

[0066] The MIC values ​​between each influencing factor and dissolved oxygen are expressed as follows: , Represented as:

[0067] ;

[0068] In the formula: The upper limit of the number of grid cells is given, where n is the number of samples in the dataset. This is the maximum mutual information value after normalization.

[0069] like Figure 3 The diagram shows the maximum information coefficient (MIC) values ​​between dissolved oxygen concentration (DO) and various other environmental factors, displayed on 1-hour and 12-hour time scales. Each small circle represents the relationship between factors; the size and color intensity of the circle indicate the strength of the correlation—the darker the color and the larger the circle, the stronger the correlation. In the 1-hour graph, DO is compared with the dissolved oxygen concentration 25 days prior (DO...). 25 The MIC values ​​for electrical conductivity (EC) are 0.64 and 0.44, respectively, and the color is very dark, indicating that DO 25、 There is a strong correlation between EC and dissolved oxygen concentration. This result is also shown in the 12-hour graph.

[0070] S2. Set the target MIC value, filter several influencing factors whose MIC values ​​are greater than the target MIC value, and arrange the influencing factors in descending order of MIC value to form a second factor set.

[0071] Specifically, the maximum mutual information coefficient (MIC) between the factor and dissolved oxygen (DO) is between 0 and 1. A higher MIC indicates a stronger non-linear correlation between DO and the environmental factor. The target MIC value can be set to 0.3. Several influencing factors with MIC values ​​≥ 0.3 are selected and arranged in descending order to form a second factor set. ={X1, X2, ..., X m}, m≤n. In this example, ={water temperature, conductivity, pH value, vapor pressure, ammonia nitrogen, total nitrogen, DO 25}

[0072] S3. Calculate the cross-wavelet power spectrum, cross-wavelet phase spectrum, and cross-wavelet coherent condensation spectrum of dissolved oxygen and each influencing factor of the second factor set using cross-wavelet transform (XWT).

[0073] Cross wavelet transform is a time-frequency domain analysis tool that can overcome some of the limitations of conventional correlation analysis methods. It can analyze two time series in both the time and frequency domains from multiple time scales, study their interrelationships, and reveal the correlation between two related variables at different periods from a multi-time scale perspective. It can also reveal the synchronicity between factors and reflect their synchronicity in the time domain. Combining the two can provide a more comprehensive analysis of the correlation between dissolved oxygen and influencing factors.

[0074] S31. Calculate the cross wavelet power spectrum. Perform continuous wavelet transform on the time series of the influence factors and the time series of dissolved oxygen in the second factor set, respectively, to obtain the continuous wavelet transform results of the time series of influence factors and the time series of dissolved oxygen. Calculate the cross wavelet power spectrum based on the continuous wavelet transform results.

[0075] This embodiment uses water temperature as an example, collecting time series data X(t) for water temperature and Y(t) for dissolved oxygen. The two data series are equally spaced, continuous, and have the same time range. Continuous wavelet transforms are then performed on the time series X(t) (water temperature) and Y(t) (dissolved oxygen), respectively, yielding the continuous wavelet transform results. and The formula is:

[0076] ;

[0077] ;

[0078] In the formula: s is the scale parameter (the reciprocal of the frequency). For translation parameters (time). The selected wavelet basis function (Morlet wavelet is commonly chosen), * represents the complex conjugate.

[0079] Based on the results of continuous wavelet transform and The cross-wavelet power spectrum can be calculated as follows:

[0080] ;

[0081] In the formula, * denotes complex conjugation. Represents the cross wavelet power spectrum. This represents the power spectral density of the cross-wavelet transform. A larger power spectral density value indicates that the dissolved oxygen and water temperature time series have more similar energy values, and that the two series are more correlated in a specific time-frequency domain. The complex-valued part can show the local correlation phase of two time series in the time-frequency domain.

[0082] S32. Based on the continuous wavelet transform results of the influence factor time series and the dissolved oxygen time series, calculate the cross wavelet phase spectrum of the influence factor time series and the dissolved oxygen time series.

[0083] Cross-wavelet phase spectra can be used to reflect the lag time characteristics of two time series in different time domains. Based on the phase, the positive or negative correlation between the two series in the time-frequency domain can be analyzed. The phase angle is represented by arrows pointing in different directions, proving that the two time series have different time-lag correlations at different scales. The formula for calculating the phase angle between two time series is:

[0084] ;

[0085] The phase angle is used to reflect the synchronicity of dissolved oxygen and water temperature. A phase angle of 0° indicates that they are in phase (positive correlation). A phase angle of ±180° indicates that they are out of phase (negative correlation). A phase angle of ±90° indicates that they are leading or lagging.

[0086] S33. Based on the continuous wavelet transform results and the cross wavelet power spectrum, calculate the cross wavelet coherence coefficients of the influence factor time series and the dissolved oxygen time series.

[0087] The correlation between two wavelet transforms in the time-frequency domain indicates how the signal changes over time; even in the low-energy region of the cross-wavelet power spectrum, it may be significant in the wavelet coherence condensation spectrum. The wavelet coherence coefficients of the dissolved oxygen and water temperature time series are shown. The calculation formula is:

[0088] ;

[0089] in, and The wavelet transform result in S31 For the cross wavelet power spectrum, For smoothing operators, The closer the coherence value is to 1, the stronger the correlation.

[0090] Specifically, the correlation between the cross-wavelet spectrum and the phase spectrum can be tested to determine whether it is significant. In this embodiment, the Monte Carlo method is used to test whether the correlation between the time series X(t) (water temperature) and Y(t) (dissolved oxygen) is significant, based on the wavelet coherence coefficients of the two time series, dissolved oxygen and water temperature. The calculation results are recorded, and the maximum coherence values ​​are compared with the wavelet coherence values ​​of the original time series. If the wavelet coherence values ​​of the original time series are greater than 95% or 99% of the maximum coherence values ​​in the Monte Carlo simulation, the coherence is considered significant.

[0091] S4. Based on the calculated cross wavelet power spectrum, cross wavelet phase spectrum, and cross wavelet coherence coefficient, plot the cross wavelet power spectrum and phase spectrum. Based on the wavelet power spectrum and phase spectrum, determine the influencing factors that are significantly correlated with dissolved oxygen at different scales and frequencies.

[0092] Cross-wavelet transform not only satisfies the correlation analysis of dissolved oxygen with various influencing factors, but also can represent the regions of common change between two sequences (including low-energy spectral bands). Cross-wavelet transform is performed on dissolved oxygen time-series data with water temperature, conductivity, pH, vapor pressure, ammonia nitrogen, total nitrogen, and dissolved oxygen from 25 days prior at the same time. This example uses dissolved oxygen and water temperature as an example to analyze the resonance period, significant time periods, and phase relationship between dissolved oxygen levels and water temperature in the time-frequency domain of this river. Figure 4-5 As shown.

[0093] S41. Based on the calculated cross-wavelet power spectrum, plot the cross-wavelet power spectrum diagram. Analyze the interaction strength between dissolved oxygen and each influencing factor at different time and frequency scales based on the cross-wavelet power spectrum diagram, and obtain the analysis results of the cross-wavelet power spectrum diagram.

[0094] Specifically, the cross wavelet power spectrum is plotted as a two-dimensional image to obtain the cross wavelet power spectrum diagram. Time is the horizontal axis and scale or frequency is the vertical axis. The color intensity represents the magnitude of the cross wavelet power; the darker the color, the greater the cross wavelet power, indicating a stronger correlation between the two variables at that time and scale.

[0095] like Figure 4The figure shows the cross-wavelet power spectrum of dissolved oxygen and water temperature, revealing the strength of their interaction at different time-frequency scales. The horizontal axis represents time, indicating the temporal variation of the analyzed signal, while the vertical axis represents scale, indicating the periodicity of the signal (higher scales correspond to lower frequencies, and lower scales correspond to higher frequencies). The color bars in the figure represent the magnitude of the cross-wavelet power; the darker the color, the stronger the interaction between the signals. The thin solid line in the figure represents the boundary of the wavelet influence cone (COD), within which is the effective spectral value region. The color represents the correlation; the darker the color, the stronger the correlation. The area enclosed by the thick solid line is the region where the energy density passes the 95% confidence level red noise test, i.e., the region with strong correlation. The short- and long-term variations in dissolved oxygen and water temperature are unevenly distributed and exhibit local characteristics. Within the main cycle of approximately 180 days (half a year), a banded area of ​​significant high energy appears and passes the significance test. The correlation between dissolved oxygen and water temperature is stable and shows a negative correlation, with dissolved oxygen exhibiting obvious seasonal variations. In the secondary cycle of approximately 16-32 days (May 2019 - September 2019), the correlation between dissolved oxygen and water temperature is unstable.

[0096] S42. Based on the calculated cross-wavelet phase spectrum and cross-wavelet coherence coefficient, plot the cross-wavelet phase spectrum. Analyze the time-frequency correlation between dissolved oxygen and each influencing factor based on the wavelet coherence coefficient values ​​shown in the cross-wavelet phase spectrum. Analyze the positive and negative correlation between dissolved oxygen and each influencing factor in the time-frequency domain based on the phase relationship shown in the cross-wavelet phase spectrum to obtain the analysis results of the cross-wavelet phase spectrum.

[0097] Specifically, based on the calculated cross-wavelet phase spectrum and cross-wavelet coherence coefficients, wavelet coherence is plotted as a two-dimensional image to obtain the cross-wavelet phase spectrum. Time is plotted on the horizontal axis, and scale or frequency on the vertical axis. The intensity of the color represents the magnitude of wavelet coherence; the darker the color, the greater the wavelet coherence, indicating a stronger linear correlation between the two variables at that time and scale. Phase differences are represented by colors or arrows, revealing the lead or lag relationship between the two variables. The direction of the arrow indicates whether one variable leads or lags the other, and the angle of the arrow indicates the magnitude of the phase difference. The specific method for interpreting the phase difference is as follows:

[0098] When the phase difference is close to 0, the two variables change essentially synchronously at that time and scale.

[0099] A phase difference close to +π / 2: the first variable leads the second variable by a quarter of a period on that time scale.

[0100] The phase difference is close to -π / 2: the first variable lags the second variable by a quarter of a period in this time and scale.

[0101] When the phase difference is close to +π or -π, the two variables are inversely correlated at that time scale (one increases while the other decreases).

[0102] like Figure 5 As shown, the cross-wavelet phase spectrum of dissolved oxygen and water temperature reveals their time-frequency correlation. The color bars represent the wavelet coherence coefficient values, ranging from 0 to 1. A wavelet coherence coefficient value close to 1 indicates a high correlation between dissolved oxygen and water temperature at that scale and time point; darker colors indicate a stronger correlation. The thin solid line in the figure represents the boundary of the wavelet influence cone (COD), with the area inside representing the effective spectral value region. Color indicates correlation, with darker colors indicating a stronger correlation. The area enclosed by the thick solid line represents the region where energy density passes the 95% confidence level red noise test, indicating a strong correlation. The short-period and long-period variations of dissolved oxygen and water temperature are unevenly distributed, exhibiting local characteristics, with a significant correlation existing within a period of approximately 16-32 days.

[0103] The positive and negative correlations between dissolved oxygen and various influencing factors in the time-frequency domain were analyzed based on the phase relationships shown in the cross-wavelet phase spectrum. For example... Figure 5 As shown in the figure, the arrows reflect the phase relationship between dissolved oxygen and water temperature. The arrows from left to right (→) indicate that the changes are in phase, showing a positive correlation; the arrows from right to left (←) indicate out-of-phase, showing a negative correlation; the arrows pointing vertically downwards (↓) and vertically upwards (↑) indicate that the wavelet transform of water temperature is ahead and behind by 1 / 4 of a cycle, respectively, showing a non-linear relationship. The fluctuations in dissolved oxygen and water temperature show a significant negative correlation with opposite directions within a period of approximately 16-32 days. The correlation between dissolved oxygen and water temperature is unstable, sometimes leading water temperature changes by approximately 90° to 180°. Dissolved oxygen changes occur 1 / 4 to 1 / 2 of the cycle (4 to 8 days) before water temperature changes, and this region is concentrated in summer and winter.

[0104] S43. Based on the analysis results of the cross-wavelet power spectrum and the cross-wavelet phase spectrum, analyze the correlation and changes between dissolved oxygen and influencing factors at different scales and frequencies. The high-frequency scale reflects the short-term changes in the correlation, and the low-frequency scale reflects the long-term changes in the correlation, thus obtaining the influencing factors that have significant correlations at different scales and frequencies.

[0105] The correlation between dissolved oxygen and influencing factors at different scales and frequencies was analyzed using cross-wavelet power spectrum analysis and cross-wavelet phase spectrum analysis results. High-frequency scales reflect short-term changes (e.g., intraday, hourly variations), while low-frequency scales reflect long-term changes (e.g., seasonal variations). Factors showing significant correlations at key time scales were identified, as shown in Table 1. The significantly correlated influencing factors of dissolved oxygen fluctuations at the annual, monthly, and daily time scales are not entirely the same. At the annual scale, dissolved oxygen concentration fluctuates with a 200-day cycle and is negatively correlated with total nitrogen. At the monthly scale, dissolved oxygen concentration fluctuates with a 20-day cycle and is negatively correlated with water temperature and vapor pressure, but not with pH and DO. 25 There is a positive correlation; on a daily scale, dissolved oxygen concentration fluctuates in a 7-day cycle and is negatively correlated with ammonia nitrogen and conductivity.

[0106] Table 1. Analysis results of factors showing significant correlation at key time scales.

[0107]

[0108] S5. Quantify the influence of each factor that is significantly correlated with dissolved oxygen on dissolved oxygen using principal component analysis (PCA), identify the key factors affecting dissolved oxygen based on the degree of influence, and output the key factors affecting dissolved oxygen.

[0109] S51. Form a significant factor set by combining the influencing factors that are significantly correlated with dissolved oxygen, standardize the data of the significant factor set and construct a variable matrix; the variable matrix contains a dataset of j influencing factors, and each influencing factor contains i monitoring values.

[0110] A significant factor set is composed of influencing factors that exhibit significant correlations at different scales and frequencies. ={water temperature, conductivity, pH value, vapor pressure, ammonia nitrogen, total nitrogen, DO 25}, for factor set The data is standardized, and a variable matrix is ​​constructed from the standardized data. For a dataset containing j influencing factors, each influencing factor contains i monitoring values. In this embodiment, the size of the variable matrix is ​​7×1095, and the variable matrix Z is as follows.

[0111] ;

[0112] In the formula, This represents the standardized value of the j-th influence factor on day i.

[0113] S52. Calculate the covariance matrix of the variable matrix, calculate the eigenvalues ​​of the covariance matrix, and calculate the corresponding eigenvectors based on the eigenvalues.

[0114] The covariance matrix is ​​used to describe the linear correlation between variables. The diagonal elements represent the variance of each variable, while the off-diagonal elements represent the covariance between two variables. The size of the covariance matrix is ​​i×j, and each element represents the covariance between two features. The formula for calculating the covariance matrix is ​​as follows:

[0115] Z;

[0116] In the formula, Represents the covariance matrix. This is the transpose of the variable matrix Z.

[0117] With water temperature, DO 25 Taking 5 days of monitoring data for 2 variables as an example, calculate Z:

[0118] ;

[0119] ;

[0120] The covariance matrix is:

[0121] ;

[0122] Calculate the eigenvalues ​​of the covariance matrix, and then calculate the corresponding eigenvectors based on the eigenvalues.

[0123] The eigenvectors represent the directions of the "principal components," and the eigenvalues ​​represent the variance projected along those directions. The formula for calculating the eigenvalues ​​is as follows:

[0124] ;

[0125] In the formula, These are the eigenvalues ​​(each corresponding to the variance of a principal component). This is the determinant (used to solve the characteristic equation). It is an identity matrix (with the same dimensions as C).

[0126] The formula for calculating the eigenvector is as follows:

[0127] ;

[0128] In the formula, For eigenvalues, For determinant, It is the identity matrix. The eigenvectors (direction vectors, used for linear combination variables) corresponding to the eigenvalues.

[0129] For matrices:

[0130] ;

[0131] Substitute:

[0132] ;

[0133] We obtain two eigenvalues: , .

[0134] S53. Several principal components are calculated based on the eigenvectors and variable matrices. The formula for calculating the principal components is as follows:

[0135] ;

[0136] In the formula, This is the k-th principal component (the result of a linear combination). Let Z be the k-th eigenvector, and Z be the variable matrix. For example, substituting the principal eigenvalues... Solving the linear equation yields:

[0137] ;

[0138] The first principal component is: PC1 = *Water temperature +0.720*DO 25 The result of a linear combination.

[0139] S54. Calculate the contribution rate and cumulative contribution rate of each principal component, set a preset range for the cumulative contribution rate, select p principal components that make the cumulative contribution rate within the preset range, and obtain the key influencing factors that ultimately affect dissolved oxygen based on the p principal components.

[0140] Calculate the contribution rate of each principal component. The formula for calculating the contribution rate is as follows:

[0141] ;

[0142] In the formula, k is the contribution rate, which indicates how much variance (information) of the original data is explained by the k-th principal component. Let be the eigenvalue (i.e., variance) of the k-th principal component, and n be the total number of variables.

[0143] Cumulative contribution rate equation:

[0144] ;

[0145] In the formula, t represents the cumulative contribution rate, which can be preset to a range of 85% to 95%. The final set of key influencing factors is obtained by taking the p principal components corresponding to the p eigenvalues ​​with a cumulative contribution rate of 85% to 95%. ={X1, X2, ..., X P}

[0146] In this embodiment, combining the results of nonlinear correlation coefficient and time-varying characteristic analysis, principal component analysis (PCA) is used to quantify the influence of various parameters on dissolved oxygen content, thereby identifying key factors of dissolved oxygen and outputting these key factors. = {Total nitrogen, ammonia nitrogen, water temperature}, the PCA calculation results of the key influencing factors of dissolved oxygen concentration are shown in Table 2.

[0147] Table 2. Key influencing factors of dissolved oxygen concentration (PCA calculation results)

[0148]

[0149] In summary, this invention combines the maximum information coefficient (MIC) method and cross-wavelet transform to analyze the correlation between dissolved oxygen (DO) and environmental influencing factors. The MIC method captures the nonlinear relationships between variables, overcoming the shortcomings of traditional linear analysis methods, revealing the complex nonlinear relationship between DO and environmental influencing factors, and improving the accuracy of correlation analysis. The cross-wavelet transform (XWT) analysis in the time-frequency domain captures the correlation between time series at different time periods and frequencies, identifying the dynamic relationship between DO and environmental factors over time, distinguishing between short-term disturbances and long-term trends. Principal component analysis quantifies the influence of each significantly correlated factor on DO, identifying key factors affecting DO based on their influence levels, accurately identifying the key factors influencing DO concentration, and providing more granular analysis results.

[0150] The above embodiments are preferred embodiments of the present invention, but the embodiments of the present invention are not limited to the above embodiments. Any changes, modifications, substitutions, combinations, or simplifications made without departing from the spirit and principle of the present invention shall be considered equivalent substitutions and shall be included within the protection scope of the present invention.

Claims

1. A method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics, characterized in that, Includes the following steps: S1. Select multiple factors affecting dissolved oxygen in rivers to construct an initial factor set, and use the maximum information coefficient method to calculate the MIC value of dissolved oxygen and each factor affecting the initial factor set. S2. Set the target value of MIC, filter several factors whose MIC value is greater than the target value of MIC, and arrange the several influencing factors in descending order of MIC value to form a second factor set. S3. Calculate the cross-wavelet power spectrum, cross-wavelet phase spectrum, and cross-wavelet coherent condensation spectrum of dissolved oxygen and each influencing factor of the second factor set using cross-wavelet transform. Step S3 includes the following steps: S31. Perform continuous wavelet transform on the time series of the influence factors and the time series of dissolved oxygen in the second factor set respectively to obtain the continuous wavelet transform results of the time series of influence factors and the time series of dissolved oxygen. Calculate the cross wavelet power spectrum based on the continuous wavelet transform results. S32. Based on the continuous wavelet transform results of the influence factor time series and the dissolved oxygen time series, calculate the cross wavelet phase spectrum of the influence factor time series and the dissolved oxygen time series. S33. Based on the continuous wavelet transform results and the cross wavelet power spectrum, calculate the cross wavelet coherence coefficients of the influence factor time series and the dissolved oxygen time series. S4. Based on the calculated cross wavelet power spectrum, cross wavelet phase spectrum and cross wavelet coherence coefficient, draw the cross wavelet power spectrum and phase spectrum. Based on the wavelet power spectrum and phase spectrum, determine the influencing factors that are significantly correlated with dissolved oxygen at different scales and frequencies. S5. Quantify the influence of each factor that is significantly correlated with dissolved oxygen on dissolved oxygen using principal component analysis. Identify the key factors affecting dissolved oxygen based on the degree of influence and output the key factors affecting dissolved oxygen.

2. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 1, characterized in that, Step S1 includes the following steps: S11. Select multiple factors affecting dissolved oxygen in rivers from meteorological, hydrological and water quality indicators to form an initial factor set. Use the initial factor set as the independent variable X and dissolved oxygen concentration as the dependent variable Y to construct dataset D. S12. Grid the scatter plot of dataset D according to the X-axis and Y-axis to obtain grid G. Calculate the mutual information of dataset D on grid G ​​with different probability distributions and take the maximum mutual information to obtain the maximum mutual information value of different probability distributions. S13. Normalize the maximum mutual information values ​​of different probability distributions to obtain the MIC values ​​between each influencing factor and dissolved oxygen.

3. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 2, characterized in that, The formula for calculating the mutual information is: ； In the formula, I(X,Y) represents the mutual information of variables X and Y; p( x , y ) is a variable x , y Joint density function; p( x ), p( y ) are variables x , y Edge density function; The MIC values ​​between each influencing factor and dissolved oxygen are expressed as follows: , Represented as: ； In the formula, The upper limit of the number of grid cells is given, where n is the number of samples in the dataset. This is the maximum mutual information value after normalization.

4. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 2, characterized in that, Step S2 includes the following steps: Set the target MIC value to 0.3, select several influencing factors with MIC values ​​≥ 0.3, arrange the influencing factors in descending order of MIC value, and form a second factor set.

5. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 1, characterized in that, Step S4 includes the following steps: S41. Draw a cross-wavelet power spectrum based on the calculated cross-wavelet power spectrum, and analyze the interaction strength between dissolved oxygen and each influencing factor at different time and frequency scales based on the cross-wavelet power spectrum to obtain the analysis results of the cross-wavelet power spectrum. S42. Based on the calculated cross-wavelet phase spectrum and cross-wavelet coherence coefficient, plot the cross-wavelet phase spectrum. Analyze the time-frequency correlation between dissolved oxygen and each influencing factor based on the wavelet coherence coefficient values ​​shown in the cross-wavelet phase spectrum. Analyze the positive and negative correlation between dissolved oxygen and each influencing factor in the time-frequency domain based on the phase relationship shown in the cross-wavelet phase spectrum to obtain the analysis results of the cross-wavelet phase spectrum. S43. Based on the analysis results of the cross-wavelet power spectrum and the cross-wavelet phase spectrum, analyze the correlation and changes between dissolved oxygen and influencing factors at different scales and frequencies. High-frequency scale reflects the short-term changes in correlation, and low-frequency scale reflects the long-term changes in correlation, thus obtaining the influencing factors that are significantly correlated with dissolved oxygen at different scales and frequencies.

6. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 5, characterized in that, Step S41 includes the following steps: plotting the cross wavelet power spectrum in the form of a two-dimensional image to obtain a cross wavelet power spectrum diagram, with time as the horizontal axis and scale or frequency as the vertical axis, and the color intensity representing the magnitude of the cross wavelet power; the darker the color, the greater the cross wavelet power, indicating a stronger correlation between the two variables at that time and scale.

7. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 5, characterized in that, Step S42 includes the following steps: plotting the wavelet coherence in the form of a two-dimensional image based on the calculated cross-wavelet phase spectrum and cross-wavelet coherence coefficients to obtain a cross-wavelet phase spectrum. With time as the horizontal axis and scale or frequency as the vertical axis, the color depth represents the magnitude of wavelet coherence. The darker the color, the greater the wavelet coherence, indicating a stronger linear correlation between the two variables at that time and scale. Arrows are used to represent phase differences, revealing the leading or lagging relationship between the two variables. The direction of the arrow indicates whether one variable leads or lags the other, and the angle of the arrow indicates the magnitude of the phase difference.

8. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 1, characterized in that, Step S5 includes the following steps: S51. Form a significant factor set by combining the influencing factors that are significantly correlated with dissolved oxygen, standardize the data of the significant factor set and construct a variable matrix; S52. Calculate the covariance matrix of the variable matrix, calculate the eigenvalues ​​of the covariance matrix, and calculate the corresponding eigenvectors based on the eigenvalues. S53. Several principal components are calculated based on the eigenvectors and variable matrices; S54. Calculate the contribution rate of each principal component and the cumulative contribution rate, set a preset range for the cumulative contribution rate, select p principal components that make the cumulative contribution rate within the preset range, and obtain the key influencing factors that ultimately affect dissolved oxygen based on the p principal components.

9. The method for identifying key factors of dissolved oxygen in rivers based on nonlinear and time-varying characteristics as described in claim 8, characterized in that, The preset range for the cumulative contribution rate is 85% to 95%.

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