Aerosol concentration inversion method and system under transient condition

Abstract

The invention provides an aerosol concentration inversion method and system under a transient working condition, and the method comprises the steps: 1, carrying out the time processing and time sequence feature construction of a transient aerosol concentration data sequence obtained by a monitoring point, and obtaining a time covariance matrix; 2, based on the time covariance matrix and the space information of the monitoring points and the target inversion points, initial inversion is carried out through a space-time Kriging model, and an initial inversion concentration value is obtained; 3, constructing and solving a nonlinear correction coefficient based on the preliminary inversion concentration value and the corresponding actual observation concentration value, and performing secondary correction on the preliminary inversion concentration value to obtain a weighted space-time Kriging inversion concentration value; and 4, carrying out local peak value matching on the weighted space-time Kriging inversion concentration value and an actual observation concentration value, and amplifying and correcting the inversion concentration value in a successfully matched peak value region to obtain a final aerosol concentration inversion result. According to the method, the precision and stability of pollutant concentration field reconstruction under the transient working condition are improved.

Description

Technical Field

[0001] This invention relates to the field of aerosol concentration inversion technology, and more specifically, to a method and system for inverting aerosol concentration under transient operating conditions. Background Technology

[0002] Accurately and quantitatively describing the diffusion behavior of environmental aerosols has significant scientific value and practical implications. This invention addresses the difficulty in accurately measuring pollutant concentration fields in high Reynolds number fluids under transient flow conditions. Based on interpolation-based inversion methods, which are currently the mainstream approach in pollutant concentration retrieval research, a pollutant concentration inversion model is constructed, enabling quantitative reconstruction of the pollutant concentration field under limited monitoring data.

[0003] Patent application CN109657363A discloses a spatiotemporally continuous PM2.5 inversion method. This patent uses ordinary kriging interpolation and inverse variance weighted fusion to study the spatiotemporal inversion of PM2.5 concentration from ground stations and satellite data, achieving the goal of generating a continuous and spatiotemporally consistent PM2.5 concentration field under limited monitoring data conditions. However, the spatiotemporal covariance parameter of this patent depends on historical monitoring data and statistical characteristics. Under conditions of transient release, limited sample size, and short time series, the fitting stability of the covariance parameter is insufficient.

[0004] Patent application CN105512464A discloses a method for retrieving spatiotemporally continuous PM2.5 concentrations by combining satellite and site observations. This patent uses satellite remote sensing data combined with ground-based spatial interpolation methods (Kriging / IDW) to conduct a fusion inversion study of PM2.5 concentrations, achieving the collaborative generation of a spatiotemporally continuous pollutant concentration field from multi-source data. However, when using IDW interpolation, this patent only assigns weights based on spatial distance, failing to incorporate the temporal dimension and the characteristics of rapid concentration changes, making it difficult to reflect the transient concentration evolution process; the interpolation parameters (distance decay index, neighbor selection, etc.) rely on empirical settings, are highly sensitive to the location and density of monitoring points, and lack adaptability under transient conditions.

[0005] Patent application CN112986990A discloses an atmospheric phase correction method and system. This patent uses the Kriging interpolation method to study the spatiotemporal field estimation of atmospheric phase data, achieving improved accuracy of atmospheric phase reconstruction under turbulent and complex meteorological conditions. However, under conditions of limited monitoring samples and short time series, the covariance parameter fitting error is easily amplified, affecting the stability of weight calculation; the pan-Kriging model still relies on global or semi-global covariance structures, making it difficult to accurately calculate transient and high-gradient concentrations. Summary of the Invention

[0006] To address the shortcomings of existing technologies, the purpose of this invention is to provide a method and system for inverting aerosol concentration under transient operating conditions.

[0007] The aerosol concentration inversion method under transient operating conditions provided by the present invention includes:

[0008] Step 1: Perform time processing and time series feature construction on the transient aerosol concentration data sequence obtained from the monitoring points to obtain the time covariance matrix; Step 2: Based on the time covariance matrix and the spatial information of the monitoring points and target inversion points, perform initial inversion using a spatiotemporal kriging model to obtain preliminary inversion concentration values; Step 3: Based on the preliminary inverted concentration value and the corresponding actual observed concentration value, construct and solve the nonlinear correction coefficient, and perform a second correction on the preliminary inverted concentration value to obtain the weighted spatiotemporal kriging inverted concentration value; Step 4: Perform local peak matching between the weighted spatiotemporal kriging inversion concentration value and the actual observed concentration value, and amplify and correct the inversion concentration value in the successfully matched peak region to obtain the final aerosol concentration inversion result.

[0009] Preferably, step 1 includes: Step 1.1: Perform time standardization on the transient aerosol concentration data series acquired from the monitoring points. The expression is:

[0010] In the formula, It is a time average; Original time point Time standard deviation; Indicates the first Standardized time points corresponding to each observation data point; Indicates the first The original time points corresponding to each observation data point; Step 1.2: Establish the time covariance function based on the exponential covariance model, with the following expression:

[0011] In the formula, The variance of the observed concentration series; For time-related scales; Indicates the time interval as The time covariance function value represents the correlation decay characteristics of concentration over time; This represents the time interval between any two observation times; Represents the natural exponential function; Step 1.3: Construct the time covariance matrix based on the time covariance function. Its elements are:

[0012] In the formula, Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Standardized time corresponding to each observation point; Step 1.4: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] To enhance numerical stability, a Nugget term is added, expressed as:

[0013] In the formula, This is used to enhance the numerical stability of the covariance matrix; Represents the covariance matrix Identity matrices of the same dimension.

[0014] Preferably, step 2 includes: Step 2.1: For the covariance matrix Perform Cholesky decomposition, the expression is:

[0015]

[0016] In the formula, Represents the covariance matrix The Cholesky lower triangular decomposition matrix; Represents the matrix transpose symbol; Step 2.2: Calculate the analytical solution for leave-one-out prediction. The expression is:

[0017] In the formula, Indicates time The actual observed concentration value at the location; Indicates the first The weighted related terms corresponding to each observation point; Represents the covariance matrix The Middle One diagonal element; Step 2.3: Calculate the prediction variance The expression is:

[0018] Step 2.4: Calculate the coordinates of the monitoring point. Coordinates of the target point are The Euclidean distance between them is expressed as:

[0019] Step 2.5: Calculate spatial weights using an exponential decay model. The expression is:

[0020] In the formula, Indicates spatially relevant scales; Step 2.6: Calculate the preliminary inversion concentration value using spatial weights, expressed as:

[0021] In the formula, Original time point The initial inversion concentration value, Original time point The analytical solution for leave-one prediction.

[0022] Preferably, step 3 includes: Step 3.1: Construct the feature matrix F, whose row vectors are derived from the feature vectors of the i-th observation point. Composition, the expression is:

[0023]

[0024]

[0025]

[0026] In the formula, Indicates zero-factor protection. For normalized residual characteristics, To predict variance, Spatial correlation intensity; Step 3.2: Construct a target quantity that reflects the degree of deviation between observed values ​​and spatiotemporal Kriging predictions. The expression is:

[0027] Step 3.3: Transform the objective into a ridge regression problem and solve for the regression weight vector of the nonlinear modified model. The expression is:

[0028] In the formula, This represents the ridge regression regularization parameter, used to suppress model overfitting and enhance numerical stability; Indicates by The vector formed; Step 3.4: Calculate the nonlinearity correction coefficients The expression is:

[0029] Step 3.5: Calculate the weighted spatiotemporal kriging inversion concentration value, expressed as:

[0030] In the formula, Original time point The weighted spatiotemporal Kriging inversion concentration value.

[0031] Preferably, step 4 includes: Step 4.1: Perform peak time-series labeling on the monitoring sequence and the initial WSTK sequence respectively;

[0032]

[0033] In the formula, Indicates the concentration peak in the observed concentration sequence; This represents the concentration peak in the WSTK inverted concentration sequence; Indicates the peak extraction operator; This represents the peak value of the observed concentration at the peak point; This indicates the peak value of the WSTK inversion concentration at the matched peak. Step 4.2: For each observed peak, find the nearest WSTK and calculate the concentration peak q;

[0034] In the formula, Indicates the time at which a concentration peak is observed; for The index; Step 4.3: Calculate the peak magnification factor by comparing the peak values ​​of the observed peak and the concentration peak. The expression is:

[0035] in, for The actual observed concentration value at that time; This represents the weighted spatiotemporal kriging inversion concentration value at the concentration peak q. Step 4.4: Calculate the peak width magnification factor by comparing the peak widths of the observed peak and the concentration peak;

[0036] In the formula, This represents the final corrected concentration inversion result; This indicates the half-width of the peak correction time window; Step 4.5: Finally, calculate the inverted concentration sequence;

[0037] In the formula, This represents the WSTK inversion concentration curve after peak correction.

[0038] The aerosol concentration inversion system under transient operating conditions provided by the present invention includes: Module M1: Performs time processing and time series feature construction on the transient aerosol concentration data sequence acquired from the monitoring points to obtain the time covariance matrix; Module M2: Based on the time covariance matrix and the spatial information of the monitoring points and target inversion points, an initial inversion is performed using a spatiotemporal kriging model to obtain preliminary inversion concentration values; Module M3: Based on the preliminary inverted concentration value and the corresponding actual observed concentration value, construct and solve the nonlinear correction coefficient, perform secondary correction on the preliminary inverted concentration value, and obtain the weighted spatiotemporal kriging inverted concentration value; Module M4: Performs local peak matching between the weighted spatiotemporal kriging inversion concentration values ​​and the actual observed concentration values, and amplifies and corrects the inversion concentration values ​​in the successfully matched peak regions to obtain the final aerosol concentration inversion result.

[0039] Preferably, the module M1 includes: Module M1.1: Performs time normalization on the transient aerosol concentration data sequence acquired from monitoring points, with the following expression:

[0040] In the formula, It is a time average; Original time point Time standard deviation; Indicates the first Standardized time points corresponding to each observation data point; Indicates the first The original time points corresponding to each observation data point; Module M1.2: Establishes the time covariance function based on the exponential covariance model, with the following expression:

[0041] In the formula, The variance of the observed concentration series; For time-related scales; Indicates the time interval as The time covariance function value represents the correlation decay characteristics of concentration over time; This represents the time interval between any two observation times; Represents the natural exponential function; Module M1.3: Constructing the time covariance matrix based on the aforementioned time covariance function. Its elements are:

[0042] In the formula, Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Standardized time corresponding to each observation point; Module M1.4: [This refers to the time covariance matrix] To enhance numerical stability, a Nugget term is added, expressed as:

[0043] In the formula, This is used to enhance the numerical stability of the covariance matrix; Represents the covariance matrix Identity matrices of the same dimension.

[0044] Preferably, the module M2 includes: Module M2.1: For the covariance matrix Perform Cholesky decomposition, the expression is:

[0045]

[0046] In the formula, Represents the covariance matrix The Cholesky lower triangular decomposition matrix; Represents the matrix transpose symbol; Module M2.2: Calculate the analytical solution for leave-one-out prediction The expression is:

[0047] In the formula, Indicates time The actual observed concentration value at the location; Indicates the first The weighted related terms corresponding to each observation point; Represents the covariance matrix The Middle One diagonal element; Module M2.3: Calculate Prediction Variance The expression is:

[0048] Module M2.4: Calculates the coordinates of the monitoring point. Coordinates of the target point are The Euclidean distance between them is expressed as:

[0049] Module M2.5: Calculates spatial weights using an exponential decay model. The expression is:

[0050] In the formula, Indicates spatially relevant scales; Module M2.6: Calculates preliminary inversion concentration values ​​using spatial weights, expressed as:

[0051] In the formula, Original time point The initial inversion concentration value, Original time point The analytical solution for leave-one prediction.

[0052] Preferably, the module M3 includes: Module M3.1: Constructs the feature matrix F, whose row vectors are derived from the feature vectors of the i-th observation point. Composition, the expression is:

[0053]

[0054]

[0055]

[0056] In the formula, Indicates zero-factor protection. For normalized residual characteristics, To predict variance, Spatial correlation intensity; Module M3.2: Constructing a target quantity that reflects the degree of deviation between observed values ​​and spatiotemporal Kriging predictions. The expression is:

[0057] Module M3.3: Transforms the objective into a ridge regression problem, solving for the regression weight vector of the nonlinear modified model. The expression is:

[0058] In the formula, This represents the ridge regression regularization parameter, used to suppress model overfitting and enhance numerical stability; Indicates by The vector formed; Module M3.4: Calculate nonlinear correction coefficients The expression is:

[0059] Module M3.5: Calculates the weighted spatiotemporal kriging inversion concentration value, expressed as:

[0060] In the formula, Original time point The weighted spatiotemporal Kriging inversion concentration value.

[0061] Preferably, the module M4 includes: Module M4.1: Performs peak time-series labeling on the monitored sequence and the initial WSTK sequence respectively;

[0062]

[0063] In the formula, Indicates the concentration peak in the observed concentration sequence; This represents the concentration peak in the WSTK inverted concentration sequence; Indicates the peak extraction operator; This represents the peak value of the observed concentration at the peak point; This indicates the peak value of the WSTK inversion concentration at the matched peak. Module M4.2: For each observed peak, find the nearest WSTK and calculate the concentration peak q;

[0064] In the formula, Indicates the time at which a concentration peak is observed; for The index; Module M4.3: Calculates the peak magnification factor by comparing the peak values ​​of the observed peak and the concentration peak. The expression is:

[0065] in, for The actual observed concentration value at that time; This represents the weighted spatiotemporal kriging inversion concentration value at the concentration peak q. Module M4.4: Calculates the peak width magnification factor by comparing the peak widths of the observed peak and the concentration peak;

[0066] In the formula, This represents the final corrected concentration inversion result; This indicates the half-width of the peak correction time window; Module M4.5: Finally, the inverted concentration sequence is calculated;

[0067] In the formula, This represents the WSTK inversion concentration curve after peak correction.

[0068] Compared with the prior art, the present invention has the following beneficial effects: This invention proposes a concentration inversion method that integrates a weighted spatiotemporal kriging model with a local peak matching amplification mechanism. Addressing the challenge of accurately measuring pollutant concentration fields in high Reynolds number fluids under transient flow conditions, this invention constructs a pollutant concentration inversion model based on interpolation-based inversion methods currently prevalent in pollutant concentration inversion research. This model achieves quantitative reconstruction of the pollutant concentration field under limited monitoring data, thereby improving the accuracy and stability of pollutant concentration field reconstruction under transient conditions. Attached Figure Description

[0069] Other features, objects, and advantages of the present invention will become more apparent from the following detailed description of non-limiting embodiments with reference to the accompanying drawings: Figure 1 Here is a flowchart of the concentration inversion calculation; Figure 2a for Inversion concentration correction comparison, Figure 2b for Inversion concentration correction comparison at random point 2. Figure 2c for Inversion concentration correction comparison, Figure 2d For the inversion concentration correction comparison at random point 1, Figure 2e For the concentration correction and comparison at random monitoring point 2; Figure 3a To compare different concentration inversion methods at monitoring point 1, Figure 3b To compare different concentration inversion methods at monitoring point 2, Figure 3c A comparison of different concentration inversion methods for monitoring point 3. Detailed Implementation

[0070] The present invention will now be described in detail with reference to specific embodiments. These embodiments will help those skilled in the art to further understand the present invention, but do not limit the invention in any way. It should be noted that those skilled in the art can make several changes and improvements without departing from the concept of the present invention. These all fall within the scope of protection of the present invention.

[0071] Example This invention addresses the problem of the difficulty in accurately measuring the pollutant concentration field in high Reynolds number fluids under transient flow conditions. Based on the interpolation-based inversion method that is currently the mainstream method in pollutant concentration inversion research, a pollutant concentration inversion model is constructed to achieve quantitative reconstruction of the pollutant concentration field under limited monitoring data.

[0072] Specifically, the steps include the following: Step 1: Time processing and time-series feature construction of monitoring data; Step 1 includes the following steps: Step 1.1: First, the transient concentration data series acquired from the monitoring points are time-normalized to eliminate the influence of dimensions and increase the condition number of the covariance matrix. The normalization method is as follows:

[0073] In the formula, It is a time average; Original time point Time standard deviation; Indicates the first Standardized time points corresponding to each observation data point; Indicates the first The original time points corresponding to each observation data point; Step 1.2: Subsequently, a time function is established based on the exponential covariance model, with the following expression:

[0074] In the formula, The variance of the observed concentration series; For time-related scales; Indicates the time interval as The time covariance function value represents the correlation decay characteristics of concentration over time; This represents the time interval between any two observation times; Represents the natural exponential function; Based on the above formula, the time covariance matrix is ​​constructed as follows:

[0075] In the formula, Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Standardized time corresponding to each observation point; Step 1.3: To enhance numerical stability, a Nugget term is added;

[0076] In the formula, ; Represents the time covariance matrix; This is used to enhance the numerical stability of the covariance matrix and avoid ill-conditioned or irreversible matrix problems; Represents the covariance matrix Identity matrices of the same dimension; Step 2: Spatiotemporal Kriging initial inversion based on Leave-One-Out Cross-Validation (LOO) to obtain preliminary inversion values; Step 2 includes the following steps: Step 2.1: For the covariance matrix Perform Cholesky decomposition:

[0077]

[0078] In the formula, Represents the covariance matrix The Cholesky lower triangular decomposition matrix; Represents the matrix transpose symbol; Step 2.2: Calculate the analytical solution for leave-one-out prediction (LOO Kriging) :

[0079] In the formula, Indicates time The actual observed concentration value at the location; Indicates the first The weighted related terms corresponding to each observation point; Represents the covariance matrix The Middle One diagonal element; Step 2.3: Calculate the prediction variance :

[0080] Step 2.4: Next, introduce the spatial attenuation term between the monitoring point and the target inversion point. The coordinates of the monitoring point are... The target point coordinates are ; and calculate the Euclidean distance between the monitoring point's location and the target point's coordinates;

[0081] Step 2.5: Calculate the spatial weights using the exponential decay model:

[0082] In the formula, Indicates spatially relevant scale (spatially relevant length). Step 2.6: Calculate the initial inversion values ​​of the STK model using spatial weights:

[0083] Step 3: Construct adaptive nonlinear correction coefficients based on the preliminary inversion results. An adaptive correction model is constructed from the concentration samples to perform a secondary correction on the concentration calculated by STK. Step 3 includes the following steps: Step 3.1: Construct the feature matrix F according to the following formula:

[0084]

[0085]

[0086] In the formula, This represents the zero-prevention factor, used to ensure that the formula can still be calculated stably when the theoretical value is close to zero; By calculating the characteristics of the normalized residual Prediction variance Spatial correlation strength Constructing feature vectors ;

[0087] Step 3.2: Construct a target quantity reflecting the degree of deviation between observed values ​​and spatiotemporal Kriging predictions, expressed as:

[0088] In the formula, Represents the target variable from all samples The target vector formed; Step 3.2: It transforms the objective into a ridge regression problem;

[0089] In the formula, This represents the regression weight vector in the nonlinear correction model, obtained by solving ridge regression. This represents the ridge regression regularization parameter, used to suppress model overfitting and enhance numerical stability; Represents the covariance matrix Identity matrices of the same dimension; Indicates by The vector formed; Step 3.3: Thus, the nonlinear regression expression for the correction function can be obtained:

[0090] Step 3.4: Calculate the correction function Weighted spatiotemporal Kriging model inversion calculation:

[0091] Step 4: Local peak matching amplification based on monitoring peak consistency. Since the peak value is often extremely narrow and the change is obvious under transient explosion conditions, WSTK may still have a lower peak value, a larger peak width, or a slight shift in peak position. This is achieved through local peak matching amplification.

[0092] Step 4 includes the following steps: Step 4.1: Perform peak time-series labeling on the monitoring sequence and the initial WSTK sequence respectively;

[0093]

[0094] In the formula, Indicates the concentration peak in the observed concentration sequence; This represents the concentration peak in the WSTK inverted concentration sequence; Indicates the peak extraction operator; This represents the peak value of the observed concentration at the peak point; This indicates the peak value of the WSTK inversion concentration at the matched peak. Step 4.2: For each observed peak, find the nearest WSTK and calculate the concentration peak q;

[0095] In the formula, Indicates the time at which a concentration peak is observed; Step 4.3: Calculate the peak magnification factor by comparing the peak values ​​of the observed peak and the concentration peak;

[0096] Step 4.4: Calculate the peak width magnification factor by comparing the peak widths of the observed peak and the concentration peak;

[0097] In the formula, This represents the final corrected concentration inversion result; This indicates the half-width of the peak correction time window; Step 4.5: Finally, calculate the inverted concentration sequence;

[0098] In the formula, This represents the WSTK inversion concentration curve after peak correction.

[0099] Figure 1 The flowchart illustrates the concentration inversion calculation process. By employing a weighted spatiotemporal kriging (WSTK) inversion method that integrates temporal covariance structure, spatial decay operators, and nonlinear correction coefficients, the model's responsiveness to concentration changes at monitoring points under transient conditions is enhanced. The concentration inversion results of this model closely approximate the true concentration in terms of peak position, peak height, and overall trend. Compared to traditional spatiotemporal kriging models, the method of this invention reduces the relative inversion error in the transient high gradient region by 33.46%, solving the problems of peak underestimation, trend drift, and insensitivity to rapid changes in existing models under unsteady diffusion conditions.

[0100] By employing a local peak matching amplification strategy, the multi-peak structure in the inversion results is corrected peak by peak, ensuring that the height, width, and peak time of the inverted concentration peaks correspond to the monitoring data. This invention reduces the peak error by 11.53% and effectively suppresses peak bifurcation, peak distortion, and peak position shift that commonly occur in traditional STK inversion, solving the problem that conventional inversion methods cannot accurately recover transient multi-peak characteristics.

[0101] A concentration correction coefficient based on residual structure, adaptive weights, and local scaling factors was constructed. This invention enables dynamic optimization of spatiotemporal inversion results, allowing the inverted sequence to maintain smoothness while accurately recovering key transient features such as abrupt changes and inflection points. Compared to unweighted methods, the WSTK model in this invention significantly improves the stability of concentration reconstruction under high noise and weak signal conditions, solving the problem of excessive smoothing and unreasonable inter-peak transitions caused by noise interference in traditional methods.

[0102] Figures 2a-2c Demonstrates the application of spatiotemporal kriging methods to point locations , , Comparison of concentration inversion results with numerical simulation results. Figure 2a shown The location is in the explosion impact response zone. The simulated data rapidly jumped to about 0.458 kg / m³ in the early stage of the explosion (0~0.01s), while the theoretical inversion value was only about 0.35 kg / m³, with a relative deviation of 23.58%, reflecting the model's insufficient adaptability to cope with high-frequency sudden changes. Figure 2b middle, The peak simulated concentration at the monitoring point was 0.055 kg / m³, while the peak inverted value was 0.039 kg / m³, with a relative deviation of 29%. Particularly in the 0.03–0.06 s timeframe, the simulated value ranged from approximately 0.08 to 0.055 kg / m³, while the theoretically calculated value fluctuated between 0.017 and 0.041 kg / m³, with an average deviation of 0.0385 kg / m³ and a relative deviation of 25.4%, indicating a significant systematic overestimation trend during this period. Figure 2c Displayed At the specified locations, the retrieved concentration remained at a low level of 0.011 kg / m³ throughout the time period, while the simulated concentration spiked to 0.013 kg / m³ at several points, indicating a significant bias. The calculated average bias was 0.002 kg / m³, with a relative bias of 12.66%, demonstrating a significantly insufficient response in high-concentration regions and a substantial underestimation of the concentration. This suggests poor model stability in low-disturbance boundary regions, potentially due to the spatial covariance approaching zero, leading to numerical instability. Figure 2d and Figure 2e This further reflects the difference between the simulated and inverted values ​​of random point 1 and random point 2. Figure 2e The two are basically consistent in peak amplitude and time series, with a simulated peak of 0.95 kg / m³ and an inverted concentration of 0.54 kg / m³, and a relative error of 43.15%.

[0103] Figures 3a-3c As shown, three concentration inversion methods were used to compare the results with simulated concentrations. Figure 3a In the study, the relative errors of STK, IDW, and WSTK relative to the CFD simulated concentrations were 29.12%, 40.94%, and 5.29%, respectively. Figure 3b In the above tests, the relative errors of STK, IDW, and WSTK were 17.58%, 21.99%, and 0.14%, respectively. Figure 3cIn the figure, the relative errors of STK, IDW, and WSTK are 27.13%, 23.46%, and 0.28%, respectively. Figure 2 illustrates the shortcomings of traditional methods and demonstrates the accuracy of WSTK in concentration inversion under transient conditions. Figure 3 shows the concentration inversion performed at newly selected points, and compares the accuracy of another traditional interpolation method (IDW interpolation) with that of the latter. Through comparative analysis, it is evident that the concentration inversion capability of this method is superior to that of traditional interpolation methods.

[0104] The present invention also provides an aerosol concentration inversion system under transient operating conditions, comprising: Module M1: Performs time processing and time series feature construction on the transient aerosol concentration data sequence acquired from the monitoring points to obtain the time covariance matrix; Module M2: Based on the time covariance matrix and the spatial information of the monitoring points and target inversion points, an initial inversion is performed using a spatiotemporal kriging model to obtain preliminary inversion concentration values; Module M3: Based on the preliminary inverted concentration value and the corresponding actual observed concentration value, construct and solve the nonlinear correction coefficient, perform secondary correction on the preliminary inverted concentration value, and obtain the weighted spatiotemporal kriging inverted concentration value; Module M4: Performs local peak matching between the weighted spatiotemporal kriging inversion concentration values ​​and the actual observed concentration values, and amplifies and corrects the inversion concentration values ​​in the successfully matched peak regions to obtain the final aerosol concentration inversion result.

[0105] The module M1 includes: Module M1.1: Performs time normalization on the transient aerosol concentration data sequence acquired from monitoring points, with the following expression:

[0106] In the formula, It is a time average; Original time point Time standard deviation; Indicates the first Standardized time points corresponding to each observation data point; Indicates the first The original time points corresponding to each observation data point; Module M1.2: Establishes the time covariance function based on the exponential covariance model, with the following expression:

[0107] In the formula, The variance of the observed concentration series; For time-related scales; Indicates the time interval as The time covariance function value represents the correlation decay characteristics of concentration over time; This represents the time interval between any two observation times; Represents the natural exponential function; Module M1.3: Constructing the time covariance matrix based on the aforementioned time covariance function. Its elements are:

[0108] In the formula, Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Standardized time corresponding to each observation point; Module M1.4: [This refers to the time covariance matrix] To enhance numerical stability, a Nugget term is added, expressed as:

[0109] In the formula, This is used to enhance the numerical stability of the covariance matrix; Represents the covariance matrix Identity matrices of the same dimension.

[0110] The module M2 includes: Module M2.1: For the covariance matrix Perform Cholesky decomposition, the expression is:

[0111]

[0112] In the formula, Represents the covariance matrix The Cholesky lower triangular decomposition matrix; Represents the matrix transpose symbol; Module M2.2: Calculate the analytical solution for leave-one-out prediction The expression is:

[0113] In the formula, Indicates time The actual observed concentration value at the location; Indicates the first The weighted related terms corresponding to each observation point; Represents the covariance matrix The Middle One diagonal element; Module M2.3: Calculate Prediction Variance The expression is:

[0114] Module M2.4: Calculates the coordinates of the monitoring point. Coordinates of the target point are The Euclidean distance between them is expressed as:

[0115] Module M2.5: Calculates spatial weights using an exponential decay model. The expression is:

[0116] In the formula, Indicates spatially relevant scales; Module M2.6: Calculates preliminary inversion concentration values ​​using spatial weights, expressed as:

[0117] In the formula, Original time point The initial inversion concentration value, Original time point The analytical solution for leave-one prediction.

[0118] The module M3 includes: Module M3.1: Constructs the feature matrix F, whose row vectors are derived from the feature vectors of the i-th observation point. Composition, the expression is:

[0119]

[0120]

[0121]

[0122] In the formula, Indicates zero-factor protection. For normalized residual characteristics, To predict variance, Spatial correlation intensity; Module M3.2: Constructing a target quantity that reflects the degree of deviation between observed values ​​and spatiotemporal Kriging predictions. The expression is:

[0123] Module M3.3: Transforms the objective into a ridge regression problem, solving for the regression weight vector of the nonlinear modified model. The expression is:

[0124] In the formula, This represents the ridge regression regularization parameter, used to suppress model overfitting and enhance numerical stability; Indicates by The vector formed; Module M3.4: Calculate nonlinear correction coefficients The expression is:

[0125] Module M3.5: Calculates the weighted spatiotemporal kriging inversion concentration value, expressed as:

[0126] In the formula, Original time point The weighted spatiotemporal Kriging inversion concentration value.

[0127] The module M4 includes: Module M4.1: Performs peak time-series labeling on the monitored sequence and the initial WSTK sequence respectively;

[0128]

[0129] In the formula, Indicates the concentration peak in the observed concentration sequence; This represents the concentration peak in the WSTK inverted concentration sequence; Indicates the peak extraction operator; This represents the peak value of the observed concentration at the peak point; This indicates the peak value of the WSTK inversion concentration at the matched peak. Module M4.2: For each observed peak, find the nearest WSTK and calculate the concentration peak q;

[0130] In the formula, Indicates the time at which a concentration peak is observed; for The index; Module M4.3: Calculates the peak magnification factor by comparing the peak values ​​of the observed peak and the concentration peak. The expression is:

[0131] in, for The actual observed concentration value at that time; This represents the weighted spatiotemporal kriging inversion concentration value at the concentration peak q. Module M4.4: Calculates the peak width magnification factor by comparing the peak widths of the observed peak and the concentration peak;

[0132] In the formula, This represents the final corrected concentration inversion result; This indicates the half-width of the peak correction time window; Module M4.5: Finally, the inverted concentration sequence is calculated;

[0133] In the formula, This represents the WSTK inversion concentration curve after peak correction.

[0134] Those skilled in the art will understand that, in addition to implementing the system, apparatus, and their modules provided by this invention in purely computer-readable program code, the same program can be implemented in the form of logic gates, switches, application-specific integrated circuits, programmable logic controllers, and embedded microcontrollers by logically programming the method steps. Therefore, the system, apparatus, and their modules provided by this invention can be considered a hardware component, and the modules included therein for implementing various programs can also be considered structures within the hardware component; alternatively, modules for implementing various functions can be considered both software programs implementing the method and structures within the hardware component.

[0135] Specific embodiments of the present invention have been described above. It should be understood that the present invention is not limited to the specific embodiments described above, and those skilled in the art can make various changes or modifications within the scope of the claims, which do not affect the essence of the present invention. Unless otherwise specified, the embodiments and features described in this application can be arbitrarily combined with each other.

Claims

1. A method for inverting aerosol concentration under transient operating conditions, characterized in that, include: Step 1: Perform time processing and time series feature construction on the transient aerosol concentration data sequence obtained from the monitoring points to obtain the time covariance matrix; Step 2: Based on the time covariance matrix and the spatial information of the monitoring points and target inversion points, perform initial inversion using a spatiotemporal kriging model to obtain preliminary inversion concentration values; Step 3: Based on the preliminary inverted concentration value and the corresponding actual observed concentration value, construct and solve the nonlinear correction coefficient, and perform a second correction on the preliminary inverted concentration value to obtain the weighted spatiotemporal kriging inverted concentration value; Step 4: Perform local peak matching between the weighted spatiotemporal kriging inversion concentration value and the actual observed concentration value, and amplify and correct the inversion concentration value in the successfully matched peak region to obtain the final aerosol concentration inversion result.

2. The aerosol concentration inversion method under transient operating conditions according to claim 1, characterized in that, Step 1 includes: Step 1.1: Perform time standardization on the transient aerosol concentration data series acquired from the monitoring points. The expression is: In the formula, It is a time average; Original time point Time standard deviation; Indicates the first Standardized time points corresponding to each observation data point; Indicates the first The original time points corresponding to each observation data point; Step 1.2: Establish the time covariance function based on the exponential covariance model, with the following expression: In the formula, The variance of the observed concentration sequence; For time-related scales; Indicates the time interval as The time covariance function value represents the correlation decay characteristics of concentration over time; This represents the time interval between any two observation times; Represents the natural exponential function; Step 1.3: Construct the time covariance matrix based on the time covariance function. Its elements are: In the formula, Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Standardized time corresponding to each observation point; Step 1.4: [The text abruptly ends here, likely due to an incomplete sentence or a formatting error.] To enhance numerical stability, a Nugget term is added, expressed as: In the formula, This is used to enhance the numerical stability of the covariance matrix; Represents the covariance matrix Identity matrices of the same dimension.

3. The aerosol concentration inversion method under transient conditions according to claim 2, characterized in that, Step 2 includes: Step 2.1: For the covariance matrix Perform Cholesky decomposition, the expression is: In the formula, Represents the covariance matrix The Cholesky lower triangular decomposition matrix; Represents the matrix transpose symbol; Step 2.2: Calculate the analytical solution for leave-one-out prediction The expression is: In the formula, Indicates time The actual observed concentration value at the location; Indicates the first The weighted related terms corresponding to each observation point; Represents the covariance matrix The Middle One diagonal element; Step 2.3: Calculate the prediction variance The expression is: Step 2.4: Calculate the coordinates of the monitoring point. Coordinates of the target point are The Euclidean distance between them is expressed as: Step 2.5: Calculate spatial weights using an exponential decay model. The expression is: In the formula, Indicates spatially relevant scales; Step 2.6: Calculate the preliminary inversion concentration value using spatial weights, expressed as: In the formula, Original time point The initial inversion concentration value, Original time point The analytical solution for leave-one prediction.

4. The aerosol concentration inversion method under transient operating conditions according to claim 3, characterized in that, Step 3 includes: Step 3.1: Construct the feature matrix F, whose row vectors are derived from the feature vectors of the i-th observation point. Composition, the expression is: In the formula, Indicates zero-factor protection. For normalized residual characteristics, To predict variance, Spatial correlation intensity; Step 3.2: Construct a target quantity that reflects the degree of deviation between observed values ​​and spatiotemporal Kriging predictions. The expression is: Step 3.3: Transform the objective into a ridge regression problem and solve for the regression weight vector of the nonlinear modified model. The expression is: In the formula, This represents the ridge regression regularization parameter, used to suppress model overfitting and enhance numerical stability; Indicates by The vector formed; Step 3.4: Calculate the nonlinearity correction coefficients The expression is: Step 3.5: Calculate the weighted spatiotemporal kriging inversion concentration value, expressed as: In the formula, Original time point The weighted spatiotemporal Kriging inversion concentration value.

5. The aerosol concentration inversion method under transient operating conditions according to claim 4, characterized in that, Step 4 includes: Step 4.1: Perform peak time-series labeling on the monitoring sequence and the initial WSTK sequence respectively; In the formula, Indicates the concentration peak in the observed concentration sequence; This represents the concentration peak in the WSTK inverted concentration sequence; Indicates the peak extraction operator; This represents the peak value of the observed concentration at the peak point; This indicates the peak value of the WSTK inversion concentration at the matched peak. Step 4.2: For each observed peak, find the nearest WSTK and calculate the concentration peak q; In the formula, This indicates the time at which a concentration peak was observed. for Index; Step 4.3: Calculate the peak magnification factor by comparing the peak values ​​of the observed peak and the concentration peak. The expression is: in, for The actual observed concentration value at that time; This represents the weighted spatiotemporal kriging inversion concentration value at the concentration peak q. Step 4.4: Calculate the peak width magnification factor by comparing the peak widths of the observed peak and the concentration peak; In the formula, This represents the final corrected concentration inversion result; This indicates the half-width of the peak correction time window; Step 4.5: Finally, calculate the inverted concentration sequence; In the formula, This represents the WSTK inversion concentration curve after peak correction.

6. An aerosol concentration inversion system under transient operating conditions, characterized in that, include: Module M1: Performs time processing and time series feature construction on the transient aerosol concentration data sequence acquired from the monitoring points to obtain the time covariance matrix; Module M2: Based on the time covariance matrix and the spatial information of the monitoring points and target inversion points, an initial inversion is performed using a spatiotemporal kriging model to obtain preliminary inversion concentration values; Module M3: Based on the preliminary inverted concentration value and the corresponding actual observed concentration value, construct and solve the nonlinear correction coefficient, perform secondary correction on the preliminary inverted concentration value, and obtain the weighted spatiotemporal kriging inverted concentration value; Module M4: Performs local peak matching between the weighted spatiotemporal kriging inversion concentration values ​​and the actual observed concentration values, and amplifies and corrects the inversion concentration values ​​in the successfully matched peak regions to obtain the final aerosol concentration inversion result.

7. The aerosol concentration inversion system under transient conditions according to claim 6, characterized in that, The module M1 includes: Module M1.1: Performs time normalization on the transient aerosol concentration data sequence acquired from monitoring points, with the following expression: In the formula, It is a time average; Original time point Time standard deviation; Indicates the first Standardized time points corresponding to each observation data point; Indicates the first The original time points corresponding to each observation data point; Module M1.2: Establishes the time covariance function based on the exponential covariance model, with the following expression: In the formula, The variance of the observed concentration sequence; For time-related scales; Indicates the time interval as The time covariance function value represents the correlation decay characteristics of concentration over time; This represents the time interval between any two observation times; Represents the natural exponential function; Module M1.3: Constructing the time covariance matrix based on the aforementioned time covariance function. Its elements are: In the formula, Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Elements of the time covariance matrix between observation times; Indicates the first Standardized time corresponding to each observation point; Module M1.4: [This refers to the time covariance matrix] To enhance numerical stability, a Nugget term is added, expressed as: In the formula, This is used to enhance the numerical stability of the covariance matrix; Represents the covariance matrix Identity matrices of the same dimension.

8. The aerosol concentration inversion system under transient operating conditions according to claim 7, characterized in that, The module M2 includes: Module M2.1: For the covariance matrix Perform Cholesky decomposition, the expression is: In the formula, Represents the covariance matrix The Cholesky lower triangular decomposition matrix; Represents the matrix transpose symbol; Module M2.2: Calculate the analytical solution for leave-one-out prediction The expression is: In the formula, Indicates time The actual observed concentration value at the location; Indicates the first The weighted related terms corresponding to each observation point; Represents the covariance matrix The Middle One diagonal element; Module M2.3: Calculate Prediction Variance The expression is: Module M2.4: Calculates the coordinates of the monitoring point. Coordinates of the target point are The Euclidean distance between them is expressed as: Module M2.5: Calculates spatial weights using an exponential decay model. The expression is: In the formula, Indicates spatially relevant scales; Module M2.6: Calculates preliminary inversion concentration values ​​using spatial weights, expressed as: In the formula, Original time point The initial inversion concentration value, Original time point The analytical solution for leave-one prediction.

9. The aerosol concentration inversion system under transient conditions according to claim 8, characterized in that, The module M3 includes: Module M3.1: Constructs the feature matrix F, whose row vectors are derived from the feature vectors of the i-th observation point. Composition, the expression is: In the formula, Indicates zero-factor protection. For normalized residual characteristics, To predict variance, Spatial correlation intensity; Module M3.2: Constructing a target quantity that reflects the degree of deviation between observed values ​​and spatiotemporal Kriging predictions. The expression is: Module M3.3: Transforms the objective into a ridge regression problem, solving for the regression weight vector of the nonlinear modified model. The expression is: In the formula, This represents the ridge regression regularization parameter, used to suppress model overfitting and enhance numerical stability; Indicates by The vector formed; Module M3.4: Calculate nonlinear correction coefficients The expression is: Module M3.5: Calculates the weighted spatiotemporal kriging inversion concentration value, expressed as: In the formula, Original time point The weighted spatiotemporal Kriging inversion concentration value.

10. The aerosol concentration inversion system under transient conditions according to claim 9, characterized in that, The module M4 includes: Module M4.1: Performs peak time-series labeling on the monitored sequence and the initial WSTK sequence respectively; In the formula, Indicates the concentration peak in the observed concentration sequence; This represents the concentration peak in the WSTK inverted concentration sequence; Indicates the peak extraction operator; This represents the peak value of the observed concentration at the peak point; This indicates the peak value of the WSTK inversion concentration at the matched peak. Module M4.2: For each observed peak, find the nearest WSTK and calculate the concentration peak q; In the formula, This indicates the time at which a concentration peak was observed. for Index; Module M4.3: Calculates the peak magnification factor by comparing the peak values ​​of the observed peak and the concentration peak. The expression is: in, for The actual observed concentration value at that time; This represents the weighted spatiotemporal kriging inversion concentration value at the concentration peak q. Module M4.4: Calculates the peak width magnification factor by comparing the peak widths of the observed peak and the concentration peak; In the formula, This represents the final corrected concentration inversion result; This indicates the half-width of the peak correction time window; Module M4.5: Finally, the inverted concentration sequence is calculated; In the formula, This represents the WSTK inversion concentration curve after peak correction.

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