A generative interpolation method for abnormally missing ozone concentration data

Abstract

The present invention discloses a generative interpolation method for abnormally missing ozone concentration data. First, the ozone data is decomposed into a time series. The decomposed seasonal component, trend component, and residual component are slid and spliced ​​with multi-source influencing factors such as the air quality index, five other indicators of air pollutants, and meteorological measured data in the time dimension. The result is used as the input sequence of the Transformer model. The state sequence that causes the change in ozone concentration is learned through the state sequence, and the state sequence is used as part of the input sequence of the diffusion model. The diffusion model reconstructs the ozone concentration time series from the noise by learning the random process of adding and removing noise, thereby achieving high-quality interpolation of abnormally missing ozone concentration data, thereby ensuring the integrity and accuracy of ozone pollution monitoring data. The present invention combines the sequence processing capability of the Transformer model with the generative capability of the diffusion model, and can significantly improve the interpolation performance of missing data.

Description

Technical Field

[0001] The present invention belongs to the technical field of air quality detection, and in particular relates to a generative interpolation method for abnormally missing ozone concentration data. Background Art

[0002] Poor monitoring environments and equipment failures can lead to unusually missing ozone concentration data. These large amounts of missing data severely impact the accuracy and value of air quality monitoring and forecasting, making it difficult to provide effective data support for environmental governance. Existing research has failed to adequately address this issue during the preprocessing of environmental monitoring data. Alternatively, traditional prediction models have been used to interpolate missing data without factoring in prior information about ozone pollution. This poor interpolation performance of prediction models for long periods of missing data will diminish the value of ozone concentration data for future applications. Summary of the Invention

[0003] The purpose of the present invention is to provide a generative interpolation method for abnormally missing ozone concentration data, which combines the sequence processing capability of the Transformer model and the generative capability of the diffusion model to achieve high-quality interpolation of abnormally missing ozone concentration data.

[0004] The present invention is achieved by adopting the following technical solutions:

[0005] A generative interpolation method for abnormally missing ozone concentration data is proposed, including:

[0006] S1, decomposing the time series of ozone concentration data to obtain component data; wherein the component data includes seasonal component, trend component and residual component;

[0007] S2, concatenates component data and multi-source influencing factors into the input sequence of the Transformer model;

[0008] S3, using the Transformer model to extract the state information of ozone concentration changes;

[0009] S4, taking the state information and ozone concentration data as inputs of the diffusion model, and using the diffusion model to perform generative interpolation operations on the ozone concentration data.

[0010] In some embodiments of the present invention, step S2 includes the step of dynamically intercepting the ozone sequence fragment, including:

[0011] Configure the decomposition window size to ,make The seasonal component, trend component and residual component of the moment are The ozone sequence within the time period is obtained by STL decomposition; among them, is the seasonal cycle parameter;

[0012] As time goes by, the decomposition window slides backward to obtain the input sequence at each moment ,in, It is the measured data of multi-source influencing factors; It is the dimension of multi-source influencing factors; are the seasonal component, trend component and residual component respectively.

[0013] In some embodiments of the present invention, step S2 includes the step of constructing a Transformer model input data sequence, including:

[0014] The input sequence of the Transformer model Set to data before and after missing:

[0015] ;

[0016] in, Indicates the length of the data intercepted before and after the missing sequence. for Multi-source measured data at each moment and the spliced ​​characteristic sequence of the three components.

[0017] In some embodiments of the present invention, in step S3:

[0018] The input sequence Perform vector representation;

[0019] Position information is encoded using sine and cosine functions of different frequencies;

[0020] The positional encoding is added to the sequence vector as input to the encoder of the Transformer model.

[0021] In some embodiments of the present invention, the diffusion process of step S4 adopts:

[0022] conduct;

[0023] State information extracted for the Transformer model; , , is the number of iteration steps; For the The variance of the step; The noise added in the rth step of the forward process obeys the standard Gaussian distribution; Output the result for step r;

[0024] The generation process uses:

[0025] conduct;

[0026] The noise added to the forward process follows a standard Gaussian distribution; ; During the generation process Predict using a neural network: , is the noise predicted by the neural network, as input to the generation process; Output the result for step r-1.

[0027] In some embodiments of the present invention, the method further comprises:

[0028] The Transformer model and the diffusion model are integrated into a Bayesian framework. The output of the Transformer model As part of the diffusion model input, the optimization of parameters during the gradient propagation during the training process is based on the total loss function Joint optimization, the parameters of the Transformer model are based on the loss function To optimize, the generation process of the diffusion model uses a neural network in the training process. get , the training of neural networks is based on the loss function conduct:

[0029] ;

[0030] in represents the loss function of the Transformer model, represents the loss function of the diffusion model.

[0031] Compared with the prior art, the advantages and positive effects of the present invention are as follows: in the generative interpolation method for abnormal missing ozone concentration data proposed by the present invention, the ozone data is first decomposed into a time series, and the decomposed seasonal component, trend component and residual component are slid and spliced ​​with multi-source influencing factors such as air quality index, five other air pollutant indicators, and meteorological measured data in the time dimension as the input sequence of the Transformer. The Transformer learns the state sequence that causes the change in ozone concentration. On this basis, the state sequence is used as part of the input sequence of the diffusion model. The diffusion model reconstructs the ozone concentration time series from the noise by learning the random process of adding and removing noise. By improving the learning ability of the denoising process, high-quality interpolation of abnormal missing ozone concentration data is achieved, thereby ensuring the integrity and accuracy of ozone pollution monitoring data. The present invention integrates the Transformer model and the diffusion model in a Bayesian framework, adopts a joint optimization strategy, and uses the state information extracted by the Transformer model as prior information. The diffusion model can more effectively focus on estimating the generated data, combining the sequence processing ability of the Transformer model with the generation ability of the diffusion model, and can significantly improve the interpolation performance of missing data.

[0032] Other features and advantages of the present invention will become more apparent after reading the detailed description of the embodiments of the present invention in conjunction with the accompanying drawings. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the description of the embodiments. Obviously, the drawings described below are only some embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on these drawings without paying any creative work.

[0034] Figure 1 This is a schematic diagram of the steps of the generative interpolation method for abnormal missing ozone concentration data proposed by the present invention;

[0035] Figure 2 This is a schematic diagram of the generative interpolation process for abnormal missing ozone concentration data proposed in the present invention;

[0036] Figure 3 Schematic diagram of the composition of the input data sequence in the method of the present invention;

[0037] Figure 4 This is a comparison of the four indicators of MAPE / R2 / MAE / RMSE between the method of the present invention and other models in the embodiments of the present invention. DETAILED DESCRIPTION

[0038] The following will clearly and completely describe the technical solutions in the embodiments of the present invention in conjunction with the accompanying drawings. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without making creative efforts are within the scope of protection of the present invention.

[0039] In the description of the present invention, it should be understood that the terms "center", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", etc., indicating the orientation or position relationship, are based on the orientation or position relationship shown in the accompanying drawings, and are only for the convenience of describing the present invention and simplifying the description, rather than indicating or implying that the device or element referred to must have a specific orientation, be constructed and operated in a specific orientation, and therefore cannot be understood as limiting the present invention.

[0040] In the description of the present invention, it should be noted that, unless otherwise expressly specified or limited, the terms "installed," "connected," and "connected" should be understood in a broad sense. For example, they can refer to fixed connections, detachable connections, or integral connections. A person of ordinary skill in the art will understand the specific meanings of the above terms in the present invention in specific circumstances. In the description of the above embodiments, specific features, structures, materials, or characteristics may be combined in any appropriate manner in any one or more embodiments or examples.

[0041] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the quantity of the technical features being referred to. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, unless otherwise specified, "plurality" means two or more.

[0042] The generative interpolation method for abnormally missing ozone concentration data proposed in this paper is a generative interpolation method that combines Transformer and diffusion models. It includes three parts: time series decomposition of ozone concentration data, state information learning of ozone concentration changes, and generative interpolation of missing data:

[0043] (1) Commonly used time series decomposition algorithms include STL, X11, SEATS, etc. In this paper, STL is used as an example to illustrate the decomposition process of ozone concentration series data. STL is a time series decomposition algorithm based on Loess smoothing, which consists of two internal and external loop mechanisms. The inner loop fits the seasonal component through local weighted regression and low-pass filtering algorithm to obtain the trend component; the outer loop is used to obtain the residual component and calculate the robustness weight in each loop to reduce the impact of outliers on the inner loop. The STL algorithm decomposes the time series into three subsequence components: seasonal component, trend component and residual component, which can capture the seasonal periodicity and medium- and long-term trend patterns of the time series to a large extent.

[0044] (2) The extraction of ozone concentration state information uses a Transformer model. The Transformer model consists of a multi-layered encoder and decoder, each of which includes a multi-head attention and a feedforward neural network sublayer. The encoder input is a sequence of the three decomposed components concatenated with multiple influencing factors such as the Air Quality Index (AQI), five other air pollutant indicators, and meteorological data. The output is a state sequence representing the change in ozone concentration.

[0045] (3) Diffusion Models include diffusion process and generation process. The diffusion process converts the input sequence Converting to a standard Gaussian distribution can be understood as a process of gradually adding noise; the generation process is to convert the samples in the standard Gaussian distribution into The samples in the image are generated by a neural network, which is a process of gradually removing noise to achieve generative interpolation of ozone loss data.

[0046] Based on the above, in order to extract the prior information contained in the ozone time series, the present invention first uses the STL time series decomposition algorithm to decompose the measured ozone concentration series into a seasonal component, a trend component, and a residual component; the three decomposed components and a spliced ​​sequence of multi-source influencing factors such as the air quality index (AQI), five other indicators of air pollutants, and meteorological measured data are used as the input of the Transformer model. The Transformer model extracts the global information of the input sequence and learns the state sequence that causes the change in ozone concentration; on this basis, with the state sequence as part of the input, the diffusion model learns the random process of adding and removing noise, and reconstructs the ozone concentration time series from the noise.

[0047] The present invention integrates the Transformer model and the diffusion model in a Bayesian framework, adopts a joint optimization strategy, and uses the state information extracted by the Transformer model as prior information. The diffusion model can more effectively focus on estimating the generated data. It combines the sequence processing capability of the Transformer model and the generation capability of the diffusion model to achieve high-quality interpolation of abnormally missing ozone concentration data, thereby ensuring the integrity and accuracy of ozone pollution monitoring data.

[0048] Specifically, such as Figure 1 As shown, the following steps are included:

[0049] S1: Decompose the time series of ozone concentration data to obtain component data; the component data include seasonal component, trend component and residual component.

[0050] Affected by a variety of factors, ozone pollution often exhibits distinct seasonal characteristics and medium- to long-term trends. High temperatures and strong sunlight in the summer are conducive to the formation of ozone pollution, resulting in generally higher concentrations, while concentrations are relatively low in the winter. Industrial activities, prevention and control measures, and pollution source structures cause ozone pollution to exhibit certain medium- and long-term trends. In addition, due to some extreme weather or special events, ozone concentrations may experience short-term fluctuations. Based on the above analysis of the empirical laws of ozone concentration changes, the present invention decomposes ozone concentration data into time series, extracts the seasonal periodicity and medium- to long-term trend patterns of the ozone series, and provides effective prior information for interpolation of missing ozone concentration data.

[0051] Commonly used time series decomposition algorithms include STL, X11, SEATS, etc. In the present invention, STL is taken as an example to illustrate the decomposition process of ozone concentration series data.

[0052] The STL algorithm decomposes ozone concentration data into seasonal component, trend component and residual component through local weighted regression (Loess). The specific decomposition result can be expressed as:

[0053] ;

[0054] in, Represents the measured ozone concentration series, seasonal component Represents the periodic fluctuation of data at different time scales, trend component Indicates the long-term trend of data, the residual component represents random noise excluding seasonal and trend components.

[0055] The STL decomposition consists of two loops, the inner loop and the outer loop, and the seasonal component is fitted by local weighted regression and low-pass filtering algorithm. , find the trend component ; The outer loop is used to obtain the remaining components , and calculate the robustness weight in each loop to reduce the impact of outliers on the inner loop.

[0056] Specifically, 、 The seasonal component and the trend component are The results of the iterations are as follows:

[0057] (1) Detrending the original series.

[0058] The trend component of the measured ozone concentration series is removed to obtain the detrended series .

[0059] (2) Smoothing periodic subsequences of detrended series.

[0060] The periodic subsequence of the detrended sequence calculated by (1) is subjected to Loess smoothing, and the robustness weight is , the result is recorded as Among them, the Loess smoothing algorithm is a point-by-point weighted regression smoothing algorithm, and its robustness weight can be recorded as , indicating a time point The corresponding robustness weight, robustness weight The size of affects the seasonal component after decomposition.

[0061] (3) Perform low-pass filtering on the result of (2).

[0062] right Perform low-pass filtering and the output sequence is recorded as , the filter includes moving average and Loess regression.

[0063] The Moving Average (MA) is a tool used in technical analysis to analyze time series. Common moving averages include the Simple Moving Average (SMA), the Weighted Moving Average (WMA), and the Exponential Moving Average (EMA). Loess regression is a non-parametric method used for local regression analysis. It primarily divides the sample into small intervals, performs polynomial fitting on the samples within these intervals, and repeats this process to obtain weighted regression curves for different intervals. The centers of these regression curves are then connected to form a complete regression curve.

[0064] (4) Detrend the results of (2).

[0065] The time series in (2) Remove the trend term and get the seasonal component, which is recorded as:

[0066] .

[0067] (5) The seasonal component is obtained by removing S4 from the measured ozone concentration series.

[0068] That is, calculate the deseasonal series .

[0069] (6) Perform trend smoothing on the deseasonalized series.

[0070] The deseasonalized series obtained from (5) Perform Loess smoothing and get Iterated trend component .

[0071] After one inner cycle, the seasonal component and trend component are 、 , from which the remaining components can be calculated for:

[0072] .

[0073] (7) Calculate the remaining component.

[0074] .

[0075] (8) The outer loop introduces robust weights To evaluate robustness.

[0076] The calculation formula is: ;

[0077] in, ; is the bisquare weight function, For time point The corresponding robust weights.

[0078] S2: Concatenate component data and multi-source influencing factors into the input sequence of the Transformer model.

[0079] The interpolation operation of ozone concentration data needs to comprehensively consider the changing patterns of multiple influencing factors such as ozone concentration data, air quality index (AQI), five other indicators of air pollutants, and meteorological measured data, so as to extract the state information contained therein that causes changes in the ozone sequence and provide a basis for data interpolation.

[0080] In the present invention, the source of the pre-extracted state information is the data within a period of time before and after the ozone sequence is missing, that is, future state information is added to the interpolation task.

[0081] The state information is extracted using a Transformer model. The input data sequence fed into the Transformer model, i.e., the data used to extract the state information, includes the three components obtained in step S1 (seasonal component, trend component, and residual component), the Air Quality Index (AQI), five other air pollutant indicators, and meteorological data. The AQI, five other air pollutant indicators, and meteorological data are measured sequences.

[0082] The preprocessing of the input data sequence includes: (a) Dynamic interception of ozone sequence fragments: When decomposing the STL, the seasonal cycle parameters are taken For N, The seasonal component, trend component and residual component of the moment are The ozone sequence in the time period is obtained by STL decomposition, and for The three components of time are The STL decomposition results of the ozone sequence within the time period, as the state information extraction time goes by, the decomposition window also slides backward, and the window size is set to The characteristic sequence at each moment is the concatenation of multi-source measured data and three components, namely ( is the dimension of multi-source measured data). (b) Construction of Transformer model input data sequence: In order to extract more comprehensive state information, the input sequence of the Transformer model is converted to Set to data before and after missing:

[0083] ;

[0084] in, Indicates the length of data intercepted before and after the missing sequence; for The output of the spliced ​​feature sequence of multi-source measured data and three components at each moment is the state information representing the change of ozone concentration. That is, when interpolating missing data, not only the information contained in the past series and the relevant information of the missing period are utilized, but also the future information within a period of time after the missing is considered.

[0085] In order to illustrate the generative interpolation performance of the method of the present invention for time series data, data missing processing was performed on the input of the model during method verification. That is, the data of the complete time series was masked using multiple different proportions to form different degrees of data missing. The model was then verified based on different missing rates, and the interpolation evaluation indicators under different missing conditions were compared.

[0086] S3: Use the Transformer model to extract the state information of ozone concentration changes.

[0087] The method proposed in the present invention adopts the Transformer model to extract the state information of ozone concentration changes as prior information for missing data interpolation.

[0088] The Transformer consists of a multi-layered encoder and decoder, each of which includes a multi-head attention and a feedforward neural network sublayer. The encoder input is the concatenated multi-source data. Embedding and position encoding are two key components of the Transformer model. The input sequence is represented as a vector, and considering the spatial correlation of sequence data, position encoding is added to the embedded input, encoding the position information using sine and cosine functions of different frequencies:

[0089] ;

[0090] ;

[0091] in, , position encoding , the positional encoding is added to the sequence vector as the input of the encoder.

[0092] The multi-head self-attention mechanism splits a single self-attention mechanism into multiple subspaces and performs self-attention on each subspace to learn different attention weights, thereby better capturing features at different levels and fusing them in the representation space. The self-attention mechanism is described as:

[0093] ;

[0094] in , and Represents query, key, and value respectively.

[0095] Multi-head self-attention concatenates the vector representations formed by each head combined with the context representation and multiplies them by the weight matrix To aggregate the information from different heads and form the final vector representation combined with the context:

[0096] ;

[0097] ;

[0098] in , Indicates the number of attention heads; , , are the weight matrices for query, key, and value, respectively. A weight matrix representing a linear transformation.

[0099] In the present invention, the input of the decoder uses the data before and after the missing data, and the output of the decoder is set as a multidimensional feature vector as needed, which is recorded as , to characterize the intermediate state information that causes changes in ozone concentration. The input takes into account the data before and after the missing data, providing the interpolation task with information on the changes in ozone concentration caused by the past, present and future based on the missing moment. Unlike simple prediction tasks, which can only consider historical data before the prediction moment, the interpolation task completed by this method can take into account the serial data within a period of time after the missing data. Because the serial data within a period of time after the data is missing is used as part of the model input in this invention, the Transformer architecture does not use the masked attention mechanism.

[0100] S4: The state information is used as part of the diffusion model input, and together with the ozone concentration monitoring data, it is used as the input of the diffusion model, and the diffusion model performs generative interpolation operations on the ozone concentration data.

[0101] In the present invention, the interpolation of abnormal missing ozone concentration data is generative interpolation using a diffusion model. The state sequence extracted by Transformer is used as part of the model input to provide more state information causing ozone concentration changes for the forward and reverse processes.

[0102] The diffusion model includes the diffusion process and the generation process:

[0103] (a) Diffusion process: The model input without adding state sequence The distribution is recorded as The standard diffusion process is to add noise to the input so that it gradually conforms to the Gaussian distribution, which can be described by the formula:

[0104] ;

[0105] The above formula can also be written as: ;

[0106] During the diffusion process, is the number of iteration steps, is a known quantity, i.e. the input of the forward process, and the process is displayed. represents a Gaussian distribution, For the The variance of the step, For the initial data The identity matrix of the same dimension. Let , ,according to and The relationship between Derived :

[0107] ;

[0108] in, Obey the standard Gaussian distribution. According to the above formula It can be calculated directly without iteration, which can improve the computational efficiency of the diffusion process. The continuous increase of the diffusion process It can be approximated as Gaussian noise to complete the forward diffusion process.

[0109] In this invention, in order to improve the interpolation performance of missing data, the state sequence learned by the Transformer model is transformed into As part of the diffusion model input sequence, it provides the diffusion model with prior information on the change of ozone concentration. The formula is optimized as follows:

[0110] .

[0111] (b) Generation process: Inversely transform the samples in the standard Gaussian distribution into The samples in the ,that is, the process of gradually removing noise using neural networks.

[0112] ;

[0113] in, Obeying the standard Gaussian distribution, ; When R is large enough, It can be regarded as a sample from the standard Gaussian distribution. Unknown, can be predicted using neural networks:

[0114] ;

[0115] As input to the generation process, the number of iteration steps r is positionally encoded. is the noise predicted by the neural network. In the proposed method, the state sequence extracted by the Transformer model is As part of the neural network input, it provides prior state information for noise prediction.

[0116] In this invention, the Transformer model and the diffusion model are integrated into a Bayesian framework, and the output of the Transformer model is As part of the diffusion model input, the optimization of parameters during the gradient propagation during the training process is based on the total loss function Jointly optimized, the parameters of the Transformer model are based on the loss function The generation process of the diffusion model is optimized by using the neural network in the training process. get , the training of neural networks is based on the loss function The goal of optimizing the parameters of the two models is to make the total loss function The common goal is to make the noise predicted in each step closer to the noise superimposed in the generation process, so that Obtained Closer to the real input of the diffusion process.

[0117] In the data interpolation framework, the model loss function consists of two parts: the Transformer model loss and the diffusion model loss. The total loss function can be expressed as:

[0118] ;

[0119] in represents the loss function of the Transformer model, represents the loss function of the diffusion model.

[0120] The state information extracted by the Transformer model is used as prior information and, together with the ozone sequence, serves as the input to the diffusion model. The Transformer model pre-trains the multi-source measured data and the STL decomposition components to learn sequence features. It extracts the time series features inherent in the sequence that cause changes in ozone concentration as state information input to the diffusion model, enabling the diffusion model to more effectively focus on estimating generated data, thereby improving data generation performance. The proposed method combines the sequence processing capabilities of the Transformer model with the generation capabilities of the diffusion model. Experimental validation based on real-world monitoring data demonstrates that the proposed method significantly improves the performance of missing data interpolation.

[0121] The following describes in detail the application process of the generative interpolation method for abnormally missing ozone concentration data proposed by the present invention using a specific embodiment.

[0122] (1) Data source: A city, from May 13, 2014 to July 31, 2023, a total of 80,808 records, each record includes the air quality index (AQI), six indicators of air pollutants (O3, CO, NO2, SO2, PM 2.5 and PM 10 ) and meteorological parameters (temperature, dew point temperature, wind speed, wind direction, and air pressure). Data from May 13, 2014, to October 15, 2020, was used as the training dataset; data from October 16, 2020, to September 12, 2021, was used as the validation dataset; and data from September 13, 2021, to July 31, 2023, was used as the test dataset.

[0123] (2) Time series decomposition: According to steps S1-S7, the ozone series is decomposed to obtain seasonal components, trend components and residual components. The seasonal cycle is verified by experiments when interpolating data with different missing rates. The best value of .

[0124] (3) Learning the state information of ozone concentration changes: First, dynamically intercept the ozone sequence in the time dimension and perform STL decomposition to obtain the seasonal component , trend component and the remaining amount Secondly, the three components were compared with the air quality index (AQI), five other indicators of air pollutants (CO, NO2, SO2, PM 2.5 、PM 10 ), meteorological measured data (temperature, dew point temperature, wind speed, wind direction, air pressure) are spliced ​​as the input sequence of the Transformer model, that is, ; Secondly, different proportions of random masking (i.e., 10%, 50%, and 90%) are applied to the input sequence; finally, the Transformer model is used to extract the state information of ozone concentration changes. The Transformer model can extract global state information of ozone concentration changes from ozone sequence components and multi-source data as prior information for accurate data interpolation, thereby improving the performance of data interpolation.

[0125] (4) Generative interpolation of ozone concentration data: A diffusion model is used to perform generative interpolation on missing data of ozone concentration anomalies. The state sequence extracted by Transformer is used as part of the model input and serves as prior information for the diffusion process and the generative process.

[0126] (a) When comparing the data interpolation results, the following four evaluation indicators are first used: mean absolute percentage error (MAPE), mean square error (R 2), mean absolute error (MAE) and root mean square error (RMSE). The interpolation performance comparison of the proposed method with other models in terms of MAPE / R2 / MAE / RMSE is shown in Figure 4 When the coverage rate (i.e., missing rate) is 10%, 50%, and 90%, the R 2 The values ​​were 0.9939, 0.9848 and 0.9658, respectively, which were better than the other comparison models, especially when the missing rate was 90%, R 2 The value still reaches 0.9658. The proposed method outperforms the other compared models in terms of R² / MAE / RMSE under the three random missing conditions. The MAPE indicator is only slightly inferior to the CSDI model when the missing rate is 90%. Comparison with other models on the four indicators shows that the proposed method demonstrates superior performance in the task of interpolating anomalously missing ozone concentration data.

[0127] (b) To further validate the interpolation performance of the proposed method, the prediction interval coverage probability (PICP) metric for data interpolation was compared among the various models. The results are shown in Table 1. The PICP of the proposed method outperforms the other comparison models at different rates of random missingness, further demonstrating that the proposed method is more effective in interpolating abnormally missing data.

[0128] Table 1 Comparison of PICP indicators of this example and other models

[0129]

[0130] There are many implementation methods of the present invention, and all technical solutions formed by equivalent transformation or equivalent transformation fall within the protection scope of the present invention.

[0131] It should be pointed out that the above description is not a limitation of the present invention, and the present invention is not limited to the above examples. Changes, modifications, additions or substitutions made by ordinary technicians in this technical field within the essential scope of the present invention should also fall within the scope of protection of the present invention.

Claims

1. A generative interpolation method for abnormal missing ozone concentration data, characterized in that: include: S1, decomposing the time series of ozone concentration data to obtain component data; wherein the component data includes seasonal component, trend component and residual component; S2, splicing the component data and the multi-source influencing factors into an input sequence for the Transformer model; wherein step S2 includes the step of dynamically intercepting the ozone sequence fragment, including: Configure the decomposition window size to P e = N, so that the seasonal component, trend component and residual component at time p are obtained by STL decomposition of the ozone sequence in the time period {p-1, p-2, ... pN}; where P e is the seasonal cycle parameter; as time goes by, the decomposition window slides backward to obtain the input sequence X={x1,x2,…,x J ,S v ,T v ,R v }, where x j is the measured data of the multi-source impact factor; J is the dimension of the multi-source impact factor; S v ,T v ,R v are seasonal component, trend component and residual component respectively; Step S2 includes the step of constructing the input data sequence of the Transformer model, including: converting the input sequence M of the Transformer model into P Set to data before and after missing: M P ={X p-L ,…X p-2 ,X p-1 ,X p ,X p+1 ,X p+2 ,…X p+L }; Among them, L represents the length of the data intercepted before and after the missing sequence, X p is the spliced ​​characteristic sequence of multi-source measured data and three components at time p; S3, using the Transformer model to extract the state information of ozone concentration changes, the state information comes from the data before and after the ozone sequence is missing; S4, taking the state information and ozone concentration data as inputs of the diffusion model, and using the diffusion model to perform generative interpolation on the ozone concentration data; wherein the diffusion process of step S4 adopts; conduct; Z0 is the state information extracted by the Transformer model; α r =1-β r , r is the number of iterations; β r is the variance of the rth step; ε r Y is the noise added in the rth step of the forward process, which obeys the standard Gaussian distribution; r Output result for step r; the generation process uses: ε is the noise added in the forward process, which obeys the standard Gaussian distribution; In the generation process ε r Predicting using a neural network: ε r ≈ε θ (Y r ,Z0,r),Y r As the input of the generation process, ε θ is the noise predicted by the neural network; Y r-1 Output the result for step r-1.

2. The generative interpolation method for abnormal missing ozone concentration data according to claim 1 is characterized in that: In step S3: Vectorize the input sequence; Position information is encoded using sine and cosine functions of different frequencies; The positional encoding is added to the sequence vector as input to the encoder of the Transformer model.

3. The generative interpolation method for abnormal missing ozone concentration data according to claim 1, characterized in that: The method further comprises: The Transformer model and the diffusion model are integrated in a Bayesian framework. The output Z0 of the Transformer model is used as part of the input of the diffusion model. The optimization of parameters during the gradient propagation of the training process is based on the total loss function. Joint optimization, the parameters of the Transformer model are based on the loss function To optimize, the generation process of the diffusion model uses a neural network in the training process by Y r Get Y r-1 , the training of neural networks is based on the loss function conduct; in represents the loss function of the Transformer model, represents the loss function of the diffusion model.

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