A deep learning-based organic aerosol concentration calibration method

Abstract

This invention relates to the field of atmospheric particulate matter analysis and discloses a deep learning-based method for calibrating organic aerosol concentrations. This invention addresses the technical problems in existing organic aerosol concentration calibration techniques, such as insufficient utilization of multi-source information, inadequate use of temporal evolution information, and fixed feature fusion methods lacking dynamic weight adjustment. By leveraging multi-source observation vectors, it fully utilizes observation information from different physical properties to establish a stable nonlinear mapping relationship under complex atmospheric conditions and mixed aerosol backgrounds. Through multi-source observation features and historical state features, the model can characterize the dynamic evolution of organic aerosol concentrations. Employing a bidirectional long short-term memory network and SE attention mechanism to process multi-source observation features and historical state features, it can automatically learn and dynamically adjust the importance weights of feature channels, effectively suppressing noise and redundant feature interference. Furthermore, it utilizes forward and backward time-series modeling to fully capture the contextual relationships between consecutive time points.

Description

Technical Field

[0001] This invention relates to the field of atmospheric particulate matter analysis, and in particular to a method for calibrating the concentration of organic aerosols based on deep learning. Background Technology

[0002] Organic aerosols (OA) are a significant component of atmospheric particulate matter, affecting not only air quality and human health but also climate through processes such as scattering and absorbing solar radiation and participating in cloud formation. Accurate, continuous, and high spatiotemporal resolution monitoring and retrieval of OA concentrations has become an important research direction in the field of atmospheric environment.

[0003] Lidar remote sensing technology is widely used in aerosol monitoring. Mie scattering lidar can acquire backscattering information of particulate matter, and Raman lidar can retrieve optical parameters such as extinction coefficient. It has been used for boundary layer structure detection and pollution transport monitoring. However, since traditional lidar mainly reflects the overall optical characteristics of particulate matter, it does not have the direct ability to identify organic components and quantitatively characterize their concentration levels. Under complex atmospheric conditions where dust, inorganic particles, bioaerosols, and pollutant particles are mixed, it is difficult to stably establish a correspondence between scattering and extinction parameters and the true concentration of organic aerosols. Although laser-induced fluorescence technology can enhance the identification of organic particles, it focuses more on qualitative classification and lacks stability in quantitative concentration calibration.

[0004] It is evident that existing technologies have the following technical problems in concentration quantitative calibration:

[0005] 1. Insufficient utilization of multi-source information, or reliance on a single optical parameter to obtain a simple combination of a few features. Under complex atmospheric conditions and mixed aerosol background, the limitation of information utilization makes it difficult for the model to establish a stable nonlinear mapping relationship, resulting in insufficient quantitative accuracy and robustness.

[0006] 2. The model does not make full use of time evolution information, making it difficult to characterize the dynamic changes in concentration. It is mostly based on single-frame observations or local time windows, and lacks targeted modeling of the effects of processes at different time scales, resulting in limited ability of the model to represent the dynamic evolution of concentration.

[0007] 3. When fusing multi-source features, direct splicing or fixed weighting is usually used, which cannot dynamically adjust the weights according to the actual contribution of the feature channels and is easily affected by noise or redundant features. Summary of the Invention

[0008] The purpose of this invention is to solve the technical problems in the existing technology of organic aerosol concentration calibration, such as insufficient utilization of multi-source information, insufficient utilization of time evolution information, fixed feature fusion method and lack of dynamic weight adjustment, and to provide an organic aerosol concentration calibration method based on deep learning.

[0009] To achieve the above-mentioned objectives, the embodiments of the present invention provide the following technical solutions:

[0010] A deep learning-based method for calibrating the concentration of organic aerosols includes the following sub-steps:

[0011] Simultaneously collect multi-channel echo signals, meteorological parameters, and organic aerosol reference concentrations, and integrate them into raw sample data;

[0012] The channel echo signal is cleaned, and the cleaned channel echo signal is time-aligned with the original sample data. The aligned channel echo signal is extracted to obtain the aerosol extinction coefficient and fluorescence-elastic scattering ratio. The channel echo signal, aerosol extinction coefficient, fluorescence-elastic scattering ratio and meteorological parameters are normalized and integrated into a multi-source observation vector. The multi-source observation vectors over continuous time are collected to obtain multi-source observation characteristics.

[0013] The organic aerosol concentration calibration model uses a bidirectional long short-term memory network and SE attention mechanism to process multi-source observation features and historical state features to obtain the predicted organic aerosol concentration.

[0014] Compared with existing technologies, the beneficial effects of this invention are as follows: By simultaneously acquiring multi-channel echo signals and meteorological parameters, and extracting multi-source features such as aerosol extinction coefficient and fluorescence-elastic scattering ratio, and forming multi-source observation vectors after normalization, this invention can fully utilize observation information with different physical properties, establish stable nonlinear mapping relationships under complex atmospheric conditions and mixed aerosol backgrounds, and significantly improve the quantitative accuracy and robustness of organic aerosol concentration calibration; by collecting continuous-time multi-source observation vectors to form a time window sequence and introducing historical state features, this invention enables the model to characterize the dynamics of organic aerosol concentration. This invention overcomes the shortcomings of single-frame observations or simple time windows in representing processes at different time scales, such as short-term disturbances, medium-term evolution, and long-term transport, by studying evolutionary patterns and improving the continuity and prediction accuracy of concentration calibration. Furthermore, this invention employs a bidirectional long short-term memory network and SE attention mechanism to process multi-source observation features and historical state features. It can automatically learn and dynamically adjust the importance weights of feature channels, effectively suppressing interference from noise and redundant features. Simultaneously, forward and reverse time-series modeling fully captures the contextual relationships between consecutive moments, thus maintaining stable calibration performance under different weather conditions and enhancing the model's adaptability and generalization.

[0015] Furthermore, a deep learning-based method for calibrating organic aerosol concentration, wherein the simultaneous acquisition of multi-channel echo signals, meteorological parameters, and organic aerosol reference concentrations, and integration into raw sample data, includes the following sub-steps:

[0016] Multi-channel echo signals are acquired using lidar; the multi-channel echo signals include elastic scattering channel signals, nitrogen Raman scattering channel signals, and fluorescence channel signals.

[0017] Meteorological parameters are collected synchronously based on the observation time of the lidar; the meteorological parameters include temperature, relative humidity, wind speed, wind direction, and air pressure;

[0018] The reference concentration of organic aerosols is obtained synchronously based on the observation time of the lidar.

[0019] In the above scheme, by simultaneously acquiring multi-channel echo signals of lidar elastic scattering, Raman scattering, and fluorescence, and combining them with meteorological parameters and organic aerosol reference concentrations at the observation time, precise alignment of multi-source heterogeneous data in the time dimension is achieved. This provides a complete original sample data foundation, including optical characteristics, environmental driving factors, and true concentration labels, for subsequent organic aerosol concentration calibration.

[0020] Furthermore, a deep learning-based method for calibrating organic aerosol concentration includes the following sub-steps: data cleaning of channel echo signals; time alignment of the cleaned channel echo signals with the original sample data; extraction of the aligned channel echo signals to obtain aerosol extinction coefficients and fluorescence-elastic scattering ratios; and integration of the channel echo signals, aerosol extinction coefficients, fluorescence-elastic scattering ratios, and meteorological parameters into a multi-source observation vector after normalization. Collecting continuous-time multi-source observation vectors to obtain multi-source observation features includes the following sub-steps:

[0021] Noise reduction, squared distance correction, smoothing, and outlier removal are performed on the echo signals of each channel to obtain the cleaned channel echo signals.

[0022] The cleaned channel echo signal is synchronized with the meteorological parameters and organic aerosol reference concentration at the same observation time in the original sample data to obtain the aligned channel echo signal;

[0023] The aerosol extinction coefficient and fluorescence-elastic scattering ratio were extracted using the aligned channel echo signals.

[0024] The aligned channel echo signals, meteorological parameters, aerosol extinction coefficients, and fluorescence-elastic scattering ratios are normalized respectively, and then integrated to obtain the multi-source observation vector at the current time.

[0025] By integrating multi-source observation vectors from consecutive time points, multi-source observation features are obtained.

[0026] In the above scheme, noise subtraction, distance squared correction, smoothing and outlier removal are performed on the echo signals of each channel in sequence, and the signals are synchronized with meteorological parameters and reference concentrations. The aerosol extinction coefficient and fluorescence-elastic scattering ratio are extracted, and after normalization, a multi-source observation vector is formed and a continuous time window sequence is constructed. This effectively eliminates noise and abnormal interference in the original signal, realizes the alignment and scale uniformity of multi-source features in the time dimension, and provides a stable and continuous multi-time series input feature foundation for the subsequent concentration calibration model.

[0027] Furthermore, a deep learning-based method for calibrating organic aerosol concentrations, wherein the multi-source observation vector at the current moment is expressed by the formula:

[0028] ;

[0029] in, Let be the multi-source observation vector at time t. This is the normalized elastic scattering channel echo signal at time t. This is the normalized nitrogen Raman scattering channel echo signal at time t. The normalized fluorescence channel signal at time t Let be the normalized aerosol extinction coefficient at time t. The normalized fluorescence-elastic scattering ratio at time t. Let be the normalized temperature at time t. Let be the normalized relative humidity at time t. Let be the normalized wind speed at time t. Let be the normalized wind direction at time t. The pressure is the normalized air pressure, and t is the current time.

[0030] In the above scheme, by constructing the normalized elastic scattering, Raman scattering, fluorescence channel signal, aerosol extinction coefficient, fluorescence-elastic scattering ratio, and temperature, relative humidity, wind speed, wind direction, and air pressure as the multi-source observation vector at the current moment, the scale unification and information integration of different physical dimension features are realized, providing a standardized and low-redundancy feature representation basis for the subsequent construction of continuous time window sequences and model inputs.

[0031] Furthermore, a deep learning-based method for calibrating the concentration of organic aerosols, wherein noise subtraction, squared distance correction, smoothing, and outlier removal are performed on the echo signals of each channel to obtain the cleaned channel echo signals, includes the following sub-steps:

[0032] Background noise is subtracted from the echo signals of each channel to obtain the background-subtracted channel echo signals;

[0033] The background-subtracted channel echo signal is subjected to squared distance correction to obtain the corrected channel echo signal;

[0034] The corrected channel echo signal is smoothed to obtain a smoothed channel echo signal.

[0035] The mean and standard deviation of all smoothed channel echo signals within a window are obtained by using a sliding window.

[0036] Outlier identification is performed using the mean and standard deviation. Outliers are then removed and replaced with the mean to obtain the cleaned channel echo signal.

[0037] In the above scheme, by performing background noise subtraction, distance squared correction, smoothing, and outlier identification and removal based on the mean and standard deviation of the sliding window sequentially on the echo signals of each channel, the influence of dark current, ambient background light, geometric attenuation, random noise and transient interference on the original signal is effectively eliminated, and high-quality, continuous and physically consistent cleaned channel echo signals are obtained, providing a reliable data foundation for subsequent feature extraction and concentration calibration.

[0038] Furthermore, a deep learning-based method for calibrating organic aerosol concentrations is provided. The organic aerosol concentration calibration model comprises, in sequence, an input layer, a branch coding layer, a multi-scale temporal feature extraction layer, an attention-gated fusion module, a bidirectional temporal modeling layer, a channel recalibration layer, and an output layer. The organic aerosol concentration calibration model processes multi-source observation features and historical state features through a bidirectional long short-term memory network and an SE attention mechanism to obtain the predicted organic aerosol concentration, including the following sub-steps:

[0039] The input layer divides the multi-source observation features into lidar features and meteorological features;

[0040] The branch coding layer extracts lidar features through the lidar branch encoder to obtain lidar coding features, the meteorological branch encoder extracts meteorological features to obtain meteorological coding features, and the state branch encoder extracts historical state features to obtain state coding features. The feature fusion layer concatenates and maps the lidar coding features, meteorological coding features, and state coding features to obtain multi-source coding fusion features.

[0041] The multi-scale temporal feature extraction layer extracts multi-source coding fusion features through short-scale convolutional branches to obtain short-scale features, medium-scale convolutional branches to extract multi-source coding fusion features to obtain medium-scale features, and long-scale convolutional branches to extract multi-source coding fusion features to obtain long-scale features.

[0042] The attention-gated fusion module extracts short-scale, medium-scale, and long-scale features through global average pooling to obtain short-scale descriptive vectors, medium-scale descriptive vectors, and long-scale descriptive vectors. It then uses gating to generate scale fusion weights corresponding to the short-scale, medium-scale, and long-scale descriptive vectors. Finally, it obtains multi-scale gated fusion features by using the scale fusion weights and the short-scale, medium-scale, and long-scale descriptive vectors.

[0043] The bidirectional temporal modeling layer processes multi-scale gated fusion features along the time-increasing direction through a forward long short-term memory network to obtain a forward hidden state sequence, and processes multi-scale gated fusion features along the time-decreasing direction through a reverse long short-term memory network to obtain a reverse hidden state sequence. The forward hidden state sequence and the reverse hidden state sequence are concatenated to obtain bidirectional temporal features.

[0044] The recalibration layer compresses and excites the bidirectional temporal features to obtain the channel weight vector. The channel recalibration features are obtained by element-wise multiplying the channel weight vector with the bidirectional temporal features.

[0045] The output layer obtains the predicted organic aerosol concentration by recalibrating the channel features.

[0046] In the above scheme, the multi-source observation features are divided into lidar and meteorological features through the input layer. The three types of features are encoded separately by the branch coding layer and fused into multi-source coded fusion features. Then, the multi-scale temporal feature extraction layer extracts short-term, medium-term, and long-term scale features in parallel. The attention-gated fusion module dynamically generates scale weights based on the global description vector and performs weighted fusion. The bidirectional temporal modeling layer uses forward and backward LSTM to capture contextual correlations. The recalibration layer generates channel weights through SE attention compression excitation and performs element-wise weighting. Finally, the output layer maps to obtain the predicted concentration. This process realizes branch coding of multi-source heterogeneous features, adaptive fusion of multi-scale temporal information, bidirectional contextual correlation modeling, and recalibration of channel features, significantly enhancing the model's ability to characterize the evolution of organic aerosol concentration and improving prediction accuracy.

[0047] Furthermore, a deep learning-based method for calibrating organic aerosol concentrations, wherein the recalibration layer compresses and excites bidirectional temporal features to obtain channel weight vectors, includes the following sub-steps:

[0048] The recalibration layer compresses bidirectional temporal features along the time dimension using global average pooling to obtain channel description vectors;

[0049] The channel weight vector is obtained by using the excitation channel description vector of the fully connected layer.

[0050] In the above scheme, channel description vectors are obtained by compressing bidirectional temporal features along the time dimension through global average pooling, and then channel weight vectors are generated by fully connected layer activation. This achieves adaptive evaluation and dynamic recalibration of the importance of each feature channel, providing accurate weight basis for subsequent element-wise weighted enhancement of effective channels and suppression of redundant noise.

[0051] Furthermore, a deep learning-based method for calibrating organic aerosol concentration is provided, wherein the organic aerosol concentration calibration model is iteratively trained with a composite loss function as the objective, and the parameters of the organic aerosol concentration calibration model are updated.

[0052] The composite loss function is constructed using a prediction error term, a physical error term, and a soft constraint term.

[0053] Furthermore, a deep learning-based method for calibrating the concentration of organic aerosols is provided, wherein the prediction error term is constructed using mean error and mean absolute error.

[0054] The physical constraints are constructed through non-negativity constraints, smoothness constraints, humidity response consistency constraints, and optical parameter consistency constraints.

[0055] The soft constraint terms are constructed through range constraint terms, order constraint terms, and operating condition prior constraint terms.

[0056] In the above scheme, a composite loss function consisting of prediction error term, physical constraint term and soft constraint term is constructed, and the model is iteratively trained with this loss function as the target. This enables the model to satisfy physical laws such as non-negativity, smoothness, humidity response consistency, and optical parameter consistency, as well as business constraints such as range, ranking, and prior operating conditions, while fitting the reference concentration. This significantly improves the physical consistency, robustness and generalization ability of the organic aerosol concentration calibration model under complex environments.

[0057] Furthermore, a deep learning-based method for calibrating organic aerosol concentration includes the following sub-steps for constructing physical constraints through non-negativity constraints, smoothness constraints, humidity response consistency constraints, and optical parameter consistency constraints:

[0058] Non-negative constraint terms are obtained by penalizing the predicted organic aerosol concentrations of the samples.

[0059] The smoothing constraint term is obtained by weighted summing and averaging the squares of the differences in the predicted organic aerosol concentrations at adjacent time points.

[0060] A humidity response consistency constraint term is obtained by penalizing the opposite of the predicted changes in organic aerosol concentration at adjacent time points and the relative humidity at adjacent time points.

[0061] An optical parameter consistency constraint term is obtained by imposing a penalty when the predicted aerosol concentration difference between sample pairs is opposite to the optical parameter difference between sample pairs.

[0062] In the above scheme, by applying non-negative penalties to the predicted concentration, weighted smoothing constraints to the concentration differences between adjacent time points, penalties to the inconsistency between the direction of concentration change and relative humidity change, and penalties to the inconsistency between the direction of concentration difference and optical parameter difference, physical constraint terms including non-negative constraints, smoothing constraints, humidity response consistency constraints, and optical parameter consistency constraints are constructed. This effectively guides the model to output prediction results that satisfy non-negative concentration, reasonable time changes, regular humidity response, and consistent optical correlation, thereby enhancing the physical credibility of the model and its stability under complex working conditions. Attached Figure Description

[0063] To more clearly illustrate the technical solutions of the embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be regarded as a limitation on the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort.

[0064] Figure 1 This is a flowchart of a deep learning-based method for calibrating the concentration of organic aerosols.

[0065] Figure 2 The structural diagram of the organic aerosol concentration calibration model. Detailed Implementation

[0066] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only a part of the embodiments of the present invention, and not all of them. The components of the embodiments of the present invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the present invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. All other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort are within the scope of protection of the present invention.

[0067] It should be noted that similar reference numerals and letters in the following figures denote similar items; therefore, once an item is defined in one figure, it does not need to be further defined and explained in subsequent figures. Furthermore, in the description of this invention, the terms "first," "second," etc., are used only for distinguishing descriptions and should not be construed as indicating or implying relative importance, or suggesting any such actual relationship or order between these entities or operations. Additionally, the terms "connected," "linked," etc., can refer to a direct connection between elements or an indirect connection via other elements.

[0068] like Figure 1 As shown, a deep learning-based method for calibrating the concentration of organic aerosols includes the following sub-steps:

[0069] S1: Simultaneously acquire multi-channel echo signals, meteorological parameters, and organic aerosol reference concentrations, and integrate them into raw sample data;

[0070] S11: Acquire multi-channel echo signals using lidar; the multi-channel echo signals include elastic scattering channel signals, nitrogen Raman scattering channel signals, and fluorescence channel signals;

[0071] In the embodiment, the elastic scattering channel is detected near 355 nm, the nitrogen Raman scattering channel is detected near 387 nm, and the fluorescence channel is detected in the range of 400 nm to 520 nm.

[0072] S12: Collect meteorological parameters synchronously based on the observation time of the lidar; the meteorological parameters include temperature, relative humidity, wind speed, wind direction, and air pressure;

[0073] S13: Simultaneously obtain the reference concentration of organic aerosols based on the observation time of the lidar.

[0074] It should be noted that reference concentrations for organic aerosols are provided by portable detectors, online monitoring devices, or other calibrated reference instruments.

[0075] S2: Perform data cleaning on the channel echo signal, align the cleaned channel echo signal with the original sample data in time, extract the aligned channel echo signal, obtain the aerosol extinction coefficient and fluorescence-elastic scattering ratio, integrate the channel echo signal, aerosol extinction coefficient, fluorescence-elastic scattering ratio and meteorological parameters after normalization into a multi-source observation vector, and collect the multi-source observation vectors over continuous time to obtain multi-source observation characteristics.

[0076] S21: Perform noise reduction, squared distance correction, smoothing and outlier removal on the echo signals of each channel to obtain the cleaned channel echo signals;

[0077] S211: Perform background noise subtraction on the echo signals of each channel to obtain the background-subtracted channel echo signals. The formula is:

[0078] ;

[0079] in, To be at the distance of the door The background echo signal is removed from the channel. To be at the distance of the door The channel echo signal, To be at the distance of the door Background noise signal at that location, Let represent the slant range of the i-th range gate (the distance between the lidar and the target), where i is the range gate number.

[0080] It should be noted that background noise subtraction is performed to eliminate dark current and ambient light interference.

[0081] S212: Perform squared distance correction on the background-subtracted channel echo signal to obtain the corrected channel echo signal, using the following formula:

[0082] ;

[0083] in, To be at the distance of the door The corrected channel echo signal.

[0084] It should be noted that squared distance correction is used to improve the comparability of channel echo signals at different distances.

[0085] S213: Smooth the corrected channel echo signal to obtain the smoothed channel echo signal, using the following formula:

[0086] ;

[0087] in, To be at the distance of the door The smoothed channel echo signal, To smoothly slide the window half-width, To smoothly slide the window length, This is the offset. To be at the distance of the door The corrected channel echo signal.

[0088] It is important to note that smoothing is used to suppress random noise.

[0089] S214: Obtain the mean and standard deviation of all smoothed channel echo signals within a sliding window using the following formula:

[0090] ;

[0091] in, Let be the mean of all smoothed channel echo signals within the window centered at the i-th distance gate, and h be the half-width of the anomaly detection sliding window. The distance to the door number within the window. To be at the distance of the door The smoothed channel echo signal, Let be the standard deviation of all smoothed channel echo signals within the window centered at the i-th distance gate.

[0092] S215: Outlier identification is performed using the mean and standard deviation. Outliers are then removed, and the mean is used to replace the outliers to obtain the cleaned channel echo signal. The formula is as follows:

[0093] ;

[0094] in, To be at the distance of the door The channel echo signal after cleaning This is the threshold coefficient for anomaly detection. If, Otherwise.

[0095] In the embodiments, .

[0096] It is important to note that eliminating outliers reduces equipment fluctuations and transient interference.

[0097] S22: Synchronously align the cleaned channel echo signal with the meteorological parameters and organic aerosol reference concentration at the same observation time in the original sample data to obtain the aligned channel echo signal;

[0098] S23: Extract the aerosol extinction coefficient and fluorescence-elastic scattering ratio using the aligned channel echo signal.

[0099] S231: The aerosol extinction coefficient is obtained by inversion using the echo signal from the aligned elastic scattering channel and the echo signal from the nitrogen Raman scattering channel;

[0100] S232: Obtain the fluorescence-elastic scattering ratio by comparing the aligned fluorescence channel signal and the elastic scattering channel echo signal.

[0101] S24: Normalize the aligned channel echo signals, meteorological parameters, aerosol extinction coefficients, and fluorescence-elastic scattering ratios respectively. Then, integrate the normalized data to obtain the multi-source observation vector for the current moment, using the following formula:

[0102] ;

[0103] in, Let be the multi-source observation vector at time t. This is the normalized elastic scattering channel echo signal at time t. This is the normalized nitrogen Raman scattering channel echo signal at time t. The normalized fluorescence channel signal at time t Let be the normalized aerosol extinction coefficient at time t. The normalized fluorescence-elastic scattering ratio at time t. Let be the normalized temperature at time t. Let be the normalized relative humidity at time t. Let be the normalized wind speed at time t. Let be the normalized wind direction at time t. The pressure is the normalized air pressure, and t is the current time.

[0104] It is important to note that before normalization, the aligned channel echo signal should be... Compression of the changing vertical profile into a scalar (e.g., taking the whole-layer average or integral) can be understood as removing... .

[0105] S25: Integrate the multi-source observation vectors from consecutive time points to obtain multi-source observation features, using the following formula:

[0106] ;

[0107] in, As a feature of multi-source observation, The length of the time window for consecutive moments. , For the feature dimensions of multi-source observation features, .

[0108] S3: The organic aerosol concentration calibration model uses a bidirectional long short-term memory network and SE attention mechanism to process multi-source observation features and historical state features to obtain the predicted organic aerosol concentration.

[0109] The historical state characteristics ;

[0110] in, This refers to the predicted organic aerosol concentration within the historical statistical window. This represents the average predicted concentration of organic aerosols within the historical statistical window. This represents the predicted rate of change in organic aerosol concentration within a historical statistical window. The standard deviation of predicted organic aerosol concentration within the historical statistical window. This is the historical prediction residual (the difference between the reference concentration and the predicted concentration of organic aerosols at the previous moment).

[0111] The organic aerosol concentration calibration model includes an input layer, a branch coding layer, a multi-scale temporal feature extraction layer, an attention-gated fusion module, a bidirectional temporal modeling layer, a channel recalibration layer, and an output layer. The branch coding layer includes a branch encoder and a feature fusion layer. The branch encoder includes a lidar branch encoder, a meteorological branch encoder, and a state branch encoder. The multi-scale temporal feature extraction layer includes a short-scale convolutional branch, a medium-scale convolutional branch, and a long-scale convolutional branch.

[0112] The connection structure of the organic aerosol concentration calibration model is as follows: the input layer, the branch coding layer, the multi-scale temporal feature extraction layer, the attention gating fusion module, and the bidirectional temporal modeling layer are connected in sequence.

[0113] Specifically, the first output of the input layer is connected to the input of the lidar branch encoder; the second output of the input layer is connected to the input of the meteorological branch encoder; the third output of the input layer is connected to the input of the state branch encoder; the output of the lidar branch encoder is connected to the first input of the feature fusion layer; the output of the meteorological branch encoder is connected to the second input of the feature fusion layer; the output of the state branch encoder is connected to the third input of the feature fusion layer; the first output of the feature fusion layer is connected to the input of the short-term convolution branch; the second output of the feature fusion layer is connected to the input of the medium-term convolution branch; the third output of the feature fusion layer is connected to the input of the long-term convolution branch; the output of the short-term convolution branch is connected to the first input of the attention-gated fusion module; the output of the medium-term convolution branch is connected to the second input of the attention-gated fusion module; the output of the long-term convolution branch is connected to the third input of the attention-gated fusion module; the output of the attention-gated fusion module is connected to the input of the bidirectional temporal modeling layer; the output of the bidirectional temporal modeling layer is connected to the input of the channel recalibration layer; and the input of the channel recalibration layer is connected to the input of the output layer.

[0114] It should be noted that the branch encoder consists of a one-dimensional convolutional layer, a normalization layer, and a non-linear activation layer.

[0115] S31: The input layer divides multi-source observation features into lidar features and meteorological features, using the following formula:

[0116] ;

[0117] in, Features of lidar As a meteorological feature, It is an elastic scattering sequence. It is a Raman scattering sequence. It is a fluorescence backscattering sequence. It is an aerosol extinction sequence. It is a fluorescence-elastic scattering ratio sequence. It is a temperature sequence. The relative humidity sequence For wind speed sequence, For wind direction sequence, It is a pressure sequence.

[0118] S32: The branch coding layer extracts lidar features from the lidar branch encoder to obtain lidar coded features, meteorological features from the meteorological branch encoder to obtain meteorological coded features, and historical state features from the state branch encoder to obtain state coded features. The feature fusion layer concatenates and maps the lidar coded features, meteorological coded features, and state coded features to obtain multi-source coded fused features, as shown in the formula:

[0119] ;

[0120] in, For LiDAR coding features, Extraction operation for LiDAR branch encoder. Meteorological coding characteristics, For meteorological branch encoder extraction operation, For state coding features, Extraction operation for state branch encoder, For multi-source coding fusion features, For splicing operations, This is a convolution mapping operation.

[0121] It is important to note that different branch encoders are assigned to the branch coding layer to reduce the mutual interference caused by the direct splicing of features with different dimensions and attributes, thereby improving the feature representation effect of subsequent time series analysis.

[0122] S33: The multi-scale temporal feature extraction layer extracts multi-source coding fusion features through short-scale convolutional branches to obtain short-scale features, medium-scale convolutional branches to extract multi-source coding fusion features to obtain medium-scale features, and long-scale convolutional branches to extract multi-source coding fusion features to obtain long-scale features. The formula is as follows:

[0123] ;

[0124] in, It is a short-time scale feature. For short-timescale convolution branch convolution operations, The equivalent receptive field parameters for short-timescale convolution (e.g., kernel size of 3, dilation rate of 1, receptive field of 3). It is a mid-timescale feature. This is a mid-timescale convolution branch convolution operation. The equivalent receptive field parameters for mesoscale convolution (e.g., kernel size of 3, dilation rate of 2, receptive field of 5~7). It is a long-term scale feature. For long-term convolution branch convolution operations, The equivalent receptive field parameters for long-term convolution (e.g., kernel size of 7 and dilation rate of 1, or kernel size of 3, dilation rate of 4, and receptive field of 9 or more).

[0125] In the embodiments, ,in, The transformed time dimension. This represents the number of channels.

[0126] In existing technologies, changes in organic aerosol concentration are typically influenced by short-term local disturbances, medium-term environmental evolution, and long-term regional transport and accumulation processes simultaneously. Therefore, a multi-scale temporal feature extraction layer is set up. The short-term convolutional branch uses a smaller convolutional kernel and a smaller dilation rate to extract local emissions, pulse fluctuations, and short-term abrupt changes. The medium-term convolutional branch uses a medium convolutional kernel and a medium dilation rate to extract boundary layer evolution, humidity changes, and medium-scale disturbance features. The long-term convolutional branch uses a larger convolutional kernel to extract regional transport, particulate matter aging, and continuous accumulation process features.

[0127] S34: The attention-gated fusion module extracts short-term, mid-term, and long-term features respectively through global average pooling, obtaining short-term, mid-term, and long-term descriptive vectors. It then uses gating to generate scale fusion weights corresponding to these vectors. Finally, it obtains multi-scale gated fusion features using these scale fusion weights and the short-term, mid-term, and long-term descriptive vectors, as shown in the formula:

[0128] ;

[0129] in, A short-time scale description vector. This is a global average pooling operation. This is a mid-timescale description vector. For long-term scale description vectors, This is the weight matrix of the first fully connected layer. This is the bias vector of the first fully connected layer. It is a non-linear activation function (such as the ReLU function). This is the weight matrix of the second fully connected layer. This is the bias vector for the second fully connected layer. For the Softmax function, such that , For scale fusion weights, For short-term fusion weights, For the mid-timescale fusion weights, For long-term scale fusion weights, This is a multi-scale gating fusion feature.

[0130] It is worth noting that the attention-gated fusion module enables the organic aerosol concentration calibration model to automatically adjust the weights of different features at short, medium, and long time scales under different weather conditions and different stages of pollution evolution. It can dynamically highlight more effective time-scale information under different operating conditions such as sunny days, haze, high humidity, and before and after precipitation, thereby improving its adaptability to complex environmental changes.

[0131] In the embodiments, temporal attention mechanism and self-attention mechanism can also be used to obtain the description vector. However, global average pooling is simpler and more efficient, requires no extra parameters, has a small computational load, and matches the gating mechanism. In contrast, temporal attention mechanism and self-attention mechanism have a large number of parameters and may overfit.

[0132] S35: The bidirectional temporal modeling layer processes multi-scale gated fusion features along the time-increasing direction using a forward long short-term memory network to obtain a forward hidden state sequence, and processes multi-scale gated fusion features along the time-decreasing direction using a reverse long short-term memory network to obtain a reverse hidden state sequence. The forward and reverse hidden state sequences are then concatenated to obtain the bidirectional temporal feature, as shown in the formula:

[0133] ;

[0134] in, This is a sequence of positive hidden states. For positive long short-term memory network processing operations, This is a reverse hidden state sequence. Reverse Long Short-Term Memory (LSTM) network processing operations, It has a bidirectional time series characteristic.

[0135] It is worth noting that the bidirectional temporal modeling layer uses both forward and reverse long short-term memory networks to more fully characterize the contextual relationships of organic aerosol concentrations during the temporal evolution process.

[0136] S36: The recalibration layer compresses and excites the bidirectional temporal features to obtain the channel weight vector. The channel recalibration features are obtained by element-wise multiplying the channel weight vector with the bidirectional temporal features.

[0137] S361: The recalibration layer compresses bidirectional temporal features along the time dimension using global average pooling to obtain channel description vectors, as shown in the formula:

[0138] ;

[0139] in, For channel description vectors, The length of the time series is a bidirectional temporal feature. For time step index;

[0140] S362: The channel weight vector is obtained using the excitation channel description vector of the fully connected layer. The formula is as follows:

[0141] ;

[0142] in, This is the channel weight vector. For the Sigmoid function, This is the weight matrix of the fourth fully connected layer. This is the weight matrix of the third fully connected layer. This is the bias vector of the third fully connected layer. This is the bias vector for the fourth fully connected layer;

[0143] S363: Element-wise multiplication of the channel weight vector and the bidirectional temporal features yields the channel recalibration features, as shown in the formula:

[0144] ;

[0145] in, For channel recalibration features, This is an element-wise product.

[0146] It should be noted that after recalibrating the layer to process the bidirectional time-series features, the obtained channel recalibration features enhance the effective feature channels that are strongly correlated with the concentration of organic aerosols, while suppressing noise channels and redundant channels.

[0147] S37: The output layer obtains the predicted organic aerosol concentration by recalibrating the features of the channels, using the following formula:

[0148] ;

[0149] in, For the predicted organic aerosol concentration, The weight matrix of the output layer. This is the bias vector for the output layer.

[0150] The organic aerosol concentration calibration model is iteratively trained using a composite loss function as the objective, and the parameters of the organic aerosol concentration calibration model are updated accordingly. The formula is as follows:

[0151] ;

[0152] in, For learning rate, for The organic aerosol concentration in each training round calibrates the model parameters. For the current training round, for The organic aerosol concentration in each training round calibrates the model parameters. For composite loss function, For composite loss function right Organic aerosol concentration calibration model parameters in training rounds The gradient.

[0153] Specifically, the composite loss function is constructed using a prediction error term, a physical error term, and a soft constraint term, and the formula is as follows:

[0154] ;

[0155] in, These are the weighting coefficients for the prediction error term. For the prediction error term, These are the weighting coefficients for the physical constraint terms. For physical constraints, These are the weighting coefficients for the soft constraint terms. This is a soft constraint.

[0156] It is important to note that physical constraints are used to penalize predictions that violate known physical laws, while soft constraints are used to guide predictions to meet operating condition experience, boundary conditions, or trend priors, while ensuring the model's learnability.

[0157] More specifically, the weighting coefficients are adjusted during the training iterations of the organic aerosol concentration calibration model, using the following formula:

[0158] ;

[0159] in, for The weighting coefficients of the prediction error term for each training epoch. These are the initial weighting coefficients for the prediction error term. The weighting increment for the prediction error term is scheduled. for The weighting coefficients of the physical constraints in each training round. These are the initial weighting coefficients for the physical constraint terms. The weighting increment for the physical constraint term. For the total number of training rounds, for The weighting coefficients of the soft constraint term in each training epoch. These are the initial weighting coefficients for the soft constraint terms. The weighting increment for soft constraint terms. , .

[0160] It is important to note that in the initial stage of training the organic aerosol concentration calibration model, let This allows the organic aerosol concentration calibration model to learn the basic mapping relationship. In the later stages of training the organic aerosol concentration calibration model, incremental improvements are achieved through weight scheduling. and The weights of these weights enable the organic aerosol concentration calibration model to further meet the requirements of physical constraints and soft constraints.

[0161] More specifically, the prediction error term is constructed using the mean error and the mean absolute error, as shown in the following formula:

[0162] ;

[0163] in, This represents the total number of samples in the current training batch. This is the index of the current training batch of samples. The predicted organic aerosol concentration for the nth sample. This is the reference concentration of organic aerosols for the nth sample. This is the balance coefficient.

[0164] More specifically, the physical constraint term is constructed through a non-negativity constraint term, a smoothing constraint term, a humidity response consistency constraint term, and an optical parameter consistency constraint term, as shown in the following formula:

[0165] ;

[0166] in, These are the weighting coefficients for the non-negativity constraint terms. The weighting coefficients for the smoothing constraint term, The weighting coefficients for the humidity response consistency constraint term. These are the weighting coefficients for the optical parameter consistency constraint term. These are non-negative constraint terms. For the smoothing constraint term, This is a humidity response consistency constraint. This is a constraint term for the consistency of optical parameters.

[0167] By applying a penalty to the predicted organic aerosol concentration of the sample, a non-negative constraint term is obtained, as shown in the formula:

[0168] ;

[0169] in, To obtain the maximum value.

[0170] It should be noted that the non-negative constraint term is used to constrain the predicted organic aerosol concentration to be no less than zero.

[0171] The smoothing constraint term is obtained by weighted summing and averaging the squares of the differences in predicted organic aerosol concentrations between adjacent time points. The formula is as follows:

[0172] ;

[0173] in, The length of the time step sequence for the current training batch. The smoothing constraint weights at time t are reduced when there is a sudden pollution source, strong convection, or drastic weather change at time t. When the time t is stationary, Take a positive value (e.g., 1). Let be the predicted concentration of organic aerosols at time t. The concentration of organic aerosols predicted at time t-1.

[0174] It should be noted that the smoothing constraint is used to suppress non-physical oscillations in the prediction results between adjacent time points when there are no sudden pollution sources, strong convection, or other drastic changes.

[0175] By penalizing the opposite of the predicted changes in organic aerosol concentration at adjacent time points and the relative humidity at adjacent time points, a humidity response consistency constraint term is obtained, as shown in the formula:

[0176] ;

[0177] in, Let t be the humidity response consistency activation factor. The relative humidity is normalized at time t-1.

[0178] It is important to note that the humidity response consistency constraint ensures that the predicted concentration changes are consistent with the hygroscopic growth pattern.

[0179] By imposing a penalty when the predicted differences in aerosol concentrations and optical parameters of a sample pair are opposite, an optical parameter consistency constraint term is obtained, the formula of which is:

[0180] ;

[0181] in, This represents the total number of sample pairs in the current training batch. For sample pair indexing, Let p be the predicted concentration of organic aerosols for the p-th sample. Let q be the predicted concentration of organic aerosols for the q-th sample. Let be the optical parameters of the p-th sample. Let be the optical parameters of the q-th sample.

[0182] The optical parameters include the normalized fluorescence channel signal, the normalized aerosol extinction coefficient, and the normalized fluorescence-elastic scattering ratio.

[0183] It should be noted that the optical parameter consistency constraint term is used to constrain the predicted organic aerosol concentration to maintain a monotonic, piecewise, or intervally correlated relationship with the fluorescence channel signal, aerosol extinction coefficient, and fluorescence-elastic scattering ratio.

[0184] More specifically, the soft constraint term is constructed through range constraint term, ordination constraint term, and prior operating condition constraint term, as shown in the formula:

[0185] ;

[0186] in, These are the weighting coefficients for the range constraint terms. These are the weight coefficients for the sorting constraint terms. These are the weighting coefficients for the prior constraints of the operating conditions. For range constraint terms, For sorting constraints, These are the prior constraints for the operating conditions.

[0187] By setting upper and lower limits for organic aerosol concentration, a penalty is applied when the predicted organic aerosol concentration of a sample exceeds these limits to obtain a range constraint term. The formula is as follows:

[0188] ;

[0189] in, This is the preset upper limit for organic aerosol concentration. This is the preset lower limit for organic aerosol concentration.

[0190] It should be noted that the range constraint ensures that the predicted organic aerosol concentration of the sample does not exceed the preset upper and lower limits of the organic aerosol concentration.

[0191] The ranking constraint term is obtained by penalizing sample pairs with a clear trend relationship (e.g., near-ground concentrations are usually higher than upper-air concentrations or concentrations show a monotonically increasing trend over time during pollution) when the trend direction is opposite to the expected trend. The formula is as follows:

[0192] ;

[0193] in, For sample pairs The expected trend direction, if expected hour, If expected hour, .

[0194] It should be noted that the sorting constraint is used to maintain the relative size regularity of the prediction results when there is a clear trend relationship between adjacent time periods, adjacent height layers, or adjacent spatial locations.

[0195] By comparing the predicted organic aerosol concentration of the sample with the empirical prior concentration of the corresponding operating condition label, and applying a penalty when there is a deviation, the prior constraint term for the operating condition is obtained, as shown in the formula:

[0196] ;

[0197] in, The operating condition label (such as sunny day, haze, high humidity, before or after precipitation, etc.) corresponds to the nth sample. The working condition label corresponding to the nth sample The pre-set empirical prior concentration is used.

[0198] It is important to note that the prior constraints on operating conditions are used to guide the model to learn reasonable response patterns under different operating conditions based on operating condition labels such as sunny days, fog and haze, high humidity, and before and after precipitation.

[0199] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the technical scope disclosed in the present invention should be included within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of the claims.

Claims

1. A deep learning-based method for calibrating concentration of organic aerosol, characterized in that, Includes the following sub-steps: Simultaneously collect multi-channel echo signals, meteorological parameters, and organic aerosol reference concentrations, and integrate them into raw sample data; The channel echo signal is cleaned, and the cleaned channel echo signal is time-aligned with the original sample data. The aligned channel echo signal is extracted to obtain the aerosol extinction coefficient and fluorescence-elastic scattering ratio. The channel echo signal, aerosol extinction coefficient, fluorescence-elastic scattering ratio and meteorological parameters are normalized and integrated into a multi-source observation vector. The multi-source observation vectors over continuous time are collected to obtain multi-source observation characteristics. The organic aerosol concentration calibration model uses a bidirectional long short-term memory network and SE attention mechanism to process multi-source observation features and historical state features to obtain the predicted organic aerosol concentration. 2.The deep learning-based organic aerosol concentration calibration method according to claim 1, wherein, The process of simultaneously acquiring multi-channel echo signals, meteorological parameters, and organic aerosol reference concentrations, and integrating them into raw sample data, includes the following sub-steps: Multi-channel echo signals are acquired using lidar; the multi-channel echo signals include elastic scattering channel signals, nitrogen Raman scattering channel signals, and fluorescence channel signals. Meteorological parameters are collected synchronously based on the observation time of the lidar; the meteorological parameters include temperature, relative humidity, wind speed, wind direction, and air pressure; The reference concentration of organic aerosols is obtained synchronously based on the observation time of the lidar. 3.The deep learning-based organic aerosol concentration calibration method according to claim 1, characterized in that, The process of cleaning the channel echo signals involves aligning the cleaned signals to the original sample data over time, extracting the aligned channel echo signals, obtaining the aerosol extinction coefficient and fluorescence-elastic scattering ratio, and then integrating the channel echo signals, aerosol extinction coefficient, fluorescence-elastic scattering ratio, and meteorological parameters into a multi-source observation vector after normalization. Collecting continuous-time multi-source observation vectors to obtain multi-source observation features includes the following sub-steps: Noise reduction, squared distance correction, smoothing, and outlier removal are performed on the echo signals of each channel to obtain the cleaned channel echo signals. The cleaned channel echo signal is synchronized with the meteorological parameters and organic aerosol reference concentration at the same observation time in the original sample data to obtain the aligned channel echo signal; The aerosol extinction coefficient and fluorescence-elastic scattering ratio were extracted using the aligned channel echo signals. The aligned channel echo signals, meteorological parameters, aerosol extinction coefficients, and fluorescence-elastic scattering ratios are normalized respectively, and then integrated to obtain the multi-source observation vector at the current time. By integrating multi-source observation vectors from consecutive time points, multi-source observation features are obtained. 4.The deep learning-based organic aerosol concentration calibration method according to claim 3, characterized in that, The formula for the multi-source observation vector at the current moment is: ； wherein, is a multi-source observation vector at time t, is a normalized elastic scattering channel echo signal at time t, is a normalized nitrogen Raman scattering channel echo signal at time t, is a normalized fluorescence channel signal at time t, is a normalized aerosol extinction coefficient at time t, is a normalized fluorescence-elastic scattering ratio at time t, is a normalized temperature at time t, is a normalized relative humidity at time t, is a normalized wind speed at time t, is a normalized wind direction at time t, is a normalized air pressure, t is the current time.

5. The method for calibrating organic aerosol concentration based on deep learning according to claim 3, characterized in that, The process of performing noise reduction, squared distance correction, smoothing, and outlier removal on the echo signals of each channel to obtain the cleaned channel echo signals includes the following sub-steps: Background noise is subtracted from the echo signals of each channel to obtain the echo signals of the channels with background noise removed. The background-subtracted channel echo signal is subjected to squared distance correction to obtain the corrected channel echo signal; The corrected channel echo signal is smoothed to obtain a smoothed channel echo signal. The mean and standard deviation of all smoothed channel echo signals within a window are obtained by using a sliding window. Outlier identification is performed using the mean and standard deviation. Outliers are then removed and replaced with the mean to obtain the cleaned channel echo signal.

6. The method for calibrating the concentration of organic aerosols based on deep learning according to claim 1, characterized in that, The organic aerosol concentration calibration model comprises, in sequence, an input layer, a branch coding layer, a multi-scale temporal feature extraction layer, an attention-gated fusion module, a bidirectional temporal modeling layer, a channel recalibration layer, and an output layer. The organic aerosol concentration calibration model processes multi-source observation features and historical state features through a bidirectional long short-term memory network and an SE attention mechanism to obtain the predicted organic aerosol concentration, including the following sub-steps: The input layer divides the multi-source observation features into lidar features and meteorological features; The branch coding layer extracts lidar features through the lidar branch encoder to obtain lidar coding features, the meteorological branch encoder extracts meteorological features to obtain meteorological coding features, and the state branch encoder extracts historical state features to obtain state coding features. The feature fusion layer concatenates and maps the lidar coding features, meteorological coding features, and state coding features to obtain multi-source coding fusion features. The multi-scale temporal feature extraction layer extracts multi-source coding fusion features through short-scale convolutional branches to obtain short-scale features, medium-scale convolutional branches to extract multi-source coding fusion features to obtain medium-scale features, and long-scale convolutional branches to extract multi-source coding fusion features to obtain long-scale features. The attention-gated fusion module extracts short-scale, medium-scale, and long-scale features through global average pooling to obtain short-scale descriptive vectors, medium-scale descriptive vectors, and long-scale descriptive vectors. It then uses gating to generate scale fusion weights corresponding to the short-scale, medium-scale, and long-scale descriptive vectors. Finally, it obtains multi-scale gated fusion features by using the scale fusion weights and the short-scale, medium-scale, and long-scale descriptive vectors. The bidirectional temporal modeling layer processes multi-scale gated fusion features along the time-increasing direction through a forward long short-term memory network to obtain a forward hidden state sequence, and processes multi-scale gated fusion features along the time-decreasing direction through a reverse long short-term memory network to obtain a reverse hidden state sequence. The forward hidden state sequence and the reverse hidden state sequence are concatenated to obtain bidirectional temporal features. The recalibration layer compresses and excites the bidirectional temporal features to obtain the channel weight vector. The channel recalibration features are obtained by element-wise multiplying the channel weight vector with the bidirectional temporal features. The output layer obtains the predicted organic aerosol concentration by recalibrating the channel features.

7. The method for calibrating organic aerosol concentration based on deep learning according to claim 6, characterized in that, The recalibration layer compresses and excites bidirectional temporal features to obtain channel weight vectors, including the following sub-steps: The recalibration layer compresses bidirectional temporal features along the time dimension using global average pooling to obtain channel description vectors; The channel weight vector is obtained by using the excitation channel description vector of the fully connected layer.

8. The method for calibrating the concentration of organic aerosols based on deep learning according to claim 1, characterized in that, The organic aerosol concentration calibration model is iteratively trained using a composite loss function as the objective, and the parameters of the organic aerosol concentration calibration model are updated accordingly. The composite loss function is constructed using a prediction error term, a physical error term, and a soft constraint term.

9. The method for calibrating the concentration of organic aerosols based on deep learning according to claim 8, characterized in that, The prediction error term is constructed using the mean error and the mean absolute error; The physical constraints are constructed through non-negativity constraints, smoothness constraints, humidity response consistency constraints, and optical parameter consistency constraints. The soft constraint terms are constructed through range constraint terms, order constraint terms, and operating condition prior constraint terms.

10. The method for calibrating the concentration of organic aerosols based on deep learning according to claim 9, characterized in that, The physical constraint terms are constructed through non-negativity constraint terms, smoothness constraint terms, humidity response consistency constraint terms, and optical parameter consistency constraint terms, including the following sub-steps: Non-negative constraint terms are obtained by penalizing the predicted organic aerosol concentrations of the samples; The smoothing constraint term is obtained by weighted summing and averaging the squares of the differences in the predicted organic aerosol concentrations at adjacent time points. A humidity response consistency constraint term is obtained by penalizing the opposite of the predicted changes in organic aerosol concentration at adjacent time points and the relative humidity at adjacent time points. An optical parameter consistency constraint term is obtained by penalizing the difference in predicted aerosol concentration between sample pairs when the difference in optical parameters between sample pairs is opposite.

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