A regression analysis-based system error compensation method for a laser ceilometer

Abstract

The application provides a laser ceilometer system error compensation method based on regression analysis, and belongs to the technical field of laser ceilometers.The application divides a measurement range into four height intervals by constructing a layered height interval step regression equation set and establishing independent nonlinear regression equations, designs a double-layer game optimization framework to realize collaborative optimization of global error minimization and local fitting accuracy maximization, performs historical data preprocessing and data set division, implements a double-layer game model collaborative optimization algorithm to determine regression equation coefficients and neural network parameters, constructs an adaptive cloud height error correction model based on a Transformer architecture to realize real-time error compensation, and maintains optimal model performance through sliding time window monitoring and automatic retraining, thereby solving the technical problem that the measurement accuracy of a laser ceilometer is significantly affected by system errors caused by changes in atmospheric environmental parameters and device parameters.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of laser ceilometer, and particularly relates to a laser ceilometer system error compensation method based on regression analysis. BACKGROUND

[0002] As a core device of modern meteorological observation and aviation meteorological guarantee, the laser ceilometer measures the cloud base height by emitting a laser beam and receiving the cloud reflection signal, and is widely used in airport meteorological observation, climate monitoring, numerical weather prediction and other fields. The traditional laser ceilometer system mainly uses a simple linear model or an empirical formula based on laser echo time ranging to calculate the cloud base height, and preliminarily corrects the measurement results by using a fixed calibration coefficient. This method can provide relatively accurate measurement results under standard atmospheric conditions. However, the traditional technology has obvious limitations in the face of complex and variable atmospheric environment, especially when the atmospheric temperature, humidity, pressure and other environmental parameters change significantly, the propagation characteristics of the laser beam will be affected to different degrees, and the fluctuations of the laser itself and the changes of the response characteristics of the photoelectric detector will also introduce additional system errors. In the current application of the laser ceilometer, due to the lack of comprehensive consideration and dynamic compensation mechanism for multi-dimensional influencing factors, the measurement accuracy is often difficult to meet the strict requirements of high-precision meteorological observation and aviation safety guarantee, that is, there is a technical problem in the prior art that the measurement accuracy of the laser ceilometer is significantly affected by the changes of the atmospheric environmental parameters and the device itself. SUMMARY

[0003] Therefore, the application provides a laser ceilometer system error compensation method based on regression analysis, which can solve the technical problem in the prior art that the measurement accuracy of the laser ceilometer is significantly affected by the changes of the atmospheric environmental parameters and the device itself.

[0004] The application is implemented in the following manner: the application provides a laser ceilometer system error compensation method based on regression analysis, which comprises the following steps: collecting laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data, and synchronously acquiring standard cloud base height measurement values by a reference laser ceilometer as dependent variable reference data for regression analysis; constructing a hierarchical height interval stepwise regression equation set, dividing the cloud base height measurement range according to different height intervals, establishing an independent nonlinear regression equation for each height interval, and the nonlinear regression equation comprises a laser parameter linear term, an atmospheric parameter nonlinear term, and an adaptive cloud height error correction model output term; establishing a double-layer game optimization framework, constructing an upper-layer optimization model with the minimum root mean square error of cloud base height measurement as an objective function and a lower-layer optimization model with the maximum fitting degree of each height interval regression equation as an objective function; implementing a double-layer game model collaborative optimization algorithm to determine the laser parameter linear coefficient and the atmospheric parameter nonlinear coefficient of each height interval nonlinear regression equation, and simultaneously optimizing the network connection weight parameter and the bias parameter of the adaptive cloud height error correction model; and constructing a real-time cloud base height error compensation algorithm, determining the height interval category to which the current measurement data belong through a height interval discrimination function, calling the nonlinear regression equation of the corresponding height interval to calculate a preliminary cloud base height prediction value, calculating an error compensation amount through the adaptive cloud height error correction model, and outputting the final cloud base height measurement result.

[0005] In the step of constructing the hierarchical height interval stepwise regression equation set, the cloud base height measurement range is divided into a low cloud interval of 30-500 m, a middle-low cloud interval of 500-2000 m, a middle-high cloud interval of 2000-5000 m, and a high cloud interval of 5000-7500 m.

[0006] In the nonlinear regression equation of each height interval, the logarithmic term of the ratio of the laser beam emission power data to the laser echo signal intensity data is added to the square root term of the product of the atmospheric temperature data and the atmospheric humidity data, and the exponential decay term of the atmospheric pressure data is subtracted, and then the product term of the quadratic coefficient of the laser beam emission power data and the atmospheric temperature data is added, and finally the adaptive cloud height error correction model output term is added.

[0007] In the upper-layer optimization model objective function, the input includes the cloud base height measurement error sequence of each height interval, the nonlinear regression equation coefficient vector, the model structure complexity index, the L2 regularization penalty parameter, and the upper-lower layer coupling weight coefficient, and the output is the optimal objective function value of the upper-layer optimization model.

[0008] The lower layer optimization model objective function is specifically used for maximizing the fitting accuracy of each height interval nonlinear regression equation to historical training data, and the input includes a training data set fitting residual vector, each regression equation decision coefficient, k-fold cross-validation error, constraint condition violation degree, and lower-upper coupling weight coefficient, and the output is an optimal objective function value of the lower layer optimization model.

[0009] Before the step of implementing the double-layer game model collaborative optimization algorithm, the method further includes performing a historical cloud height measurement data preprocessing procedure, performing outlier detection and elimination on collected laser beam transmission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, and standard cloud base height measurement values, eliminating abnormal measurement data using a 3 times standard deviation criterion, and performing normalization processing on the data after eliminating outliers, and dividing the data set according to a 70% training set and a 30% verification set ratio.

[0010] The height interval discriminant function is specifically used for automatically identifying the height interval category to which the cloud base height belongs according to the current laser measurement parameters and atmospheric environment parameters, and the input includes laser beam transmission power data, laser echo signal intensity data, atmospheric temperature data, and preliminary cloud base height estimation values, and the output is a corresponding height interval category identifier.

[0011] After the step of constructing the real-time cloud base height error compensation algorithm, the method further includes designing a dynamic model parameter updating mechanism, continuously monitoring cloud base height measurement error statistical indicators using a sliding time window method, and when the root mean square error of continuous measurement errors exceeds a preset error threshold, automatically starting a model retraining procedure, re-executing the double-layer game model collaborative optimization algorithm, and updating the parameters of each height interval nonlinear regression equation and the parameters of the adaptive cloud height error correction model.

[0012] The adaptive cloud height error correction model is specifically a sequence processing architecture based on a Transformer encoder, includes an input feature embedding layer, maps five-dimensional parameters such as laser beam transmission power, laser echo signal intensity, atmospheric temperature, humidity, and pressure to a unified feature space through linear transformation, uses a learned position embedding vector to represent the importance weight of different parameters in a position encoding layer, and uses a Transformer encoder to capture complex nonlinear relationships between parameters through a self-attention mechanism.

[0013] The number of layers of the Transformer encoder is dynamically adjusted according to the rate of change of the data environment parameter, when the environmental parameter changes little (the similarity of the adjacent environmental parameters of the input is greater than or equal to 90%), a 3-layer encoder is used to reduce the calculation overhead, when the environmental parameter changes greatly (the similarity of the adjacent environmental parameters of the input is less than 90%), the number of layers is increased to 6 to improve the representation ability, and finally the high-dimensional features are mapped to the cloud base height error compensation value through a multi-head fully connected output layer, and a residual connection and layer normalization mechanism are introduced to improve the training stability and generalization performance of the model.

[0014] The adaptive cloud height error correction model training data set is constructed, specifically, laser cloud height instrument measurement sample data under different weather conditions are collected, covering six typical atmospheric conditions of clear weather, little cloudy weather, cloudy weather, overcast weather, precipitation weather and haze weather, not less than 15000 groups of effective measurement samples are collected for each weather condition, the laser beam emission power data, the laser echo signal intensity data, the atmospheric temperature data, the atmospheric humidity data and the atmospheric pressure data are taken as the network input features, and the corresponding cloud base height measurement error is taken as the network output label. The training data set is constructed, specifically, the original training data set is expanded to 90000 training samples through data enhancement technology and noise injection method, and the data set is divided into training set, validation set and test set three subsets in time sequence order. The adaptive cloud height error correction model training process is specifically that the AdamW optimization algorithm is used for network parameter gradient update, the initial learning rate is set to 0.0001, the batch processing size is 128, the total training iteration number is 300 rounds, the cosine annealing learning rate decay strategy is used to dynamically adjust the learning rate, the model performance index is evaluated on the validation set every 20 rounds, when the validation set loss function value does not appear for 15 consecutive rounds, the training process is terminated in advance, and the network parameters with the optimal performance of the validation set are selected as the final adaptive cloud height error correction model parameters.

[0015] Further, the adaptive cloud height error correction model specifically further includes an image block adjustment function for dynamically optimizing the feature extraction granularity of the adaptive cloud height error correction model according to the real-time atmospheric environmental conditions and the laser measurement parameters. The image block adjustment function calculates a block adjustment factor based on the three key environmental parameters of the laser echo signal intensity data, the atmospheric humidity data and the atmospheric pressure data.

[0016] The image block adjustment function is specifically: when the block adjustment factor belongs to a low sensitivity numerical range, a larger image block size is adopted to reduce the calculation complexity and improve the processing efficiency; when the block adjustment factor belongs to a medium sensitivity numerical range, a medium image block size is adopted to balance the feature extraction accuracy and the calculation efficiency; and when the block adjustment factor belongs to a high sensitivity numerical range, a smaller image block size is adopted to obtain a more fine feature representation and a higher error correction accuracy, so that the image block parameters of the adaptive cloud height error correction model are dynamically adjusted.

[0017] Further, the laser ceilometer multi-parameter synchronous data acquisition system is also included, which is a sensor network platform integrated with core functions of coordinating and controlling multiple sensor modules to realize accurate synchronous acquisition of laser measurement parameters and environmental parameters, ensuring that the laser beam emission power data and the laser echo signal intensity data are strictly consistent with the atmospheric temperature, humidity, pressure and other environmental parameters in the time dimension through a high-precision clock synchronization mechanism, and simultaneously integrating a reference laser ceilometer device to obtain a standard cloud base height measurement reference value, and adopting a distributed data acquisition architecture, each sensor node communicates with the central processing unit through a CAN bus or an Ethernet protocol.

[0018] The present application effectively solves the technical problem of significant system error of the traditional laser ceilometer system by constructing a hierarchical height interval stepwise regression equation set and a double-layer game optimization framework, and combining an adaptive cloud height error correction model. The present application establishes independent nonlinear regression equations for different height intervals, fully considers the differentiated influence law of laser parameters and atmospheric parameters in different height ranges, realizes the collaborative optimization of global error minimization and local fitting accuracy maximization through a double-layer game optimization model, overcomes the defects that the traditional method cannot simultaneously consider the overall performance and local accuracy, and simultaneously introduces an adaptive error correction model based on the Transformer architecture, which can dynamically capture the complex nonlinear relationship between parameters and adjust the compensation strategy in real time. The present application also designs a dynamic model parameter updating mechanism, monitors and automatically re-trains through a sliding time window, ensures that the compensation model can continuously adapt to environmental changes, and fundamentally solves the problem that the system error fluctuates with the change of environmental conditions. In summary, the present application solves the technical problem that the measurement accuracy of the laser ceilometer is affected by the change of atmospheric environmental parameters and device parameters, resulting in significant system error. BRIEF DESCRIPTION OF DRAWINGS

[0019] Figure 1 The flowchart of the method of the present application. DETAILED DESCRIPTION

[0020] In order to make the purposes, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be described clearly and completely below with reference to the drawings in the embodiments of the present application.

[0021] As Figure 1 shown is a flowchart of a laser ceilometer system error compensation method based on regression analysis provided by the present application, and the method comprises the following steps:

[0022] S01, a laser ceilometer multi-parameter synchronous data acquisition system is established, laser beam transmission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data are synchronously acquired, and a standard cloud base height measurement value is synchronously acquired by a reference laser ceilometer as dependent variable reference data for regression analysis;

[0023] S02, a hierarchical height interval stepwise regression equation set is constructed, the cloud base height measurement range is divided into a low cloud interval of 30-500 meters, a middle-low cloud interval of 500-2000 meters, a middle-high cloud interval of 2000-5000 meters, and a high cloud interval of 5000-7500 meters, an independent nonlinear regression equation is established for each height interval, and the nonlinear regression equation comprises a laser parameter linear term, an atmospheric parameter nonlinear term, and an adaptive cloud height error correction model output term;

[0024] S03, a double-layer game optimization framework is established, an upper-layer optimization model with minimization of cloud base height measurement root mean square error as an objective function and a lower-layer optimization model with maximization of fitting goodness of each height interval regression equation as an objective function are constructed, the upper-layer optimization model objective function comprises a measurement error square sum term, a regression coefficient regularization penalty term, a model complexity control term, and an upper-lower layer coupling constraint term, and the lower-layer optimization model objective function comprises a fitting residual square sum term, a determination coefficient maximization term, a cross-validation error minimization term, and a lower-upper layer coupling constraint term;

[0025] S04, a historical cloud height measurement data preprocessing procedure is performed, abnormal value detection and elimination are performed on the acquired laser beam transmission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, and standard cloud base height measurement value, 3 times of standard deviation criterion is adopted to eliminate abnormal measurement data, normalization processing is performed on the data after elimination of abnormal values, and the data set is divided according to a proportion of 70% for a training set and 30% for a verification set;

[0026] S05, a double-layer game model collaborative optimization algorithm is implemented, through an iterative solving process of the upper-layer optimization model and the lower-layer optimization model, laser parameter linear coefficients of each height interval nonlinear regression equation and atmospheric parameter nonlinear coefficients are determined, and network connection weight parameters and bias parameters of an adaptive cloud height error correction model are simultaneously optimized;

[0027] S06, constructing a real-time cloud base height error compensation algorithm, according to the current measurement obtained laser beam transmit power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, determining the height interval category through the height interval discrimination function, calling the nonlinear regression equation of the corresponding height interval to calculate the preliminary cloud base height prediction value, and then calculating the error compensation amount through the adaptive cloud height error correction model, and outputting the final cloud base height measurement result;

[0028] S07, designing a dynamic model parameter updating mechanism, using a sliding time window method to continuously monitor cloud base height measurement error statistical indicators, when the root mean square error of continuous measurement error exceeds the preset error threshold, automatically starting the model retraining process, and re-executing the double-layer game model collaborative optimization algorithm to update the nonlinear regression equation parameters and adaptive cloud height error correction model parameters of each height interval.

[0029] The mathematical form of the nonlinear regression equation of each height interval is the logarithmic term of the ratio of laser beam transmit power data and laser echo signal intensity data, plus the square root term of the product of atmospheric temperature data and atmospheric humidity data, minus the exponential decay term of atmospheric pressure data, plus the product term of the quadratic term coefficient of laser beam transmit power data and atmospheric temperature data, and finally plus the output term of the adaptive cloud height error correction model.

[0030] The upper layer optimization model objective function is used to minimize the overall measurement error of the entire laser cloud height instrument system, and the input includes the cloud base height measurement error sequence of each height interval, the nonlinear regression equation coefficient vector, the model structure complexity index, the L2 regularization penalty parameter, and the upper and lower layer coupling weight coefficient. The output is the optimal objective function value of the upper layer optimization model.

[0031] The lower layer optimization model objective function is used to maximize the fitting accuracy of each height interval nonlinear regression equation to historical training data, and the input includes the training data set fitting residual vector, the regression equation determination coefficient, the k-fold cross-validation error, the constraint condition violation degree, and the lower and upper layer coupling weight coefficient. The output is the optimal objective function value of the lower layer optimization model.

[0032] The height interval discrimination function is used to automatically identify the height interval category of the cloud base height according to the current laser measurement parameters and atmospheric environment parameters, and the input includes laser beam transmit power data, laser echo signal intensity data, atmospheric temperature data, and preliminary cloud base height estimate value. The output is the corresponding height interval category identifier.

[0033] The network architecture of the adaptive cloud height error correction model adopts a sequence processing architecture based on a Transformer encoder to replace the original visual processing mode. The network structure includes an input feature embedding layer, which maps the five-dimensional parameters of laser beam transmission power, laser echo signal strength, atmospheric temperature, humidity, and pressure to a unified feature space through linear transformation; the position encoding layer uses a learnable position embedding vector to represent the importance weight of different parameters; among them, the number of layers of the Transformer encoder is dynamically adjusted according to the rate of change of the data environment parameters, when the environmental parameters change less (the similarity of adjacent environmental parameters is greater than or equal to 90%), a 3-layer encoder is used to reduce the computational overhead, when the environmental parameters change greatly (the similarity of adjacent environmental parameters is less than 90%), the number of layers is increased to 6 to improve the representation ability, and finally the high-dimensional features are mapped to the cloud base height error compensation value through a multi-head fully connected output layer, and the residual connection and layer normalization mechanism are introduced to improve the training stability and generalization performance of the model.

[0034] The construction of the training data set of the adaptive cloud height error correction model includes collecting laser cloud height instrument measurement sample data under different weather conditions, covering six typical atmospheric conditions: clear sky weather, few cloud weather, cloudy weather, overcast weather, precipitation weather, and haze weather. Each weather condition collects not less than 15000 groups of valid measurement samples. The laser beam transmission power data, laser echo signal strength data, atmospheric temperature data, atmospheric humidity data, and atmospheric pressure data are used as network input features, and the corresponding cloud base height measurement error is used as network output label. Through data enhancement technology and noise injection method, the original training data set is expanded to 90000 training samples. The data set is divided into training set, validation set and test set three subsets in time sequence order.

[0035] The training process of the adaptive cloud height error correction model includes updating the network parameter gradient using the AdamW optimization algorithm, setting the initial learning rate to 0.0001, the batch processing size to 128, and the total training iteration number to 300 rounds. The cosine annealing learning rate decay strategy is used to dynamically adjust the learning rate, and the model performance indicators are evaluated on the validation set every 20 rounds. When the validation set loss function value does not appear for 15 consecutive rounds, the training process is terminated in advance. The network parameters with the best performance on the validation set are selected as the final adaptive cloud height error correction model parameters.

[0036] The image block adjustment function is used to dynamically optimize the feature extraction granularity of the adaptive cloud height error correction model according to real-time atmospheric environmental conditions and laser measurement parameters. The image block adjustment function calculates a block adjustment factor based on three key environmental parameters, i.e., laser echo signal intensity data, atmospheric humidity data, and atmospheric pressure data. When the block adjustment factor belongs to a low sensitivity numerical range, a larger image block size is used to reduce the computational complexity and improve the processing efficiency. When the block adjustment factor belongs to a medium sensitivity numerical range, a medium image block size is used to balance the feature extraction accuracy and the computational efficiency. When the block adjustment factor belongs to a high sensitivity numerical range, a smaller image block size is used to obtain a more fine feature representation and a higher error correction accuracy, thereby dynamically adjusting the image block parameters of the adaptive cloud height error correction model.

[0037] The multi-parameter synchronous data acquisition system of the laser ceilometer is an integrated sensor network platform, and its core function is to coordinate and control multiple sensor modules to realize accurate synchronous acquisition of laser measurement parameters and environmental parameters. The system ensures that the laser beam emission power data and the laser echo signal intensity data are strictly consistent with the environmental parameters such as atmospheric temperature, humidity, and pressure in the time dimension through a high-precision clock synchronization mechanism, and integrates a reference laser ceilometer device to obtain a standard cloud base height measurement reference value. The system adopts a distributed data acquisition architecture, and each sensor node communicates with the central processing unit through CAN bus or Ethernet protocol to ensure the real-time and reliability of data transmission, and has data preprocessing, storage management, and quality control function modules, providing high-quality multidimensional input data for subsequent regression analysis and error compensation algorithms.

[0038] The specific implementation of the above steps is described in detail below.

[0039] The specific implementation of step S01 is to first build a hardware synchronization control platform, using a high-precision global positioning system clock chip as the main time sequence generator to ensure that the data acquisition timestamp error of each sensor module is controlled within 1 millisecond. The laser emission power sensor monitors the laser output power in real time through a photodiode array, with a sampling frequency set to 1 kilohertz and a measurement accuracy of 0.1 watts. The laser echo signal strength detection module uses avalanche photodiode technology, combined with a low-noise preamplifier circuit, to achieve high-sensitivity detection of weak echo signals. The atmospheric temperature sensor uses a platinum resistance thermometer, with a measurement range of -40°C to 60°C and an accuracy of 0.1°C. The atmospheric humidity sensor is based on the capacitive humidity detection principle, with a relative humidity measurement range of 0% to 100% and an accuracy of 2%. The atmospheric pressure sensor uses silicon piezoresistive pressure detection technology, with a measurement range of 80 kilopascals to 110 kilopascals and an accuracy of 0.1 kilopascals. Each sensor is connected to the data acquisition controller through a controller area network bus, realizing distributed real-time data transmission. The reference laser ceilometer equipment provides the reference cloud base height measurement value through a standard serial communication interface, with a data update frequency of 10 times per second.

[0040] The specific implementation of step S02 is to divide the measurement range into four height intervals according to the cloud height distribution characteristics and atmospheric physical properties. The low cloud interval is set to 30 meters to 500 meters, mainly for the measurement requirements of stratus and fog-like clouds. The low-mid cloud interval is set to 500 meters to 2000 meters, covering typical cloud types such as stratocumulus and rain layer clouds. The mid-high cloud interval is set to 2000 meters to 5000 meters, corresponding to high cumulus and high-level clouds. The high cloud interval is set to 5000 meters to 7500 meters, mainly dealing with cirrus and convective clouds. An independent nonlinear regression equation is established for each height interval, with the equation structure containing the natural logarithm term of the ratio of laser beam emission power to echo signal strength, reflecting the attenuation law of laser in the atmosphere. The square root term of the product of atmospheric temperature and humidity reflects the influence of water vapor condensation on optical propagation. The exponential decay term of atmospheric pressure describes the influence law of height change on atmospheric density. The product term of laser emission power quadratic term and atmospheric temperature represents the nonlinear influence of temperature on the working state of the laser. The adaptive error correction model output term is used to compensate for systematic errors under complex environmental conditions.

[0041] The specific implementation of step S03 is to construct a hierarchical optimization solution architecture. The upper layer optimization model takes minimizing the overall measurement error as the core objective. The objective function includes the quadratic sum of the cloud base height measurement error, reflecting the overall accuracy level of the system. The L2 regularization penalty term of the regression coefficient prevents model overfitting, and the regularization coefficient is set to 0.01. The model complexity control term evaluates the model structure rationality through the Akaike information criterion. The upper and lower layer coupling constraint term ensures the coordination consistency of the two-layer optimization problem, and the coupling weight coefficient is set to 0.5. The lower layer optimization model focuses on improving the fitting accuracy of each height interval regression equation. The fitting residual sum of squares term measures the approximation degree of the regression equation to the training data. The determination coefficient maximization term requires the explanation ability of each regression equation to be above 0.85. The k-fold cross-validation error minimization term uses a 5-fold cross-validation strategy to evaluate the model generalization performance. The lower and upper layer coupling constraint term maintains the parameter consistency with the upper layer model. The two-layer game structure realizes the coordination and unity of the upper and lower layer optimization objectives through Nash equilibrium theory.

[0042] The specific implementation of step S04 is to establish a complete data quality control process. First, the original measurement data is identified and removed. The 3 standard deviation criterion is used to detect laser power data, and when a measurement value exceeds the average value plus or minus 3 times the standard deviation, it is determined to be an outlier and is removed. The laser echo signal strength data uses the box plot quartile range method to identify outliers, and data points exceeding the first quartile minus 1.5 times the quartile range or the third quartile plus 1.5 times the quartile range are marked as outliers. The atmospheric parameter data is smoothed by the sliding window median filtering method, and the window length is set to 5 sampling points. After removing the outliers, the remaining data is normalized. The laser parameter uses the maximum and minimum value normalization method to map the value to the 0 to 1 interval. The atmospheric parameter uses the zero mean unit variance standardization method to ensure the comparability of parameters with different dimensions. The data set is divided using the time series segmentation method, with the first 70% of the time series data as the training set for model parameter learning, and the last 30% of the data as the validation set to evaluate the model performance, ensuring time continuity to avoid data leakage problems.

[0043] The specific implementation of step S05 is to realize the iterative solution algorithm of the two-layer game model. Genetic algorithm is used to solve the upper layer optimization problem. The population size is set to 100 individuals, and the chromosome coding method uses real number coding to represent the regression coefficient vector. The selection operation uses the tournament selection strategy, and the tournament size is 3. The crossover operation uses the simulated binary crossover method, and the crossover probability is set to 0.8. The mutation operation uses the polynomial mutation strategy, and the mutation probability is set to 0.1. The lower layer optimization problem is solved by particle swarm optimization algorithm, and the particle swarm size is set to 50 particles. The inertia weight uses a linear decreasing strategy, with an initial value of 0.9 and a final value of 0.4. The acceleration factor and Both are set to 2.0. The upper and lower layer iterative solution process realizes parameter coordination through bidirectional information exchange. The upper layer optimization result is used as the constraint condition of the lower layer optimization, and the lower layer optimization result is fed back to the upper layer model to adjust the search direction. The iteration termination condition is set to less than 20 consecutive generations of optimal solution improvement amplitude or reaches the maximum iteration number of 500 generations. The adaptive error correction model parameters are optimized synchronously through the back propagation algorithm, and the learning rate is dynamically adjusted according to the gradient change using an adaptive adjustment strategy.

[0044] The specific implementation of step S06 is to establish a real-time cloud bottom height compensation calculation process. First, the height interval category corresponding to the current measurement condition is determined through a height interval discrimination function. The discrimination function is based on fuzzy logic reasoning method, and the input parameters include laser beam transmission power, laser echo signal strength, atmospheric temperature and preliminary height estimation value. The fuzzy process converts continuous input variables into fuzzy set membership degrees, and triangular and trapezoidal membership functions are used to describe the fuzzy intervals of each parameter. The reasoning rule base contains 24 if-then rules to describe the correspondence between different parameter combinations and height intervals. The defuzzification process uses the barycentric method to calculate the final height interval category probability distribution. According to the discrimination result, the nonlinear regression equation of the corresponding height interval is called to calculate the preliminary cloud bottom height prediction value, and the Newton-Raphson iteration method is used to ensure numerical stability. The adaptive error correction model calculates the error compensation value through forward propagation, inputs the five-dimensional environmental parameters measured at present into the Transformer encoder network, and obtains high-dimensional feature representation through multi-layer nonlinear transformation. Finally, it is mapped to the cloud bottom height error compensation value through the fully connected layer. The compensation value and the preliminary prediction value are added to obtain the final cloud bottom height measurement result.

[0045] The specific implementation of step S07 is to establish a dynamic model update monitoring mechanism. The sliding time window method is used to continuously monitor the measurement error statistical indicators. The time window length is set to 1 hour, and the root mean square error, mean absolute error and maximum absolute error of the measurement error in the window are calculated every 10 minutes. When the root mean square error exceeds the preset threshold of 20 meters for 3 consecutive calculation periods, the system automatically triggers the model retraining process. The retraining process first collects the measurement data of the last 72 hours as new training samples, and mixes them with historical training data according to a ratio of 3:7 to form an updated training set. Model retraining uses an incremental learning strategy to fine-tune the original parameters rather than completely retrain them to maintain the model's historical knowledge and speed up convergence. The parameter update uses the exponential moving average method, and the fusion weight of new and old parameters is set to 0.2:0.8 to ensure model stability. After retraining, the performance of the updated model is evaluated by an independent validation set. When the performance improvement is more than 5%, the new model parameters are deployed, otherwise the original model continues to run. The model update history is stored in the database for easy tracing and analysis of model evolution trends.

[0046] The adaptive cloud height error correction model adopts a deep learning architecture based on a Transformer encoder, with strong sequence modeling and feature learning capabilities. The network structure first includes an input feature embedding layer, which maps the input parameters of laser beam transmission power, laser echo signal intensity, atmospheric temperature, atmospheric humidity, and atmospheric pressure in five dimensions to a unified 128-dimensional feature space through linear transformation. Each input parameter corresponds to a learnable embedding matrix with dimensions 1 x 128, which realizes linear mapping of the parameter vector to a high-dimensional feature vector through a fully connected layer. The position encoding layer uses a learnable position embedding vector to assign a 128-dimensional position encoding to each input parameter, representing the importance weight of different parameters in the error correction process. The position encoding is added to the feature embedding to form the final input representation, which is input to the subsequent Transformer encoder module.

[0047] The Transformer encoder module is the core computing unit of the network, consisting of a stack of multiple encoder layers. Each encoder layer consists of a multi-head self-attention mechanism and a feedforward neural network. The multi-head self-attention mechanism uses 8 attention heads, each with a query, key, and value vector dimension of 16. The attention weight distribution is obtained by calculating the dot product of the query vector and the key vector, and the weight distribution is normalized by softmax before being multiplied by the value vector to obtain the weighted feature representation. The output of the multi-head attention is combined into a 128-dimensional feature vector through concatenation. The feedforward neural network consists of two fully connected layers, the first layer expands the 128-dimensional input to 512 dimensions and uses the ReLU activation function, and the second layer compresses the 512-dimensional features back to 128 dimensions. Each sub-module is followed by a residual connection and layer normalization operation. The residual connection alleviates the gradient vanishing problem through a skip connection, and the layer normalization accelerates the training convergence by standardizing the feature distribution. The number of encoder layers is dynamically adjusted according to the complexity of the environmental conditions. When the atmospheric parameter changes less than 10%, a 3-layer encoder is used to reduce computational complexity, and when the environmental conditions change dramatically, the number of encoder layers is increased to 6 to improve the model's representation ability.

[0048] The output layer uses a multi-head fully connected structure to map high-dimensional features to cloud base height error compensation values. The first fully connected layer maps the 128-dimensional encoder output to 64-dimensional intermediate features, using Dropout regularization to prevent overfitting with a Dropout probability of 0.1. The second fully connected layer maps the 64-dimensional features to 32 dimensions, also using Dropout regularization. The final output layer is a single neuron that uses a linear activation function to output the cloud base height error compensation value, with a range of -100 meters to 100 meters, covering most error correction needs.

[0049] The training dataset establishment process includes comprehensive data collection and preprocessing steps. The data collection stage is carried out in different geographical locations and climate conditions for long-term continuous observation, covering six typical weather types: clear, few clouds, many clouds, overcast, precipitation, and haze. 15000 samples are collected under clear weather conditions, with visibility greater than 20 kilometers and cloud cover less than 10%. 15000 samples are collected under few cloud weather, with cloud cover between 10% and 30% and uniform cloud base height distribution. 15000 samples are collected under many cloud weather, with cloud cover between 30% and 70% and multiple cloud structures. 15000 samples are collected under overcast weather, with cloud cover greater than 70% and relatively stable cloud base height. 15000 samples are collected under precipitation weather, including measurement data under rainfall and snowfall conditions. 15000 samples are collected under haze weather, with atmospheric visibility less than 5 kilometers and the presence of aerosol particles.

[0050] Data augmentation techniques expand the number of training samples through various methods. Time series data augmentation uses a sliding window sampling strategy to divide continuous measurement data into different time steps to generate new training samples. Noise injection method adds Gaussian white noise to the original data, with noise intensity set to 5% of the signal standard deviation, simulating random errors in actual measurement. Parameter perturbation technique applies small random perturbations to laser power and atmospheric parameters, with perturbation amplitude controlled within 2% of the original value, enhancing the model's robustness to parameter fluctuations. Interpolation generation method generates new data points between existing samples through cubic spline interpolation, maintaining data distribution continuity and smoothness. After data augmentation, the original 90000 training samples are expanded to 270000, providing sufficient learning samples for model training.

[0051] The data set division uses stratified sampling strategy to ensure that the sample proportion of various weather conditions in the training set, validation set and test set remains consistent. The training set accounts for 60% of the total samples for model parameter learning, the validation set accounts for 20% for hyperparameter tuning and early stopping strategy, and the test set accounts for 20% for final performance evaluation. Sample label construction obtains cloud base height error by comparing the difference between laser ceilometer measurement value and reference equipment standard value, and the error value is smoothed to eliminate high-frequency noise as the model training supervision signal. Data preprocessing also includes outlier detection and missing value filling to ensure the quality and integrity of the training data.

[0052] The analysis of key technical ideas shows that the application has four core innovations. The layered height interval stepwise regression equation set technology establishes a regression model for the physical property differences of different height clouds, significantly improves the adaptability of the model to complex atmospheric environment compared with the traditional single regression equation, effectively captures the nonlinear characteristics of laser-atmosphere interaction in different height intervals through segmented modeling, and avoids the problems of fitting precision loss and insufficient generalization ability caused by global modeling. The double-layer game optimization framework technology realizes the unification of global error minimization and local fitting precision maximization through upper and lower layer cooperative optimization, which can better balance the relationship between model complexity and prediction accuracy compared with the traditional single objective optimization method. The game theory mechanism ensures the coordination consistency of the regression equation of each height interval, avoiding the problem of local optimization falling into suboptimal solution. The adaptive error correction model technology based on the Transformer encoder deeply mines the nonlinear relationship between multi-dimensional environmental parameters by using the self-attention mechanism, which has stronger feature learning and pattern recognition ability than traditional neural networks, can automatically find the complex mapping rule between laser measurement error and environmental factors, and realizes the intelligentization and adaptivity of error compensation. The dynamic model parameter updating mechanism technology has stronger environmental adaptability and long-term stability compared with static model by real-time monitoring of system performance indicators and automatic triggering of retraining process, effectively solving the problem of model performance degradation caused by changes in atmospheric environment.

[0053] The synergistic effect of the four key technical ideas forms a complete intelligent error compensation technology system. Layered regression modeling provides basic prediction capability for different cloud environments, double-layer game optimization ensures the global coordination of each layered model, Transformer error correction network provides fine compensation capability, and dynamic updating mechanism guarantees the long-term performance stability of the system. Compared with the single linear regression or simple neural network method commonly used in existing technologies, the collaborative technology architecture of the application realizes a leap from rough approximation to accurate prediction, and still maintains stable high-precision measurement performance in complex and variable atmospheric environment, providing a solid technical foundation for the wide application of laser ceilometer systems in meteorological observation, aviation safety, environmental monitoring and other fields.

[0054] It should be noted that the present application also solves the technical problems that the existing laser ceilometer system lacks a compensation mechanism for the differences in cloud layer characteristics in different height intervals, resulting in inconsistent measurement accuracy in different height ranges. Traditional laser ceilometers use a unified measurement model and calibration parameters to process cloud base height measurements in all height ranges, ignoring the significant differences in atmospheric density, humidity distribution, temperature gradient, and cloud droplet size distribution in different height intervals such as low clouds, mid-low clouds, mid-high clouds, and high clouds. These physical property differences directly affect the scattering characteristics and attenuation of the laser beam, resulting in significant differences in the applicability of the same set of measurement parameters in different height intervals. The present application builds a layered height interval step regression equation set, establishes independent nonlinear regression equations for four different height intervals of 30 meters to 500 meters, 500 meters to 2000 meters, 2000 meters to 5000 meters, and 5000 meters to 7500 meters, respectively. Each equation fully considers the unique physical laws of laser propagation and cloud scattering in the corresponding height interval, and optimizes the regression coefficients of each interval through a double-layer game optimization framework, so that the measurement compensation can accurately adapt to the differences in cloud layer characteristics in different height intervals, thereby solving the problem of inconsistent measurement accuracy in different height ranges in traditional methods.

[0055] The existing laser ceilometer system lacks multi-parameter collaborative modeling in complex atmospheric environments, resulting in limited error compensation effect. Traditional compensation methods usually only consider a single or a few influencing factors, such as temperature correction or simple humidity compensation, which cannot fully describe the complex coupling relationship and nonlinear interaction effect between laser power, return intensity, temperature, humidity, pressure, and other multi-dimensional parameters. Especially in extreme weather conditions such as fog, precipitation, and rapid changes in temperature and humidity, the mutual influence between parameters is more complex, and traditional linear or simple nonlinear models are difficult to accurately model such multi-dimensional nonlinear relationships. The present application designs an adaptive cloud height error correction model based on the Transformer encoder architecture, which simultaneously processes five-dimensional parameters such as laser beam launch power, laser return signal intensity, atmospheric temperature, humidity, and pressure using the self-attention mechanism, automatically learns and models the complex nonlinear coupling relationship between parameters, gradually extracts deep feature representations through a multi-layer encoder structure, and dynamically adjusts the network depth according to the environmental complexity. In simple environments, 3-layer encoders are used to improve computational efficiency, while in complex environments, 6-layer encoders are expanded to enhance representation ability, while residual connection and layer normalization mechanisms are combined to improve model stability and generalization performance, thereby achieving high-precision error compensation under multi-parameter collaborative modeling.

[0056] Specifically, the principle of this invention is as follows: The core principle that enables this invention to solve the significant error problem of laser cloud height measurement systems lies in establishing a multi-dimensional parameter coupling hierarchical error compensation mechanism and an intelligent dynamic optimization framework. First, this invention constructs a hierarchical set of step regression equations for different cloud base height ranges, addressing the differences in physical characteristics across these ranges. Each height range independently establishes a regression equation containing linear terms for laser parameters and nonlinear terms for atmospheric parameters. This hierarchical modeling strategy can accurately characterize the differentiated performance of laser propagation characteristics and atmospheric scattering patterns within different height ranges, avoiding the problem of insufficient fitting accuracy of traditional single models across the entire height range. Second, the design of the two-layer game-theoretic optimization framework is based on multi-objective optimization theory. The upper-layer model aims to minimize the global measurement error, while the lower-layer model aims to maximize the local fitting accuracy. The two models achieve collaborative optimization through coupling constraint terms. This game-theoretic mechanism can optimize the local accuracy of each sub-range while ensuring overall system performance, resolving the contradiction that traditional optimization methods struggle to balance global and local optima. Furthermore, the adaptive cloud height error correction model based on the Transformer architecture captures the complex nonlinear relationships between multidimensional parameters such as laser power, echo intensity, temperature, humidity, and pressure through a self-attention mechanism. Compared to traditional linear or simple nonlinear models, it can more accurately model the coupling effects and interactions between parameters, thereby achieving more precise error prediction and compensation. Finally, the dynamic model parameter update mechanism is based on statistical process control theory. It monitors the statistical characteristics of errors in real time through a sliding time window. When the error exceeds a preset threshold, it automatically triggers a retraining process. This adaptive mechanism ensures that the compensation model can continuously track environmental changes and maintain optimal compensation performance, thus completely solving the problem of system errors accumulating with changes in time and environmental conditions.

[0057] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0058] In this embodiment, the specific implementation of step S01 is the same as described above, and will not be repeated in detail here.

[0059] The specific implementation of step S02 is to establish nonlinear regression equations for each altitude interval, as shown below:

[0060] ;

[0061] In the formula, For the first Predicted cloud base height for each altitude range, in meters; This data represents the laser beam emission power, expressed in watts. This is data on laser echo signal intensity, in watts per square meter. These are atmospheric temperature data, in Kelvin. is atmospheric humidity data, in percentage; is atmospheric pressure data, in pascal; is standard atmospheric pressure, taking the value of 101325 pascal; is the regression coefficient of the height interval; is the adaptive cloud height error correction model output item, in meters; is the random error item, in meters. The height interval is divided into corresponding to 30 meters to 500 meters, corresponding to 500 meters to 2000 meters, corresponding to 2000 meters to 5000 meters, corresponding to 5000 meters to 7500 meters.

[0062] The parameter acquisition method is: The output power of the laser is monitored in real time by using a photodiode array, and the sampling frequency is 1 kilohertz; The avalanche photodiode technology is used in conjunction with a low-noise preamplifier circuit to obtain; The measurement is obtained by using a platinum resistance thermometer, and the measurement accuracy is 0.1 kelvin; The accuracy is 2% by using the capacitance type humidity detection principle; The accuracy is 0.1 kilopascal by using the silicon piezoresistive pressure detection technology; The calculation is obtained by the adaptive cloud height error correction model; The range of is -5 meters to 5 meters.

[0063] The specific implementation of step S03 is to construct the objective function of the double-layer game optimization framework. The objective function of the upper optimization model is specifically represented as follows:

[0064] ;

[0065] In the formula, is the objective function value of the upper optimization model; is the total number of measurement samples; is the cloud base height measurement value of the measurement, in meters; is the standard cloud base height reference value of the measurement, in meters; is the L2 regularization penalty parameter, taking the value of 0.01; is the model complexity control parameter, taking the value of 0.05; is the upper and lower coupling weight coefficient, taking the value of 0.5; is the Akaike information criterion value; The calculation formula of the coupling constraint term between the upper and lower layers is wherein and are the local objective function values of the upper and lower layer models in the first height interval.

[0066] The objective function of the lower optimization model is specifically represented as follows:

[0067]

[0068] wherein is the objective function value of the lower optimization model; is the number of training samples in the first height interval; is the predicted value of the first sample in the first height interval, in meters; is the observed value of the first sample in the first height interval, in meters; is the lower optimization weight parameter, and is respectively 1.0, 0.8, 0.3, and 0.5; is the determination coefficient of the first height interval; is the cross-validation error of the first height interval; is the constraint condition violation degree, and the calculation formula is wherein is the minimum threshold of the determination coefficient, and is 0.85. wherein, the parameter acquisition method is: and

[0069] synchronous measurement by the laser ceilometer and the reference equipment is obtained; is calculated and obtained by using the formula wherein is the number of model parameters, is the likelihood function value; is calculated and obtained by using the formula wherein is the residual sum of squares of the first interval, is the total sum of squares of the first interval; is calculated and obtained by using 5-fold cross-validation; and are the components of the upper and lower objective functions in the first height interval; is the lower limit of the determination coefficient.

[0070] ​​​​​The specific implementation of step S04 is the same as described above, and will not be repeated in detail here.

[0071] The specific implementation of step S05 is to implement a two-layer game model collaborative optimization algorithm. The upper-layer optimization adopts a genetic algorithm, and the individual fitness function is specifically expressed as follows:

[0072] ;

[0073] In the formula, This represents the individual fitness value. This represents the objective function value of the upper layer. The lower layer optimization uses a particle swarm optimization algorithm, and the particle position update formula is expressed as follows:

[0074] ;

[0075] ;

[0076] In the formula, For the first The particle velocity vector of the next iteration; For the first The particle velocity vector of the next iteration; As an inertial weight, a linear decreasing strategy is adopted to decrease it from 0.9 to 0.4; The acceleration factor is 2.0. A random number between 0 and 1; This is the optimal position vector in the particle's history. The global optimal position vector; For the first The particle position vector of the next iteration; For the first The particle position vector of the next iteration.

[0077] The parameter acquisition method is as follows: and Obtained by comparing historical fitness values; The numbers are obtained using a pseudo-random number generator; the iteration termination condition is that the improvement of the optimal solution for 20 consecutive generations is less than [a certain value]. Or it can reach the maximum number of iterations, 500 generations.

[0078] The specific implementation of step S06 is to construct a height interval discrimination function, which is specifically expressed as follows:

[0079] ;

[0080] in, ;

[0081] In the formula, The height range category identifier for determination; For the first Membership function for each height interval; This is a preliminary estimate of the cloud base height, in meters. For the first The interval is the first The weighting coefficients of each parameter; For the first Input parameters In the Membership function values ​​for each interval; The final formula for calculating the cloud base height is as follows:

[0082] ;

[0083] In the formula, The final cloud base height measurement result is in meters; The results of the regression equation calculation for the corresponding height range; This is the output value of the adaptive error correction model for the corresponding height range.

[0084] The parameter acquisition method is as follows: Based on the basic principles of laser ranging Calculation and acquisition, where At the speed of light, This refers to the round-trip time of the laser. Determined through expert experience and historical data analysis; The calculation is performed using triangular and trapezoidal membership functions.

[0085] The specific implementation of step S07 is to establish a dynamic model parameter update monitoring mechanism. The formula for calculating the root mean square error of the sliding window is as follows:

[0086] ;

[0087] In the formula, The root mean square error of the sliding window is expressed in meters. This is the length of the time window, with a value of 360 sampling points corresponding to 1 hour; This refers to the current time point; For the first The final measurement result of the time; For the first The standard baseline value at time 1. The specific formula for updating the model parameters is as follows:

[0088] ;

[0089] In the formula, This is the updated model parameter vector; is the original model parameter vector; is the model parameter vector obtained by retraining; is the parameter fusion weight, and the value is 0.2.

[0090] The parameter acquisition method is as follows: is obtained in real time by referring to a laser ceilometer; when trigger retraining when the threshold value of 20 meters is exceeded for 3 consecutive calculation periods; is obtained by re-executing the double-layer game optimization algorithm.

[0091] The upper-layer optimization model objective function is specifically represented as follows:

[0092] ;

[0093] The meanings of the parameters are the same as defined in step S03. The objective function optimizes system performance by minimizing the overall measurement error, the regularization term prevents overfitting, the complexity control term maintains model simplicity, and the coupling constraint term ensures consistency between the upper and lower layers.

[0094] The lower-layer optimization model objective function is specifically represented as follows:

[0095] ;

[0096] The meanings of the parameters are the same as defined in step S03. The objective function optimizes local modeling effect by maximizing the fitting accuracy of each height interval, the determination coefficient term ensures the explanation ability, the cross-validation term improves the generalization performance, and the constraint term maintains the feasibility of the solution.

[0097] The height interval discrimination function is specifically represented as follows:

[0098] ;

[0099] The meanings of the parameters are the same as defined in step S06. The discrimination function automatically identifies the interval to which the cloud base height belongs through fuzzy logic reasoning, avoids the instability of traditional hard classification methods at the boundary, and improves the accuracy and robustness of interval division.

[0100] The adaptive cloud height error correction model adopts a Transformer encoder architecture to map multi-dimensional environmental parameters to error compensation values, and uses a self-attention mechanism to mine the non-linear correlations between parameters, thereby realizing intelligent error correction. The model outputs directly as the compensation term of the regression equation, dynamically adjusting the prediction result to adapt to complex environmental changes.

[0101] It should be noted that the non-linear regression equation of each height interval establishes a prediction model for different cloud layer physical characteristics through a piecewise modeling strategy, and the logarithmic term Lambert-Beer law embodying laser atmospheric attenuation wherein is the light intensity after attenuation, is the initial light intensity, is the atmospheric attenuation coefficient, is the light propagation distance, square root term reflects the nonlinear effect of water vapor condensation, exponential attenuation term describes the atmospheric pressure height distribution law, quadratic product term captures the nonlinear modulation effect of temperature on laser performance. Compared with the traditional single linear model, the hierarchical regression equation significantly improves the prediction accuracy and adaptability in complex atmospheric environment, avoiding the cumulative fitting error problem of global modeling. The two-layer game optimization framework realizes the unification of global error minimization and local precision maximization through the upper and lower layer coordination mechanism, and the game equilibrium ensures the parameter coordination of each interval model, effectively avoiding the local optimal trap and parameter conflict problem compared with the independent optimization method. The high degree interval discriminant function overcomes the instability of traditional hard classification in the boundary region through the soft classification mechanism of fuzzy logic, and improves the accuracy and continuity of interval identification through multi-parameter comprehensive judgment. The sliding window dynamic monitoring mechanism and adaptive parameter update maintains the stability and accuracy of the model in long-term operation, and significantly improves the adaptability and robustness of the system to environmental changes compared with static models.

[0102] In order to better understand and implement the present application, the following provides an embodiment 2 of a specific application scenario of the present application: a technical team receives a task to build a high-precision laser ceilometer measurement system for a weather observation station. The observation station faces complex atmospheric environmental conditions, including large diurnal temperature difference, severe humidity change, low air pressure and other characteristics, and the traditional laser ceilometer has large measurement error in this environment. The technical team decides to use the laser ceilometer system error compensation method based on regression analysis to solve this technical problem.

[0103] The technical team first establishes a laser ceilometer multi-parameter synchronous data acquisition system. The system core uses a wavelength of 905 nanometers semiconductor laser, and the laser emission power is monitored in real time by a high-precision photodiode array with a sampling frequency of 1 kilohertz. The laser return signal strength detection uses avalanche photodiode technology, combined with a gain-adjustable low-noise preamplifier. Atmospheric environmental parameter monitoring includes platinum resistance thermometer to measure atmospheric temperature, capacitive sensor to measure relative humidity, and silicon piezoresistive sensor to measure atmospheric pressure. All sensors are connected to the data acquisition controller through the controller area network bus, achieving microsecond-level time synchronization. The reference laser ceilometer uses imported equipment to provide a standard cloud base height reference value, with a data update frequency of 10 times per second.

[0104] During the 30-day continuous observation period, the technical team collected measurement data under different weather conditions. As shown in Table 1, effective measurement samples under six typical atmospheric conditions in plateau areas were covered.

[0105] Table 1 Measurement sample statistics under different weather conditions

[0106]

[0107] According to the cloud distribution characteristics, the technical team divided the measurement range into four height intervals to establish a hierarchical regression equation. The low cloud interval of 30-500 meters mainly corresponds to the terrain cloud and radiation fog, the low-mid cloud interval of 500-2000 meters covers the plateau cumulus cloud, the mid-high cloud interval of 2000-5000 meters corresponds to the altostratus cloud, and the high cloud interval of 5000-7500 meters contains the cirrus system. Through the double-layer game optimization algorithm, the technical team determined the nonlinear regression equation coefficients of each height interval. As shown in Table 2, the regression coefficients of different height intervals reflect the differences in laser-atmosphere interaction at each height layer.

[0108] Table 2 Nonlinear regression equation coefficient table for each height interval

[0109]

[0110] The technical team constructed an adaptive cloud height error correction model based on the Transformer encoder. The network architecture includes a 128-dimensional feature embedding layer, 8 heads of self-attention mechanism, and 3 layers of encoder structure. The training process uses the AdamW optimization algorithm, with an initial learning rate of 0.0001, a batch size of 128, and 300 rounds of training. The optimal performance of the model on the validation set appears in the 187th round, at which time the root mean square error of the validation set reaches a minimum value of 6.8 meters. The technical team uses a height interval discrimination function to achieve dynamic interval recognition, and the fuzzy logic reasoning rule base contains 24 if-then rules, with a mixed triangular and trapezoidal membership function.

[0111] During the real-time measurement phase, the technical team conducted a 7-day performance test on the system. During the test period, various complex weather conditions were encountered, including sandstorm weather, snow weather, and strong wind weather. As shown in Table 3, the measurement accuracy of the system under different weather conditions was stable.

[0112] Table 3 Real-time measurement performance statistics

[0113]

[0114] The technical team established a dynamic model parameter updating mechanism and used a sliding time window method to monitor system performance. The window length was set to 1 hour, and the root mean square error was calculated every 10 minutes. When the root mean square error of 3 consecutive calculation periods exceeded the preset threshold of 20 meters, the system automatically triggered the model retraining process. During the test, the retraining was triggered 4 times, each time consuming about 45 minutes, and the system performance was effectively restored after retraining. The parameter update used an exponential moving average strategy, with a new and old parameter fusion weight of 0.2:0.8, ensuring model stability.

[0115] The technical team compared and analyzed the performance differences between the traditional method and the method of the application. As shown in Table 4, the application is significantly better than the traditional method in terms of measurement accuracy, adaptability and stability.

[0116] Table 4 Performance comparison table of traditional method and method of the application

[0117]

[0118] The technical team further analyzed the distribution characteristics of the error compensation effect. The adaptive error correction model has different compensation capabilities in different height intervals. The compensation effect is best in the low cloud interval, with an average compensation of -3.2 meters, -4.7 meters in the low-mid cloud interval, -6.1 meters in the mid-high cloud interval, and -8.5 meters in the high cloud interval. The increasing trend of compensation with increasing height conforms to the physical properties of the plateau atmosphere, reflecting the model's adaptive learning ability to environmental conditions.

[0119] In long-term operation tests in different seasons, the technical team found that the system performance remained stable. The average root mean square error during the spring test was 8.9 meters, 9.2 meters in summer, 10.1 meters in autumn, and 11.4 meters in winter. Seasonal differences are mainly due to changes in atmospheric stability in different seasons in the plateau region, but the system effectively adapts to this change through a dynamic parameter updating mechanism. The model retraining frequency is once a week in spring, twice a week in summer, three times a week in autumn, and four times a week in winter, reflecting the adaptive adjustment capability.

[0120] It should be noted that the variables involved in the application are explained in detail in Tables 5 and 6.

[0121] Table 5 Variable explanation table (first part)

[0122]

[0123] Table 6 Variable explanation table (second part)

[0124]

[0125] The above merely illustrates the specific embodiments of the present application, but the protection scope of the present application is not limited thereto, any person skilled in the art can easily think of the changes or replacements within the technical range disclosed by the present application, which should be covered in the protection scope of the present application.

Claims

1. A method for compensating system error of a laser ceilometer based on regression analysis, characterized in that, Comprise: Collecting laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, and obtaining standard cloud base height measurement values synchronously through a reference laser ceilometer as dependent variable benchmark data for regression analysis; constructing a hierarchical height interval stepwise regression equation set, dividing the cloud base height measurement range according to different height intervals, establishing an independent nonlinear regression equation for each height interval, and the specific steps are as follows: ； wherein, is the cloud base height prediction value for the height interval, is the laser beam emission power data, is the laser return signal strength data, is the atmospheric temperature data, is the atmospheric humidity data, is the atmospheric pressure data, is the standard atmospheric pressure, is the cloud base height prediction value for the height interval, is the regression coefficient for the height interval, is the adaptive cloud height error correction model output term, is the random error term. Next, a double-layer game optimization framework is established, an upper optimization model with the objective function of minimizing the root mean square error of cloud base height measurement and a lower optimization model with the objective function of maximizing the fitting degree of the regression equation of each height interval are constructed; a double-layer game model collaborative optimization algorithm is implemented to determine the linear coefficients of laser parameters and the nonlinear coefficients of atmospheric parameters of the nonlinear regression equation of each height interval, and to optimize the network connection weight parameters and bias parameters of the adaptive cloud height error correction model; a real-time cloud base height error compensation algorithm is constructed, the height interval category to which the current measurement data belongs is determined through a height interval discrimination function, the preliminary cloud base height prediction value is calculated by calling the nonlinear regression equation of the corresponding height interval, and the error compensation amount is calculated through the adaptive cloud height error correction model to output the final cloud base height measurement result; The specific expression of the objective function of the upper optimization model is as follows: ； In the formula, To optimize the objective function value of the upper-level model, This represents the total number of measurement samples. For the first The cloud base height measurement value of this measurement. For the first The standard cloud base height reference value for this measurement The parameter is the L2 regularization penalty parameter. These are parameters for controlling model complexity. These are the coupling weights between the upper and lower layers. This is the value of the Akaike Information Criterion. The upper and lower layer coupling constraint terms are calculated using the following formula: ,in and The upper and lower layer models are respectively in the first and second layers. Local objective function values ​​for each height interval; The specific expression of the objective function of the lower optimization model is as follows: ； In the formula, To optimize the objective function value of the lower-level model, For the first Number of training samples in each height range For the first The height range is the first The predicted value for each sample, For the first The height range is the first Observations of a sample To optimize the weight parameters for the lower layer, For the first The coefficient of determination for each height range For the first Cross-validation error for each height interval, The formula for calculating the degree of constraint violation is as follows: ,in The minimum threshold for the coefficient of determination; The adaptive cloud height error correction model adopts a Transformer encoder architecture to map multi-dimensional environmental parameters to error compensation values, and uses a self-attention mechanism to mine the nonlinear correlations between parameters, thereby achieving intelligent error correction. The model output is directly used as a compensation term of a regression equation to dynamically adjust the prediction results to adapt to complex environmental changes.

2. The method of claim 1, wherein, The step of constructing the hierarchical height interval stepwise regression equation set is specifically to divide the cloud base height measurement range into a low cloud interval of 30-500 meters, a medium-low cloud interval of 500-2000 meters, a medium-high cloud interval of 2000-5000 meters, and a high cloud interval of 5000-7500 meters.

3. The method of claim 2, wherein, Before the step of implementing the double-layer game model collaborative optimization algorithm, a historical cloud height measurement data preprocessing process is further included, which detects and eliminates abnormal values from the collected laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, atmospheric humidity data, atmospheric pressure data, and standard cloud base height measurement values, eliminates abnormal measurement data according to the 3-standard deviation criterion, and normalizes the data after eliminating abnormal values, and divides the data set according to the proportions of 70% training set and 30% validation set.

4. The method according to claim 3, wherein, The height interval discrimination function is specifically used to automatically identify the height interval category to which the cloud base height belongs according to the current laser measurement parameters and atmospheric environmental parameters, and the input includes laser beam emission power data, laser echo signal intensity data, atmospheric temperature data, and preliminary cloud base height estimation value, and the output is the corresponding height interval category identifier.

5. The method according to claim 4, wherein, After the step of constructing the real-time cloud base height error compensation algorithm, a dynamic model parameter updating mechanism is further designed, a sliding time window method is used to continuously monitor cloud base height measurement error statistical indicators, and when the root mean square error of continuous measurement error exceeds a preset error threshold, a model retraining process is automatically started, the double-layer game model collaborative optimization algorithm is re-executed, and the parameters of the nonlinear regression equation of each height interval and the parameters of the adaptive cloud height error correction model are updated.

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