A Hyperspectral Water Quality Parameter Estimation Method Optimized and Accelerated by LBFGS for Multilayer Sensing Networks

Abstract

This application discloses an LBFGS-optimized and accelerated method for estimating hyperspectral water quality parameters using a multilayer sensing network. The method includes: acquiring an initial hyperspectral image of the study area; extracting the hyperspectral image of the target water body area from the initial image; using Pearson correlation analysis to select characteristic spectral bands with high correlation to non-optical water quality parameter concentrations as input; setting an objective function; establishing a network structure with multiple different numbers of hidden layers; minimizing the value of the objective function by adjusting the number of hidden layers to obtain a multilayer sensing neural network model; optimizing and accelerating the model using the LBFGS algorithm to improve the performance of the estimation model; estimating the concentration of non-optical water quality parameters; evaluating the performance of the estimation model using three indicators: coefficient of determination, root mean square error, and mean absolute error; and predicting the spatial distribution of water quality parameter concentrations in the target area based on the constructed optimal model, providing theoretical support for urban water environment monitoring and water quality management.

Description

Technical Field

[0001] This application relates to the field of non-optical water quality data processing technology, and in particular to a method, system, terminal, and computer-readable storage medium for estimating hyperspectral water quality parameters using an LBFGS-optimized and accelerated multilayer sensing network. Background Technology

[0002] Water resources are among the most precious resources on Earth, playing a vital role in human society, the ecological environment, and economic development. Water is the source of life, sustaining the survival and reproduction of all organisms on Earth; it is also the foundation supporting all human activities, from drinking water and agricultural irrigation to industrial production and ecological protection. However, under the dual pressures of human activities and climate change, aquatic ecosystems face increasingly severe challenges, especially serious water pollution, which directly threatens the physical and mental health of residents. Water quality monitoring is a crucial aspect of water pollution control, enabling accurate assessment of water body health and timely adjustments to control strategies, thereby ensuring the health and stability of the water environment.

[0003] In existing technologies, traditional water quality parameter monitoring methods involve manual sampling of water bodies or fixed-point sampling at monitoring stations. These methods assess various water indicators through steps such as sample collection, sample processing, and laboratory testing, offering advantages in accuracy and reliability. However, manual sampling methods are time-consuming and resource-intensive, and cannot achieve real-time or remote monitoring. While station-based monitoring methods can continuously monitor water body trends over long periods, the fixed locations of the monitoring equipment limit coverage to the specific areas where the monitoring stations are set up, failing to comprehensively reflect the overall water quality of the entire body.

[0004] Existing technologies further utilize remote sensing technology. As one of the Earth observation technologies, remote sensing technology has advantages such as spatial continuity, wide monitoring range, and low cost. It has been incorporated into the national ecological and environmental assessment field and has become the primary monitoring method for water ecological assessment indicators. It provides strong support for obtaining water body monitoring results accurately, quickly, simply and effectively and for establishing and improving water quality monitoring mechanisms.

[0005] Specifically, remote sensing water quality parameter inversion utilizes remote sensing technology to acquire surface reflectance spectral information of water bodies and uses mathematical models and algorithms to calculate the concentrations of various water quality parameters, such as the optical characteristic parameter chlorophyll a concentration and non-optical characteristic parameters total phosphorus, total nitrogen, and ammonia nitrogen concentration. This method typically uses sensors carried by remote sensing satellites or aircraft to acquire water reflectance spectral data, then compares and analyzes this data with sample data of known water quality parameters to establish an inversion model for quantitative estimation of water quality parameters. This enables rapid monitoring and assessment of large-scale water bodies, providing a scientific basis for water environment protection and management. Hyperspectral remote sensing technology, in particular, organically combines spectral information reflecting the composition of substances with spatial image information reflecting the location of ground features, offering the unique advantage of integrated image and spectral data. Furthermore, this technology enables the detection of targets undetectable in broadband multispectral remote sensing in hyperspectral remote sensing, achieving significant breakthroughs in ecological monitoring and environmental management, and providing a powerful tool for monitoring water environment and aquatic ecosystem elements.

[0006] In recent years, with the rapid development of UAVs and hyperspectral remote sensing technologies, UAVs equipped with hyperspectral imagers have achieved significant improvements in spectral and spatial resolution. Using hyperspectral remote sensing technology for water quality monitoring, with its convenient and efficient sampling methods, low sampling costs, broad analytical range, and rapid analysis speed, has greatly promoted the development of the water quality monitoring field and has become an important research direction in current water quality analysis. Hyperspectral remote sensing data covers multiple spectral bands, including visible light, near-infrared, mid-infrared, and thermal infrared, each with unique material response characteristics, thus providing multifaceted information for remote sensing interpretation. Many scholars both domestically and internationally have successfully used hyperspectral information to establish linear, exponential, logarithmic, and polynomial statistical regression models, or combined them with machine learning algorithms for application in the field of water quality monitoring, achieving good research results. These technologies, by fully utilizing the rich spectral features in hyperspectral images, have greatly improved the accuracy and real-time performance of water quality monitoring. The powerful computing capabilities of machine learning algorithms enable us to process large amounts of spectral data in a short time, uncover potential features related to water quality parameters, and train inversion models with high accuracy and strong generalization ability, providing strong algorithmic support for water environment monitoring.

[0007] While these technologies provide crucial support for water quality monitoring, some shortcomings remain. Regarding parameter selection, current inversion studies primarily focus on optically relevant parameters such as suspended solids and chlorophyll a, while research on non-optically relevant parameters (important indicators of water nutrient status), such as total phosphorus, total nitrogen, and ammonia nitrogen, is relatively limited. In terms of model inversion methods, statistical regression models, including linear, exponential, logarithmic, and polynomial models, are generally built based on spectral bands. While the principles are simple, they lack the ability to capture the complex relationships between water quality parameters and hyperspectral data, resulting in poor model generalization. Random forest and XGBoost machine learning models can handle nonlinear relationships to some extent, but these models require calculation and evaluation for each feature and split point, consuming significant computational resources and training time. Furthermore, traditional machine learning algorithms mainly handle feature-level relationships and do not fully utilize the band correlations between hyperspectral data, potentially leading to the loss of some information. Furthermore, for decision tree-based algorithms such as random forests, their optimization methods employ a stepwise strategy. At each node split, a greedy algorithm is used to select the best feature for the split. This means that at each step, only the best choice is considered, which may lead to getting stuck in local optima and failing to find the global optimum. At the same time, once a choice is made, the greedy algorithm usually cannot backtrack and modify it. If a subsequent choice leads to an infeasible or bad solution, the greedy algorithm cannot correct its previous decision by backtracking, which may result in poor estimation accuracy of the model.

[0008] In addition, existing technologies have also used Baiyangdian water as a research object, analyzing the correlation between water spectral reflectance values, first-order derivative values, reflectance ratios and total phosphorus and total nitrogen in the water to extract characteristic bands, constructing various linear inversion models with single-band and multi-band inputs, and comparing and analyzing the model performance, discussing the inversion effect of modeling with different sample concentrations. Furthermore, existing technologies have also used nearshore waters as a research object, establishing a semi-empirical linear regression method combining characteristic bands of water spectral reflectance peaks and absorption valleys using satellite hyperspectral imagery to monitor water pollution in the nearshore areas of Hong Kong. The inversion models constructed in these studies can capture the spectral characteristics of specific water areas to a certain extent. Based on the above studies, traditional empirical / semi-empirical models of non-optical water quality parameters such as linear, polynomial, exponential, and logarithmic models constructed using single-band, dual-band, or multi-band combinations of spectral features as model inputs, although simple in principle, have very limited efficiency in utilizing the spectral features of hyperspectral data and the model's generalization ability.

[0009] In addition, researchers have conducted remote sensing estimation studies on total phosphorus concentration in Taihu Lake. By comprehensively considering the lake's optical properties and the speciation of total phosphorus in the water, they proposed a limit gradient boosting framework for total phosphorus concentration inversion. This technique is a machine learning model based on decision tree ensemble, which can effectively mine the correlation between phytoplankton index and total phosphorus in Taihu Lake. Other researchers have used fractional derivatives and discrete wavelet transform methods to mine potential spectral information in UAV hyperspectral images and selected sensitive features of various water quality parameters through filters and genetic algorithms, proposing an effective machine learning-based framework for water quality parameter inversion. However, as the authors state, this method may result in unstable results or overfitting. Furthermore, using satellite hyperspectral imagery data and ground-based measured data, support vector machines, partial least squares, K-nearest neighbors, and XGBoost regression models were established to invert various non-optical water quality parameters of river bodies. The constructed estimation models exhibit instability and biases at high and low concentrations. The aforementioned research indicates that while traditional machine learning algorithms demonstrate good estimation performance in the inversion of non-optical water quality parameters from hyperspectral remote sensing, tree-based machine learning methods such as XGBoost and Random Forest divide the data into multiple subsets and construct the final regression model by combining subtrees, resulting in long training times. These techniques often employ greedy optimization strategies (such as decision trees, random forests, and XGBoost models) or do not use optimization strategies (such as the K-nearest neighbors algorithm), which may lead to getting stuck in local optima and failing to obtain the global optimum. Summary of the Invention

[0010] In view of this, this application provides a method, system, terminal and computer-readable storage medium for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks, in order to solve the problem that in the prior art, non-optical water quality parameter estimation methods have limited efficiency in utilizing the spectral features of hyperspectral data and model estimation performance, and may get stuck in local optima and make it difficult to obtain the global optimum.

[0011] This application proposes a method for estimating hyperspectral water quality parameters using an LBFGS-optimized and accelerated multilayer sensing network. The method includes:

[0012] An initial hyperspectral image of the study area is acquired, and the target water body region is extracted from the initial hyperspectral image to obtain a hyperspectral image that only covers the target water body;

[0013] After removing noise bands from the hyperspectral image, Pearson correlation analysis is used to screen out characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the hyperspectral image after removing noise bands, and these bands are used as inputs for the estimation method.

[0014] A target function is defined, and a network structure with a variety of different numbers of hidden layers is established. By adjusting the number of hidden layers, the value of the target function is minimized, thus obtaining a multilayer perceptron neural network model.

[0015] The LBFGS algorithm is used to optimize and accelerate the multilayer sensing neural network model, thereby improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters.

[0016] The performance of the estimation model is evaluated using three metrics: coefficient of determination, root mean square error, and mean absolute error.

[0017] The spatial distribution of water quality parameter concentrations in the target area is predicted based on the constructed optimal model.

[0018] Optionally, the step of acquiring an initial hyperspectral image of the study area, extracting the target water body region from the initial hyperspectral image, and obtaining a hyperspectral image covering only the target water body specifically includes:

[0019] An initial hyperspectral image of the study area is acquired, and the target water body region is extracted from the initial hyperspectral image using the normalized water index and threshold segmentation method to obtain a hyperspectral image that only covers the target water body.

[0020] The formula for calculating the normalized water index is as follows:

[0021] ;

[0022] in, Indicates the normalized water quality index. This represents the reflectance value of a hyperspectral image in the green band. This represents the reflectance value of a hyperspectral image in the near-infrared band.

[0023] Optionally, after removing noise bands from the hyperspectral image, Pearson correlation analysis is used to screen characteristic spectral bands with high correlation to the concentration of non-optical water quality parameters from the noise-removed hyperspectral image, which are then used as inputs to the estimation method. Specifically, this includes:

[0024] After removing the noise bands from the hyperspectral image, the hyperspectral image with the noise bands removed is obtained. On the hyperspectral image with the noise bands removed, the reflectance values ​​of all the pixels where the sampling points are located are extracted in all spectral bands according to the multiple sampling points set during data acquisition. The vector composed of all the reflectance values ​​is used as a multidimensional spectral vector.

[0025] The Pearson correlation analysis method is used to calculate the correlation between the spectral information of all the sampling points and each non-optical water quality parameter using the multidimensional spectral vector, so as to obtain the correlation coefficient between each non-optical water quality parameter and each spectral band.

[0026] A first threshold is set for each of the non-optical water quality parameters based on the correlation coefficient. Feature selection is performed based on the first threshold to filter out the characteristic spectral bands corresponding to the non-optical water quality parameters when the correlation coefficient is greater than the first threshold, which are then used as inputs to the estimation method.

[0027] Optionally, the correlation coefficient is calculated using the following formula:

[0028] ;

[0029] ;

[0030] ; ;

[0031] ;

[0032] ;

[0033] in, Represents the correlation coefficient. express and covariance, Represents the spectral vector. Indicates the first A vector of values ​​for non-optical water quality parameters. Represents the spectral vector standard deviation Indicates non-optical water quality parameters standard deviation It is the number of sampling points. It is a spectral vector The mean, Water quality parameter values The mean, Represents the spectral vector The One element, This represents the i-th element in the value vector of the k-th non-optical water quality parameter.

[0034] Optionally, the step of setting an objective function, establishing a network structure with multiple different numbers of hidden layers, and minimizing the value of the objective function by adjusting the number of hidden layers to obtain a multilayer perceptron neural network model specifically includes:

[0035] Define an objective function, establish network structures with various numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers.

[0036] By combining the characteristic spectral bands of the non-optical water quality parameters to be estimated, the search range of all the hidden layers is determined;

[0037] Within the search range, the comprehensive performance of all the hidden layers is analyzed using a traversal method combined with the objective function to obtain the optimal comprehensive performance.

[0038] The optimal number of hidden layers is obtained based on the optimal overall performance, and a multilayer perceptron neural network model is obtained based on the optimal number of hidden layers.

[0039] Optionally, the step of using the LBFGS algorithm to optimize and accelerate the multilayer perceptron neural network model, improving the performance of the estimation model, and thus estimating the concentration of non-optical water quality parameters, specifically includes:

[0040] The LBFGS algorithm is used to optimize and accelerate the multilayer perceptron model, and the approximate inverse matrix of the Hessian matrix is ​​constructed by iterating the parameter vector multiple times.

[0041] The approximate inverse matrix is ​​used to estimate the update direction and step size of the parameter vector, thereby improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters.

[0042] The method for estimating hyperspectral water quality parameters using LBFGS-optimized accelerated multilayer sensing networks is characterized by the following formulas for calculating the coefficient of determination, the root mean square error, and the mean absolute error:

[0043] ;

[0044] ;

[0045] ;

[0046] in, The coefficient of determination is represented by RMSE, and the mean absolute error is represented by MAE. This represents the predicted values ​​of water quality parameters. This represents the measured values ​​of water quality parameters. This represents the average value of the measured water quality parameters, and n represents the number of sample points.

[0047] This application also proposes a hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks, the hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks comprising:

[0048] The target water body region extraction module is used to acquire an initial hyperspectral image of the study area, extract the target water body region from the initial hyperspectral image, and obtain a hyperspectral image that only covers the target water body.

[0049] The spectral feature selection module is used to remove noise bands from the hyperspectral image and then use Pearson correlation analysis to select characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the hyperspectral image after removing noise bands, as input to the estimation method.

[0050] The network layer analysis module is used to set the objective function, establish network structures with various numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers to obtain a multilayer perceptron neural network model.

[0051] The model optimization and acceleration module is used to optimize and accelerate the multilayer perceptron model using the LBFGS algorithm, thereby improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters.

[0052] The model accuracy evaluation module is used to evaluate the performance of the estimation model using three indicators: coefficient of determination, root mean square error, and mean absolute error.

[0053] The concentration spatial visualization module is used to predict the spatial distribution of water quality parameter concentrations in a target area based on the constructed optimal model.

[0054] This application also proposes a terminal, the terminal comprising: a memory, a processor, and a hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network stored in the memory and executable on the processor, wherein when the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation program is executed by the processor, it implements the steps of the hyperspectral water quality parameter estimation method for an LBFGS-optimized and accelerated multilayer sensing network as described above.

[0055] This application also proposes a computer-readable storage medium storing a hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network. When executed by a processor, the hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network implements the steps of the hyperspectral water quality parameter estimation method for an LBFGS-optimized and accelerated multilayer sensing network as described above.

[0056] The beneficial effects of this application are as follows: Firstly, unlike existing technologies, this application obtains an initial hyperspectral image of the study area and extracts the target water body region from it, resulting in a hyperspectral image covering only the target water body, effectively reducing computational load. Secondly, after removing noise bands from the hyperspectral image, this application uses Pearson correlation analysis to screen characteristic spectral bands with high correlation to non-optical water quality parameter concentrations from the noise-removed hyperspectral image, using these as inputs for the estimation method. This not only improves computational efficiency but also meets the requirements for inversion accuracy. Thirdly, this application sets an objective function and establishes a network structure with various numbers of hidden layers, adjusting the number of hidden layers to achieve the desired objective function value. The optimal multilayer perceptron neural network model is obtained by minimizing the model size. This model can effectively mine and utilize potential spectral information. The LBFGS algorithm is used to optimize and accelerate the model, which can more accurately determine the direction of parameter updates and accelerate the model's learning of parameters. This allows the model to converge faster while approaching the global optimum, thereby improving the performance of the estimation model. The performance of the estimation model is evaluated using three indicators: coefficient of determination, root mean square error, and mean absolute error. This evaluation can comprehensively and objectively reflect the model's generalization performance. In addition, this application predicts the spatial distribution of water quality parameter concentrations in the target area based on the constructed optimal model, providing a theoretical basis and reference for comprehensively assessing the river water condition and providing theoretical support for urban water environment monitoring and water quality management.

[0057] It should be understood that the above general description and the following detailed description are exemplary and explanatory only, and are not intended to limit this application. Attached Figure Description

[0058] To more clearly illustrate the technical solutions in the embodiments of this application, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the accompanying drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0059] Figure 1 This is a flowchart of a preferred embodiment of the hyperspectral water quality parameter estimation method for LBFGS-optimized and accelerated multilayer sensing networks in this application;

[0060] Figure 2 This is a flowchart of the hyperspectral water quality parameter estimation method using LBFGS-optimized and accelerated multilayer sensing network in the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation method of this application.

[0061] Figure 3 This is the LBFGS optimized and accelerated multilayer sensing network model in the hyperspectral water quality parameter estimation method of the LBFGS optimized and accelerated multilayer sensing network in this application;

[0062] Figure 4 This is a schematic diagram of a preferred embodiment of the hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks in this application;

[0063] Figure 5 This is a schematic diagram of the operating environment of a preferred embodiment of the terminal of this application. Detailed Implementation

[0064] To enable those skilled in the art to better understand the technical solutions of this application, the hyperspectral water quality parameter estimation method, system, terminal, and computer-readable storage medium of the LBFGS optimized and accelerated multilayer sensing network provided in this application will be further described in detail below with reference to the accompanying drawings and specific embodiments. It is understood that the described embodiments are merely some embodiments of this application, and not all embodiments. All other embodiments obtained by those skilled in the art based on the embodiments of this application without creative effort are within the scope of protection of this application.

[0065] The terms “comprising” and “having”, and any variations thereof, used in this application are intended to cover non-exclusive inclusion. For example, a process, method, system, product, or apparatus that includes a series of steps or units is not limited to the steps or units listed, but may optionally include steps or units not listed, or may optionally include other steps or units inherent to such process, method, product, or apparatus.

[0066] This application provides a method, system, terminal, and computer-readable storage medium for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks. This addresses the problem in existing non-optical water quality parameter estimation methods that have limited efficiency in utilizing the spectral features of hyperspectral data and limited model estimation performance, which may lead to getting stuck in local optima and making it difficult to obtain the global optimum.

[0067] Please see Figures 1 to 3 , Figure 1 This is a flowchart of a preferred embodiment of the hyperspectral water quality parameter estimation method for LBFGS-optimized and accelerated multilayer sensing networks in this application; Figure 2 This is a flowchart of the hyperspectral water quality parameter estimation method using LBFGS-optimized and accelerated multilayer sensing network in the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation method of this application. Figure 3 This is the LBFGS optimized and accelerated multilayer sensing network model in the hyperspectral water quality parameter estimation method of the LBFGS optimized and accelerated multilayer sensing network in this application.

[0068] This application proposes a hyperspectral water quality parameter estimation method using LBFGS-optimized and accelerated multilayer sensing networks. The non-optical water quality parameters used in this application can be water quality parameters such as total phosphorus, total nitrogen, and ammonia nitrogen, which do not possess strong optical properties. Figure 1 As shown, the LBFGS-optimized and accelerated hyperspectral water quality parameter estimation method for multilayer sensing networks includes the following steps:

[0069] Step S100: Obtain an initial hyperspectral image of the study area, extract the target water body region from the initial hyperspectral image, and obtain a hyperspectral image that only covers the target water body.

[0070] Specifically, by acquiring the initial hyperspectral image of the study area, the target water body region is extracted from the initial hyperspectral image, resulting in a hyperspectral image that only covers the target water body, which can effectively reduce the amount of computation.

[0071] Specifically, step S100 involves acquiring an initial hyperspectral image of the study area, extracting the target water body region from the initial hyperspectral image, and obtaining a hyperspectral image that only covers the target water body.

[0072] An initial hyperspectral image of the study area is acquired, and the target water body region is extracted from the initial hyperspectral image using the normalized water index and threshold segmentation method to obtain a hyperspectral image that only covers the target water body.

[0073] The formula for calculating the normalized water index is as follows:

[0074] ;

[0075] in, Indicates the normalized water quality index. This represents the reflectance value of a hyperspectral image in the green band. This represents the reflectance value of a hyperspectral image in the near-infrared band.

[0076] Specifically, NDWI (Normalized Difference Water Index) is an index used to extract water information from remote sensing images. It distinguishes water bodies from other land features based on the normalized ratio of reflectance in the green band to the near-infrared band, primarily utilizing the strong absorption characteristic of water bodies in the near-infrared band. Therefore, by acquiring an initial hyperspectral image of the study area, using the normalized water index and threshold segmentation method, the target water body region is extracted from the initial hyperspectral image, resulting in a hyperspectral image that only covers the target water body. This allows for processing only the target water body region during water quality inversion, effectively reducing computational load.

[0077] Assuming the hyperspectral image is ,in, , and The normalized water index, representing the length, width, and number of bands of the hyperspectral image, is calculated using the following formula to extract the target water body region:

[0078] ;

[0079] in, This represents the reflectance value of a hyperspectral image in the green band. This represents the reflectance value of a hyperspectral image in the near-infrared band.

[0080] Usually, when At that time, the surface type in the pixel is water or covered by rain or snow; when At that time, the surface type in the pixel is covered by bare soil or rock; when At that time, the ground surface in the pixel is covered by vegetation.

[0081] In this application, the water body is affected by the external environment, and the extraction of water body area... The threshold for the index is often not set to zero, but rather a suitable threshold is set based on the remote sensing images of the study area.

[0082] The normalized water index can also be replaced by the MNDWI index (Modified Normalized Difference Water Index) and the NDMI index (Normalized Difference Water Index), both of which fall within the scope of protection of this application.

[0083] Step S200: After removing noise bands from the hyperspectral image, Pearson correlation analysis is used to screen out characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the hyperspectral image after removing noise bands, and these bands are used as inputs for the estimation method.

[0084] Specifically, after removing noise bands from the hyperspectral image, Pearson correlation analysis is used to screen out characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the noise-removed hyperspectral image. These bands are then used as input for the estimation method, which not only improves computational efficiency but also meets the requirements for inversion accuracy.

[0085] Specifically, step S200 involves removing noise bands from the hyperspectral image and then using Pearson correlation analysis to select characteristic spectral bands with high correlation to non-optical water quality parameter concentrations from the noise-removed hyperspectral image as input for the estimation method.

[0086] After removing the noise bands from the hyperspectral image, the hyperspectral image with the noise bands removed is obtained. On the hyperspectral image with the noise bands removed, the reflectance values ​​of all the pixels where the sampling points are located are extracted in all spectral bands according to the multiple sampling points set during data acquisition. The vector composed of all the reflectance values ​​is used as a multidimensional spectral vector.

[0087] The Pearson correlation analysis method is used to calculate the correlation between the spectral information of all the sampling points and each non-optical water quality parameter using the multidimensional spectral vector, so as to obtain the correlation coefficient between each non-optical water quality parameter and each spectral band.

[0088] A first threshold is set for each of the non-optical water quality parameters based on the correlation coefficient. Feature selection is performed based on the first threshold to filter out the characteristic spectral bands corresponding to the non-optical water quality parameters when the correlation coefficient is greater than the first threshold, which are then used as inputs to the estimation method.

[0089] Specifically, after removing noise bands from the hyperspectral image, a noise-removed hyperspectral image is obtained. On this noise-removed hyperspectral image, based on multiple sampling points set during data acquisition, the reflectance values ​​of all pixels at each sampling point are extracted across all spectral bands. The vector composed of all reflectance values ​​is then used as a multidimensional spectral vector. The multidimensional spectral data vector is used to calculate the correlation between the spectral information of all sampling points and each non-optical water quality parameter using Pearson correlation analysis. Correlation coefficients with each spectral band A first threshold is set for each non-optical water quality parameter based on the correlation coefficient. Feature selection is performed to identify the characteristic spectral bands corresponding to non-optical water quality parameters whose correlation coefficients are greater than a first threshold; that is, only those bands are retained. The characteristic spectral bands are used as the final input features.

[0090] make This represents the pixel spectral information of the corresponding water body sampling point in the hyperspectral image, where, This represents the number of spectral bands for the sample. Each pixel This represents the reflectance values ​​of the sampling point across all spectral bands, which together constitute a... A dimensional spectral data vector. The vector of dimension will be further input into the Pearson correlation analysis algorithm to calculate the correlation between the spectral information of that pixel and various non-optical water quality parameters. In the Pearson correlation analysis stage, firstly for each water quality parameter... Calculate its spectral vector relative to the sampling point respectively. Pearson correlation coefficient Then set the first threshold. Only keep those The spectral bands are used as the final input features. Specifically, the total number of water quality parameters that need to be estimated is... ,set up For the first Water quality parameters.

[0091] The formula for calculating the correlation coefficient is as follows:

[0092] ;

[0093] ;

[0094] ; ;

[0095] ;

[0096] ;

[0097] in, Represents the correlation coefficient. express and The covariance, i.e. and The degree of correlation between them Represents the spectral vector. Indicates the first A vector of values ​​for non-optical water quality parameters. Represents the spectral vector standard deviation Used to measure the degree of data dispersion Indicates non-optical water quality parameters standard deviation Used to measure the degree of data dispersion It is the number of sampling points. It is a spectral vector The mean, Water quality parameter values The mean, Represents the spectral vector The One element, This represents the i-th element in the value vector of the k-th non-optical water quality parameter.

[0098] After calculating the correlation coefficients between the required estimated water quality parameters and each spectral band, an appropriate first threshold is set for each water quality parameter. Feature selection is performed. The first threshold is selected. The screening process should improve computational efficiency while also meeting the requirements for inversion accuracy.

[0099] Set the objective function as The function takes its minimum value under the conditions of achieving a given accuracy and computational efficiency. The calculation formula is as follows:

[0100] ;

[0101] in, To indicate the model's accuracy, it needs to be greater than a set threshold. ; The efficiency of a model (e.g., computation speed or consumption of computational resources) must be less than a set threshold. , This represents a comprehensive consideration of model accuracy and computational efficiency.

[0102] Pearson correlation coefficient can be replaced by Spearman correlation coefficient, both of which are within the scope of protection of this application.

[0103] Step S300: Set the objective function, establish a network structure with a variety of different numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers to obtain a multilayer perceptron neural network model.

[0104] Specifically, an objective function is set, and a network structure with a variety of different numbers of hidden layers is established. By adjusting the number of hidden layers, the value of the objective function is minimized, resulting in a multilayer perceptron neural network model. This effectively mines and utilizes potential spectral information, improving the performance of the estimation model.

[0105] Specifically, step S300 involves setting an objective function, establishing network structures with varying numbers of hidden layers, and minimizing the objective function by adjusting the number of hidden layers to obtain a multilayer perceptron neural network model.

[0106] Define an objective function, establish network structures with various numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers.

[0107] By combining the characteristic spectral bands of the non-optical water quality parameters to be estimated, the search range of all the hidden layers is determined;

[0108] Within the search range, the comprehensive performance of all the hidden layers is analyzed using a traversal method combined with the objective function to obtain the optimal comprehensive performance.

[0109] The optimal number of hidden layers is obtained based on the optimal overall performance, and a multilayer perceptron neural network model is obtained based on the optimal number of hidden layers.

[0110] Specifically, the number of hidden layers in a multilayer sensing network plays a crucial role in its structure. Deeper networks can learn and represent more complex features and abstract concepts, enabling the model to capture the intricate relationships between hyperspectral features and non-optical water quality parameters. However, an excessive number of layers can also lead to increased computational complexity and overfitting. Therefore, it is necessary to determine an appropriate number of hidden layers, and thus, set an objective function. A network structure with multiple different numbers of hidden layers is established. The value of the objective function is minimized by adjusting the number of hidden layers. The search range of all hidden layers is determined by combining the characteristic spectral bands of the non-optical water quality parameters to be estimated. Within the search range, the comprehensive performance of all numbers of hidden layers is analyzed by combining the objective function with the traversal method to obtain the optimal comprehensive performance. The optimal number of hidden layers is obtained based on the optimal comprehensive performance. The multilayer perceptron neural network model is obtained based on the optimal number of hidden layers.

[0111] Wherein, objective function The calculation formula is as follows:

[0112] ;

[0113] in, This represents the loss of a network model with L hidden layers on the validation set. This represents the time required to train the model. and These are the weight coefficients, reflecting preferences for model performance and training time.

[0114] In defining the objective function Then, by combining the characteristic spectral bands of the non-optical water quality parameters to be estimated, the search range for the number of hidden layers is determined. Then, within the determined search range, a traversal approach is used in conjunction with the objective function. The overall performance of different numbers of hidden layers is analyzed, the optimal overall performance is obtained by comparison, the optimal number of hidden layers is obtained based on the optimal overall performance, and the multilayer perceptron neural network model is obtained based on the optimal number of hidden layers.

[0115] The specific steps are as follows: First, based on the number of hidden layers... Construct the initial multilayer perceptron neural network model During model training, a function is used to calculate the training time of the model. Record training time : After the model training is complete, the loss of the model is calculated using the validation set: .in, This is the loss function, which takes a model and a set of validation data and outputs the model's loss value on that validation data. Through the above steps, we obtain the parameters needed to determine the overall performance objective function of multilayer perceptrons with different numbers of hidden layers. and Substitute the obtained parameters into By finding the minimum value of this function within the search range, we can obtain the optimal number of hidden layers in the network within the search range.

[0116] The loss function can be replaced, such as mean absolute error, Huber loss, etc., all of which are within the scope of protection of this application.

[0117] Step S400: The LBFGS algorithm is used to optimize and accelerate the multilayer perceptron neural network model, improve the performance of the estimation model, and then estimate the concentration of non-optical water quality parameters.

[0118] Specifically, the LBFGS algorithm (Limited Memory Quasi-Newton algorithm) is used to optimize the multilayer perceptron neural network model, which can more accurately determine the update direction of the multilayer perceptron neural network model parameters, obtain a faster convergence speed, improve the performance of the estimation model, and thus estimate the concentration of non-optical water quality parameters.

[0119] Specifically, step S400 involves optimizing and accelerating the multilayer perceptron neural network model using the LBFGS algorithm to improve the performance of the estimation model and thereby estimate the concentration of non-optical water quality parameters.

[0120] The LBFGS algorithm is used to optimize and accelerate the multilayer perceptron model, and the approximate inverse matrix of the Hessian matrix is ​​constructed by iterating the parameter vector multiple times.

[0121] The approximate inverse matrix is ​​used to estimate the update direction and step size of the parameter vector, thereby accelerating the convergence speed, improving the performance of the estimation model, and thus estimating the concentration of non-optical water quality parameters.

[0122] Specifically, the LBFGS algorithm is adopted. The LBFGS algorithm is used to adjust the parameters of the model in order to minimize the loss function on the training set. It constructs an approximate inverse matrix of the Hessian matrix by iterating the parameter vector multiple times. The approximate inverse matrix is ​​used to estimate the update direction and step size of the parameter vector, which accelerates the convergence speed and efficiency of the training of the multilayer perceptron model, improves the performance of the estimation model, and thus estimates the concentration of non-optical water quality parameters.

[0123] The LBFGS (Limited Memory Quasi-Newton) algorithm is used for optimization and acceleration, and the parameters of the neural network are randomly initialized. Then, in each subsequent iteration, the parameter update process is as follows:

[0124] ;

[0125] in, It is the gradient of the loss function L at the parameter position in the k-th step. This represents the parameter vector in the k-th step; This represents the learning rate in step k. The learning rate is updated using an adaptive strategy. If the model's performance does not improve within a certain number of consecutive iterations, the learning rate is multiplied by a factor less than 1 to gradually decrease the learning rate. The specific formula is as follows:

[0126] ;

[0127] Here, factor is a factor less than 1, used to control the rate at which the learning rate decreases; It is an approximate inverse of the Hessian matrix, which is usually calculated from information from the past few steps in the LBFGS algorithm.

[0128] The formula for the approximate inverse of the Hessian matrix is ​​as follows:

[0129] ;

[0130] ;

[0131] in, It is the approximate Hessian matrix at the k-th step. , representing the amount of change in the parameter. It is the change in gradient. It is an updated scale parameter. It is an identity matrix.

[0132] By continuously repeating the above steps before the termination conditions are met (reaching the maximum number of iterations, the model's loss on the validation set being less than a certain threshold, etc.), the curvature information of the loss function can be analyzed through the approximation of the Hessian matrix, allowing for a more accurate determination of the parameter update direction and achieving a faster convergence speed.

[0133] The learning rate adjustment strategy can be replaced, such as step decay or Cyclic Learning Rate, all of which are within the scope of protection of this application.

[0134] Step S500: Evaluate the performance of the estimation model using three indicators: coefficient of determination, root mean square error, and mean absolute error.

[0135] Specifically, the determination coefficients of the optimized multilayer perceptron neural network model are obtained. The accuracy of non-optical water quality parameters estimated by the optimized multilayer sensing neural network model is evaluated and analyzed based on three indicators: root mean square error (RMSE) and mean absolute error (MAE). The RMSE can reflect the inversion model's ability to interpret data. It can reflect the error between the true value and the predicted value of the sample, thereby judging the model's performance. The MAE can avoid the problem of errors canceling each other out.

[0136] The formulas for calculating the coefficient of determination, the root mean square error, and the mean absolute error are as follows:

[0137] ;

[0138] ;

[0139] ;

[0140] in, The coefficient of determination is represented by RMSE, and the mean absolute error is represented by MAE. This represents the predicted values ​​of water quality parameters. This represents the measured values ​​of water quality parameters. This represents the average value of the measured water quality parameters, and n represents the number of sample points.

[0141] Step S600: Predict the spatial distribution of water quality parameter concentrations in the target area based on the constructed optimal model.

[0142] Specifically, the characteristic spectral bands are input into the LBFGS-optimized and accelerated multilayer perceptron neural network model and evaluated. The estimation model with the best accuracy is used to predict the concentration of non-optical water quality parameters of river water based on pixel-by-pixel characteristics, and spatial mapping of concentration is performed, providing theoretical support for urban water environment monitoring and water quality management.

[0143] Specifically, the water body pixels selected in step S100 are traversed, and their spectral values ​​are input into the LBFGS-MLP model (a multilayer perceptron model with finite memory quasi-Newton algorithm) to estimate the corresponding water quality parameters:

[0144] ;

[0145] in, It is the spectral reflectance value of the water body. These are the predicted values ​​of water quality parameters based on model predictions.

[0146] Finally, based on the concentration matrices of three non-optical water quality parameters—total phosphorus, total nitrogen, and ammonia nitrogen—estimated by the model, the spatial distribution of these water quality parameters is visualized, providing a theoretical basis and reference for a comprehensive assessment of river water conditions.

[0147] This application improves the accuracy and stability of estimating non-optical water quality parameters by fully mining and utilizing the spectral information of hyperspectral images. The multilayer sensing network (MLN) mainly consists of a spectral feature input layer, a feature extraction hidden layer, and a water quality parameter output layer. Adjacent layers are connected using a fully connected approach. Each hidden layer introduces a nonlinear activation function for effectively learning and representing spectral features. The LBFGS optimization algorithm is mainly used to accelerate and iteratively update the weights and bias parameters in the MLF, adjusting the model parameters to minimize the loss function, thereby improving the performance of the estimation model. The MLF can effectively approximate nonlinear functions, enabling it to handle the complex nonlinear relationship between non-optical water quality parameters and hyperspectral features, exhibiting higher generalization ability compared to other models. Regarding spectral features, the MLF can fully learn the optimal feature representation from the training data, effectively mining and utilizing potential spectral information to improve the performance of the estimation model. In terms of adjustment strategies, the MLF automatically adjusts the network structure and weights through optimization algorithms such as backpropagation, reducing manual intervention and training time. The LBFGS optimization algorithm offers significant advantages for training multilayer perceptron models, particularly in complex tasks such as estimating non-optical water quality parameters based on hyperspectral data. Its efficient and stable parameter update strategy plays a positive role in improving training efficiency, reducing overfitting risk, and accelerating model convergence. This algorithm utilizes the second-order curvature information of the loss function to more accurately determine the direction of parameter updates, accelerating the model's parameter learning and thus achieving faster model convergence while approaching the global optimum.

[0148] Please see Figures 4 to 5 , Figure 4 This is a schematic diagram of a preferred embodiment of the hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks in this application; Figure 5 This is a schematic diagram of the operating environment of a preferred embodiment of the terminal of this application.

[0149] In some embodiments, such as Figure 4 As shown, based on the above-mentioned method for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks, this application also proposes a hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks. The hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks includes:

[0150] The target water body region extraction module 51 is used to acquire an initial hyperspectral image of the study area, extract the target water body region from the initial hyperspectral image, and obtain a hyperspectral image that only covers the target water body.

[0151] The spectral feature selection module 52 is used to remove noise bands from the hyperspectral image and then use Pearson correlation analysis to select characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the hyperspectral image after removing noise bands, as input to the estimation method.

[0152] The network layer analysis module 53 is used to set the objective function, establish a network structure with a variety of different numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers to obtain a multilayer perceptron neural network model.

[0153] The model optimization and acceleration module 54 is used to optimize and accelerate the multilayer perceptron model using the LBFGS algorithm, improve the performance of the estimation model, and then estimate the concentration of non-optical water quality parameters.

[0154] The model accuracy evaluation module 55 is used to evaluate the performance of the estimation model using three indicators: coefficient of determination, root mean square error, and mean absolute error.

[0155] Concentration spatial visualization module 56 is used to predict the spatial distribution of water quality parameter concentrations in the target area based on the constructed optimal model.

[0156] In some embodiments, such as Figure 5 As shown, based on the above-mentioned LBFGS-optimized accelerated multilayer sensing network hyperspectral water quality parameter estimation method and system, this application also proposes a terminal, which includes: a memory 20, a processor 10, and a display 30. Figure 5 Only some of the terminal components are shown; however, it should be understood that it is not required to implement all of the components shown, and more or fewer components may be implemented instead.

[0157] In some embodiments, the memory 20 may be an internal storage unit of the terminal, such as a hard drive or memory. In other embodiments, the memory 20 may be an external storage device of the terminal, such as a plug-in hard drive, smart media card (SMC), secure digital card (SD), flash card, etc. Furthermore, the memory 20 may include both internal and external storage units. The memory 20 is used to store application software and various types of data installed on the terminal, such as the program code installed on the terminal. The memory 20 can also be used to temporarily store data that has been output or will be output.

[0158] In one embodiment, the memory 20 stores a hyperspectral water quality parameter estimation program 40 for LBFGS-optimized and accelerated multilayer sensing networks. This hyperspectral water quality parameter estimation program 40 for LBFGS-optimized and accelerated multilayer sensing networks can be executed by the processor 10, thereby realizing the hyperspectral water quality parameter estimation method for LBFGS-optimized and accelerated multilayer sensing networks in this application.

[0159] In some embodiments, the processor 10 may be a central processing unit (CPU), a microprocessor, or other data processing chip, used to run program code stored in the memory 20 or process data, such as executing the LBFGS-optimized and accelerated hyperspectral water quality parameter estimation method for multilayer sensing networks.

[0160] In some embodiments, the display 30 may be an LED display, a liquid crystal display, a touch-sensitive liquid crystal display, or an OLED (Organic Light-Emitting Diode) touchscreen. The display 30 is used to display information on the terminal and to display a visual user interface. The components 10-30 of the terminal communicate with each other via a system bus.

[0161] This application also proposes a computer-readable storage medium storing a hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network. When the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation program is executed by a processor, it implements the steps of the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation method as described above.

[0162] In summary, this application obtains an initial hyperspectral image of the study area, extracts the target water body region from the initial hyperspectral image, and obtains a hyperspectral image covering only the target water body, effectively reducing the computational load. Secondly, after removing noise bands from the hyperspectral image, this application uses Pearson correlation analysis to screen characteristic spectral bands with high correlation to the concentration of non-optical water quality parameters from the noise-removed hyperspectral image, which are then used as input for the estimation method. This not only improves computational efficiency but also meets the requirements for inversion accuracy. Thirdly, this application sets an objective function, establishes a network structure with multiple different numbers of hidden layers, and adjusts the number of hidden layers to minimize the value of the objective function, thus obtaining a multilayer perceptron neural network. By effectively mining and utilizing potential spectral information through a network model, and optimizing and accelerating the model using the LBFGS algorithm, the direction of parameter updates is accurately determined, accelerating the model's learning of parameters. This allows the model to converge faster while approaching the global optimum, improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters. The performance of the estimation model is evaluated using three indicators: coefficient of determination, root mean square error, and mean absolute error, to comprehensively and objectively reflect the model's generalization performance. Furthermore, this application predicts the spatial distribution of water quality parameter concentrations in the target area based on the constructed optimal model, providing a theoretical basis and reference for comprehensively assessing the river water condition and offering theoretical support for urban water environment monitoring and water quality management.

[0163] It should be noted that the various optional implementation methods described in the embodiments of this application can be combined with each other or implemented individually, and the embodiments of this application do not limit this.

[0164] The above embodiments are described with reference to the accompanying drawings. Other different forms and embodiments are also feasible without departing from the principles of this application, and therefore this application should not be construed as limiting the embodiments set forth herein. Rather, these embodiments are provided to make this application complete and perfect, and to convey the scope of this application to those skilled in the art. In the drawings, component dimensions and relative dimensions may be exaggerated for clarity. The terminology used herein is for the purpose of describing particular embodiments only and is not intended to be limiting. The terms “comprising” and / or “including”, when used in this specification, indicate the presence of said features, integers, elements, and / or components, but do not exclude the presence or addition of one or more other features, integers, elements, components, and / or groups thereof. Unless otherwise shown, numerical ranges, when stated, include the upper and lower limits of the range and any subranges therebetween.

[0165] The above description is only a part of the embodiments of this application and does not limit the scope of protection of this application. Any equivalent device or equivalent process transformation made based on the content of this application specification and drawings, or directly or indirectly applied to other related technical fields, are similarly included in the patent protection scope of this application.

Claims

1. A method for estimating hyperspectral water quality parameters using an LBFGS-optimized and accelerated multilayer sensing network, characterized in that, include: Acquire an initial hyperspectral image of the study area, extract the target water body region from the initial hyperspectral image, and obtain a hyperspectral image that only covers the target water body; After removing noise bands from the hyperspectral image, Pearson correlation analysis is used to screen out characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the hyperspectral image after removing noise bands, and these bands are used as inputs for the estimation method. A target function is defined, and a network structure with a variety of different numbers of hidden layers is established. By adjusting the number of hidden layers, the value of the target function is minimized, thus obtaining a multilayer perceptron neural network model. The LBFGS algorithm is used to optimize and accelerate the multilayer sensing neural network model, thereby improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters. The performance of the estimation model is evaluated using three indicators: coefficient of determination, root mean square error, and mean absolute error. Predict the spatial distribution of water quality parameter concentrations in the target area based on the constructed optimal model; After removing noise bands from the hyperspectral image, Pearson correlation analysis is used to screen characteristic spectral bands with high correlation to the concentration of non-optical water quality parameters from the noise-removed hyperspectral image, which are then used as inputs for the estimation method. Specifically, this includes: After removing the noise bands from the hyperspectral image, the hyperspectral image with the noise bands removed is obtained. On the hyperspectral image with the noise bands removed, the reflectance values ​​of all the pixels where the sampling points are located are extracted in all spectral bands according to the multiple sampling points set during data acquisition. The vector composed of all the reflectance values ​​is used as a multidimensional spectral vector. The Pearson correlation analysis method is used to calculate the correlation between the spectral information of all the sampling points and each non-optical water quality parameter using the multidimensional spectral vector, so as to obtain the correlation coefficient between each non-optical water quality parameter and each spectral band. A first threshold is set for each of the non-optical water quality parameters based on the correlation coefficient. Feature selection is performed based on the first threshold to filter out the characteristic spectral bands corresponding to the non-optical water quality parameters when the correlation coefficient is greater than the first threshold, which are then used as inputs to the estimation method. The objective function is set, and a network structure with various numbers of hidden layers is established. By adjusting the number of hidden layers, the value of the objective function is minimized, resulting in a multilayer perceptron neural network model, specifically including: Define an objective function, establish network structures with various numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers. By combining the characteristic spectral bands of the non-optical water quality parameters to be estimated, the search range of all the hidden layers is determined; Within the search range, the comprehensive performance of all the hidden layers is analyzed using a traversal method combined with the objective function to obtain the optimal comprehensive performance. The optimal number of hidden layers is obtained based on the optimal overall performance, and a multilayer perceptron neural network model is obtained based on the optimal number of hidden layers.

2. The method for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks according to claim 1, characterized in that, The process of acquiring an initial hyperspectral image of the study area, extracting the target water body region from the initial hyperspectral image, and obtaining a hyperspectral image covering only the target water body specifically includes: An initial hyperspectral image of the study area is acquired, and the target water body region is extracted from the initial hyperspectral image using the normalized water index and threshold segmentation method to obtain a hyperspectral image that only covers the target water body. The formula for calculating the normalized water index is as follows: ； in, Indicates the normalized water quality index. This represents the reflectance value of a hyperspectral image in the green band. This represents the reflectance value of a hyperspectral image in the near-infrared band.

3. The method for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks according to claim 1, characterized in that, The formula for calculating the correlation coefficient is as follows: ； ； ； ； ； ； in, Represents the correlation coefficient. express and covariance, Represents the spectral vector. Indicates the first A vector of values ​​for non-optical water quality parameters. Represents the spectral vector standard deviation Indicates non-optical water quality parameters standard deviation It is the number of sampling points. It is a spectral vector The mean, Water quality parameter values The mean, Represents the spectral vector The One element, This represents the i-th element in the value vector of the k-th non-optical water quality parameter.

4. The method for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks according to claim 1, characterized in that, The optimization and acceleration of the multilayer perceptron neural network model using the LBFGS algorithm improves the estimation model performance and thus estimates the concentration of non-optical water quality parameters. Specifically, this includes: The LBFGS algorithm is used to optimize and accelerate the multilayer perceptron model, and the approximate inverse matrix of the Hessian matrix is ​​constructed by iterating the parameter vector multiple times. The approximate inverse matrix is ​​used to estimate the update direction and step size of the parameter vector, thereby improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters.

5. The method for estimating hyperspectral water quality parameters using LBFGS-optimized and accelerated multilayer sensing networks according to claim 1, characterized in that, The formulas for calculating the coefficient of determination, the root mean square error, and the mean absolute error are as follows: ； ； ； in, The coefficient of determination is represented by RMSE, and the mean absolute error is represented by MAE. This represents the predicted values ​​of water quality parameters. This represents the measured values ​​of water quality parameters. This represents the average value of the measured water quality parameters, and n represents the number of sample points.

6. A hyperspectral water quality parameter estimation system for LBFGS-optimized and accelerated multilayer sensing networks, wherein the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation system is used to implement the hyperspectral water quality parameter estimation method for LBFGS-optimized and accelerated multilayer sensing networks as described in any one of claims 1-5, characterized in that, The LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation system includes: The target water body region extraction module is used to acquire an initial hyperspectral image of the study area, extract the target water body region from the initial hyperspectral image, and obtain a hyperspectral image that only covers the target water body. The spectral feature selection module is used to remove noise bands from the hyperspectral image and then use Pearson correlation analysis to select characteristic spectral bands that are highly correlated with the concentration of non-optical water quality parameters from the hyperspectral image after removing noise bands, as input to the estimation method. The network layer analysis module is used to set the objective function, establish network structures with various numbers of hidden layers, and minimize the value of the objective function by adjusting the number of hidden layers to obtain a multilayer perceptron neural network model. The model optimization and acceleration module is used to optimize and accelerate the multilayer perceptron model using the LBFGS algorithm, thereby improving the performance of the estimation model and estimating the concentration of non-optical water quality parameters. The model accuracy evaluation module is used to evaluate the performance of the estimation model using three indicators: coefficient of determination, root mean square error, and mean absolute error. The concentration spatial visualization module is used to predict the spatial distribution of water quality parameter concentrations in a target area based on the constructed optimal model.

7. A terminal, characterized in that, The terminal includes: a memory, a processor, and a hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network stored in the memory and executable on the processor. When the processor executes the hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network, it implements the steps of the hyperspectral water quality parameter estimation method for an LBFGS-optimized and accelerated multilayer sensing network as described in any one of claims 1-5.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a hyperspectral water quality parameter estimation program for an LBFGS-optimized and accelerated multilayer sensing network. When the LBFGS-optimized and accelerated multilayer sensing network hyperspectral water quality parameter estimation program is executed by a processor, it implements the steps of the hyperspectral water quality parameter estimation method for an LBFGS-optimized and accelerated multilayer sensing network as described in any one of claims 1-5.

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