Abstract
In view of the importance of the concentration of engine tail flame components to the infrared spectrum radiation intensity, an efficient infrared spectrum concentration solution model is proposed, namely the CARS-CNN-GRU model which combines the competitive adaptive reweighted sampling (CARS) algorithm with the convolutional neural network (CNN)-gated recurrent unit (GRU) deep learning algorithm. This method uses the CARS algorithm to select the key wavelengths and obtain the tail flame component concentration information. Then the CNN-GRU model is used to perform long-range dependency analysis on the sequence data to achieve multi-scale feature extraction. Simulation results show that compared with the traditional models, the CARS-CNN-GRU model has higher accuracy in solving H2O and CO2 concentrations. Its root mean square error (RMSE) is reduced to 0.0014 and 0.0017, respectively. The R² value is 0.999 and 0.998, respectively; the mean absolute error (MAE) is 0.0011 and 0.0014, respectively. The CARS-CNN-GRU model proposed in this paper shows superior performance in solving infrared spectral concentration. Compared with traditional methods, it has higher accuracy, stability and reliability, and provides strong support for stealth technology, environmental monitoring and combustion efficiency evaluation in the military and civil aviation fields.
Introduction
The infrared radiation characteristics of the engine tail flame are important feature bases for detecting, identifying, warning and tracking aircraft using infrared detection equipment [1]. As an important infrared radiation source of aircraft, the radiation spectrum of the engine tail flame mainly depends on its composition and temperature. The tail flame is a high-temperature, high-speed airflow ejected by the aircraft engine. Its main components are high-temperature gases such as H2O, CO2, N2, and CO. Among them, H2O and CO2 are the main active components that generate infrared radiation energy [2]. Different aviation kerosene combustion will produce different concentrations of H2O and CO2, so it is very important to solve the concentration of engine tail flame components.
With the rapid advancement of computer technology, the combination of machine learning algorithms and infrared spectroscopy technology to accurately detect the concentration of mixed gas components [3] has become a key research direction. Traditional gas detection methods are easily disturbed by external conditions (such as temperature and air pressure changes) , resulting in poor stability of measurement results. Usually, other technologies must be used to ensure that the detection purpose is achieved. At present, infrared spectroscopy is considered to be one of the most ideal gas detection methods.
Infrared spectroscopy detection technology has attracted great attention from scholars in this field and has been widely used in practical fields [4]. Fang L et al. [5] used genetic algorithms to identify unknown components in Fourier transform infrared (FTIR) spectroscopy analysis. Evseev V [6] and Bharadwaj SP [7] et al. used the HITEMP database and CDSD database to obtain the infrared spectrum of CO2 gas under high temperature conditions and discussed the spectral characteristics of CO2 under high temperature. Yu Duanhui [8] used the radial basis neural network algorithm to identify five gases including CO. Shao L et al. [9] used FTIR technology to measure air and obtained a large number of spectral samples. They established the Classical Least Squares (CL Squares (CLS) and partial least squares (PLS) quantitative models were used to obtain the concentration information of gases such as NH3 and CH4 in the spectrum. Zhang L et al. [10] used chaos optimization to estimate the concentration of formaldehyde and benzene, and the prediction errors were reduced by 26.03% and 16.4% respectively.
Convolutional Neural Network (CNN) has the ability to extract image features quickly and does not require data preprocessing, so it is used to process spectral data. Cai Y et al. [11] proposed a multi-gas component measurement method that combines CNN with a long short-term memory (LSTM) network, but the interference of the on-site environment can cause significant errors in the prediction of low-concentration gas results.
Based on this, this paper established a CARS-CNN-GRU model. The CARS algorithm is used to remove useless variables, and the CNN-GRU model is used to accurately solve the engine tail flame spectral concentration. CNN has a strong feature extraction capability for one-dimensional spectral data [12], while the GRU network makes up for the shortcomings of ordinary recurrent networks that bring gradient vanishing and gradient explosion, making it difficult to train the network, and can better adapt to time series signals [13]. The combination of the two is expected to greatly enhance the generalization ability and robustness of the model. At the same time, in terms of spectral data dimensionality reduction, the CARS algorithm can effectively remove uninformative variables while minimizing the impact of collinear variables on the model, and finally select the variables that are most critical to the solution target [14].
1 Data acquisition and modeling
1.1 Construction of mixed gas dataset
The HITRAN database was used to obtain 100 sets of absorbance spectra of H2O and CO2 mixed gases of different concentrations and used as experimental data. The wavelength range obtained was 2－5 μm, and each spectrum contained 3000 discrete data points (interval 0.001 μm) .80% of the data was used as a training set, and the remaining20% of the data was used as a test set. The training set was used to train the neural network, and the test set was used to evaluate the performance of each gas concentration solution model. Some mixed gas spectral data are shown in Figure1.
Fig.1Spectra of some mixed gases.
1.2 CARS Algorithm
CARS algorithm [15] is a method for variable selection, which is particularly suitable for spectral data analysis. It can effectively select the most informative features from a large number of variables. The core of the CARS algorithm is to determine the optimal variable subset through an iterative process, combined with the strategy of adjusting the weights of variables and gradually eliminating unimportant variables. The following is a simplified version of the CARS algorithm process and its mathematical description.
(1) Initialization process
Assume we have 𝑁 samples, each sample contains 𝑝 variables (features) . Initially, the weight of each variable ωi is 1, where 𝑖 =1, 2, ..., 𝑝 .
(2) PLS regression
Using PLS regression analysis, the solution model is calculated based on the current weight vector 𝑤 . PLS is a linear modeling technique that is particularly suitable for high-dimensional data. It looks for potential linear combinations that explain the relationship between the response variable and the solution variable.
(3) Weight update
Calculate an importance measure for each variable, such as the absolute value of the variable's coefficient |βi|. The weight of the variable is usually updated using formula (1) :
(1)
(4) Competitive Adaptive Sampling
Based on the updated weights, a certain proportion of variables are selected as "winners". These variables will be retained to participate in the next round of iterations. The remaining "loser" variables will be eliminated or their weights will be further reduced until the stopping criterion is met.
(5) Iteration process
The above process needs to be repeated until the termination condition is met, such as the number of iterations reaches a preset upper limit or the weight change is lower than a certain critical value .
(6) Final model
Finally, the final model is constructed from the retained variables. These variables are considered to be the most representative and informative features of the dataset.
The CARS algorithm dynamically adjusts sample weights and feature subsets so that important features receive higher weights, thereby improving the effects of feature selection and dimensionality reduction. The algorithm has good robustness and generalization capabilities.
1.3 CNN
The design of CNN is inspired by the working mechanism of biological visual cortex. Its architecture effectively captures and extracts valuable information while reducing the data size by staggering convolutional layers and pooling layers. With the continuous and unremitting exploration and improvement of researchers around the world, CNN has been rapidly updated and developed. The network consists of five main parts: input layer, several convolutional layers, pooling layer, fully connected layer and output layer. Its structure is shown in Figure2.
Fig.2CNN structure diagram.
1.4 GRU Network
The GRU network is a member of the Recurrent Neural Network (RNN) family. Its design concept is derived from the improvement of the LSTM network. The LSTM network effectively alleviates the gradient vanishing and gradient exploding problems faced by RNN when dealing with long-term dependencies by introducing innovative input gating, output gating, and forgetting gating mechanisms [16] . The GRU network is built on this basis, and its core component is also the gated recurrent unit.
As a variant of the LSTM network, the GRU network has a simpler structure. Therefore, on the basis of achieving the same effect, it has a faster training speed with fewer parameters and can reduce the risk of overfitting. Compared with the triple gate mechanism of the LSTM network, the GRU network simplifies the gate function and only has an update gate and a reset gate.
The RNN structure is shown in Figure3. In the GRU network, each traditional RNN node in the hidden layer is replaced by GRU. The structure of each unit node is shown in Figure4.
Fig.3RNN structure.
Fig.4GRU node model.
In Figure4, xt represents the input information at the current moment; ht-1 represents the hidden state at the previous moment. The hidden state serves as the memory carrier of the neural network and contains the characteristic information of the data received at the previous time steps; ht represents the hidden state passed forward to the next moment; is the candidate hidden state; is the reset gate; and zt is the update gate.
The reset gate determines how to combine new input information with previous memory. This relationship is expressed in mathematical formula form as follows:
(2)
Where σ is the logistic sigmoid function; Wr is the weight vector. The formula used for the candidate hidden state after solving rt is:
(3)
From formula (3) , we can see that the larger the rt value is, the more the previous moment is combined with the current moment. If the rt value is 1, it means that the hidden state information of the previous moment will be completely retained; if the rt value is 0, it means that the hidden state information of the previous moment will be completely ignored. Therefore, when processing time series data, the reset gate can effectively identify and capture short-term dependency relationships.
The update gate is used to update the memory, and its mathematical formula is as follows:
(4)
The expression for updating memory is as follows:
(5)
The final memory ht forgets some of the ht-1 information passed down and adds some of the information input by the current node. The closer zt is to 1, the more data is "remembered"; the closer zt is to 0, the more data is "forgotten".
1.5 CARS-CNN-GRU model establishment
When solving the spectral concentration of mixed gases, the CARS algorithm is used to select characteristic bands. At the same time, the CNN-GRU model is used as the algorithm basis for the selected data, which can effectively extract and utilize the characteristic information in the spectrum, thereby improving the solution accuracy. Therefore, this section combines the above algorithm with the model to obtain the CARS-CNN-GRU model, and compares it with other algorithms. The modeling process of the model is shown in Figure5.
Fig.5CARS-CNN-GRU network modeling diagram.
The CARS-CNN-GRU model includes an input layer, a CARS algorithm, a convolution layer, a pooling layer, a GRU layer, a fully connected layer, and an output layer. The absorbance spectrum data of the mixed gas in the characteristic band is input, and the concentration is solved using different models.
1.6 Model Evaluation Metrics
Root mean square error (RMSE) , mean absolute error (MAE) and R2 determination coefficient are introduced to effectively evaluate the error of mixed gas concentration solution. The expressions of RMSE, MAE and R2 are as follows:
(6)
(7)
(8)
2 Experimental results analysis
2.1 Characteristic wavelength extraction
A 50-round variable selection process (the process is targeted at the spectral absorption band of the mixed gas) was performed using the CARS algorithm. As the number of Monte Carlo sampling iterations increases, the number of selected wavelengths gradually decreases, and the deceleration tends to be gentle. This process shows the trend of wavelength selection from broad to fine. By comparing the root mean square error of cross-validation (RMSECV) of each iteration, the whole process continues until the iteration corresponding to the minimum RMSECV value is found, thereby determining the wavelength containing the optimal variable subset .
Figure6 Schematic diagram of CARS characteristic band selection. It can be seen that with the increase in the number of iterations, the number of selected wavelengths shows a decreasing trend, while the RMSECV curve shows a trend of first fluctuating down to the lowest point and then gradually recovering. This change process shows that in the initial stage, by eliminating irrelevant wavelength variables, the RMSECV value can be reduced; however, in the subsequent stage, excessive elimination of related variables leads to information loss, and the RMSECV value increases accordingly. Specifically, when the CARS algorithm is applied to the infrared radiation spectrum of the engine tail flame, its RMSECV value reaches the minimum value when the iteration is carried out for the10th time. At this time, the number of wavelength variables determined is 112.
Fig.6Schematic diagram of CARS characteristic band selection.
In order to verify the effective improvement of the CARS algorithm on the model accuracy, this paper also uses the Differential Evolution (DE) algorithm and the Sequential Projection Algorithm (SPA) to select feature bands, and compares them with the CARS algorithm.
2.2 Model solution results and analysis
The data after the CARS feature band selection is input into the trained CNN-GRU gas concentration solution model, and the concentration of the gas samples in the test set is solved by the neural network. At the same time, five additional methods, CARS-GRU, SPA-GRU, SPA-CNN-GRU, DE-GRU, and DE-CNN-GRU, are used to invert the concentration of the test set data, and then the results are compared with the solution results of the CARS-CNN-GRU model. The RMSE and MAE of all samples in the test set and the solution are used as evaluation indicators of algorithm performance.
Solution results of the CARS-CNN-GRU model for H2O and CO2 gas concentration are shown in Figure7 (a) and Figure7 (b) .
Fig.7Solution of mixed gas concentration: (a) H2O; (b) CO2.
In order to intuitively reflect the superiority of the CARS-CNN-GRU model proposed in this paper, the RMSE, MAE and R2 comparison are shown in Figure8.
Fig.8Comparison of model error indicators: (a) RMSE; (b) MAE; (c) R2.
Table1 lists the RMSE, MAE and of each algorithm R2 for solving H2O and CO2 concentrations. Combining Figure8 and Table1, it can be concluded that in terms of RMSE, CARS-CNN-GRU<DE-CNN-GRU<SPA-CNN-GRU<DE-GRU<SPA-GRU<CARS-GRU; in terms of MAE, CARS-CNN-GRU<SPA-CNN-GRU<DE-CNN-GRU<DE-GRU<SPA-GRU<CARS-GRU; in terms of R2, CARS-CNN-GRU>SPA-CNN-GRU>DE-CNN-GRU>DE-GRU>SPA-GRU>CARS-GRU. This shows that the CARS-CNN-GRU model has the smallest solution error, the best degree of consistency between the solution value and the true value, and all samples have obtained good concentration solutions, proving that the CARS-CNN-GRU model has good generalization ability.
Table1Model solution results
The gas concentration solution error of the CARS-CNN-GRU model is lower than that of other hybrid models, indicating that using the CARS algorithm to extract data features and then using the CNN algorithm to deeply extract features can reduce the error and enhance the solution performance of the GRU network.
In general, the CARS-CNN-GRU gas concentration solution model has the smallest MSE value and the smallest MAE value. The R2 value is the largest . Therefore, CARS-CNN-GRU is the model with the best performance in solving gas concentration.
3 Conclusion
In order to solve the concentration value of the mixed gas components in the tail flame of the aircraft, this paper adds a CNN network to the GRU network and constructs a CNN-GRU model; at the same time, the CARS algorithm is used to extract the features of the data, and finally a tail flame infrared spectrum concentration solution method based on the CARS-CNN-GRU model is proposed. At the same time, five additional methods, CARS-GRU, SPA-GRU, SPA-CNN-GRU, DE-GRU, and DE-CNN-GRU are used to solve the concentration of the test set data, and the results are compared with the prediction results of the CARS-CNN-GRU model. The simulation results show that the CARS-CNN-GRU model has higher accuracy in solving infrared spectrum concentration than other models. The RMSE values of H2O and CO2 concentrations are as low as 0.0014 and 0.0017, respectively, the R2 values are 0.999 and 0.998, and the MAE values are 0.0011 and 0.0014, respectively. Therefore, the model has a good ability to solve tail flame concentration.
The concentration solution model in this article is currently only applicable to the solution of high-concentration gases. In the future, the solution of trace gases in the tail flame will also be carried out to expand the applicable conditions of the algorithm.