Method for predicting concentration of SO2 gas in fire coal through combination of photoacoustic spectrometry and Stacking model

Abstract

The invention discloses a fire coal SO2 gas concentration prediction method based on combination of photoacoustic spectroscopy and a Stacking model. The fire coal SO2 gas concentration prediction method comprises the following steps: acquiring a spectral data set of SO2 gas through an experiment; dividing the collected spectral data set into a training set and a test set according to a ratio of 8: 2; carrying out wavelet transform denoising on the divided spectral data, and then carrying out SPA wavelength screening on the denoised data; establishing a Stacking model of the SO2 gas concentration of the photoacoustic spectrum; optimizing the Stacking model by using an improved Arctic Sea-Sharrow algorithm (IPAO); and inputting spectral data to test the model. According to the fire coal SO2 gas detection method based on the SPAO optimized Stacking model, the photoacoustic spectrometry technology is utilized, the Stacking model constructed through the method has the advantage of efficiently processing complex data, and accurate prediction of the concentration of fire coal SO2 gas is achieved; therefore, the method is very suitable for the demand of accurately predicting the SO2 gas concentration in industrial production field and environment detection.

Description

Technical Field

[0001] The present invention relates to the field of pollutant detection, and specifically relates to a method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy and a Stacking model. Background Technique

[0002] The SO2 gas emitted during the coal combustion process is a major source of air pollution and health problems. Accurately predicting the concentration of these pollutants is crucial for environmental protection and public health. By establishing an accurate prediction model, it can help the government and enterprises optimize emission control measures, reduce the harm of pollutants to the environment and human body, and thus achieve the goal of sustainable development.

[0003] Existing SO2 prediction methods such as empirical formula method and traditional statistical modeling perform poorly in the face of complex non-linear problems, while a single machine learning model is sensitive to noise and overfitting and is difficult to process high-dimensional spectral data. The limitations of these methods restrict the accurate prediction of the concentration of coal-fired SO2 gas and affect the reliability in practical applications.

[0004] The combination of spectral technology and the Stacking model can make up for the above deficiencies. Photoacoustic spectroscopy technology has high sensitivity and selectivity and can provide characteristic data with high signal-to-noise ratio; while the Stacking model enhances the ability to capture complex non-linear relationships by integrating multiple base learners. Combined with the characteristic wavelength selection algorithm, this method not only improves the accuracy and generalization ability of the model, but also can better cope with the prediction challenges in complex data environments. Summary of the Invention

[0005] The present invention proposes a method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy and a Stacking model, aiming to solve the deficiencies existing in the existing methods.

[0006] The technical solution adopted by the present invention is as follows: A method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy and a Stacking model, comprising the following steps:

[0007] S1. Acquisition of the photoacoustic spectroscopy data set of coal-fired SO2 gas;

[0008] S2. Divide the data set into a data set and a test set according to a ratio of 8:2;

[0009] S3. Preprocess the photoacoustic spectroscopy data of the training set and the test set;

[0010] S4. Establish a photoacoustic spectroscopy SO2 gas Stacking model;

[0011] S5. Optimize the hyperparameters of the Stacking model with an improved puffin algorithm (PAO);

[0012] S6. Input the spectral data to test the model.

[0013] In step S1, a quantum cascade laser is selected to excite SO2 gas, and a photoacoustic spectroscopy data set of SO2 gas is obtained.

[0014] In step S2, the data collected from the experiment is divided, and the data is divided into a training set and a test set according to the ratio of 8:2.

[0015] In step S3, the photoacoustic spectroscopy is preprocessed. The main steps include:

[0016] S31. Denoising is performed using wavelet transform as follows:

[0017] S311. Select a suitable wavelet basis function: Since the db wavelet basis function has better adaptability in wavelet threshold denoising, the db wavelet basis function is selected.

[0018] S312. Perform wavelet decomposition: The photoacoustic spectroscopy data is decomposed by multi-level wavelet decomposition. Wavelet decomposition can decompose the signal into components of different frequencies, usually the high-frequency detail part and the low-frequency approximation part. The L-level wavelet decomposition can be expressed as:

[0019] c A,L =∑ x s(x)φ A,L (x)

[0020] c D,L =∑ x s(x)φ D,L (x)

[0021] In the formula, c A,L is the approximation coefficient, c D,L is the detail coefficient, φ A,L and φ D,L are the low-pass and high-pass filters in wavelet decomposition respectively.

[0022] S313. Threshold processing of wavelet coefficients: Threshold processing is performed on the coefficients after wavelet decomposition to remove noise. The threshold processing methods include hard threshold and soft threshold. The hard threshold processing formula:

[0023]

[0024] The soft threshold processing formula:

[0025]

[0026] In the formula: c(i) is the original wavelet coefficient, identifies the wavelet coefficient after processing, and λ is the threshold.

[0027] S314. Signal reconstruction: Use the processed coefficients for wavelet reconstruction to obtain the denoised photoacoustic spectrum data. The reconstruction formula is as follows:

[0028]

[0029] In the formula: s′(x) is the reconstructed signal, is the processed wavelet coefficient, and φ i (x) is the corresponding wavelet function;

[0030] S32. Use the SPA algorithm for characteristic wavelength screening. The specific method is as follows:

[0031] S321. Standardization preprocessing: Perform standardization processing on the denoised photoacoustic spectrum data to ensure that the spectrum data at different wavelengths have the same scale. The standardization formula is as follows:

[0032]

[0033] In the formula: X ij is the denoised spectrum data, representing the absorption value of the i-th sample at the j-th wavelength. μ j and σ j are respectively the mean and standard deviation of the absorption values at the j-th wavelength;

[0034] S322. Initialization: Select an initial wavelength λ1, usually a wavelength with a relatively high correlation with the output variable, as the starting point;

[0035] S323. Step-by-step projection: Select uncorrelated wavelengths through step-by-step projection. The specific steps are as follows:

[0036] (1) Calculate the projection vector: For the currently selected wavelength set, calculate the projection vector of each unselected wavelength, aiming to find the wavelength that is least correlated with the selected wavelength set. The calculation formula is as follows:

[0037]

[0038] In the formula: X j is the spectral vector corresponding to the to-be-selected wavelength j, X k is the spectral vector corresponding to the selected wavelength, S is the currently selected wavelength set, and p j is the projection vector of wavelength j, indicating its linear independence from the selected wavelengths;

[0039] (2) Select the next wavelength: Select the wavelength with the smallest modulus of the projection vector p j as the next characteristic wavelength, that is, select the wavelength that is least correlated with the selected wavelength set. The selection criterion is:

[0040]

[0041] S324. Repeat step S323: Repeat the wavelength selection step until the predetermined number of wavelengths is reached or the model error reaches the threshold;

[0042] S325. Screen the final characteristic wavelengths: The characteristic wavelengths screened through the above process will be used as the input variables for subsequent modeling. These wavelengths have the lowest collinearity and, at the same time, maximize the key information of the spectrum.

[0043] In step S4, a photoacoustic spectroscopy SO2 gas Stacking model is constructed, which is characterized by constructing a prediction model;

[0044] The Stacking model combines the prediction results of three base learners, namely support vector regression (SVR), backpropagation neural network (BP), and decision tree (DT), and uses an XGBoost meta-learner to further optimize these predictions, thereby improving the overall performance of the model; the combinations of these base learners in the Stacking model can complement each other, improving the performance and generalization ability of the overall model. The generalization ability of SVR and the non-linear modeling ability of the BP neural network, combined with the interpretability and fast prediction ability of the decision tree, can form a powerful integrated learning model;

[0045] The specific process of establishing the Stacking model is as follows:

[0046] S41. Conduct base learner training: The training dataset is The base learners are respectively trained to obtain prediction models f1(x), f2(x), f3(x), then:

[0047]

[0048] S42. Generate the second-layer training data: Combine the prediction results of the base learners into a new training dataset for training the meta-learner. Assuming there are m samples, the input dataset for the second layer is:

[0049]

[0050] S43. Meta-learner training: Use XGBoost as the meta-learner, and the training data is Z. The goal of the meta-learner is to improve the final prediction by learning the relationship between the output of the base learners and the true label y i between them:

[0051]

[0052] where g is the XGBoost model;

[0053] S44. Prediction stage: For a new sample x during the testing stage, first obtain the initial prediction through the base learner:

[0054]

[0055] Input these prediction results into the meta-learner XGBoost for the final prediction:

[0056]

[0057] In step S5, aiming at the overfitting problem and difficult parameter tuning of the Stacking model, the improved puffin algorithm (IPAO) is used to optimize the parameters of the base learner and meta-learner of the Stacking model. When facing some complex optimization problems, the behavior transformation factor in the original PAO algorithm cannot provide sufficient adaptability, resulting in deficiencies in the algorithm's balance between exploration and exploitation phases. If the global exploration phase ends too quickly, the algorithm may prematurely fall into a local optimum. Therefore, an enhanced behavior transformation factor is added, that is, by utilizing the non-linear characteristics of the sine function and the change of the fitness value of the objective function, the algorithm is adaptively and dynamically adjusted, enabling the algorithm to more flexibly balance global exploration and local exploitation, better find suitable hyperparameter combinations, thereby reducing the risk of overfitting. In addition, IPAO can combine the advantages of multiple base learners and meta-learners, optimize the fusion effect of the overall model, improve the generalization ability, and make the model perform better on unknown data;

[0058] Furthermore, the content of IPAO is as follows:

[0059] S51. Aerial search stage:

[0060] S511. Aerial search: Puffins mainly live in groups. When going out to hunt, they often fly in formation to search for prey. This collaborative hunting method greatly increases the chance of successful predation. The position update formula is as follows:

[0061]

[0062] R = round(0.5 * (0.05 + rand)) * α

[0063] α ~ Normal(0,1)

[0064] In the formula: r is a random number between [1, N - 1], represents the i-th individual of the current population, represents an individual randomly selected from the current population, L(D) is a random number generated by Levy, D is the dimension constant, and α is a random number following the normal distribution with load;

[0065] S512, Pouncing Predation: In this stage, a speed coefficient S is introduced to adjust the state of the puffin during the dive. The position update formula is as follows:

[0066]

[0067] S = tan((rand - 0.5) * π)

[0068] During the aerial search stage, on the one hand, the puffin conducts a global search through the Levy flight strategy, and on the other hand, a speed coefficient S is introduced to balance the state of the puffin when diving towards the prey, in order to obtain the optimal individual and optimal population in this stage. To better calculate and screen the optimal solution, the position update formulas for the two cases are combined and updated to obtain:

[0069]

[0070]

[0071] In the formula: sort sorts in ascending order according to the fitness value and selects a better population;

[0072] S52, Underwater Foraging Stage:

[0073] S521, Gathering Foraging: During the process of assisting in predation, the puffin often flies around the fish school. This formation flight method also makes it easier for the group to prey on the prey. When the puffin without a target docks on the ground, it will also observe the behavior of other members and identify the underwater heat source and the movement direction of the prey. The position update formula is as follows:

[0074]

[0075] In the formula: F represents the cooperation factor, and its main role is to regulate the predation behavior of the puffin. r1, r2, r3 are random numbers in the range of [1, N - 1], is the randomly selected candidate optimal population;

[0076] S522, Enhanced Search: When the puffin searches or preys in a specific area for a period of time, it will measure whether there are still remaining resources in this area. If it is found that the remaining resources do not meet the needs of the group's life, the puffin population will choose to search for the next area. The position update formula is as follows:

[0077]

[0078] In the formula: T represents the total number of iterations, t represents the current iteration number, and rand represents a random number;

[0079] S523. Avoiding predators: When razorbills are hunting or searching for prey, if they detect natural enemies or predators around them, they will emit a call to alert other individuals in the population and change their positions, flying to a safe area to avoid danger. The position update formula is as follows:

[0080]

[0081] Where: β is a random number between [0, 1];

[0082] During the underwater hunting stage, the razorbill algorithm updates positions in different states. To ensure that the optimal populations and optimal solutions in the three sub-stages do not conflict or make mistakes, the following formula is used for merging:

[0083]

[0084] In IPAO, to better achieve the transition from the aerial search stage to the foraging stage, a transition coefficient B and a specific parameter C are introduced here:

[0085] B = 2 × log(1 / rand) × sin((1 - t / T) × (π / 2)) × H

[0086]

[0087] Where t represents the current iteration number, T is the total number of iterations, rand is a random number between 0 and 1, and f(X best ) and f(X worst ) represent the best fitness value and the worst fitness value respectively.

[0088] S53. Steps for IPAO to optimize the hyperparameters of the Stacking model:

[0089] S531. Hyperparameter definition: Set the hyperparameter spaces of the base learners (SVR, BP, DT) and the meta-learner XGBoost;

[0090] S532. Initialization: Randomly generate a set of initial solutions (i.e., hyperparameter combinations), and initialize the initial positions and velocities of the razorbills;

[0091] S533. Fitness evaluation: For each hyperparameter combination, perform k-fold cross-validation, and use MSE or R 2 Calculate the model performance of each combination as the fitness function:

[0092] f(p) = CV_score(p)

[0093] S534. Global Search: IPAO conducts a global search in the hyperparameter space. By using the position and velocity formulas, it searches for the optimal hyperparameter combination. The formulas are as follows:

[0094] v(t + 1) = wv(t) + c1r1(p best - x(t)) + c2r2(g best - x(t))

[0095] x(t + 1) = x(t) + v(t + 1)

[0096] S635. Local Search: Refinement search is carried out near potential high-quality solutions, and the search radius is dynamically adjusted as:

[0097] x i (t + 1) = x i (t) + α·rand(0, 1)·(g(t) - x i (t))

[0098] S536. Update Strategy: Update the global optimal solution based on the fitness value, and gradually approach the hyperparameter combination.

[0099] In step S6, relevant data of the input SO2 gas concentration is tested to adjust various parameters in the model; using the tuned prediction model, spectral data is input for testing to predict the SO2 gas concentration for a period of time in the future. Description of the Drawings

[0100] Figure 1 is a flowchart of a method for predicting the concentration of coal-fired SO2 gas using a photoacoustic spectroscopy combined with a Stacking model;

[0101] Figure 2 is a flowchart of using an improved Arctic tern algorithm (IPAO) to optimize the hyperparameters of the Stacking model in a method for predicting the concentration of coal-fired SO2 gas using a photoacoustic spectroscopy combined with a Stacking model. Detailed Embodiment

[0102] The following combines the attached Figure 1 and the attached Figure 2 , and describes in detail a specific embodiment of the present invention. However, it should be understood that the protection scope of the present invention is not limited by the specific embodiment.

[0103] The present invention proposes a method for predicting the concentration of coal-fired SO2 gas using a photoacoustic spectroscopy combined with a Stacking model, aiming to solve the problems existing in the existing methods and provide a more effective solution for the detection of coal-fired SO2 gas concentration.

[0104] To achieve the above object, this embodiment proposes a method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy with a Stacking model. The Stacking model is used as a regression model. Laser is used to excite the gas to obtain photoacoustic spectroscopy data, and the relevant data that affects the concentration of SO2 gas is used to train the model. Aiming at the problems of easy overfitting and difficult parameter tuning of the Stacking model, the improved puffin algorithm (IPAO) is used to optimize the parameters of the base learner and meta-learner of the Stacking model. IPAO can combine the advantages of multiple base learners and meta-learners, optimize the fusion effect of the overall model, improve the generalization ability, and make the model perform better on unknown data.

[0105] It should be noted that the regression model of the present invention is based on the ensemble learning Stacking model. Through the combination of multiple base learners and meta-learners, the Stacking model can make full use of the advantages of different algorithms, further improve the performance of the detection system, effectively reduce the bias and variance of a single model, improve the generalization ability on new data, reduce the dependence on a single model by combining the predictions of multiple models, and enhance the stability and robustness of the prediction.

[0106] Combined with the attached Figure 1 As shown in the figure, this embodiment of the present invention provides a method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy with a Stacking model to solve all or part of the deficiencies of the current technology, including the following steps:

[0107] S1. Obtain the photoacoustic spectroscopy dataset of coal-fired SO2 gas;

[0108] S2. Divide the dataset into a training set and a test set according to a ratio of 8:2;

[0109] S3. Preprocess the photoacoustic spectroscopy data of the training set and the test set;

[0110] S4. Establish a photoacoustic spectroscopy SO2 gas Stacking model;

[0111] S5. Optimize the hyperparameters of the Stacking model with the improved puffin algorithm (IPAO);

[0112] S6. Input the spectral data to test the model.

[0113] In step S1, a quantum cascade laser is selected to excite SO2 gas to obtain the photoacoustic spectroscopy dataset of SO2 gas.

[0114] In step S2, the data collected in the experiment is divided, and the data is divided into a training set and a test set according to a ratio of 8:2.

[0115] In step S3, preprocessing operations are performed on the data of the training set and the test set respectively. The wavelet transform denoising algorithm is used to denoise the spectral data, which can effectively suppress random noise and improve the signal-to-noise ratio. After denoising, the spectral data is subjected to SPA feature wavelength screening to extract the main features, reduce the data dimension, and improve the data processing efficiency.

[0116] In step S4, first, the preprocessed photoacoustic spectroscopy dataset is divided into a training set and a test set by using the cross-validation method. The training set is used to train the Stacking model to determine the parameters of the Stacking model, and the trained Stacking model is obtained.

[0117] In step S5, aiming at the problems that the Stacking model is prone to overfitting and difficult to tune parameters, the improved puffin algorithm (IPAO) is used to optimize the hyperparameters of the Stacking model.

[0118] In further step S6, relevant data affecting the concentration of SO2 gas is input for testing, and various parameters in the model are adjusted; using the tuned prediction model, spectral data is input for testing, and the detection effect of the Stacking model is analyzed.

[0119] The present invention constructs a photoacoustic spectroscopy regression model for coal-fired SO2 gas based on the IPAO-optimized Stacking model, and proposes a method for predicting the concentration of coal-fired SO2 gas by combining the photoacoustic spectroscopy with the Stacking model, which can detect the concentration of coal-fired SO2 gas more quickly, effectively and accurately. With the advantage of the Stacking model in efficiently processing complex data, accurate detection of coal-fired SO2 gas is realized. This method not only has high sensitivity and high accuracy, but also has the characteristics of real-time and strong adaptability, and is suitable for the detection requirements of SO2 gas in industrial production sites and environmental detection.

[0120] Embodiment:

[0121] As Figure 2 shown, in step S5, aiming at the problems that the Stacking model is prone to overfitting and difficult to tune parameters, the improved puffin algorithm (IPAO) is used to optimize the parameters of the base learner and the meta-learner of the Stacking model. The penalty coefficient C and kernel function parameter γ of the SVR of the base learner and meta-learner of the Stacking model optimized by IPAO, the learning rate and the number of hidden layers of the BP neural network, the maximum depth of the DT, the learning rate and the number of trees of the XGBoost and other parameters are as follows:

[0122] S51: Determine the search range of each learner's hyperparameters and generate an initial hyperparameter combination:

[0123] SVR: Initial range of C: [0.1, 100], initial range of γ: [0.001, 1];

[0124] BP: Initial range of learning rate: [0.001, 0.1], initial range of number of hidden layers: [1, 5];

[0125] DT: Initial range of maximum depth: [3, 15];

[0126] XGBoost: Initial range of learning rate: [0.01, 0.3], initial range of number of trees: [50, 300];

[0127] S52: Evaluate fitness: Perform k-fold cross-validation for each initial combination, and calculate the mean squared error MSE as the fitness value;

[0128] S53: Global search and local search: Update parameters using IPAO, and the updated parameters may be:

[0129] SVR: C = 10, γ = 0.05;

[0130] BP: Learning rate = 0.01, number of hidden layers = 3;

[0131] DT: Maximum depth = 10;

[0132] XGBoost: Learning rate = 0.05, number of trees = 150;

[0133] S54: Determine whether the maximum number of iterations is reached: Set the maximum number of iterations to 500 times. If the number of iterations n is less than 500, then update the speed and position of the puffin, and ensure that the position and speed of the puffin are within the set range, and then go to step S53; if the number of iterations n is greater than 500, then execute S55;

[0134] S55: Output the optimal hyperparameter combination, initialize the Stacking model using the optimal hyperparameters, train the Stacking model, and test the performance of the Stacking model.

[0135] For those skilled in the art, it is obvious that the present invention is not limited to the details of the above exemplary embodiments, and without departing from the spirit or basic characteristics of the present invention, the present invention can be implemented in other specific forms. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-limiting. The scope of the present invention is defined by the appended claims rather than the above description. Therefore, all changes falling within the meaning and scope of the equivalent elements of the claims are intended to be included in the present invention. Any reference signs in the claims should not be regarded as limiting the claims involved.

[0136] In addition, it should be understood that although this specification is described in terms of embodiments, not every embodiment contains only an independent technical solution. This narrative manner of the specification is only for clarity. Those skilled in the art should regard the specification as a whole, and the technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art.

Claims

1. A method for predicting the concentration of coal - fired SO2 gas by combining photoacoustic spectroscopy with a Stacking model, characterized in that, It includes the following steps: S1. Obtain the photoacoustic spectroscopy dataset of coal-fired SO2 gas; S2. Divide the dataset into a training set and a test set according to a ratio of 8:2; S3. Preprocess the photoacoustic spectroscopy data of the training set and the test set, including wavelet transform denoising and SPA feature wavelength screening; S4. Establish a photoacoustic spectroscopy SO2 gas Stacking model, where the Stacking model includes three base learners: support vector regression (SVR), backpropagation neural network (BP), and decision tree (DT), and an XGBoost meta-learner; S5. Optimize the hyperparameters of the Stacking model using the improved puffin algorithm (IPAO); S6. Input the spectral data to test the model and predict the concentration of coal-fired SO2 gas.

2. The method for predicting the concentration of coal-fired SO2 gas by using photoacoustic spectroscopy combined with the Stacking model according to claim 1, wherein, In step S1, a quantum cascade laser is used to excite SO2 gas to obtain the photoacoustic spectroscopy dataset.

3. The method for predicting the concentration of coal-fired SO2 gas by using photoacoustic spectroscopy combined with the Stacking model according to claim 1, wherein, The preprocessing in step S3 includes: S31. Perform denoising using wavelet transform, specifically including selecting the db wavelet basis function, performing wavelet decomposition, wavelet coefficient threshold processing, and signal reconstruction; S32. Perform feature wavelength screening using the SPA algorithm, specifically including standardization preprocessing, initialization, stepwise projection, repeated screening, and determination of the final feature wavelength.

4. The method for predicting the concentration of coal - fired SO2 gas by combining photoacoustic spectroscopy with a Stacking model according to claim 1, wherein, In step S4, the establishment process of the Stacking model includes: S41. Train the base learners to obtain the prediction model; S42. Generate the second-layer training data and combine the prediction results of the base learners into a new training dataset; S43. Use XGBoost as the meta-learner and train the meta-learner to improve the final prediction; S44. In the test stage, perform the final prediction through the base learners and the meta-learner.

5. The method for predicting the concentration of coal-fired SO2 gas by photoacoustic spectroscopy combined with the Stacking model according to claim 1, characterized in that, In step S5, the improved puffin algorithm (IPAO) includes: S51. The aerial search stage, including aerial search and pouncing predation; S52. The underwater foraging stage, including foraging collection, enhanced search, and predator avoidance; S53. IPAO optimizes the hyperparameters of the Stacking model, including hyperparameter definition, initialization, fitness evaluation, global search, local search, and update strategy.

6. The method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy with a Stacking model according to claim 5, characterized in that In step S53, the hyperparameter definition includes: The penalty coefficient C and kernel function parameter γ of SVR; The learning rate and the number of hidden layers of the BP neural network; The maximum depth of DT; The learning rate and the number of trees of XGBoost.

7. The method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy with the Stacking model according to claim 1, wherein The Stacking model can effectively reduce the bias and variance of a single model and improve the generalization ability on new data by integrating multiple base learners and meta-learner.

8. The method for predicting the concentration of coal-fired SO2 gas by combining photoacoustic spectroscopy with the Stacking model according to claim 1, wherein The improved puffin algorithm (IPAO) can adaptively and dynamically adjust the global exploration and local exploitation of the algorithm, optimize the hyperparameter combination, and reduce the risk of overfitting by introducing an enhanced behavior conversion factor.

Images