Rapid evaluation of texture parameters of Tan mutton using hyperspectral imaging with optimization algorithms

Combining Vis-NIR and NIR hyperspectral imaging techniques with a data fusion strategy for prediction of norfloxacin residues in mutton

Norfloxacin is an antibacterial compound that belongs to the fluoroquinolone family. Currently, hyperspectral imaging (HSI) for the detection of antibiotic residues focuses mostly on individual systems. Attempts to integrate different HSI systems with complementary spectral ranges are still lacking. This study investigates the feasibility of applying data fusion strategies with two HSI techniques (Visible near-infrared and near-infrared) in combination to predict norfloxacin residue levels in mutton. Spectral data from the two spectral techniques were analyzed using partial least squares regression (PLSR), support vector regression (SVR) and stochastic configuration networks (SCN), respectively, and the two data fusion strategies were fused at the data level (low-level fusion) and feature level (middle-level fusion, mid-level fusion). The results indicated that the modeling performance of the two fused datasets was better than that of the individual systems. Mid-level fusion data achieved the best model based on uninformative variable elimination (UVE) combined with SCN, in which the determination coefficient of prediction set (R2p) of 0.9312, (root mean square error of prediction set) RMSEP of 0.3316 and residual prediction deviation (RPD) of 2.7434, in comparison with all others. Therefore, two HSI systems with complementary spectral ranges, combined with data fusion strategies and feature selection, could be used synergistically to improve the detection of norfloxacin residues. This study may provide a valuable reference for the non-destructive detection of antibiotic residues in meat.

Data fusion of near-infrared and Raman spectroscopy: An innovative tool for non-destructive prediction of the TVB-N content of salmon samples

Total volatile basic nitrogen (TVB-N) serves as a crucial indicator for evaluating the freshness of salmon. This study aimed to achieve accurate and non-destructive prediction of TVB-N content in salmon fillets stored in multiple temperature settings (-20, 0, -4, 20 °C, and dynamic temperature) using near-infrared (NIR) and Raman spectroscopy. A partial least square support vector machine (LSSVM) regression model was established through the integration of NIR and Raman spectral data using low-level data fusion (LLDF) and mid-level data fusion (MLDF) strategies. Notably, compared to a single spectrum analysis, the LLDF approach provided the most accurate prediction model, achieving an R2P of 0.910 and an RMSEP of 1.922 mg/100 g. Furthermore, MLDF models based on 2D-COS and VIP achieved R2P values of 0.885 and 0.906, respectively. These findings demonstrated the effectiveness of the proposed method for precise quantitative detection of salmon TVB-N, laying a technical foundation for the exploration of similar approaches in the study of other meat products. This approach has the potential to assess and monitor the freshness of seafood, ensuring consumer safety and enhancing product quality.

A new comprehensive quantitative index for the assessment of essential amino acid quality in beef using Vis-NIR hyperspectral imaging combined with LSTM

The quality of beef is usually predicted by measuring a single index rather than a comprehensive index. To precisely determine the essential amino acid (EAA) contents in 360 beef samples, the feasibility of optimized spectral detection techniques based on the comprehensive EAA index (CEI) and comprehensive weight index (CWI) constructed by factor analysis was explored. Two-dimensional correlation spectroscopy (2D-COS) was used to analyse the mechanisms of spectral peak shifts in complex disturbance systems with CEI and CWI contents, and 15 sensitive feature variables were extracted to establish a quantitative analysis model of a long short-term memory network (LSTM). The results indicated that 2D-COS had good predictive performance in both CEI-LSTM (R2P of 0.9095 and RPD of 2.76) and CWI-LSTM (R2P of 0.8449 and RPD of 2.45), which reduced data information by 88%. This indicates that utilizing 2D-COS can eliminate collinearity and redundant information among variables while achieving data dimensionality reduction and simplification of calibration models. Furthermore, a spatial distribution map of the comprehensive EAA content was generated by combining the optimal prediction model. This study demonstrated that the comprehensive index method furnishes a new approach to rapidly evaluate EAA content.

Application of colorimetric sensor array coupled with chemometric methods for monitoring the freshness of snakehead fillets

Total volatile basic nitrogen content (TVB-N) is an important index of freshness for snakehead. This paper attempted the feasibility of determining TVB-N content level in snakehead fillets by a colorimetric sensor array (CSA) composed of twelve porphyrin materials and eight pH indicators. The nine feature variables in RGB, HSV and CIE L*a*b* color spaces were obtained by differentiating the images of the CSA before and after exposure to the headspace-gas of the samples. Competitive adaptive reweighted sampling combined with partial least squares regression (CARS-PLS) was used to build the relationship between the TVB-N content and the feature variables of CSA, and to select meaningful color-sensitive materials. The results showed that CARS-PLS had a correlation coefficient of 0.9325 in the prediction set and selected 13 informative color-sensitive materials. This study demonstrated that the CSA with CARS-PLS algorithm could be used successfully to quantify and monitor the TVB-N in snakehead fillets.

Crater-Spectrum Feature Fusion Method for Panax notoginseng Cadmium Detection Using Laser-Induced Breakdown Spectroscopy

Panax notoginseng (P. notoginseng) is a valuable herbal medicine, as well as a dietary food supplement known for its satisfactory clinical efficacy in alleviating blood stasis, reducing swelling, and relieving pain. However, the ability of P. notoginseng to absorb and accumulate cadmium (Cd) poses a significant environmental pollution risk and potential health hazards to humans. In this study, we employed laser-induced breakdown spectroscopy (LIBS) for the rapid detection of Cd. It is important to note that signal uncertainty can impact the quantification performance of LIBS. Hence, we proposed the crater-spectrum feature fusion method, which comprises ablation crater morphology compensation and characteristic peak ratio correction (CPRC), to explore the feasibility of signal uncertainty reduction. The crater morphology compensation method, namely, adding variables using multiple linear regression (MLR) analysis, decreased the root-mean-square error of the prediction set (RMSEP) from 7.0233 μg/g to 5.4043 μg/g. The prediction results were achieved after CPRC pretreatment using the calibration curve model with an RMSEP of 3.4980 μg/g, a limit of detection of 1.92 μg/g, and a limit of quantification of 6.41 μg/g. The crater-spectrum feature fusion method reached the lowest RMSEP of 2.8556 μg/g, based on a least-squares support vector machine (LSSVM) model. The preliminary results suggest the effectiveness of the crater-spectrum feature fusion method for detecting Cd. Furthermore, this method has the potential to be extended to detect other toxic metals in addition to Cd, which significantly contributes to ensuring the quality and safety of agricultural production.

Discrimination among Fresh, Frozen-Stored and Frozen-Thawed Beef Cuts by Hyperspectral Imaging

The detection of the storage state of frozen meat, especially meat frozen-thawed several times, has always been important for food safety inspections. Hyperspectral imaging (HSI) is widely applied to detect the freshness and quality of meat or meat products. This study investigated the feasibility of the low-cost HSI system, combined with the chemometrics method, to classify beef cuts among fresh (F), frozen-stored (F-S), frozen-thawed three times (F-T-3) and frozen-thawed five times (F-T-5). A compact, low-cost HSI system was designed and calibrated for beef sample measurement. The classification model was developed for meat analysis with a method to distinguish fat and muscle, a CARS algorithm to extract the optimal wavelength subset and three classifiers to identify each beef cut among different freezing processes. The results demonstrated that classification models based on feature variables extracted from differentiated tissue spectra achieved better performances, with ACCs of 92.75% for PLS-DA, 97.83% for SVM and 95.03% for BP-ANN. A visualization map was proposed to provide detailed information about the changes in freshness of beef cuts after freeze-thawing. Furthermore, this study demonstrated the potential of implementing a reasonably priced HSI system in the food industry.

Rapid discrimination of urine specific gravity using spectroscopy and a modified combination method based on SPA and spectral index

To achieve high-accuracy urine specific gravity discrimination and guide the design of four-waveband multispectral sensors. A modified combination strategy was attempted to be proposed based on the successive projections algorithm (SPA) and the spectral index (SI) in the present study. First, the SPA was used to select four spectral variables in the full spectra. Second, the four spectral variables were mathematically transformed by SI to obtain SI values. Then, SPA gradually fusions the SI values and establishes models to identify USG. The results showed that the SPA can screen out the four characteristic wavelengths related to the measured sample attributes. SIs can be used to improve the performance of constructed prediction models. The best model only involves four spectral variables and 1 SI value, with high accuracy (91.62%), sensitivity (0.9051), and specificity (0.9667). The results reveal that m-SPA-SI can effectively distinguish USG and provide design guidance for 4-wavelength multispectral sensors.

Improving prediction model robustness with virtual sample construction for near-infrared spectra analysis

In a qualitative analysis of near-infrared spectroscopy (NIRS), when the samples to be analyzed are difficult to obtain or there are few counterexamples, the robustness of the models is poor, resulting in the decline of the generalization ability of the models. In this case, the effective method is to construct virtual samples to achieve the balance of categories. In this contribution, three virtual spectrum construction strategies including Synthetic Minority Oversampling Technique (SMOTE), Adaptive Synthetic Sampling (ADASYN), and Deep Convolutional Generative Adversarial Network (DCGAN) were explored to deal with the problem of insufficient or imbalanced sample numbers in NIRS analysis. The strategies were tested with the melamine and Yali pears two spectral datasets. The PLS-DA and Correct Recognition Rate (CRR) were used for discriminant model construction and accuracy evaluation, respectively. The results show that SMOTE, ADASYN, and DCGAN processing strategies can all improve the global CRR (CRRglob). The SMOTE and ADASYN can improve the CRR for majority class sample (CRRmaj), but the CRR for minority class sample (CRRmin) has decreased. For the DCGAN method, the CRRglob, CRRmaj, and CRRmin were all improved. The standard deviation of the results of the multiple parallel calculations demonstrates the robustness of DCGAN generation method. Therefore, the DCGAN method has good reliability and practicability, and can increase the robustness and generalization ability of the NIRS model.

Rapid and Non-Invasive Assessment of Texture Profile Analysis of Common Carp (Cyprinus carpio L.) Using Hyperspectral Imaging and Machine Learning

Hyperspectral imaging (HSI) has been applied to assess the texture profile analysis (TPA) of processed meat. However, whether the texture profiles of live fish muscle could be assessed using HSI has not been determined. In this study, we evaluated the texture profile of four muscle regions of live common carp by scanning the corresponding skin regions using HSI. We collected skin hyperspectral information from four regions of 387 scaled and live common carp. Eight texture indicators of the muscle corresponding to each skin region were measured. With the skin HSI of live common carp, six machine learning (ML) models were used to predict the muscle texture indicators. Backpropagation artificial neural network (BP-ANN), partial least-square regression (PLSR), and least-square support vector machine (LS-SVM) were identified as the optimal models for predicting the texture parameters of the dorsal (coefficients of determination for prediction (rp) ranged from 0.9191 to 0.9847, and the root-mean-square error for prediction ranged from 0.1070 to 0.3165), pectoral (rp ranged from 0.9033 to 0.9574, and RMSEP ranged from 0.2285 to 0.3930), abdominal (rp ranged from 0.9070 to 0.9776, and RMSEP ranged from 0.1649 to 0.3601), and gluteal (rp ranged from 0.8726 to 0.9768, and RMSEP ranged from 0.1804 to 0.3938) regions. The optimal ML models and skin HSI data were employed to generate visual prediction maps of TPA values in common carp muscles. These results demonstrated that skin HSI and the optimal models can be used to rapidly and accurately determine the texture qualities of different muscle regions in common carp.

Qualitative and quantitative detection of aflatoxins B1 in maize kernels with fluorescence hyperspectral imaging based on the combination method of boosting and stacking

The most widespread, toxic, and harmful toxin is aflatoxins B1 (AFB1). The fluorescence hyperspectral imaging (HSI) system was employed for AFB1 detection in this study. This study developed the under sampling stacking (USS) algorithm for imbalanced data. The results indicated that the USS method combined with ANOVA for featured wavelength achieved the best performance with the accuracy of 0.98 for 20 or 50 μg /kg threshold using endosperm side spectra. As for the quantitative analysis, a specified function was used to compress AFB1 content, and the combination of boosting and stacking was used for regression. The support vector regression (SVR)-Boosting, Adaptive Boosting (AdaBoost), and extremely randomized trees (Extra-Trees)-Boosting were used as the base learner, while the K nearest neighbors (KNN) algorithm was used as the meta learner could obtain the best results, with the correlation coefficient of prediction (R_p) was 0.86. These results provided the basis for developing AFB1 detection and estimation technologies.

Non-Destructive Detection of the Freshness of Air-Modified Mutton Based on Near-Infrared Spectroscopy

Monitoring and identifying the freshness levels of meat holds significant importance in the field of food safety as it directly relates to human dietary safety. Traditional packaging methods for lamb meat quality assessment present issues such as cumbersome operations and irreversible damage. This research proposes a quality assessment method for modified atmosphere packaging lamb meat using near-infrared spectroscopy and multi-parameter fusion. Fresh lamb meat quality is taken as the research subject, comparing various physicochemical indicators and near-infrared spectroscopic information under different temperatures (4 °C and 10 °C) and different modified atmosphere packaging combinations. Through precision parameter comparison, rebound and TVB-N values are selected as the modeling parameters. Six spectral preprocessing methods (multi-scatter calibration, MSC; standard normal variate transformation, SNV; normalization; Savitzky-Golay smoothing, SG; Savitzky-Golay 1 derivative, SG-1st; and Savitzky-Golay 2 derivative, SG-2nd), and three feature wavelength selection methods (competitive adaptive reweighted sampling, CARS; successive projections algorithm, SPA; and uninformative variable elimination, UVE) are compared. Partial least squares (PLS) and support vector machine (SVM) are used to construct prediction models for chilled fresh lamb meat quality. The results show that when rebound is used as a parameter, the SG-2nd-SPA-PLSR model has the highest accuracy, with a determination coefficient R²p of 0.94 for the prediction set. When TVB-N is used as a parameter, the MSC-UVE-SVM model has the highest accuracy, with an R²p of 0.95 for the prediction set. In conclusion, the use of near-infrared spectroscopic analysis enables rapid and non-destructive prediction and evaluation of lamb meat freshness, including its textural characteristics and TVB-N content under different modified atmosphere packaging. This study provides a theoretical basis and technical support for further encapsulating the models into portable devices and developing portable near-infrared spectrometers to rapidly determine lamb meat freshness.

Application of portable Vis-NIR spectroscopy for rapid detection of myoglobin in frozen pork

Myoglobin content is considered as a crucial index to evaluate the quality of frozen pork. In this study, a portable visible and near-infrared (Vis-NIR) spectrometer combined with chemometrics was used to detect myoglobin content in frozen pork. Metmyoglobin, deoxymyoglobin, oxymyoglobin, and total myoglobin were assessed spectrophotometrically. The raw Vis-NIR spectra of frozen pork samples were pre-processed using 1^st derivatives (FD). Afterward, Synergy Interval Partial Least Square (Si-PLS) coupled Competitive Adaptive Reweighted Sampling algorithm (Si-CARS-PLS) was applied to select characteristic variables. The Si-CARS-PLS models revealed the probability of estimating myoglobin content in frozen pork, with predictive correlation coefficients (R_p) for metmyoglobin, deoxymyoglobin, oxymyoglobin, and total myoglobin as 0.9095, 0.9004, 0.8578, and 0.9133, respectively. The findings of this study showed that Vis-NIR spectroscopy coupled with Si-CARS-PLS is a promising method and offered a way forward for determining the myoglobin content in frozen pork.

Nondestructive detection of nutritional parameters of pork based on NIR hyperspectral imaging technique

Nondestructive detection of the nutritional parameters of pork is of great importance. This study aimed to investigate the feasibility of applying hyperspectral image technology to detect the nutrient content and distribution of pork nondestructively. Hyperspectral cubes of 100 pork samples were collected using a line-scan hyperspectral system, the effects of different preprocessing methods on the modeling effects were compared and analyzed, the feature wavelengths of fat and protein were extracted, and the full-wavelength model was optimized using the regressor chains (RC) algorithm. Finally, pork's fat, protein, and energy value distributions were visualized using the best prediction model. The results showed that standard normal variate was more effective than other preprocessing methods, the feature wavelengths extracted by the competitive adaptive reweighted sampling algorithm had better prediction performance, and the protein model prediction performance was optimized after using the RC algorithm. The best prediction models were developed, with the correlation coefficient of prediction (R_P) = 0.929, the root mean square error in prediction (RMSEP) = 0.699% and residual prediction deviation (RPD) = 2.669 for fat, and R_P = 0.934, RMSEP = 0.603% and RPD = 2.586 for protein. The pseudo-color maps were helpful for the analysis of nutrient distribution in pork. Hyperspectral image technology can be a fast, nondestructive, and accurate tool for quantifying the composition and assessing the distribution of nutrients in pork.

Combination of hyperspectral imaging and entropy weight method for the comprehensive assessment of antioxidant enzyme activity in Tan mutton

The antioxidant enzymes play the crucial role in inhibiting mutton spoilage. In this study, visible near-infrared (Vis-NIR) hyperspectral imaging (HSI) combined with entropy weight method (EWM) was developed for the first time to evaluate the antioxidant properties of Tan mutton. The comprehensive index of antioxidant enzymes (AECI) consisting of peroxidase (49.34%), catalase (37.97%) and superoxidase (12.69%) was constructed by the EWM. Partial least squares regression, least squares support vector machine and artificial neural networks (ANN) were developed based on characteristic wavelengths extracted by successful projections algorithm, uninformative variable selection, iteratively retains informative variables (IRIV), regression coefficient and competitive adaptive reweighted sampling (CARS). The textural features (TF) were extracted by the gray level co-occurrence matrix and fused with the spectral data to establish models. Visualization of the changes in antioxidant enzyme activity was constructed from the optimal model. In addition, two-dimensional correlation spectra (2D-COS) with AECI as a perturbation variable was used to identify spectral features, revealing chemical bond changes order under the characteristic peaks at 612-799-473-708-559 nm. The results showed that the IRIV-CARS-TF-ANN model performed the best, with prediction set coefficient of determination (R_P²) of 0.8813, which improved 2.12%, 1.11% and 2.77% over the R_P² of full band, IRIV and IRIV-CARS, respectively. It was suggested that fusion data of HSI may effectively predict the activity of antioxidant enzymes in Tan mutton.

Sodium alginate edible coating to reduce oil absorption of French fries with maintaining overall acceptability: Based on a water replacement mechanism

The effect of sodium alginate (SA) coating on the oil content and quality of fries was evaluated, and the inhibitory mechanism of SA on oil absorption was analyzed based on the water replacement theory. Compared to uncoated samples, the penetrated surface oil (PSO), structure oil (STO), and total oil (TO) contents, a*, and b* of coated fries decreased, whereas moisture content, L* and hardness increased with no significant difference revealed by sensory evaluation of all samples. The water contact angle of the films correlated negatively with the water content and hardness of the fries. In contrast, it correlated positively with PSO, STO, and TO contents. The TO content of fries with 1 % SA film which had a compact microstructure, was the lowest, reduced by 52.5 % compared to the control sample. SA coating reduces the pores and roughness on the fries' surface, which inhibits the oil from penetrating into the samples. SA coating decreased the T₂₁, T₂₂, and pores of the starch, and increased the P_2b, P₂₁, relative crystallinity, and ΔH significantly (P < 0.05). Therefore, SA coating inhibits the oil absorption in fries by reducing water evaporation which is attributed to the increase in double helices and crystallinity of starch.

Hyperspectral Imaging Combined with Chemometrics Analysis for Monitoring the Textural Properties of Modified Casing Sausages with Differentiated Additions of Orange Extracts

The textural properties (hardness, springiness, gumminess, and adhesion) of 16-day stored sausages with different additions of orange extracts to the modified casing solution were estimated by response surface methodology (RSM) and a hyperspectral imaging system in the spectral range of 390-1100 nm. To improve the model performance, normalization, 1st derivative, 2nd derivative, standard normal variate (SNV), and multiplicative scatter correction (MSC) were applied for spectral pre-treatments. The raw, pretreated spectral data and textural attributes were fit to the partial least squares regression model. The RSM results show that the highest R² value achieved at adhesion (77.57%) derived from a second-order polynomial model, and the interactive effects of soy lecithin and orange extracts on adhesion were significant (p < 0.05). The adhesion of the PLSR model developed from reflectance after SNV pretreatment possessed a higher calibration coefficient of determination (0.8744) than raw data (0.8591). The selected ten important wavelengths for gumminess and adhesion can simplify the model and can be used for convenient industrial applications.

A Combination of Near-Infrared Hyperspectral Imaging with Two-Dimensional Correlation Analysis for Monitoring the Content of Alanine in Beef

Alanine (Ala), as the most important free amino acid, plays a significant role in food taste characteristics and human health regulation. The feasibility of using near-infrared hyperspectral imaging (NIR-HSI) combined with two-dimensional correlation spectroscopy (2D-COS) analysis to predict beef Ala content quickly and nondestructively is first proposed in this study. With Ala content as the external disturbance condition, the sequence of chemical bond changes caused by synchronous and asynchronous correlation spectrum changes in 2D-COS was analyzed, and local sensitive variables closely related to Ala content were obtained. On this basis, the simplified linear, nonlinear, and artificial neural network models developed by the weighted coefficient based on the feature wavelength extraction method were compared. The results show that with the change in Ala content in beef, the double-frequency absorption of the C-H bond of CH₂ in the chemical bond sequence occurred prior to the third vibration of the C=O bond and the first stretching of O-H in COOH. Furthermore, the wavelength within the 1136-1478 nm spectrum range was obtained as the local study area of Ala content. The linear partial least squares regression (PLSR) model based on effective wavelengths was selected by competitive adaptive reweighted sampling (CARS) from 2D-COS analysis, and provided excellent results (R²_C of 0.8141, R²_P of 0.8458, and RPDp of 2.54). Finally, the visual distribution of Ala content in beef was produced by the optimal simplified combination model. The results show that 2D-COS combined with NIR-HSI could be used as an effective method to monitor Ala content in beef.

Non-Destructive Techniques for the Analysis and Evaluation of Meat Quality and Safety: A Review

With the continuous development of economy and the change in consumption concept, the demand for meat, a nutritious food, has been dramatically increasing. Meat quality is tightly related to human life and health, and it is commonly measured by sensory attribute, chemical composition, physical and chemical property, nutritional value, and safety quality. This paper surveys four types of emerging non-destructive detection techniques for meat quality estimation, including spectroscopic technique, imaging technique, machine vision, and electronic nose. The theoretical basis and applications of each technique are summarized, and their characteristics and specific application scope are compared horizontally, and the possible development direction is discussed. This review clearly shows that non-destructive detection has the advantages of fast, accurate, and non-invasive, and it is the current research hotspot on meat quality evaluation. In the future, how to integrate a variety of non-destructive detection techniques to achieve comprehensive analysis and assessment of meat quality and safety will be a mainstream trend.

Recent advances in muscle food safety evaluation: Hyperspectral imaging analyses and applications

As there is growing interest in process control for quality and safety in the meat industry, by integrating spectroscopy and imaging technologies into one system, hyperspectral imaging, or chemical or spectroscopic imaging has become an alternative analytical technique that can provide the spatial distribution of spectrum for fast and nondestructive detection of meat safety. This review addresses the configuration of the hyperspectral imaging system and safety indicators of muscle foods involving biological, chemical, and physical attributes and other associated hazards or poisons, which could cause safety problems. The emphasis focuses on applications of hyperspectral imaging techniques in the safety evaluation of muscle foods, including pork, beef, lamb, chicken, fish and other meat products. Although HSI can provide the spatial distribution of spectrum, characterized by overtones and combinations of the C-H, N-H, and O-H groups using different combinations of a light source, imaging spectrograph and camera, there still needs improvement to overcome the disadvantages of HSI technology for further applications at the industrial level.

Design of predictive model to optimize the solubility of Oxaprozin as nonsteroidal anti-inflammatory drug

These days, many efforts have been made to increase and develop the solubility and bioavailability of novel therapeutic medicines. One of the most believable approaches is the operation of supercritical carbon dioxide fluid (SC-CO₂). This operation has been used as a unique method in pharmacology due to the brilliant positive points such as colorless nature, cost-effectives, and environmentally friendly. This research project is aimed to mathematically calculate the solubility of Oxaprozin in SC-CO₂ through artificial intelligence. Oxaprozin is a nonsteroidal anti-inflammatory drug which is useful in arthritis disease to improve swelling and pain. Oxaprozin is a type of BCS class II (Biopharmaceutical Classification) drug with low solubility and bioavailability. Here in order to optimize and improve the solubility of Oxaprozin, three ensemble decision tree-based models including random forest (RF), Extremely random trees (ET), and gradient boosting (GB) are considered. 32 data vectors are used for this modeling, moreover, temperature and pressure as inputs, and drug solubility as output. Using the MSE metric, ET, RF, and GB illustrated error rates of 6.29E-09, 9.71E-09, and 3.78E-11. Then, using the R-squared metric, they demonstrated results including 0.999, 0.984, and 0.999, respectively. GB is selected as the best fitted model with the optimal values including 33.15 (K) for the temperature, 380.4 (bar) for the pressure and 0.001242 (mole fraction) as optimized value for the solubility.