Back Propagation Neural Network Model Research Articles

Various carbon-based MgAl2O4 adsorbents and their removal efficiency of CR dye and antibiotics in aqueous media: High selective adsorption capacity, performance prediction and mechanism insight

Various carbon -based MgAl2O4 (MAO) adsorbents were synthesized by a simple ultrasound irradiation technology with the activated carbon (AC), carbon quantum dots (CQDs), C3N4 (CN) and graphene oxide (GO) as carbon sources. The optimum synthesis conditions for the carbon -based MAO adsorbents were determined by the study of the addition of different types of carbon and different mass ratios of mVarious carbon: mMAO = 2.5%, 5.0%, 7.5% and 10%. The carbon -based MAO adsorbents were used for the adsorption of Congo red (CR) dye, tetracycline hydrochloride (TCH), oxytetracycline hydrochloride (OCH), ciprofloxacin (CIP), naproxen sodium (NPS) and tetrabromobisphenol A (TBBPA) and the seven factors affecting the adsorption behavior were discussed, including the type of carbon, AC content, initial dye concentration (CCR), adsorbent dosage (Ccarbon -based MAO adsorbents), adsorption time (At), pH value and reaction temperature (T). The corresponding adsorption isotherm models such as Langmuir, Tempkin, Koble-Corrigan, Toth and Freundlich models and thermodynamics of carbon -based MAO adsorbents for the adsorption of CR dye were also studied. When pH = 7.8, CCR = 200 mg/L, At = 90 min, T = 287 K and CAC 5.0 wt%-MAO = 1 g/L, the removal rate of CR dye reaches 89.7%. The back propagation (BP) neural network model was used to predict the adsorption percentage of carbon-based MAO adsorbents, which was consistent with the experimental results. The high adsorption capacity of AC 5.0 wt%-MAO adsorbents for the adsorption of CR dye can be assigned to the synergistic effects of electrostatic interaction, intermolecular force, n-π interaction and hydrogen bonding, while for the adsorption of TCH, OCH and CIP can be ascribed to the electrostatic interaction. This study demonstrated a huge potential of carbon -based MAO adsorbents as an eco-friendly adsorbent for the adsorption of dyes and drugs.

Efficiency of Orange Yellow II Degradation by Synergistic Hydroxylamine with Fe2+ to Activate Peroxymonosulfate Oxidation: Machine Learning Prediction and Performance Optimization

A back-propagation neural network (BPNN) was used to model and optimize the process of hydroxylamine (HA)-enhanced Fe2+ activating peroxymonosulfate (PMS). Using HA-enhanced Fe2+ to activate PMS is a cost-effective method to degrade orange II (AO7). We investigated the individual and interactive effects of the concentrations of Fe2+, HA, and PMS on the degradation of AO7. The R2 of the BPNN model was 0.99852, and the data were distributed around y = x. Sensitivity analysis showed that the relative importance of each factor was as follows: HA > Fe2+ > PMS. The optimized results obtained by the genetic algorithm were as follows: the concentration of Fe2+ was 35.33 μmol·L−1, HA was 0.46 mmol·L−1, and PMS was 0.93 mmol·L−1. Experiments verified that the AO7 degradation effect within 5 min was 95.7%, whereas the predicted value by the BPNN was 96.2%. The difference between predicted and experimental values is 0.5%. This study provides a new tool (machine learning) to accurately predict the concentrations of HA, Fe2+, and PMS to degrade AO7 under various conditions.

Laser Electrochemical Deposition Hybrid Preparation of an Oil-Water Separation Mesh with Controllable Pore Diameter Based on a BP Neural Network.

With the increasing problem of water pollution, oil-water separation technology has attracted widespread attention worldwide. In this study, we proposed laser electrochemical deposition hybrid preparation of an oil-water separation mesh and introduced a back-propagation (BP) neural network model to realize the regulation of metal filter mesh. Among them, the coating coverage and electrochemical deposition quality were improved by laser electrochemical deposition composite processing. Based on the BP neural network model, the pore size after electrochemical deposition could be obtained only by inputting the processing parameters into the model, enabling the prediction and control of the pore size of the processed stainless-steel mesh (SSM), and the maximum residual difference between the predicted value and the experimental value was 1.5%. According to the oil-water separation theory and practical requirements, the corresponding electrochemical deposition potential and electrochemical deposition time were determined by the BP neural network model, which reduced the cost and time loss. In addition, the prepared SSM was found to achieve efficient separation of oil and water mixtures, reaching 99.9% separation efficiency in a combination with oil-water separation, along with other performance tests without chemical modification. The prepared SSM showed good mechanical durability and the separation efficiency exceeded 95% after sandpaper abrasion, thus, still maintaining the separation ability of oil-water mixture. Compared to other similar preparation methods, the method proposed in this study has the advantages of controllable pore size, simplicity, convenience, environmental friendliness, and durable wear resistance, offering important application potential in the treatment of oily wastewater.

Investigation of Favorable Neural Network Methods to Estimate Traffic Components

Neural networks provide the opportunity to estimate specific components of engineering problems. They are decomposed complex problems into different parts. Thus, it can be easy to compete with each of them through neural networks. In this paper, it was purposed to estimate the average speed of a 6-line road’s cross-section by observed traffic variables, such as numbers of vehicles and occupancy values, using radial basis function neural network (RBFNN), generalized regression neural network (GRNN) and the feed-forward back propagation neural network (FFBPNN) models. A comparison was fulfilled between different neural networks and checked against multivariate linear regression (MVLR), a conventional statistical model. After each simulation of neural networks, results show that different forecasts were obtained under the same conditions. The best forecasting is made by FFBPNN, GRNN, and RBFNN, respectively. When compared with multivariate linear regression (MVLR), FFBPNN performs better than MVLR, but GRNN and RBFNN perform lower than it.

Using EEMD mode decomposition in combination with machine learning models to improve the accuracy of monthly sea level predictions in the coastal area of China

In the context of climate change and human activities, the global sea level is facing a rising trend, which poses serious challenges to the ecological environment of coastal areas. In this study, we selected the monthly mean sea level (MSL) time series of 9 stations in the coastal areas of China as the research object. First, we analyzed the spatiotemporal distribution characteristics of the monthly MSL in the coastal areas of China. Secondly, we analyzed the ability of ensemble empirical mode decomposition (EEMD) to decompose the monthly MSL series. Finally, we choose three machine learning models, namely Back Propagation (BP), K-Nearest Neighbor (KNN), and Long Short-Term Memory (LSTM) neural network models to compare model prediction effect between single machine learning models with machine learning models combined with EEMD. The results show that except for the YANTAI (YT) station, which showed an insignificant downward trend, the monthly MSL of other stations showed an upward trend, indicating that the coastal areas of China are facing the risk of sea level rise. EEMD can effectively reduce the complexity of the original monthly MSL time series, and different intrinsic mode functions (IMFs) reflect changes in monthly MSL at different frequencies. Comparing the single machine learning model and the machine learning model combined with EEMD, it is found that the simulation effect of the machine learning model combined with EEMD is better than that of the single model. The model with the best prediction effect on monthly MSL in the coastal areas of China is LSTM-EEMD, followed by KNN-EEMD. This study provides an important reference for systematically understanding sea level changes and selecting an appropriate monthly MSL prediction model in the coastal areas of China.

Application of grey feed forward back propagation-neural network model based on wavelet denoising to predict the residual settlement of goafs.

To study the residual settlement of goaf's law and prediction model, we investigated the Mentougou mining area in Beijing as an example. Using MATLAB software, the wavelet threshold denoising method was used to optimize measured data, and the grey model (GM) and feed forward back propagation neural network model (FFBPNN) were combined. A grey feed forward back propagation neural network (GM-FFBPNN) model based on wavelet denoising was proposed, the prediction accuracy of different models was calculated, and the prediction results were compared with original data. The results showed that the prediction accuracy of the GM-FFBPNN was higher than that of the individual GM and FFBPNN models. The mean absolute percentage error (MAPE) of the combined model was 7.39%, the root mean square error (RMSE) was 49.01 mm, the scatter index (SI) was 0.06%, and the BIAS was 2.42%. The original monitoring data were applied to the combination model after wavelet denoising, and MAPE and RMSE were only 1.78% and 16.05 mm, respectively. Compared with the combined model before denoising, the prediction error was reduced by 5.61% and 32.96 mm. Thus, the combination model optimized by wavelet analysis had a high prediction accuracy, strong stability, and accorded with the law of change of measured data. The results of this study will contribute to the construction of future surface engineering in goafs and provide a new theoretical basis for similar settlement prediction engineering, which has strong popularization and application value.

Prediction of the geological indicators in TBM tunnel based on optimized proportion of surrounding rock grades

With tunnel boring machine being used in underground engineering, accurate geological indicators have been the important basis for tunnel boring machine (TBM) construction. Back propagation neural network (BPNN) has been used to predict the geological indicators of tunnels in previous studies. Nevertheless, these studies ignored the imbalance proportion of surrounding rock grades, leading to the indiscriminate use of data, thus affecting the predictive effect of BPNN. In order to prove the importance of the proportion of surrounding rock grade in geological prediction, we mainly attempt to utilize particle swarm optimization (PSO) to optimize the proportion of sample data, and integrate with BPNN to establish a PSO-BPNN theoretical model to predict geological indicators. At the same time, combined with the actual engineering data, 5 tunneling indicators were selected as input and 4 geological indicators were selected as output by a variety of dimensionality reduction methods. The geological indicators are density, uniaxial compressive strength, internal friction angle (φ) and Poisson's ratio (ε). On this basis, the PSO-BPNN prediction model was established in detail. By comparing the prediction of traditional BPNN, PSO-BPNN and other optimization-integrated models, the result shows that optimized proportion of surrounding rock grades reduces the prediction error and improves the interpretability of the prediction model. Meanwhile, we combined the theory of surrounding rock partition to illustrate the rationality of surrounding rock proportion in PSO result, that is, the proportion of complex surrounding rock should be increased appropriately to improve the prediction result. Ultimately, based on the optimization-integrated models with engineering data and the surrounding rock classification theory, the importance of proportion of surrounding rock grades for tunnel geological prediction is confirmed.

Gaussian Process Regression for Quantitative Degree of Polymerization Analysis of Oil-Paper Insulation by EPO-NIRS: A Solution to Field Moisture

In recent years, the near infrared (NIR) spectroscopy has been used in prediction of the degree of polymerization (DP) of oil-paper insulation, but the practices show that the field moisture has a significant influence on the acquired spectra. In this paper, an EPO-GPR model is proposed to eliminate the interference of external moisture and hence to improve the prediction performance of DP of insulating paper in the laboratory as well as on-site experiments. In this model, external parameter orthogonalization (EPO) extracts the differences between the insulating paper samples with varying moisture contents and builds a projection matrix orthogonal to the moisture spectral information; the Gaussian process regression (GPR) with optimized Matérn kernel is employed to mapping the correlation between the spectra and DP of insulating paper. Compared with classical PLS and BPNN models, the EPO-GPR model achieves high prediction accuracy in the laboratory testing (RMSE of 71) and field experiments (RMSE of ∼ 60). The proposed EPO-GPR model can provide a solution to field moisture when using the NIR spectroscopy technique to on-site assess the aging condition of insulating papers.

Streamflow simulation using conceptual and neural network models in the Hemavathi sub-watershed, India

Water is one of the most valuable natural resources and a major element of a state's and country's socio-economic growth. The world's water resources and India are under huge pressure because of rising demand and a limited supply. Proper water management is the only solution for ensuring a close gap between demand and supply. Hydrological modeling offers an answer to this issue by establishing relationships between different hydrological processes. Several models have been developed in the past decade to simulate the rainfall and runoff relations. Some models are simple conceptual models based on spatially distributed event-based or continuous and artificial intelligence (AI) models. This study aims to compare two conceptual daily-based models and one AI model developed for the Hemavathi sub-watershed in the Cauvery Basin (India). Two daily runoff models are implemented using conceptual models, i.e., Sacramento and the Australian water balance model (AWBM) using Rainfall-Runoff Library (RRL) tool and Feed forward Backpropagation neural network (FFBPNN) model. The models were calibrated for daily streamflow values from 1990 to 2006 and then validated from 2007 to 2015. The effectiveness of model runoff predictions is evaluated using statistical parameters such as Nash-Sutcliffe efficiency (NSE) and Correlation coefficient (CC) values. The NSE values for the FFBPNN is 0.88 (calibration) and 0.74 (validation), Sacramento model is 0.66 (calibration) and 0.48 (validation), and 0.63 (calibration) and 0.44 (validation) for the AWBM model. From the obtained results, the FFBPNN model performs well in terms of NSE and CC compared to Sacramento and AWBM models.

Reinforced quantum-behaved particle swarm-optimized neural network for cross-sectional distortion prediction of novel variable-diameter-die-formed metal bent tubes

Abstract With light weight, high strength, and high performance, metal bent tubes have attracted increasing applications in aeronautics. However, the growing demand for customized tubular parts has led to a significant increase in the cost of conventional tube-bending processes, as they can only process tubes of a specific diameter. To this end, this paper proposes a variable diameter die (VDD) scheme which can bend tubes with a specific range of diameters. To investigate the formability of VDD-processed tubes for practical VDD applications, an accurate and reliable prediction method of cross-sectional distortion is imperative. Hence, we pioneer a novel intelligent model based on quantum-behaved particle swarm optimization (QPSO)-optimized back-propagation neural network (BPNN) to predict a rational cross-sectional distortion characterization index: average distortion rate. The adaptive adjustment of coefficients and the Gaussian distributed random vector are introduced to QPSO, which balance the search and enhance the diversity of the population, respectively. For further improvement in optimization performance, the informed initialization strategy is applied to QPSO. The efficiency of the proposed reinforced QPSO (RQPSO)-optimized BPNN model is evaluated by comparing the results with those of the BPNN, BPNN with Xavier initialization, several different particle swarm optimization variants-optimized BPNN models, and variants of popular machine learning models. The results indicated the superiority of RQPSO over other methods in terms of the coefficient of determination (${R}^2$), variance account for, root mean square error (MSE), mean absolute error, and standard deviation of MSE. Thus, the proposed novel algorithm could be employed as a reliable and accurate technique to predict the cross-sectional distortion of VDD-processed tubes.

Postmortem Interval Estimation Using Protein Chip Technology Combined with Multivariate Analysis Methods.

To estimate postmortem interval (PMI) by analyzing the protein changes in skeletal muscle tissues with the protein chip technology combined with multivariate analysis methods. Rats were sacrificed for cervical dislocation and placed at 16 ℃. Water-soluble proteins in skeletal muscles were extracted at 10 time points (0 d, 1 d, 2 d, 3 d, 4 d, 5 d, 6 d, 7 d, 8 d and 9 d) after death. Protein expression profile data with relative molecular mass of 14 000-230 000 were obtained. Principal component analysis (PCA) and orthogonal partial least squares (OPLS) were used for data analysis. Fisher discriminant model and back propagation (BP) neural network model were constructed to classify and preliminarily estimate the PMI. In addition, the protein expression profiles data of human skeletal muscles at different time points after death were collected, and the relationship between them and PMI was analyzed by heat map and cluster analysis. The protein peak of rat skeletal muscle changed with PMI. The result of PCA combined with OPLS discriminant analysis showed statistical significance in groups with different time points (P<0.05) except 6 d, 7 d and 8 d after death. By Fisher discriminant analysis, the accuracy of internal cross-validation was 71.4% and the accuracy of external validation was 66.7%. The BP neural network model classification and preliminary estimation results showed the accuracy of internal cross-validation was 98.2%, and the accuracy of external validation was 95.8%. There was a significant difference in protein expression between 4 d and 25 h after death by the cluster analysis of the human skeletal muscle samples. The protein chip technology can quickly, accurately and repeatedly obtain water-soluble protein expression profiles in rats' and human skeletal muscles with the relative molecular mass of 14 000-230 000 at different time points postmortem. The establishment of multiple PMI estimation models based on multivariate analysis can provide a new idea and method for PMI estimation.

Gear contact fatigue life prediction based on transfer learning

The gear contact fatigue test is characterised by extraordinarily high costs and a long period of testing. A transfer learning algorithm was applied to develop a gear contact fatigue life prediction strategy to fully use other low-cost fatigue test data, such as twin-disc test data. The twin-disc contact fatigue test data were incorporated into the neural network model to explore the combined effects of surface integrity and stress level on fatigue life, which was further transferred for gear contact fatigue life prediction. The results indicate that this method enables an effective gear fatigue life prediction under minor gear sample conditions. With a small sample amount of 7, the prediction error in the fatigue life of the model with transfer learning is 46.33%, while the typical back-propagation neural network (BPNN) model without transfer learning is 101.66%. To control life prediction error to within 50%, the model without transfer learning requires at least 17 gear samples, while the transfer model calls for only 7 gear samples. The proposed data transfer learning framework can be used to predict the gear contact fatigue S-N curve under minor sample conditions and is straightforwardly applied to extended applications.

Experimental and numerical studies on lithium-ion battery heat generation behaviors

Current predictions of battery HGR (heat generation rate) mainly rely on Bernardi’s empirical equations, which suffer from limitations of adaptability for thermal use. A novel scheme based on experiments and BPNN (BP (back propagation) neural network is a multilayer feedforward neural network trained according to the error back propagation algorithm) is proposed in this paper. In the experiments, the thermal generation behavior of 18650 batteries under 108 different operating conditions was investigated, and the Ta (ambient temperature) as well as ID (discharge current) were extracted as inputs to the BPNN model. The experimental results show that the heat generation performance of the battery is strongly influenced by Ta and ID. The higher Ta and ID, the more obvious this effect is. The maximum error of the battery HGR obtained by using Bernardi’s empirical equations can reach 45.2 %. The predicted battery HGR using BPNN has good accuracy with error control within 5%. Accordingly, this paper provides the technical basis for proposing a promising thermal management solution.

Simultaneous measurement of chemical oxygen demand and turbidity in water based on broad optical spectra using backpropagation neural network

How to overcome the measurement interference between chemical oxygen demand (COD) and turbidity in absorption spectra of water has attracted lots of attention recently. Previous studies focused on eliminating the influence of turbidity, which could not measure COD and turbidity simultaneously. In this paper, we proposed a new method based on ultraviolet-visible-near infrared (UV-Vis-NIR) absorption measurements using a backpropagation neural network (BPNN). The BPNN model was established within the Tensorflow framework. And the absorbance of the wavelength ranges of 240–1040 nm and the actual values of COD and turbidity in the training set were defined as input and output, respectively. Then the BPNN model was trained with training sets of different sizes. And the original absorbance in the test set without any compensation was used to test the performance of the trained BPNN, which indicated that the larger the sample size, the better the adjustment effect of the model. The optimal training sample size was 2400. The correlation coefficient of the model is greater than 0.9998, and the RMSE between the predicted value and the actual value of COD and turbidity is 0.19 mg/L and 0.34 NTU, respectively. Our results show that the method based on BPNN not only can eliminate the influence of turbidity on the accuracy of COD but also realize the accurate measurement of turbidity itself. Furthermore, this method provides a potential strategy for the simultaneous and rapid measurement of other water quality parameters by using the absorption spectrum.

Prevalence of depressive symptoms and associated factors during the COVID-19 pandemic: A national-based study

BackgroundPrevious studies have reported that the prevalence of depression and depressive symptoms was significantly higher than that before the COVID-19 pandemic. This study aimed to explore the prevalence of depressive symptoms and evaluate the importance of influencing factors through Back Propagation Neural Network (BPNN). MethodsData were sourced from the psychology and behavior investigation of Chinese residents (PBICR). A total of 21,916 individuals in China were included in the current study. Multiple logistic regression was applied to preliminarily identify potential risk factors for depressive symptoms. BPNN was used to explore the order of contributing factors of depressive symptoms. ResultsThe prevalence of depressive symptoms among the general population during the COVID-19 pandemic was 57.57 %. The top five important variables were determined based on the BPNN rank of importance: subjective sleep quality (100.00 %), loneliness (77.30 %), subjective well-being (67.90 %), stress (65.00 %), problematic internet use (51.20 %). ConclusionsThe prevalence of depressive symptoms in the general population was high during the COVID-19 pandemic. The BPNN model established has significant preventive and clinical meaning to identify depressive symptoms lay theoretical foundation for individualized and targeted psychological intervention in the future.

Application of MLR, BP and PCA-BP Neural Network for Predicting FeO in Bottom-Blowing O2-CaO Converter

In order to accurately predict the FeO content of slag in the bottom-blowing O2-CaO process of the dephosphorization converter, multiple linear regression model, backpropagation (BP) neural network model and principal component analysis–backpropagation (PCA-BP) combined with neural network model were established to predict the FeO content of slag. It was found that the PCA-BP combined neural network model has the highest prediction accuracy by using principal component analysis to reduce the dimension of influencing factors of FeO content in slag and eliminate the correlation between input variables. The average absolute error is 1.178%, which is 0.78% lower than that of multiple linear regression model and 0.453% lower than that of multiple linear regression model. When the prediction error range is 3.0%, the prediction hit rate of the model is 96%, and when the prediction error range is 2.0%, the prediction hit rate of the model is 78%. The prediction model has important reference value for actual production.

Performance audit evaluation of marine development projects based on SPA and BP neural network model

Abstract Accurately grasping the comprehensive cost-benefit and influencing factors of various marine development projects is of great significance to the promotion of high-quality marine development. This work screened and constructed the performance audit evaluation index system of comprehensive cost-benefit of marine development projects from the four aspects including society, economy, resources, and environment. The entropy weight set pair analysis (SPA) was used to audit and evaluate the comprehensive cost-benefit of 15 marine development projects during the construction and operation period. The back propagation (BP) neural network model was used to test the results. The main influencing factors were analyzed by the grey relational analysis (GRA) model. It was found that the comprehensive cost-benefit performance audit evaluation index of the six projects of marine protected area and offshore wind power were higher than the other nine projects of mariculture, sewage dumping, and port industry. The main influencing factors were economic net income, loss of wetland ecological service value, environmental pollution prevention and control cost, new addition employment rate, etc. The countermeasures suggestions were put forward.

Valuing carbon quota assets of power generation companies based on Lasso-Back propagation neural network

Carbon quota assets have become an increasingly important new type of asset in the production and operation of power generation companies, and evaluating carbon quota assets for the sustainable development of power generation companies is an urgent issue. Herein, we propose a method for evaluating carbon quota assets based on the Lasso- Back Propagation Neural Network model (Lasso-BPNN). Firstly, we further consider the impact of company operations on the value of carbon quota assets, and analyze the ways in which company size, profitability and emission reduction capacity affect the value of carbon quota assets. Secondly, we innovatively introduce intelligent algorithms into the field of carbon asset value assessment, scientifically reflecting the function mapping between carbon quota assets value and influencing factors, and build a Lasso-BPNN model to improve the accuracy of carbon quota asset value assessment. Finally, by valuing the carbon quota assets of company H in the secondary market of the Hubei pilot, power generation companies can improve their carbon quota assets value in terms of three aspects: company size, profitability, and emission reduction capacity. The study provides an effective way to assess the value of carbon quota assets and optimize the carbon assets management of power generation companies.

Estimation of Spring Maize Evapotranspiration in Semi-Arid Regions of Northeast China Using Machine Learning: An Improved SVR Model Based on PSO and RF Algorithms

Accurate estimation of crop evapotranspiration (ETc) is crucial for effective irrigation and water management. To achieve this, support vector regression (SVR) was applied to estimate the daily ETc of spring maize. Random forest (RF) as a data pre-processing technique was utilized to determine the optimal input variables for the SVR model. Particle swarm optimization (PSO) was employed to optimize the SVR model. This study used data obtained from field experiments conducted between 2017 and 2019, including crop coefficient and daily meteorological data. The performance of the innovative hybrid RF–SVR–PSO model was evaluated against a standalone SVR model, a back-propagation neural network (BPNN) model and a RF model, using different input meteorological variables. The ETc values were calculated using the Penman–Monteith equation, which is recommended by the FAO, and used as a reference for the models’ estimated values. The results showed that the hybrid RF–SVR–PSO model performed better than all three standalone models for ETc estimation of spring maize. The Nash–Sutcliffe efficiency coefficient (NSE), root mean square error (RMSE), mean absolute error (MAE) and coefficient of determination (R2) ranges were 0.956–0.958, 0.275–0.282 mm d−1, 0.221–0.231 mm d−1 and 0.957–0.961, respectively. It is proved that the hybrid RF–SVR–PSO model is appropriate for estimation of daily spring maize ETc in semi-arid regions.

Fast Detection of Heavy Metal Content in Fritillaria thunbergii by Laser-Induced Breakdown Spectroscopy with PSO-BP and SSA-BP Analysis.

Fast detection of heavy metals is important to ensure the quality and safety of herbal medicines. In this study, laser-induced breakdown spectroscopy (LIBS) was applied to detect the heavy metal content (Cd, Cu, and Pb) in Fritillaria thunbergii. Quantitative prediction models were established using a back-propagation neural network (BPNN) optimized using the particle swarm optimization (PSO) algorithm and sparrow search algorithm (SSA), called PSO-BP and SSA-BP, respectively. The results revealed that the BPNN models optimized by PSO and SSA had better accuracy than the BPNN model without optimization. The performance evaluation metrics of the PSO-BP and SSA-BP models were similar. However, the SSA-BP model had two advantages: it was faster and had higher prediction accuracy at low concentrations. For the three heavy metals Cd, Cu and Pb, the prediction correlation coefficient (Rp2) values for the SSA-BP model were 0.972, 0.991 and 0.956; the prediction root mean square error (RMSEP) values were 5.553, 7.810 and 12.906 mg/kg; and the prediction relative percent deviation (RPD) values were 6.04, 10.34 and 4.94, respectively. Therefore, LIBS could be considered a constructive tool for the quantification of Cd, Cu and Pb contents in Fritillaria thunbergii.