Back Propagation Neural Network Model Research Articles

Prediction model of moisture content in spray drying of ceramic slurry based on IMFO-BPNN

The final particle moisture content of ceramic slurry spray drying affects the processing, product quality, and process energy consumption. While the real-time moisture content determination is very difficult for spray drying process due to nonlinear, severe lag, interference factors, and complexity of the systems, the high temperature, high humidity drying environment and short drying process. In current work, an improved moth optimization (IMFO) algorithm combined with backpropagation neural network (BPNN) was proposed to predict the moisture content of ceramic slurry particles during spray drying. The performance of the model is trained and tested. Results demonstrate that IMFO has better convergence ability and speed compared to other algorithms such as particle swarm optimization (PSO) and gravitational search algorithm (GSA). The IMFO-BPNN model achieves a MAE of 0.0293, RMSE of 0.0383, and R2 value of 0.9113, outperforming the prediction performance of BPNN and MFO-BPNN models. The absolute error rate of the IMFO-BPNN model (0–5%) is lower compared to BPNN (5–10%) and MFO-BPNN model (>10%), showcasing superior accuracy in predicting moisture content. This mathematical model established in the study provides an efficient, accurate, and nondestructive method for predicting the drying endpoint of ceramic slurry spray drying.

Prediction of flash flood peak discharge in hilly areas with ungauged basins based on machine learning

ABSTRACT Peak discharge is an essential element of hydrological forecasting. Due to rapid outbreaks of flash floods in hilly areas and the lack of measured data, the fast and accurate estimation of peak discharge is crucial for flash flood hazard management. Three machine learning algorithms were applied to estimate peak discharge; this estimation was compared with the results of hydrological–hydraulic models, and the results were verified with measured watershed data. In this paper, 10 hydrological and geomorphological parameters were selected to predict the flood peak discharge in 103 watersheds in Taiyi Mountain North District. The results show that the particle swarm optimization backpropagation (PSO-BP) neural network model outperforms the BP neural network and random forest regression in prediction performance. PSO-BP has a lower mean absolute error (2.51%), root mean square error (3.74%), and mean absolute percentage error (2.74%) than the other models, which indicates that PSO-BP has high prediction accuracy. Importance analysis revealed that rainfall, early impact rainfall, catchment area, and rain intensity are the key input parameters of PSO-BP. The proposed method was confirmed to be a fast and relatively accurate algorithm for estimating the peak discharge of flash floods in ungauged basins.

Volatilization of benzene on soil surface under different factors: evaluation and modeling

The volatilization of volatile organic compounds following a leakage event is a crucial mechanism that influences their migration and transformation in the soil. It is noteworthy that this process is intricately shaped by soil properties and environmental factors, exhibiting highly complex nonlinear relationships. However, there is currently no reliable mathematical model to predict the nonlinear relationship. To address this gap, the study conducted dynamic experiments considering various factors, including particle size, organic matter content, temperature, wind speed and moisture content. The volatilization rate (k\\documentclass[12pt]{minimal} \\usepackage{amsmath} \\usepackage{wasysym} \\usepackage{amsfonts} \\usepackage{amssymb} \\usepackage{amsbsy} \\usepackage{mathrsfs} \\usepackage{upgreek} \\setlength{\\oddsidemargin}{-69pt} \\begin{document}$$k$$\\end{document}), an important parameter in volatilization kinetics reflecting the speed of volatilization, was calculated by first-order kinetic principle. Finally, an innovative approach was introduced using a Back Propagation Neural Network (BPNN) model for prediction. The findings indicate that wind speed exerts the most significant impact on the volatilization rate of benzene among the examined factors. The application of BPNN demonstrates the model's accuracy in simulating benzene volatilization rates under diverse conditions. The results of K-fold cross-validation alleviate concerns of potential over-prediction, affirming the reliability of the constructed model. This research introduces a novel methodology for predicting volatilization parameters in real-world scenarios.

Few shot intelligent assessment method for compaction quality of earthwork considering uncertainty

Current practices lack reliable models for continuously assessing compaction quality from limited data, which hinders effective compaction quality control and the acceptance of earthwork. Using material source parameters as inputs for assessment models makes it infeasible to achieve a real-time assessment of the compaction quality in earthwork. These issues have hindered the popularization of emerging intelligent compaction (IC) and intelligent rolling compaction (IRC) technologies. Therefore, this study addresses the need for small-sample training by introducing an uncertainty-based multi-population genetic algorithm fused with a backpropagation neural network model (UB-MPGA-BP), enabling the real-time intelligent assessment of compaction quality based on few-shot learning. In case studies involving high- and low-liquid limit silts, existing models trained on large datasets were notably inadequate for small-sample evaluation tasks. However, the proposed method not only performed well in silt cases but also exhibited high performance in rockfill materials. The analysis revealed that in small-sample scenarios without reliance on material source parameters, the proposed method has the advantages of real-time accuracy, generalization, few-shot data-driven, and simple input parameters, which enable the rapid assessment of compaction quality. The model can potentially facilitate IC/IRC applications in other engineering practices.

Vibration analysis of Ti-SiC composite airfoil blade based on machine learning

In this study, machine learning (ML) methods are integrated with Rayleigh-Ritz method and first-order shear deformation theory (FSDT) to predict the vibration properties of Ti-SiC fiber-reinforced composite airfoil blade. The natural vibration characteristics of airfoil blade are largely determined by various geometric and material parameters, which leads to the high computational cost of numerical methods. Therefore, the low-cost ML models in conjunction with Ti-SiC fiber-reinforced composite material is developed to replace traditional numerical methods in order to predict the vibration characteristics of airfoil blade. Random Forest (RF), Gradient Boosting Decision Tree (GBDT) and Back Propagation (BP) neural network models are utilized to compare the predicted results with existing data. Among these models, the BP neural network demonstrates superior performance. Additionally, the SHapley Additive exPlanation (SHAP) method is utilized to elucidate BP neural network model, facilitating the prioritization of input features. This approach offers a feasible auxiliary solution for investigating the vibration characteristics of airfoil blade.

Structural Optimization of a Giant Magnetostrictive Actuator Based on BP-NSGA-II Algorithm

This study introduces an integrated structural optimization design method based on a BP neural network and NSGA-II multi-objective genetic algorithm. Initially, a two-dimensional axisymmetric finite element model of the Giant Magnetostrictive Actuator (GMA) was established, and the coupling simulation of the electromagnetic field, structural field, and temperature field was conducted to obtain the GMA’s performance parameters. Subsequently, the structural parameters of the GMA magnetic circuit, including the magnetic conducting ring, magnetic conducting sidewall, magnetic conducting body, and coil, were used as inputs, and the axial magnetic induction intensity, uniformity of axial magnetic induction intensity, and coil loss on the Giant Magnetostrictive Material (GMM) rod were used as outputs to establish a back propagation (BP) neural network model. This model delineated the nonlinear relationship between structural parameters and performance parameters. Then, the BP-NSGA-II algorithm was applied to perform multi-objective optimization on the actuator’s structural parameters, resulting in a set of Pareto optimal non-dominated solutions, from which a set of optimal solutions was obtained using the entropy weight method. Finally, simulation analysis of this optimal solution was conducted, indicating that under a 5 A power supply excitation, the maximum axial magnetic induction intensity on the optimized GMM rod increased from 0.87 T to 1.12 T; the uniformity of axial magnetic induction intensity improved from 93.1% to 96.5%; and the coil loss decreased from 7.79 × 104 W/m3 to 4.97 × 104 W/m3. Based on the optimization results, a prototype actuator was produced, and the test results of the prototype’s output characteristics proved the feasibility of this optimization design method.

Advanced soft-sensing techniques for predicting furnace temperature in industrial organic waste gasification

Accurately real-time monitoring furnace temperature in multi-component industrial organic waste gasification presents considerable challenges due to the process’s inherent complexity and variability. Herein, we have developed a sophisticated soft-sensing model that utilizes data-driven methods for precise temperature prediction, using input variables measured in industrial process. The data, primarily centered on cooling water, were derived from an in-depth analysis of heat transfer within the gasifier. Three distinct machine learning models were constructed and demonstrated enhanced performance compared to conventional heat transfer model. The Back Propagation Neural Network (BPNN) model, exhibiting a remarkable R2 value of 0.94, emerged as the most effective. Employing SHapley Additive exPlanations (SHAP) and Partial Dependence Plots (PDP), we further revealed the critical role of cooling water temperature in furnace temperature prediction. Overall, the application of data-driven models into the furnace temperature prediction offers a significant advancement in handling the complexities inherent in industrial processes.

Study on hysteresis performance of four-limb CFST latticed column-box girder joints based on GA-BP neural network

This study investigates the seismic performance and energy dissipation capacity of the concrete-filled steel tube (CFST) latticed column-box girder joints. A low-cycle reciprocating load test was carried out on the CFST latticed column-box girder joints with three different connection forms. Based on the test results, a genetic algorithm (GA) is developed in combination with the back propagation neural network (BPNN) model for prediction research. Using a training set of joints with single-limb diagonal and cross-diagonal braces (training set), the development of load-displacement hysteresis curves of joints with transverse diaphragm plate (test set) under low-cycle reciprocating loads is predicted. The test results are compared with those obtained from the traditional algorithms and finite element simulations. The results on the joint hysteresis performance show that all three types of joints have a good seismic performance and energy dissipation capacity. Compared with the traditional algorithms, the GA-BP model predicts more accurate results and is therefore used to predict the load-displacement hysteresis curves of CFST latticed column-box girder joints, which is shown to be convenient and feasible.

Data-driven shear strength predictions of prestressed concrete hollow-core slabs

Although providing sufficient shear strength is crucial in the design of hollow-core slabs (HCS) to prevent shear failure, conventional shear equations for HCS could not always represent the non-linear relationship between the shear strength and influencing parameters, especially for deep HCS. Back-propagation-neural-network- (BPNN)-based models could be a possible solution since they have been widely used in predicting structural behaviour of other concrete structures. However, the feasibility of such an application has not been examined previously. Therefore, a set of BPNN-based models with and without optimisation algorithms were proposed for predicting the shear strength of prestressed HCS. The proposed BPNN-based models were trained and verified against a database of 227 HCS tested in shear. Comparisons between BPNN-based and mechanics-based models were also performed. The corresponding performances of different models were evaluated by the mean Vut/Vpre, R2, RMSE, MAE and MAPE criteria. To the author's best knowledge, this is the first study to apply hybrid-BPNN-based models for shear strength prediction of HCS. The study found that all proposed BPNN models were effective in predicting the shear strength, while the ACO-BPNN model yielded the best predictions among all the BPNNs. It was also shown that the ACO-BPNN model provided better predictions than the ACI 318 code provisions with/without the size effect factor. Besides, the well-trained ACO-BPNN model could present the size effect of slab thickness on shear strength, which was not explicitly considered in ACI 318. In summary, the ACO-BPNN-based model could a rational tool for predicting shear strength for HCS.

Prediction of the fundamental viscoelasticity of asphalt mixtures using ML algorithms

The complex modulus (E*) and phase angle (δ) are fundamental viscoelastic (VE) properties of asphalt material, crucial for pavement performance analysis and modeling. This study presents a novel approach to predict the fundamental VE properties of asphalt mixtures using 20 study mixes with disparate mix design information including different Performance Graded (PG grade) binders, recycled asphalt (RAP) contents, with/without polymer modifications, and mix volumetric properties. By employing the XGBoost model for feature importance analysis, integrating the Bailey method to streamline gradation information, and utilizing master curve shape parameters for modeling, this study has effectively reduced data redundancy and dimensionality. Among four machine learning (ML) models compared, the Multi-Hidden-Layer Backpropagation Neural Network (Multi BP) model demonstrates superior applicability to the asphalt mixture dataset, providing accurate predictions for VE properties at any temperature and frequency combinations. Notably, this predictive model relies solely on the mixture design information as inputs, minimizing the need for laborious laboratory experiments. The developed model can be integrated with Mechanistic-Empirical (ME) design, predicting the variations in rutting and cracking performance of asphalt mixtures over the entire service life. This provides essential foundational input support for long-lasting pavement design.

Improved multi-input parameter optimization method for camera colorimetric characterization

In order to improve the accuracy of camera colorimetric characterization, a multi-input parameter optimization method was proposed in this paper. The input parameters of the traditional camera characterization method were generally RGB values; in the proposed method, the luminance parameter L was introduced in addition to RGB values, and the four-input parameters of RGBL were used as input parameters for the conversion model. In the experiment, 549 colors were uniformly selected from the Munsell Book of Color (Matte Edition), and the RGBL values and corresponding CIEXYZ values of the selected colors were measured by a spectroradiometer and three cameras, including an imaging luminance meter, respectively. Then, a polynomial model and a backpropagation (BP) neural network model were employed to establish the improved color conversion model with RGBL four-input parameters, which was compared with three-input parameter models to verify the effectiveness of the proposed method. Experimental results show that the proposed method can significantly improve the conversion accuracy and reduce the color difference with a maximum reduction of 57.7% in CIELAB.

Analyzing brain-activation responses to auditory stimuli improves the diagnosis of a disorder of consciousness by non-linear dynamic analysis of the EEG

Although auditory stimuli benefit patients with disorders of consciousness (DOC), the optimal stimulus remains unclear. We explored the most effective electroencephalography (EEG)-tracking method for eliciting brain responses to auditory stimuli and assessed its potential as a neural marker to improve DOC diagnosis. We collected 58 EEG recordings from patients with DOC to evaluate the classification model’s performance and optimal auditory stimulus. Using non-linear dynamic analysis (approximate entropy [ApEn]), we assessed EEG responses to various auditory stimuli (resting state, preferred music, subject’s own name [SON], and familiar music) in 40 patients. The diagnostic performance of the optimal stimulus-induced EEG classification for vegetative state (VS)/unresponsive wakefulness syndrome (UWS) and minimally conscious state (MCS) was compared with the Coma Recovery Scale-Revision in 18 patients using the machine learning cascade forward backpropagation neural network model. Regardless of patient status, preferred music significantly activated the cerebral cortex. Patients in MCS showed increased activity in the prefrontal pole and central, occipital, and temporal cortices, whereas those in VS/UWS showed activity in the prefrontal and anterior temporal lobes. Patients in VS/UWS exhibited the lowest preferred music-induced ApEn differences in the central, middle, and posterior temporal lobes compared with those in MCS. The resting state ApEn value of the prefrontal pole (0.77) distinguished VS/UWS from MCS with 61.11% accuracy. The cascade forward backpropagation neural network tested for ApEn values in the resting state and preferred music-induced ApEn differences achieved an average of 83.33% accuracy in distinguishing VS/UWS from MCS (based on K-fold cross-validation). EEG non-linear analysis quantifies cortical responses in patients with DOC, with preferred music inducing more intense EEG responses than SON and familiar music. Machine learning algorithms combined with auditory stimuli showed strong potential for improving DOC diagnosis. Future studies should explore the optimal multimodal sensory stimuli tailored for individual patients.Trial registration: The study is registered in the Chinese Registry of Clinical Trials (Approval no: KYLL-2023-414, Registration code: ChiCTR2300079310).

Predictive Analysis of a Building’s Power Consumption Based on Digital Twin Platforms

Colleges and universities are large consumers of energy, with a huge potential for building energy efficiency, and need to reduce energy consumption to build a low-carbon, energy-saving campus. Predicting the energy consumption of campus buildings can help to accurately manage the electricity consumption of buildings and reduce the energy consumption of buildings. However, the electricity consumption of a building’s operation is affected by many factors, and it is difficult to establish a model for analysis and prediction. Therefore, in this study, the training building of the BIM education center on campus was selected as the research object, and a digital twin O&M platform was established by integrating IoT, digital twin technology (DDT), smart meter monitoring devices, and indoor environment monitoring devices. The O&M management platform can monitor real-time changes in indoor power consumption data and environmental parameters, and organize data on multiple influencing factors and power consumption. Following training, validation, and testing, the machine learning models (back propagation neural network, support vector model, and multiple linear regression model) were assessed and compared for accuracy. Following the multiple linear regression and support vector models, the backpropagation neural network model exhibited the highest accuracy. Consistent with the actual power consumption detection results in the BIM education center, the backpropagation neural network model produced results. Consequently, the BP model created in this study demonstrated its dependability and ability to forecast campus building power usage, assisting the university in organizing its energy supply and creating a campus that prioritizes conservation.

Prediction of Surface Subsidence in Mining Areas Based on Ascending-Descending Orbits Small Baseline Subset InSAR and Neural Network Optimization Models.

Surface subsidence hazards in mining areas are common geological disasters involving issues such as vegetation degradation and ground collapse during the mining process, which also raise safety concerns. To address the accuracy issues of traditional prediction models and study methods for predicting subsidence in open-pit mining areas, this study first employed 91 scenes of Sentinel-1A ascending and descending orbits images to monitor long-term deformations of a phosphate mine in Anning City, Yunnan Province, southwestern China. It obtained annual average subsidence rates and cumulative surface deformation values for the study area. Subsequently, a two-dimensional deformation decomposition was conducted using a time-series registration interpolation method to determine the distribution of vertical and east-west deformations. Finally, three prediction models were employed: Back Propagation Neural Network (BPNN), BPNN optimized by Genetic Algorithm (GA-BP), and BPNN optimized by Artificial Bee Colony Algorithm (ABC-BP). These models were used to forecast six selected time series points. The results indicate that the BPNN model had Mean Absolute Errors (MAE) and Root Mean Squared Errors (RMSE) within 7.6 mm, while the GA-BP model errors were within 3.5 mm, and the ABC-BP model errors were within 3.7 mm. Both optimized models demonstrated significantly improved accuracy and good predictive capabilities.

Utilizing Enterprise Economic Benefit Evaluation Methods in Edge Intelligent Neural Network Applications

The core of enterprise economic benefit evaluation lies in the development of a quantitative identification model. The Back Propagation (BP) neural network possesses robust parallel computing, adaptive learning, and error correction capabilities, which can effectively reveal the economic benefits of enterprises and their relationship with influencing factors. This study establishes an economic benefit evaluation model for express delivery enterprises based on the BP neural network. The model takes the annual profit rate of enterprises as the quantitative index of economic benefits and selects 13 factors, both external and internal, influencing the annual profit rate of express delivery enterprises as inputs for the BP neural network model. The economic benefit evaluation model based on BP neural network meets the requirement of objective mean square error in the 300th training cycle. The research results demonstrate that the BP model significantly saves computing time and enables rapid, comprehensive, and objective evaluation of the economic benefits of industrial enterprises.

Predicting the impermeability and mechanical properties of manufactured sand polymer waterproof mortar using an optimised back-propagation neural network

Owing to its complex composition, accurately predicting the performance of polymer waterproof mortar (PWM) using ordinary equations is difficult. To quickly and accurately obtain the proportions of various components of high-performing PWM, in this study, we designed a back-propagation neural network (BPNN) model with a topology structure of 5–12–2 and optimised it using the particle swarm optimisation (PSO) algorithm, whale optimisation algorithm (WOA), and genetic algorithm (GA). The input layer of the model included cement (OPC), a waterproofing additive (WPA), dispersible polymer powder (DPP), tuff stone powder (SP), and fly ash (FA), whereas the output layer included the chloride-ion electric flux and compressive strength of PWM. The model dataset comprised 378 samples, of which 228 were used for model establishment and 150 were used for model validation. Correlation analysis was conducted to determine the relationship between the raw materials and the impermeability and mechanical properties of PWM; further, principal component analysis was performed on the PWM dataset. At 7 and 28 d, the dosages of WPA and DPP in the PWM were negatively correlated with the chloride-ion electric flux and positively correlated with the compressive strength. In addition, at 28 d, the OPC dosage was positively correlated with the chloride-ion electric flux and negatively correlated with the compressive strength; the SP and FA dosages were correlated negatively and positively with the chloride-ion electric flux and compressive strength, respectively. Group B4 performed the best in this study, and group E4 had the optimal ratio of mineral admixtures. The WOA-BPNN achieved the highest prediction accuracy for both the PWM chloride-ion electric flux and compressive strength, with prediction evaluation parameters of R2 = 0.98, MAE = 17.4, MAPE = 0.09, and RMSE = 21.2 and R2 = 0.98, MAE = 15.4, MAPE = 0.07, and RMSE = 21.0, respectively. Using the WOA-BPNN to predict the impermeability and mechanical properties of PWM is viable, and the WOA-BPNN can offer scientific guidance for the proportionate design of PWM.

Optimizing the extraction process of total saponins from Panax vietnamensis based on response surface analysis and backpropagation neural network-genetic algorithm

Panax vietnamensis (PV), a member of the Araliaceae family, is noted for its saponin-rich roots and rhizomes. Recent pharmacological studies have shown its anti-inflammatory, anti-cancer, anti-myocardial ischemia, and hypoglycemic effects, establishing PV as a highly valuable variety of ginseng worldwide. Herein, we used an ultrasound-assisted method to optimize the extraction of total saponins from PV, and developed a genetic algorithm (GA) to optimize the backpropagation (BP) neural network model and predict the best process conditions. The best process with an ethanol concentration of 65.8 %, extraction times of 4.0, ultrasonic temperature of 40.7°C, and an extraction rate of 4.4103 % was achieved through response surface optimization. Conversely, the best process optimized by the GA-BP neural network model had an ethanol concentration of 70.0 %, extraction times of 4.0, ultrasonic temperature of 41.0°C, and an extraction rate of 4.5492 %. Moreover, 254 terpenoids, consisting of 182 triterpenes, 33 monoterpenes, 19 sesquiterpenes, and 20 diterpenes, along with various types of saponins, were identified through ultra-high performance liquid chromatography-MS/MS (UPLC-MS/MS). Specifically, 87 dammarane-type saponins were detected, including 46 protopanaxadiol types, 41 protopanaxatriol types, 5 octilonol types, and 18 oleanolic acid types. The total saponin extraction rate achieved through the GA-BP neural network model surpassed that of the response surface optimization process, indicating the superiority and stability of the GA-BP neural network optimized process and thus revealing the optimal method for PV total saponin extraction. The comprehensive analysis of PV saponins using UPLC-MS/MS enhanced our understanding of total saponins in PV, laying the foundations for the strategic development and utilization of PV plant resources.

Prediction of Geometric Characteristics of Laser Cladding Layer Based on Least Squares Support Vector Regression and Crested Porcupine Optimization.

The morphology size of laser cladding is a crucial parameter that significantly impacts the quality and performance of the cladding layer. This study proposes a predictive model for the cladding morphology size based on the Least Squares Support Vector Regression (LSSVR) and the Crowned Porcupine Optimization (CPO) algorithm. Specifically, the proposed model takes three key parameters as inputs: laser power, scanning speed, and powder feeding rate, with the width and height of the cladding layer as outputs. To further enhance the predictive accuracy of the LSSVR model, a CPO-based optimization strategy is applied to adjust the penalty factor and kernel parameters. Consequently, the CPO-LSSVR model is established and evaluated against the LSSVR model and the Genetic Algorithm-optimized Backpropagation Neural Network (GA-BP) model in terms of relative error metrics. The experimental results demonstrate that the CPO-LSSVR model can achieve a significantly improved relative error of no more than 2.5%, indicating a substantial enhancement in predictive accuracy compared to other methods and showcasing its superior predictive performance. The high accuracy of the CPO-LSSVR model can effectively guide the selection of laser cladding process parameters and thereby enhance the quality and efficiency of the cladding process.

The application of IGA in urban landscape design optimization

SummaryThe foundation of urban landscape design optimization is the precise evaluation of the effectiveness. To address the issues of strong subjectivity, low efficiency, and poor accuracy in urban landscape design evaluation methods, an intelligent evaluation method combining improved genetic algorithm and error backpropagation neural network is proposed. First, based on Maslow's demand theory and questionnaire survey results, it selects indicators to construct an evaluation index system for urban landscape design. Second, in response to the performance defects of the error backpropagation neural network model, the moth flame algorithm is used to optimize it. Then, in response to the defect that the optimization effect of the moth flame algorithm is not ideal enough, a multiple strategy including improved genetic algorithm is adopted to optimize it. Finally, an urban landscape design evaluation model is constructed based on improved error backpropagation neural network. The experimental results show that the fitting coefficient of the model is 0.9523, with a minimum deviation of less than 1%. The above results indicate that the proposed model can effectively improve the accuracy and efficiency of urban landscape design evaluation, providing data support for urban landscape design optimization. The research on the intelligent development of urban landscape design is of reference significance and has to some extent promoted the development of urban landscape design.

Predicting bridge condition index using an improved back-propagation neural network

The predicted Bridge Condition Index (BCI) is a guiding indicator for formulating preventive maintenance strategies for bridges and is hardly available even if using the most advanced neural network prediction model, owing to the few measured BCIs and neural network model defects. In this paper, an improved Back-Propagation Neural Network (BPNN) model named CPSO-BP-MC is proposed to predict BCI, which has a BPNN as its core, combined with the Coordinated Particle Swarm Optimization (CPSO) algorithm aims to faster convergence and avoid local optimal solution even with less training sample, and the Markov Chain (MC) algorithm aims to further revise the fluctuation of CPSO-BP prediction output due to maintenance and reinforcement. A case study is presented to demonstrate the efficiency of CPSO-BP-MC predicting BCI with fewer training samples. Comparing the predicted BCI of CPSO-BP-MC with the measured BCI and other models, the results show that CPSO-BP-MC converges faster than other models, and can predict the BCI more stably and accurately, and the error between prediction and measured BCI is less than 3 %.