High-quality development means that the knowledge-intensive economic structure will gradually replace the labour-intensive economic structure, and human resources will gradually replace the fundamental position of natural resources. In addition, the low price of labour force will no longer be competitive, and making a strong accumulation of human capital will become the greatest advantage [1, 2]. At present, human capital has become an irreplaceable core in the process of high-quality economic development. The premise of making human capital play a better role is to elucidate the actual role of human capital in economic and social development at present. Previous studies have shown that [3, 4] human capital is vital in the process of economic growth, which can impact monetary development in numerous ways. On the other hand, the change and redesigning of modern construction is a dire undertaking in China. In this manner, it is of pragmatic importance to concentrate on the impact of human resources, especially to clarify the influence effect of current human capital.

With the increasing role of knowledge and technology in economy, human capital has become the decisive factor of economic development and social progress. Measuring, evaluating or predicting the level of regional human capital within a country can grasp the investment policy of human capital as a whole. The theories and methods of predicting and evaluating the level of human capital at home and abroad are mostly classical calculation methods under precise thinking, without considering that human capital is a typical complex system with the characteristics of nonlinearity, uncertainty and fuzziness [5–7]. These methods have achieved good results, but in the actual evaluation, the weight assignment is extremely subjective, the amount of information is lost in dimension reduction, and the information contained in the evaluation index system cannot be fully utilised, which is lack of self-learning and self-adapting ability. There are many factors influencing human capital investment, which have a complex nonlinear mapping relationship [8, 9] between themselves and the level of human capital. Therefore, further research on the prediction of regional human capital level is a work of practical significance and application value.

Human capital exists relative to physical capital, and it shows the knowledge, skills, experience and health possessed by people. It mainly includes [10] the capital of simple labour, education, health and technology. The first three are investment capital, which can only be obtained through certain investment, and they constitute the core content of human capital. Any investment that can improve workers’ knowledge, skills and physical strength is called human capital investment. Human capital investment is concentrated in the followings:

Medical care offices and administration, including all expenses that influence people’s future, actual strength and perseverance, energy and imperativeness;

On-the-job training, hands on preparing, including the old apprenticeship framework coordinated by the organisation;

Formal essential, optional and advanced education;

Adult training programmes that are not coordinated by the organisation, particularly off-grounds concentrate on programmes in agribusiness;

Individual and family migration to adapt to changing employment opportunities.

Therefore, human capital is summed up as education and training, medical care, scientific and technological experience and labour force.

Migration, social security and other five aspects of investment formation.

To assess the degree of human capital in various regions of China more accurately and objectively, we need to construct a reasonable evaluation index system of human capital investment. Considering the availability and comparability of data, based on the principle of reflecting the inherent requirements of human capital and facilitating management, in this paper, 15 original indicators or generated indicators based on 5 categories are selected to constitute the index system of regional human capital investment evaluation, which is described in Table 1.

Index system of regional human capital investment evaluation.

Category | Index system |
---|---|

Educational training | |

Development of science and technology | |

Medical care | |

Labour migration | |

Social security |

There is correlation among the evaluation indexes of regional human capital investment in China. To accurately evaluate the degree of regional human capital, it is necessary to reduce its dimension. Principal component analysis (PCA) can better solve the correlation problem among indicators. PCA is a multivariate statistical analysis of data compression and feature extraction, which uses the idea of dimension reduction. The original numerous and relevant indicators are recombined into low-dimensional and unrelated comprehensive indicators, and these comprehensive indicators can reflect the main information of the original multiple indicators [11]. According to 15 evaluation indexes of regional human capital investment in China, PCA is carried out by using the evaluation method of economic and social indicators by experts from China Economic Reform and Development Research Institute of Renmin University of China, as shown in Figure 1.

Taking 31 regions in China as evaluation objects, and 15 evaluation indexes of human capital investment:

Standardise the original data matrix

Calculate the sample correlation coefficient matrix: _{ij}_{i}_{j}

Find the correlation coefficient matrix by Jacobian method _{i}

The first

Calculate the principal component score as:

According to the corresponding

BP neural network is a feed-forward network with blunder back engendering calculation as its learning calculation, which has strong nonlinear mapping ability. For a given sample set:

Therefore, we can regard the prediction of human capital level as a functional mapping from investment index of human capital to evaluation conclusion, and then an evaluation model reflecting the nonlinear mapping relationship can be established, as shown in Figure 2.

In addition, BP network can accurately describe the mapping relationship between factors without establishing a specific mathematical function model, which shows that it is feasible to predict the level of human capital.

In the research of prediction, BP neural network and PSO algorithm are all suitable for solving nonlinear problems, but with their own characteristics [12, 13].

BP neural network has the characteristics of nonlinear mapping, distributed storage and parallel processing of information, self-organisation, self-learning and self-adaptation, which is suitable for modelling complex systems with uncertain factors. However, its error function has local minimum, and its convergence speed is slow;

Determine the structure of BP neural network, provide preliminary optimisation results by using the mutation ability and global search ability of PSO, and roughly search the weights and thresholds in the optimal solution space;

Adopt PSO to strengthen local search, improve convergence speed, and carry out fine search to get the optimal weights and thresholds for BP network training;

Take the loads and edges obtained above as the underlying loads and edges of BP brain network preparing.

Improving BP network with PSO algorithm is mainly to optimise the weights of network connection and neuron thresholds. The specific implementation method is as follows:

The neural network trained by PSO algorithm adopts real number coding; matrix

The code string used for PSO algorithm optimisation comprises four sections: the association weight of stowed away layer and information layer, the association weight of result layer and secret layer, the edge of stowed away layer and the edge of result layer. Arranging matrices

To obtain satisfactory optimisation results, the mixing degree of the PSO algorithm can be quantified by the ratio of PSO population number

Coding: For numerical optimisation, the average efficiency of real coding is higher than that of binary coding, which avoids the tedious back-and-forth coding and decoding, so real coding is selected in this paper.

Fitness function (individual evaluation method) is vital to the genetic algorithm. Because of the fitness, there exists competition among individuals, and the result of the competition is that the surviving individuals are getting better and better, and the individuals with the highest fitness are the individuals that best meet the solution objectives (optimal solutions). The function of individual fitness is called Fitness function _{i}_{i}

Plan the hereditary operator: the determination activity utilises the corresponding choice operator, the hybrid activity utilises the single-point hybrid operator and the transformation activity utilises the essential digit change operator.

Determine the operating parameters of genetic algorithm, where population size is _{c}_{m}

In the prediction of improved BP network model, the benchmark data of regional human capital is divided into _{n×P}, and training target set matrix _{n×Q}, where

The establishment of BP network must be based on a large number of sample data training, so providing sufficient and comprehensive training samples is the key to establish a correct and practical network. In the prediction simulation of human capital level based on BP network, it is found that the data of

According to the 15 evaluation indexes of human capital investment, the PCA is completed by using the evaluation method of economic and social indexes by experts from the university. The first

If the input value is too large, the neurons may be saturated and lose their learning ability, so it is necessary to limit the input data to a certain range. In addition, to eliminate the influence of dimension and the magnitude difference, we must standardise the expanded raw data [14]. Therefore, the original data is initialised by the mapminmax function in MATLAB software, and normalised to the interval [1, 1] as the input data after the initialisation of BP network.

The neural network toolbox is one of the magnificent tool compartments created in the MATLAB era. In light of the hypothesis of fake brain organisation, the MATLAB programming language is taken to build numerous commonplace brain network actuation capacities, which is convenient for users to call the design, training and simulation programs of neural network. The MATLAB2019 simulation platform is selected to combine the PSO-optimised algorithm with BP network toolbox, construct a prediction model, and simulate the prediction of regional human capital level.

Adopt MATLAB to program, complete PCA, determine the original data needed for prediction and initialise the original data.

In this paper, a ‘noise sample’ is added to the original data to make it an expanded original data. Specifically, in the programming, rand function in MATLAB is used to make each element _{i}

Establish the BP neural network prediction model of regional human capital level optimised by PSO, and the parameters of the prediction model are set, so that the level of regional human capital can be predicted and simulated.

The parameter settings in MATLAB programming are as follows:

The population number _{c}

Considering the availability and comparability of data, based on the principle of not only reflecting the inherent requirements of human capital, but also being easy to operate, this paper selects 15 original indexes or generated indexes from five aspects, namely education and training, medical care, scientific and technological experience, labour migration and social security, to constitute the evaluation index system of regional human capital. The data of the model simulation come from the National Statistical Bulletin of Science and Technology from 2015 to 2021, and so on. The evaluation data of regional human capital investment in China from 2014 to 2020 are selected. Taking the PCA of China’s regional human capital level in 2020 as an example, through PCA, the first four principal components are selected to replace the original 15 indicators, and the principal component scores of the corresponding human capital levels in 31 regions in China are obtained, as shown in Table 2.

Regional horizontal principal component scores in some areas.

Region (Province) | Y1 | Y2 | Y3 | Y4 |
---|---|---|---|---|

Beijing | 11.217 | 0.938 | 3.883 | −1.760 |

Tianjin | 4.726 | −2.299 | −1.106 | 1.099 |

Hebei | −0.855 | 0.347 | −0.961 | −0.722 |

Shanxi | −0.259 | −1.389 | −0.267 | −0.514 |

Inner Mongolia | −0.006 | −1.334 | −0.849 | −0.682 |

Liaoning | 2.087 | 0.348 | −1.545 | −0.742 |

Jilin | 0.983 | −1.553 | −1.373 | −1.341 |

Shanghai | 7.810 | −0.796 | −1.076 | 2.797 |

Jiangsu | 0.999 | 3.112 | −2.064 | 0.140 |

Zhejiang | 1.402 | 2.707 | 0.203 | 1.371 |

Hubei | −0.635 | 0.342 | −0.684 | −0.349 |

Hunan | −1.025 | 0.553 | 0.093 | −0.424 |

Guangdong | 0.672 | 2.268 | −0.675 | 1.032 |

Guangxi | −2.387 | −0.182 | 0.979 | 0.200 |

Hainan | −1.519 | −1.519 | 0.544 | 0.513 |

Chongqing | −1.551 | −0.034 | 1.473 | 0.480 |

Sichuan | −1.858 | 1.224 | 0.367 | −0.126 |

Compared with the prediction of standard BP network, the improved model is feasible has certain advantages for the prediction of regional human capital level. In order to test the simulation performance of the optimised BP neural network, the MATLAB command

As can be seen from Figure 4, the actual output of human capital level in 31 regions in 2020 is obtained, and compared with the target output, the output result of the prediction model is basically consistent with the reality, which indicates that the improved prediction model is more accurate.

To clearly explain the advantages in the prediction of human capital level, the error analysis of the prediction results is carried out. The relative error and test error are selected for testing. Table 3 shows the comparison results.

Error comparison of simulation results.

Region | Beijing | Tianjin | Hebei | Shanxi | Inner Mongolia | Liaoning | Jilin | |||
---|---|---|---|---|---|---|---|---|---|---|

Relative error | Improved BP network | 7.87 | 2.51 | 14.83 | 18.0 | 14.9 | 1.05 | 42.89 | ||

BP network | 6.24 | 21.9 | 35.14 | 44.6 | 88.5 | 16.1 | 290.6 | |||

Shanghai | Jiangsu | Zhejiang | Anhui | Fujian | Jiangxi | Shandong | Henan | Hubei | Hunan | Guangdong |

8.2 | 6.83 | 1.57 | 5.85 | 9.68 | 6.99 | 140.4 | 12.0 | 19.8 | 18.1 | 3.05 |

4.8 | 29.51 | 6.74 | 7.29 | 9.24 | 9.54 | 152.05 | 5.54 | 35.51 | 15.80 | 10.64 |

Hainan | Chongqing | Sichuan | Guizhou | Yunnan | Tibet | Shaanxi | Gansu | Qinghai | Ningxia | Xinjiang |

2.06 | 4.66 | 10.41 | 4.39 | 3.96 | 2.38 | 40.44 | 1.80 | 4.40 | 8.75 | 29.84 |

5.90 | 3.83 | 5.81 | 10.34 | 7.11 | 6.51 | 106.08 | 5.88 | 7.33 | 9.19 | 177.05 |

The results show that compared with BP neural network, the dimension of the training samples in the optimised model is reduced, so the calculation of the model is relatively reduced, so that the prediction accuracy is improved and the error is smaller.

Further research on the prediction of regional human capital level is a work of practical significance and application value. In this paper, the evaluation index system of human capital is constructed, and the data of various regions in China are selected according to the generated index to form the original data sample set. After the data are initialised, the optimised BP neural network model is derived, and the prediction model of regional human capital level is obtained. The test results show that, compared with the BP neural network, the dimension of training samples of the optimised model is reduced, so the calculation of the model is relatively reduced, the prediction accuracy is improved and the error is smaller. At the same time, the output results of the prediction model are basically consistent with the reality, which can provide decision support for the development of regional human capital.

#### Regional horizontal principal component scores in some areas.

Region (Province) | Y1 | Y2 | Y3 | Y4 |
---|---|---|---|---|

Beijing | 11.217 | 0.938 | 3.883 | −1.760 |

Tianjin | 4.726 | −2.299 | −1.106 | 1.099 |

Hebei | −0.855 | 0.347 | −0.961 | −0.722 |

Shanxi | −0.259 | −1.389 | −0.267 | −0.514 |

Inner Mongolia | −0.006 | −1.334 | −0.849 | −0.682 |

Liaoning | 2.087 | 0.348 | −1.545 | −0.742 |

Jilin | 0.983 | −1.553 | −1.373 | −1.341 |

Shanghai | 7.810 | −0.796 | −1.076 | 2.797 |

Jiangsu | 0.999 | 3.112 | −2.064 | 0.140 |

Zhejiang | 1.402 | 2.707 | 0.203 | 1.371 |

Hubei | −0.635 | 0.342 | −0.684 | −0.349 |

Hunan | −1.025 | 0.553 | 0.093 | −0.424 |

Guangdong | 0.672 | 2.268 | −0.675 | 1.032 |

Guangxi | −2.387 | −0.182 | 0.979 | 0.200 |

Hainan | −1.519 | −1.519 | 0.544 | 0.513 |

Chongqing | −1.551 | −0.034 | 1.473 | 0.480 |

Sichuan | −1.858 | 1.224 | 0.367 | −0.126 |

#### Index system of regional human capital investment evaluation.

Category | Index system |
---|---|

Educational training | |

Development of science and technology | |

Medical care | |

Labour migration | |

Social security |

#### Error comparison of simulation results.

Region | Beijing | Tianjin | Hebei | Shanxi | Inner Mongolia | Liaoning | Jilin | |||
---|---|---|---|---|---|---|---|---|---|---|

Relative error | Improved BP network | 7.87 | 2.51 | 14.83 | 18.0 | 14.9 | 1.05 | 42.89 | ||

BP network | 6.24 | 21.9 | 35.14 | 44.6 | 88.5 | 16.1 | 290.6 | |||

Shanghai | Jiangsu | Zhejiang | Anhui |
Fujian | Jiangxi | Shandong | Henan | Hubei | Hunan | Guangdong |

8.2 | 6.83 | 1.57 | 5.85 | 9.68 | 6.99 | 140.4 | 12.0 | 19.8 | 18.1 | 3.05 |

4.8 | 29.51 | 6.74 | 7.29 | 9.24 | 9.54 | 152.05 | 5.54 | 35.51 | 15.80 | 10.64 |

Hainan | Chongqing | Sichuan | Guizhou | Yunnan | Tibet | Shaanxi | Gansu | Qinghai | Ningxia | Xinjiang |

2.06 | 4.66 | 10.41 | 4.39 | 3.96 | 2.38 | 40.44 | 1.80 | 4.40 | 8.75 | 29.84 |

5.90 | 3.83 | 5.81 | 10.34 | 7.11 | 6.51 | 106.08 | 5.88 | 7.33 | 9.19 | 177.05 |

_{2} emissions and economic growth: Empirical evidence from Indonesia [J]. International Journal of Energy Economics and Policy, 2019, 9(2): 98–104._{2} emissions and economic growth: Empirical evidence from Indonesia [J]

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Index Evaluation Based on Logistic Distribution Fitting Transition Probability Function Children's Educational Curriculum Evaluation Management System in Mathematical Equation Model Query Translation Optimization and Mathematical Modeling for English-Chinese Cross-Language Information Retrieval The Effect of Children’s Innovative Education Courses Based on Fractional Differential Equations Fractional Differential Equations in the Standard Construction Model of the Educational Application of the Internet of Things Optimization research on prefabricated concrete frame buildings based on the dynamic equation of eccentric structure and horizontal-torsional coupling Optimization in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Green building considering image processing technology combined with CFD numerical simulation Research on identifying psychological health problems of college students by logistic regression model based on data mining Abnormal Behavior of Fractional Differential Equations in Processing Computer Big Data Mathematical Modeling Thoughts and Methods Based on Fractional Differential Equations in Teaching Research on evaluation system of cross-border E-commerce platform based on the combined model A mathematical model of PCNN for image fusion with non-sampled contourlet transform Nonlinear Differential Equations in Computer-Aided Modeling of Big Data Technology The Uniqueness of Solutions of Fractional Differential Equations in University Mathematics Teaching Based on the Principle of Compression Mapping Financial customer classification by combined model Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Recognition of Electrical Control System of Flexible Manipulator Based on Transfer Function Estimation Method Automatic Knowledge Integration Method of English Translation Corpus Based on Kmeans Algorithm Real Estate Economic Development Based on Logarithmic Growth Function Model Design of Tennis Mobile Teaching Assistant System Based on Ordinary Differential Equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis High Simulation Reconstruction of Crowd Animation Based on Optical Flow Constraint Equation Construction of Intelligent Search Engine for Big Data Multimedia Resource Subjects Based on Partial Least Squares Structural Equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm Analysis of the Teaching Quality of Physical Education Class by Using the Method of Gradient Difference The Summation of Series Based on the Laplace Transformation Method in Mathematics Teaching Optimal Solution of the Fractional Differential Equation to Solve the Bending Performance Test of Corroded Reinforced Concrete Beams under Prestressed Fatigue Load Animation VR scene mosaic modeling based on generalized Laplacian equation Radial Basis Function Neural Network in Vibration Control of Civil Engineering Structure Optimal Model Combination of Cross-border E-commerce Platform Operation Based on Fractional Differential Equations The influence of accounting computer information processing technology on enterprise internal control under panel data simultaneous equation Research on Stability of Time-delay Force Feedback Teleoperation System Based on Scattering Matrix BIM Building HVAC Energy Saving Technology Based on Fractional Differential Equation Construction of comprehensive evaluation index system of water-saving irrigation project integrating penman Montei the quation Human Resource Management Model of Large Companies Based on Mathematical Statistics Equations Data Forecasting of Air-Conditioning Load in Large Shopping Malls Based on Multiple Nonlinear Regression Analysis of technical statistical indexes of college tennis players under the win-lose regression function equation Automatic extraction and discrimination of vocal main melody based on quadratic wave equation Analysis of wireless English multimedia communication based on spatial state model equation Optimization of Linear Algebra Core Function Framework on Multicore Processors Application of hybrid kernel function in economic benefit analysis and evaluation of enterprises Research on classification of e-commerce customers based on BP neural network The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Fractional Differential Equations in Electronic Information Models BIM Engineering Management Oriented to Curve Equation Model Leakage control of urban water supply network and mathematical analysis and location of leakage points based on machine learning Analysis of higher education management strategy based on entropy and dissipative structure theory Prediction of corporate financial distress based on digital signal processing and multiple regression analysis Mathematical Method to Construct the Linear Programming of Football Training Multimedia sensor image detection based on constrained underdetermined equation The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Application of Numerical Computation of Partial Differential Equations in Interactive Design of Virtual Reality Media Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Knowledge Analysis of Charged Particle Motion in Uniform Electromagnetic Field Based on Maxwell Equation Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Term structure of economic management rate based on parameter analysis of estimation model of ordinary differential equation Influence analysis of piano music immersion virtual reality cooperation based on mapping equation Chinese painting and calligraphy image recognition technology based on pseudo linear directional diffusion equation Label big data compression in Internet of things based on piecewise linear regression Animation character recognition and character intelligence analysis based on semantic ontology and Poisson equation Design of language assisted learning model and online learning system under the background of artificial intelligence Study on the influence of adolescent smoking on physical training vital capacity in eastern coastal areas Application of machine learning in stock selection Comparative analysis of CR of ideological and political education in different regions based on improved fuzzy clustering Action of Aut( G ) on the set of maximal subgroups ofp -groupsStudy on transmission characteristics in three kinds of deformed finlines based on edge-based finite element method Research on loyalty prediction of e-commerce customer based on data mining Algebraic Equations in Educational Model of College Physical Education Course Education Professional English Translation Corpus Under the Binomial Theorem Coefficient Geometric Tolerance Control Method for Precision Machinery Based on Image Modeling and Novel Saturation Function Retrieval and Characteristic Analysis of Multimedia Tester Based on Bragg Equation Semiparametric Spatial Econometric Analysis of Household Consumption Based on Ordinary Linear Regression Model Video adaptive watermark embedding and detection algorithm based on phase function equation English Learning Motivation of College Students Based on probability Distribution Scientific Model of Vocational Education Teaching Method in Differential Nonlinearity Research on mobile Awareness service and data privacy Protection based on Linear Equations computing protocol Vocal Music Teaching Model Based on Finite Element Differential Mathematical Equations Studying a matching method combining distance proximity and buffer constraints The trend and influence of media information Propagation based on nonlinear Differential equation Research on the construction of early warning model of customer churn on e-commerce platform Evaluation and prediction of regional human capital based on optimised BP neural network Study on inefficient land use determination method for cities and towns from a city examination perspective A sentiment analysis method based on bidirectional long short-term memory networks A study of local smoothness-informed convolutional neural network models for image inpainting Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model Computational Algorithm to Solve Two–Body Problem Using Power Series in Geocentric System Decisions of competing supply chain with altruistic retailer under risk aversion Optimization of Color Matching Technology in Cultural Industry by Fractional Differential Equations The Marketing of Cross-border E-commerce Enterprises in Foreign Trade Based on the Statistics of Mathematical Probability Theory Application of Linear Partial Differential Equation Theory in Guiding Football Scientific Training Nonlinear Channel Estimation for Internet of Vehicles Some Necessary Conditions for Feedback Functions of de Bruijn Sequences The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function System Model of Shipping Enterprise Safety Culture Based on Dynamic Calculation Matrix Model An empirical research on economic growth from industrial structure optimisation in the Three Gorges Reservoir area The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Analysis and Research on Influencing Factors of Ideological and Political Education Teaching Effectiveness Based on Linear Equation Study of agricultural finance policy information extraction based on ELECTRA-BiLSTM-CRF Fractional Differential Equations in Sports Training in Universities Examination and Countermeasures of Network Education in Colleges and Universities Based on Ordinary Differential Equation Model Innovative research of vertical video creation under the background of mobile communication Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model Chinese-English Contrastive Translation System Based on Lagrangian Search Mathematical Algorithm Model Genetic algorithm-based congestion control optimisation for mobile data network