According to the water characteristics of the coastal waters of Hebei Province, this paper selects the data of the Marine Environmental Quality Bulletin of Hebei Province from 2009 to 2018 published on the website of the Department of Natural Resources of Hebei Province, and proposes a red tide monitoring method based on decision tree classification for the pre-processed MODIS 1B image data. The most important thing in the construction of decision tree is the determination of threshold, and this process is finally determined according to the value of Entropy. In this paper, the newly constructed red tide monitoring method is used to extract the occurrence area of red tide and count the red tide area. Finally, the decision tree classification method is compared with other typical red tide monitoring methods. The experimental results show that the red tide occurrence area and statistical area extracted by the red tide monitoring method based on decision tree classification are closer to the data displayed in the Ocean Bulletin, which demonstrates that this method is suitable for red tide monitoring in the coastal waters of Hebei Province.

#### Keywords

- MODIS Image
- Red tide monitoring
- Decision tree classification
- Pre-process
- Coastal water

Hebei Province is adjacent to the Bohai Sea, and the sea area under its jurisdiction is about 7,200 km^{2}. Three of the 11 prefecture level cities in the province are coastal cities. With the development of economy, red tides occur frequently in the coastal waters of Hebei Province in recent years. Through consulting the Bulletin of Marine Environmental Quality of Hebei Province [1], it is found that there are five times of super large red tide information with an area of more than 1000km^{2}: a red tide with an area of about 1000km^{2} occurred in the coastal waters of Qinhuangdao from late June to early September 2009, and a red tide with an area of about 3350km^{2} was found on June 24, 2010, from June 8 to August 20, 2012, The maximum area of water colour anomaly area monitored from June 8 to August 20, 2012 is about 3400km^{2}, the maximum area of red tide found from June 20 to August 31, 2013 is about 1450km^{2}, and the maximum area of red tide found in the offshore area of Qinhuangdao from May 15 to August 7, 2014 is about 2000km^{2}. In addition to these extra-large red tides, there are many other types of red tides that have been occurring almost every year, including large red tides with an area of hundreds of kilometres, medium red tides with an area of 50–100 km and small red tides with an area of less than 50 km. Red tides endanger marine life, marine fishery production and human health and safety, and their occurrence additionally affects tourism, aquatic resources and fishery income in Hebei Province. The means to take scientific and effective methods to monitor red tides in time is of great significance. Hebei Normal University of Science and Technology is located in the beautiful coastal city of Qinhuangdao. In recent years, based on the need for transformation and development of theoretical knowledge about algal behaviour into practical application in attenuating the effect of red tides, the University attaches great importance to the integration of teaching and scientific research with local industries and local economy. For improving the marine environment and promoting the development of marine economy in Hebei Province, the University encourages teachers to actively carry out marine related research and focus on the methods of monitoring marine red tide, which will contribute to the marine development of Hebei Province.

MODIS medium resolution imaging spectrometer mounted on Terra and Aqua satellites can obtain 36 bands of image data by scanning the global surface [2]. The resolution of image data in different bands is 250 m, 500 m or 1,000 m. MODIS images in various bands cover observation information about atmosphere, land and ocean [3], and MODIS images can be downloaded free of charge on NASA websites or some domestic websites, and this ready availability provides convenient conditions for using MODIS images for red tide monitoring [4] and real-time reflection of red tide changes [5]. Many scholars have applied MODIS remote sensing images to different sea areas and water bodies, and put forward different characteristic red tide monitoring methods. According to the water characteristics of the coastal waters of Hebei Province and the pre-processed MODIS 1B image data, a red tide monitoring method based on decision tree classification is proposed in this paper. Using this method, the occurrence region of red tide is extracted, and the red tide area is counted. Finally, this method is compared with other typical red tide monitoring methods that are based on MODIS remote sensing images. The red tide data used in this paper are from the Marine Environmental Quality Bulletin of Hebei Province from 2009 to 2018 published on the website of Hebei Provincial Department of Natural Resources. The remote sensing images used are MODIS Aqua 1B products downloaded from NASA website.

Since the data quality of MODIS images is greatly affected by time and space, it is necessary to select high-quality images to facilitate the later red tide extraction. According to the Marine Environmental Quality Bulletin of Hebei Province, the red tide with the largest area of 2,000 km^{2} occurred in the coastal waters of Qinhuangdao from 15 May to 7 August, 2014. After comparison, the MODIS images of the Bohai Bay waters on 26 May 2014 were selected. The present study provides a detailed description of the red tide monitoring method based on decision tree classification, together with its experimental verification. There are two main reasons for selecting the images corresponding to 26 May 2014. First, the MODIS 1B image data quality of that day is relatively good, and the area of this red tide monitored by GOCI image is close to the maximum on that day [6]. Therefore, the experiment using the image of 26 May 2014 can be compared with the maximum area of red tide published in the Bulletin of Marine Environmental Quality of Hebei Province. Second, for the adaptability analysis of common red tide monitoring methods in Qinhuangdao sea area in document [7], the MODIS image of the same day is also used. The same scene image is used for the experiment, and thus it becomes convenient to compare the experimental results with the extraction results of other red tide monitoring methods.

Figure 1 shows the original MODIS image obtained on 26 May 2014, and Figure 2 shows the pre-processed image. The pre-processing operations in this paper mainly include the following steps: geometric correction, radiometric calibration, solar zenith angle correction and target area clipping. The decision tree classification method is described below based on the pre-processed image.

The main principle of decision tree classification [8, 9] is to obtain the classification rules through certain methods, and then divide the remote sensing images level by level according to the classification rules. According to the relevant properties of decision tree, the decision tree classification method can be used to extract red tide information and achieve the purpose of monitoring red tides.

In order to make it easier to distinguish the red tide occurrence region, the values of bands 1, 4 and 3 of the pre-processed image are used for true colour synthesis in this paper, and the obtained true colour image is shown in Figure 3. The dark blue ocean and the dark brown land can be distinguished from Figure 3. However, the colours of algae and phytoplankton in the ocean are somewhat similar to the surface of the sea, and thus these cannot be well distinguished. In order to make the colour of the image closer to human visual habits, the stretching method of the true colour image is adjusted from the original default linear stretching to histogram equalisation stretching, and the resultant enhanced image is shown in Figure 4. As can be seen from Figure 4, the ocean is blue, the soil is yellowish brown, the land vegetation is green or dark green and the algae and phytoplankton on the water body are light green, indicating that the overall tone level of the stretched image is relatively clear and in line with human visual habits. Therefore, the true colour image in Figure 4 is used as a reference diagram for interpreting red tide information.

Since the establishment of decision rules is the key to determine the classification quality of decision tree [10], only the establishment of scientific decision rules can better extract red tide. The red tide monitoring decision rules of MODIS Image are analysed as below.

First, according to the characteristics of remote sensing reflectance of MODIS Image, the specific method to distinguish land, red tide water and clean water in true colour image is determined.
_{3} and R_{5} are the remote sensing reflectance of band 3 and band 5, respectively. The formula is a new method obtained by improving the normalised difference water body index method. The improved formula can further strengthen the ratio of water body and reduce the water body index of background objects, which is conducive to the segmentation of threshold.
_{1}, R_{3} and R_{4} are the remote sensing reflectance of bands 1, 3 and 4, respectively.

Then, in order to determine the critical values of A and R in the classification process, 12 point data are selected in the land, water colour anomaly area and clean water area of remote sensing image, respectively, and the values of each point are calculated by Eqs (1) and (2). The calculation results are shown in Table 1. It can be clearly seen from Table 1 that among the 12 samples, the A values of land points are all less than 0, while the A values of abnormal water and clean water points are all greater than 0. Therefore, based on whether the A value is greater than 0, it becomes possible to distinguish water and land. For the distinction between red tide water and clean water, the value range of R can be determined by in-depth analysis of water colour anomaly area and clean water area. After repeated experimental verification, the threshold of R is finally determined as 0.45.

Sample calculation results

Sample point | Land | Abnormal water area | Clean water area | |||
---|---|---|---|---|---|---|

A | R | A | R | A | R | |

1 | –0.490186 | 0.431966 | 0.208190 | 0.520284 | 0.157197 | 0.343478 |

2 | –0.515848 | 0.436719 | 0.197401 | 0.511940 | 0.224858 | 0.336290 |

3 | –0.488859 | 0.328717 | 0.195482 | 0.518240 | 0.179280 | 0.350442 |

4 | –0.456237 | 0.349821 | 0.176524 | 0.524408 | 0.245110 | 0.403250 |

5 | –0.341247 | 0.420170 | 0.167894 | 0.473622 | 0.159053 | 0.331198 |

6 | –0.451948 | 0.454620 | 0.180254 | 0.535965 | 0.376934 | 0.249489 |

7 | –0.392420 | 0.459112 | 0.189532 | 0.505973 | 0.342486 | 0.267309 |

8 | –0.398071 | 0.518295 | 0.197775 | 0.519787 | 0.318415 | 0.143954 |

9 | –0.477858 | 0.515863 | 0.218227 | 0.510321 | 0.230179 | 0.421184 |

10 | –0.502500 | 0.504848 | 0.183310 | 0.522109 | 0.248343 | 0.393807 |

11 | –0.502628 | 0.430932 | 0.172382 | 0.467220 | 0.141973 | 0.334235 |

12 | –0.461805 | 0.554743 | 0.169851 | 0.525808 | 0.149018 | 0.372128 |

According to the above methods and threshold analysis, a red tide monitoring model based on decision tree classification can be established, as shown in Figure 5.

According to the red tide monitoring model based on the decision tree shown in Figure 5, the classification rules for extracting land, clean water and red tide water can be summarised as follows: (1) Land: A < 0. (2) Clean water area: A ≥ 0 and R ≥ 0.45. (3) Red tide water body area: A ≥ 0 and R < 0.45.

In order to evaluate the actual effect of the red tide monitoring model based on decision tree, this section applies the model to the MODIS 1B image on May 26 for experimental verification.

First, the method of extracting water body is tested. Figure 6 shows the band grey map of the pre-processed image. According to the decision tree classification rules, the threshold of Eq. (1) is set to 0 to obtain the image after extracting water body, as shown in Figure 7. It can be seen from Figure 7 that the Bohai Bay is well identified as a whole, which lays a foundation for determining the Qinhuangdao sea area.

Then, according to the method of judging whether the water colour is abnormal, the result shown in Figure 8 is obtained after processing Figure 7. The red part in Figure 8 represents the red tide water body and the blue part represents the clean water body. Based on comparing with the true colour image in Figure 4, the sea area of Qinhuangdao is marked with an ellipse. Using ENVI area statistics tool, it is calculated that the area of red tide water in Qinhuangdao sea area is about 1,943 km^{2}, which is consistent with the red tide occurrence area and the maximum red tide area of 2,000 km^{2} in Qinhuangdao sea area shown in Hebei Marine Environmental Quality Bulletin in 2014. Therefore, it can be determined that the decision tree classification method can extract red tide information.

In order to verify whether the decision tree classification method provides a performance that is better than those of other methods, MODIS images corresponding to the same scene were also tested using the typical red tide monitoring methods (i.e. chlorophyll method [11, 12], single band ratio method [13, 14] and multi-band difference ratio method [15]).

The inversion results of

Figure 11 is the synthetic pseudo-colour image, which is the inversion result of ^{3} (this value is the measured data of the year), the seawater surface is abnormal. The results are shown in Figure 12, in which the abnormal area (the red and orange part) is exactly the sea area of Qinhuangdao, and the concentration changes are also shown in the same figure.

The method used for the extraction of red tide water based on single band is shown below:
_{3} is the reflectivity of MODIS channel 3, R_{4} is the reflectivity of MODIS channel 4 and Cr is a constant. The ratio of Eq. (4) mainly reflects the concentration of chlorophyll

The red tide monitoring method based on the multi-band difference ratio is to use Eq. (2) to monitor the red tide information in the Qinhuangdao sea area, and the effect is shown in Figure 15. Through the analysis of the DN value of the Qinhuangdao sea area, the results are obtained after repeated experiments. When R < 0.45, it is a non-red tide water body, and when R > 0.45, it is a red tide water body. The results are shown in Figure 16.

The areas of red tide water bodies extracted based on the four methods mentioned above are shown in Table 2.

Red tide area extracted by various methods

Red tide monitoring method | Red tide area |
---|---|

Chlorophyll method | 1,548 km^{2} |

Single band ratio method | 2,780 km^{2} |

Multi-band difference ratio method | 1,866 km^{2} |

Decision tree classification | 1,943 km^{2} |

The comparative analysis of the experimental results shows that the red tide areas extracted by chlorophyll method, multi-band difference ratio method and decision tree classification method are basically the same. The red tide area extracted by chlorophyll method is about 1,548 km^{2}, the red tide area extracted by single band ratio method is about 2,780 km^{2}, the red tide area extracted by multi-band difference ratio method is about 1,866 km^{2} and the red tide area extracted by decision tree classification method is 1,943 km^{2}. Compared with the 2,000 km^{2} red tide area shown in the Ocean Bulletin, the error of the decision tree classification method is smallest. Among the four methods mentioned above, the red tide area extracted by single band ratio method far exceeds the actual maximum area, which is similar to the verification results available in the literature [6]. The measurement error is the largest, indicating that this method extracts more false red tide information and is not suitable for red tide monitoring in the coastal waters of Hebei Province. It is normal that the red tide area extracted by the other three methods is less than the actual maximum area, because the red tide is developing and changing, and the red tide on that day does not reach the maximum area. Through comparative analysis, it can be seen that the red tide area extracted by the decision tree classification method is the closest to the data shown in the Hebei Provincial Marine Environmental Quality Bulletin, indicating that the decision tree classification method has better red tide monitoring effect and higher accuracy than other methods. In order to test the adaptability of the decision tree classification method to other types of red tides, some large, medium and small red tides were selected from the red tides from 2009 to 2018. In order to assess the red tide extraction area more intuitively, the red tide monitoring effect map and red tide area based on the decision tree classification method from 20 June 2009 to 12 July 2009 are given below. The comparison of its true colour map and decision tree classification is shown in Figures 17 to 28.

Based on analysing the results of the six groups of image data, it can be inferred that there is no large area of abnormal colour in the Qinhuangdao sea area in Figure 17. At the same time, similar results are also obtained in the decision tree model result diagram in Figure 18, with only sporadic red tide areas. In Figure 19, it can be seen that there is a large area of abnormal colour in the Qinhuangdao waters. Meanwhile, it can be seen that there is a large red tide area in the result of the decision tree model in Figure 20. Until 24 June 2009, the red tide expanded very fast, and the affected area was also very large. In Figure 23–26, it can be seen that the area of red tide gradually shrinks from 26 June to 3 July, 2009. In Figures 27 and 28, the red tide area is shown to be significantly smaller.

In order to facilitate the sorting out of the occurrence process of red tides, the red tide area on June 20, 22, 24 and 26 and July 3 and 12, 2009 is now displayed in the form of a curve graph. The red tide area statistical chart is shown in Figure 29.

Figure 29 indicates the changes in the area of red tides clearly. The early stage of red tide outbreaks commenced on 20 June 2009, and large-scale outbreaks began on 22 June 2009. The outbreak of red tides in Qinhuangdao waters was the most serious on 24 June 2009, and the area of red tides began to shrink gradually between 25 June and 3 July.

Through the verification, it was found that the decision tree classification method has a good effect on the detection of red tides above 100 km^{2}, and the monitoring area is highly consistent with the publicly displayed data. The monitoring effect of red tides below 100 km^{2} is relatively poor, and especially, the error of the extracted area is large, which is related to the resolution limit of the MODIS images themselves, and the error of ENVI area statistics tool. The maximum resolution of each band of MODIS Image is 250 m. The larger the area, the easier it is to distinguish the red tide. The boundary and area statistics are relatively accurate. It is difficult to define the red tide boundary using an area that is too small. Of course, the accuracy of area statistics cannot be guaranteed.

In general, the red tide monitoring method based on decision tree classification can extract the red tide occurrence area more accurately, and this method is more suitable than other methods for red tide monitoring in the coastal waters of Hebei Province.

The red tide monitoring method based on decision tree classification uses the reflectance of the 3rd and 5th bands of MODIS Image to extract the water body. This method avoids the error caused by manual mask and can accurately separate the water body and land. The red tide monitoring method based on decision tree classification provides a new scheme for red tide monitoring using MODIS remote sensing images. However, due to the complex inducing conditions of red tides, and the occurrence time of red tides generally lasting for several days to several months, the use of a single MODIS Image can only reflect the current situation of red tides, and cannot enable an understanding of red tide dynamics. In the future, MODIS Image will be used to continuously monitor the development process of red tides, and to constantly explore the inducing causes and influencing factors of red tides. Moreover, the red tide monitoring method based on multi-source remote sensing images will continue to be studied, and the red tide monitoring method based on the combination of multi-source remote sensing images and decision tree classification method will be studied.

#### Red tide area extracted by various methods

Red tide monitoring method | Red tide area |
---|---|

Chlorophyll method | 1,548 km^{2} |

Single band ratio method | 2,780 km^{2} |

Multi-band difference ratio method | 1,866 km^{2} |

Decision tree classification | 1,943 km^{2} |

#### Sample calculation results

Sample point | Land | Abnormal water area | Clean water area | |||
---|---|---|---|---|---|---|

A | R | A | R | A | R | |

1 | –0.490186 | 0.431966 | 0.208190 | 0.520284 | 0.157197 | 0.343478 |

2 | –0.515848 | 0.436719 | 0.197401 | 0.511940 | 0.224858 | 0.336290 |

3 | –0.488859 | 0.328717 | 0.195482 | 0.518240 | 0.179280 | 0.350442 |

4 | –0.456237 | 0.349821 | 0.176524 | 0.524408 | 0.245110 | 0.403250 |

5 | –0.341247 | 0.420170 | 0.167894 | 0.473622 | 0.159053 | 0.331198 |

6 | –0.451948 | 0.454620 | 0.180254 | 0.535965 | 0.376934 | 0.249489 |

7 | –0.392420 | 0.459112 | 0.189532 | 0.505973 | 0.342486 | 0.267309 |

8 | –0.398071 | 0.518295 | 0.197775 | 0.519787 | 0.318415 | 0.143954 |

9 | –0.477858 | 0.515863 | 0.218227 | 0.510321 | 0.230179 | 0.421184 |

10 | –0.502500 | 0.504848 | 0.183310 | 0.522109 | 0.248343 | 0.393807 |

11 | –0.502628 | 0.430932 | 0.172382 | 0.467220 | 0.141973 | 0.334235 |

12 | –0.461805 | 0.554743 | 0.169851 | 0.525808 | 0.149018 | 0.372128 |

Law of interest rate changes in financial markets based on the differential equation model of liquidity Basalt fibre continuous reinforcement composite pavement reinforcement design based on finite element model Industrial transfer and regional economy coordination based on multiple regression model Satisfactory consistency judgement and inconsistency adjustment of linguistic judgement matrix Spatial–temporal graph neural network based on node attention A contrastive study on the production of double vowels in Mandarin Research of cascade averaging control in hydraulic equilibrium regulation of heating pipe network Mathematical analysis of civil litigation and empirical research of corporate governance Health monitoring of Bridges based on multifractal theory Health status diagnosis of the bridges based on multi-fractal de-trend fluctuation analysis Performance evaluation of college laboratories based on fusion of decision tree and BP neural network Application and risk assessment of the energy performance contracting model in energy conservation of public buildings Sensitivity analysis of design parameters of envelope enclosure performance in the dry-hot and dry-cold areas The Spatial Form of Digital Nonlinear Landscape Architecture Design Based on Computer Big Data Analysis of the relationship between industrial agglomeration and regional economic growth based on the multi-objective optimisation model Constraint effect of enterprise productivity based on constrained form variational computing The impact of urban expansion in Beijing and Metropolitan Area urban heat Island from 1999 to 2019 TOPSIS missile target selection method supported by the posterior probability of target recognition Ultrasonic wave promoting ice melt in ice storage tank based on polynomial fitting calculation model The incentive contract of subject librarians in university library under the non-linear task importance Application of Fuzzy Mathematics Calculation in Quantitative Evaluation of Students’ Performance of Basketball Jump Shot Visual error correction of continuous aerobics action images based on graph difference function Application of Higher Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast Application of Forced Modulation Function Mathematical Model in the Characteristic Research of Reflective Intensity Fibre Sensors Radioactive source search problem and optimisation model based on meta-heuristic algorithm Research on a method of completeness index based on complex model Fake online review recognition algorithm and optimisation research based on deep learning Research on the sustainable development and renewal of Macao inner harbour under the background of digitisation Support design of main retracement passage in fully mechanised coal mining face based on numerical simulation Study on the crushing mechanism and parameters of the two-flow crusher Interaction design of financial insurance products under the Era of AIoT Modeling the pathway of breast cancer in the Middle East Corporate social responsibility fulfilment, product-market competition and debt risk: Evidence from China ARMA analysis of the green innovation technology of core enterprises under the ecosystem – Time series data Reconstruction of multimodal aesthetic critical discourse analysis framework Image design and interaction technology based on Fourier inverse transform What does students’ experience of e-portfolios suggest Research on China interregional industrial transformation slowdown and influencing factors of industrial transformation based on numerical simulation The medical health venture capital network community structure, information dissemination and the cognitive proximity Data mining of Chain convenience stores location The optimal model of employment and entrepreneurship models in colleges and universities based on probability theory and statistics A generative design method of building layout generated by path Parameter Id of Metal Hi-pressure State Equation Analysis of the causes of the influence of the industrial economy on the social economy based on multiple linear regression equation Research of neural network for weld penetration control P-Matrix Reasoning and Information Intelligent Mining Intelligent Recommendation System for English Vocabulary Learning – Based on Crowdsensing Regarding new wave distributions of the non-linear integro-partial Ito differential and fifth-order integrable equations Research on predictive control of students’ performance in PE classes based on the mathematical model of multiple linear regression equation Beam control method for multi-array antennas based on improved genetic algorithm The influence of X fuzzy mathematical method on basketball tactics scoring Application of regression function model based on panel data in bank resource allocation financial risk management Research on aerobics training posture motion capture based on mathematical similarity matching statistical analysis Application of Sobolev-Volterra projection and finite element numerical analysis of integral differential equations in modern art design Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Research on motion capture of dance training pose based on statistical analysis of mathematical similarity matching Application of data mining in basketball statistics Application of B-theory for numerical method of functional differential equations in the analysis of fair value in financial accounting Badminton players’ trajectory under numerical calculation method Research on the influence of fuzzy mathematics simulation model in the development of Wushu market Study on audio-visual family restoration of children with mental disorders based on the mathematical model of fuzzy comprehensive evaluation of differential equation Difference-in-differences test for micro effect of technological finance cooperation pilot in China Application of multi-attribute decision-making methods based on normal random variables in supply chain risk management Exploration on the collaborative relationship between government, industry, and university from the perspective of collaborative innovation The impact of financial repression on manufacturing upgrade based on fractional Fourier transform and probability AtanK-A New SVM Kernel for Classification Validity and reliability analysis of the Chinese version of planned happenstance career inventory based on mathematical statistics Visual positioning system for marine industrial robot assembly based on complex variable function Mechanical behaviour of continuous girder bridge with corrugated steel webs constructed by RW Research on the influencing factors of agricultural product purchase willingness in social e-commerce situation Study of a linear-physical-programming-based approach for web service selection under uncertain service quality A mathematical model of plasmid-carried antibiotic resistance transmission in two types of cells Burnout of front-line city administrative law-enforcing personnel in new urban development areas: An empirical research in China Calculating university education model based on finite element fractional differential equations and macro-control analysis Educational research on mathematics differential equation to simulate the model of children's mental health prevention and control system Analysis of enterprise management technology and innovation based on multilinear regression model Verifying the validity of the whole person model of mental health education activities in colleges based on differential equation RETRACTION NOTE Innovations to Attribute Reduction of Covering Decision System Based on Conditional Information Entropy Research on the mining of ideological and political knowledge elements in college courses based on the combination of LDA model and Apriori algorithm Adoption of deep learning Markov model combined with copula function in portfolio risk measurement Good congruences on weakly U-abundant semigroups Research on the processing method of multi-source heterogeneous data in the intelligent agriculture cloud platform Mathematical simulation analysis of optimal detection of shot-putters’ best path Internal control index and enterprise growth: An empirical study of Chinese listed-companies in the automobile manufacturing industry Determination of the minimum distance between vibration source and fibre under existing optical vibration signals: a study Nonlinear differential equations based on the B-S-M model in the pricing of derivatives in financial markets Nonlinear Differential Equations in the Teaching Model of Educational Informatisation Fed-UserPro: A user profile construction method based on federated learning The evaluation of college students’ innovation and entrepreneurship ability based on nonlinear model Smart Communities to Reduce Earthquake Damage: A Case Study in Xinheyuan, China Response Model of Teachers’ Psychological Education in Colleges and Universities Based on Nonlinear Finite Element Equations Institutional investor company social responsibility report and company performance Mathematical analysis of China's birth rate and research on the urgency of deepening the reform of art education First-principles calculations of magnetic and mechanical properties of Fe-based nanocrystalline alloy Fe _{80}Si_{10}Nb_{6}B_{2}Cu_{2}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 in Mathematics Modeling and Processing of New Type Silicate Glass Ceramics Has the belt and road initiative boosted the resident consumption in cities along the domestic route? – evidence from credit card consumption MCM of Student’s Physical Health Based on Mathematical Cone Attitude control for the rigid spacecraft with the improved extended state observer Sports health quantification method and system implementation based on multiple thermal physiology simulation Research on visual optimization design of machine–machine interface for mechanical industrial equipment based on nonlinear partial equations 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 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 Influence of displacement ventilation on the distribution of pollutant concentrations in livestock housing Cognitive Computational Model Using Machine Learning Algorithm in Artificial Intelligence Environment Application of Higher-Order Ordinary Differential Equation Model in Financial Investment Stock Price Forecast 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 Informatisation of educational reform based on fractional differential equations Financial Crisis Early Warning Model of Listed Companies Based on Fisher Linear Discriminant Analysis Research on the control of quantitative economic management variables under the numerical method based on stochastic ordinary differential equations Network monitoring and processing accuracy of big data acquisition based on mathematical model of fractional differential equation 3D Animation Simulation of Computer Fractal and Fractal Technology Combined with Diamond-Square Algorithm 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 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 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 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 System dynamics model of output of ball mill Optimisation of Modelling of Finite Element Differential Equations with Modern Art Design Theory Mathematical function data model analysis and synthesis system based on short-term human movement Sensitivity Analysis of the Waterproof Performance of Elastic Rubber Gasket in Shield Tunnel Human gait modelling and tracking based on motion functionalisation Analysis and synthesis of function data of human movement The Control Relationship Between the Enterprise's Electrical Equipment and Mechanical Equipment Based on Graph Theory Financial Accounting Measurement Model Based on Numerical Analysis of Rigid Normal Differential Equation and Rigid Functional Equation Mathematical Modeling and Forecasting of Economic Variables Based on Linear Regression Statistics Design of Morlet wavelet neural network to solve the non-linear influenza disease system Nonlinear Differential Equations in Cross-border E-commerce Controlling Return Rate Differential equation model of financial market stability based on Internet big data 3D Mathematical Modeling Technology in Visualized Aerobics Dance Rehearsal System Children’s cognitive function and mental health based on finite element nonlinear mathematical model Motion about equilibrium points in the Jupiter-Europa system with oblateness Fractional Differential Equations in Electronic Information Models Badminton players’ trajectory under numerical calculation method BIM Engineering Management Oriented to Curve Equation Model Optimal preview repetitive control for impulse-free continuous-time descriptor systems Development of main functional modules for MVB and its application in rail transit Study on the impact of forest fire prevention policy on the health of forest resources Mathematical Method to Construct the Linear Programming of Football Training The Size of Children's Strollers of Different Ages Based on Ergonomic Mathematics Design Stiffness Calculation of Gear Hydraulic System Based on the Modeling of Nonlinear Dynamics Differential Equations in the Progressive Method Relationship Between Enterprise Talent Management and Performance Based on the Structural Equation Model Method Value Creation of Real Estate Company Spin-off Property Service Company Listing Selection by differential mortality rates Digital model creation and image meticulous processing based on variational partial differential equation Dichotomy model based on the finite element differential equation in the educational informatisation teaching reform model Nonlinear Dissipative System Mathematical Equations in the Multi-regression Model of Information-based Teaching The modelling and implementation of the virtual 3D animation scene based on the geometric centre-of-mass algorithm The policy efficiency evaluation of the Beijing–Tianjin–Hebei regional government guidance fund based on the entropy method The transfer of stylised artistic images in eye movement experiments based on fuzzy differential equations Research on behavioural differences in the processing of tenant listing information: An eye-movement experiment A review of the treatment techniques of VOC Some classes of complete permutation polynomials in the form of ( x ^{pm}−x +δ )^{s}+ax ^{pm}+bx overF _{p2m}The consistency method of linguistic information and other four preference information in group decision-making Research on the willingness of Forest Land’s Management Rights transfer under the Beijing Forestry Development A mathematical model of the fractional differential method for structural design dynamics simulation of lower limb force movement step structure based on Sanda movement Fractal structure of magnetic island in tokamak plasma Numerical calculation and study of differential equations of muscle movement velocity based on martial articulation body ligament tension Study on the maximum value of flight distance based on the fractional differential equation for calculating the best path of shot put Sports intensity and energy consumption based on fractional linear regression equation Analysis of the properties of matrix rank and the relationship between matrix rank and matrix operations Study on Establishment and Improvement Strategy of Aviation Equipment Research on Financial Risk Early Warning of Listed Companies Based on Stochastic Effect Mode Characteristics of Mathematical Statistics Model of Student Emotion in College Physical Education Mathematical Calculus Modeling in Improving the Teaching Performance of Shot Put Application of Nonlinear Differential Equation in Electric Automation Control System Nonlinear strategic human resource management based on organisational mathematical model Higher Mathematics Teaching Curriculum Model Based on Lagrangian Mathematical Model 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 The Evolution Model of Regional Tourism Economic Development Difference Based on Spatial Variation Function The Inner Relationship between Students' Psychological Factors and Physical Exercise Based on Structural Equation Model (SEM) Fractional Differential Equations in Sports Training in Universities Higher Education Agglomeration Promoting Innovation and Entrepreneurship Based on Spatial Dubin Model