Applied Mathematics and Nonlinear Sciences

With the development of history, some folk dances are annihilated and lost in the inheritance. In order to protect and inherit national intangible cultural heritage and promote the construction of advanced socialist culture, this paper uses information fusion technology, combines national aesthetic personality, and refers to multi-factor theory, construction theory


Introduction
As one of the eight art forms, dance is an artistic expression that draws on the richness and diversity of human beings themselves [1][2][3][4].It fully combines musical accompaniment, regular movements, and other props to shape and build multiple artistic images.From the perspective of the formation and development of dance, dance presents the interactions, rituals, rituals, etc., in human society with the help of human body movements.Folk dance is an organic blend of folklore, regionality, genre, complete plot, distinctive image, rich body language, and various artistic elements [5][6][7][8].This dance form not only has a history of thousands of years but also has the spiritual education and entertainment function of art and the practical function of life [9].For example, after work or festive celebrations, people use cheerful dances to express their cheerfulness and meet the requirements of entertainment and aesthetics.Through performance, the charm of national art is shown to the audience, and the character traits and aesthetic interests of the people are expressed [10][11][12].Since the 1980s, dance education in colleges and universities has been gradually integrated into the practice of quality education in China, and it has received the attention of educators and learners as an important discipline.With the rapid development and progress of the social economy, people gradually start to pursue higher-level needs after satisfying the basic needs of survival, such as clothing, food, housing, and transportation [13].Therefore, the strategy of the innovative folk dance education model especially emphasizes the need to integrate students' cognition of ethnic minorities with ethnic minority emotions and then rise from abstract cognition to concrete perception [14][15].In short, it is to use innovative strategies of artistic practice to integrate knowledge, emotion, and feeling to achieve the cognition of knowledge from the outside to the cognition of emotion from the inside [16].
The art of dance, as the mother of arts, has the comprehensive artistic characteristics of kinesthetic and tactile sensations.This cannot be replaced by music and art.Through the practice of dance, it can effectively promote the integration and fusion of resources from multiple fields.Scholars from all over the world have never stopped researching and exploring this art form of dance.For example, the literature [17] produced a series of structured contemporary improvised dance concerts, as well as a collection of poems inspired by the United Kingdom and the United States, to assess how the cultural backgrounds of different audiences affected their perceptions of the dance they saw.The literature [18] invited more than one hundred senior citizens to participate in traditional Greek dance classes, verifying that dance is one of the most important elements of lifestyle, contributing to good health and longer life expectancy in older adults.The literature [19] addressed patients with chronic obstructive pulmonary disease and explored the impact and effects of music, dance, and harmonica on this population.The literature [20] used intra-group correlation coefficients to assess the retest reliability, internal consistency, structural validity, sensitivity, and responsiveness of the Dance Functional Outcome Survey among professional and pre-service adult dancers.The results showed that the Dance Functional Outcome Survey could be a useful tool for monitoring health status and functional limitations in adult ballet and contemporary dancers after lower extremity or low back injuries.The literature [21] talks about the benefits of "significant stimulation."That is, patients who listen to music associated with them during radiation therapy are more likely to reduce stress than other patients.Patients with dementia improved their balance and stride length when they listened to their favorite songs, and patients with Parkinson's disease improved their balance and stride length when they danced to music that was meaningful to them.The promotion of art forms such as music and dance in hospital settings can benefit potential patients and their caregivers.The literature [22] invited several moderately active older women to participate in a study with the goal of analyzing the effects of virtual dance exercises on skeletal muscle structure and function in community-based older women.After analyzing the data using ANOVA mixed model test, it was found that performing virtual dance exercises increased muscle mass and helped to improve function and avoid falls in older women.In the literature [23], dance movement therapy was used to treat patients with mood disorders and alleviate their depressive symptoms.The "bachata" and later more spontaneous dances were used as rehabilitation tools.The physical expression of emotions overcomes the fear of judgment, prejudice against mental illness, and social stigma.The literature [24] used a two-armed subgroup randomized controlled study to examine the effects of dance therapy on children with specific learning disabilities.The data showed that dance therapy was an effective method for improving selfesteem, attention, concentration, and emotional recognition in children with SLD.Statistics of the literature revealed that the current direction of dance research is mostly therapeutic, and there is a lack of research in dance education and teaching.This is not conducive to the transmission and development of dance.
In folk dance teaching and dance training, there are factors such as difficulty in recording movement data, inconsistency in demonstration and instruction, and lack of digital dance resources.Information fusion technology can provide new ideas for the inheritance and development of folk dance, as well as novel training methods and interactive experiences for folk dance learners in colleges and universities.This paper takes dance as a carrier, combining visual and audible expressions with the aesthetic concepts, interests, and ideals of different ethnic groups.Using multi-factor theory, construction theory, and distillation theory, the artistic practice model of folk dance education is designed.Based on the multi-frame data collected by multiple Kinect sensors, the Kalman filter algorithm is selected to establish the human skeletal motion model, fuse the information of dancers' skeletal joint points, and repair the obscured joint points.The research is proposed to achieve practical innovation in folk dance education in colleges and universities and to improve the comprehensive level of folk dance.Through information fusion technology, the practical form of the art of folk dance education in colleges and universities is made more popular, increasing the sense of achievement of dancers' training and giving fun, cultural protection, and attraction to folk dance.

Construction of art practice model of folk dance education
The art practice mode of folk dance education aims to cultivate students' national breasts, diversify artistic literacy and enhance national identity.Dance is used as a carrier to achieve the goals of passing on ethnic culture, enhancing humanistic literacy, and improving students' cross-cultural understanding and aesthetic ability.The overall design ideas of the model's applicability concept, course objectives, purposes and objects, specific theories of course construction, and learning contents are shown in Figure 1 and briefly described as follows: 1) The aesthetic personality of the nation is formed gradually in the long-term aesthetic practice.
It consists of two levels of structure: one is the external pattern and surface structure, i.e., the specific visible and audible expressions.Secondly, it has a deep structure or inner meaning, that is, the aesthetic concepts, interests, and ideals of different peoples [25][26].The course content should basically contain these two levels of content, trying to let students experience the aesthetic patterns of different people from the outside and inside [27].
2) Multi-factor theory.In the link multi-factor theory, nomads, marine fishing and hunting peoples, and agricultural peoples are placed in the multi-factor theory.The reason for this is that these three categories of ethnic groups are "based on cultural typology and aesthetic practices of ethnic minorities" and have viable theoretical support [28].This classification allows for an orderly organization of the different ethnic groups within the curriculum and a clearer identification of the differences between them.It is more conducive to the development of teaching materials to avoid misunderstandings and misjudgments among ethnic groups by students due to the similarities that exist among them.
3) Constructing theory.The folk aesthetic education course is a dance art-based course that differs from the general folk dance teaching in that the course boldly and innovatively incorporates three major parts: humanities, art appreciation, and art practice.The purpose is to break the single way of teaching folk dance and let students understand the basic humanities of ethnic groups from the macro level of customs, food, clothing, housing, and various arts [29].From the meso level to experience the audio-visual impact of different ethnic myths and legends, dance, music, painting, and other arts [30].After fully cognizing and feeling the charm of a nation's humanities and arts, they can better practice art and feel the simple, sincere, and friendly emotions of ethnic minorities.

Dancer skeletal motion modeling
Due to the redundancy of multi-frame data from multiple Kinect sensors, the need for low-level realtime dynamic data processing, and the characteristics of skeletal point data updates, the Kalman filter algorithm was selected to establish a human skeletal motion model to provide a database for the next step of information fusion work on skeletal joint points [31][32].
For human joint point data acquisition, it is necessary to the first model and determines a suitable mathematical model so that the corresponding state transfer matrix, observation matrix, and system parameter values in the formula can be solved.Since the data acquisition is performed at 30 frames per second in Kinect, the human skeletal point motion can be understood as a variable acceleration linear motion, and the time interval between every two frames is defined as △ , which is the sampling time. is the frame number, which is the discrete-time point.Then can represent the position of the joint point in the direction of axes at the moment  △ , is the velocity of the joint point in the direction of axes at the moment  △ , and any joint point of the human body is defined as , and the position and velocity of the joint point motion in axes are and respectively.Then the mathematical model of the state matrix of the dancer's skeletal joint point in the 3D coordinate system is: is the state transfer matrix of the system.Using as the covariance matrix of the process noise , which is usually diagonal, can be valued by the acceleration during the motion of the skeletal points.
The mathematical model of the observation matrix is as follows: (2) The observed variables are , is the measurement matrix and the measurement noise is .

Dancer node information fusion
In the human skeletal information fusion of this paper, two Kinect sensors are used to monitor the target human 3D skeletal point data simultaneously.The decentralized information fusion method is used, combining the Kalman filter principle with the information fusion algorithm under skeletal nodes and dividing the information fusion process into the Kalman filter estimation process and the subsequent data fusion process.That is, the filtered values under different skeletal points are first obtained by using two Kinects according to the Kalman filtering principle after filtering estimation, and then the filtered values under two Kinects are used to reach the final fused values.Simultaneous filter estimation is performed for both Kinects, firstly based on the initial measured estimates, which are continuously updated using temporal updates and measurement updates.The time update process, i.e., the prediction process, is used to obtain the estimates of the next step in one step and to solve the prediction covariance array for the next step.The time update equation is: where represents the prior, ^ represents the estimate, and  & ' represents the prior state estimate at moment , i.e., the predicted result at moment  based on the optimal estimate before step , which can be seen as the result of the prediction equation. & ! and  & !"# represent the posterior state estimates at moments  and  − 1, i.e., the updated results. ! and  !"# represent the posterior estimated covariance at times  and  − 1 as one of the results after the filtering. !$ is the prior estimated covariance at time  as an intermediate calculation of the filtering process.
The measurement update process is the calibration process.The Kalman gain matrix is first calculated to obtain the corrected estimate, and then the error covariance is updated.The measurement update equation is: ( Where represents the Kalman gain, which is the intermediate calculation of the filtering.is the state-to-observation transition matrix.
is the input to the filtering, which is the observed value of the system.
The two processes are iteratively looped continuously to obtain more accurate skeletal data estimates, and finally, the final fusion result is obtained based on the two estimates.As shown in Figure 2, the flow chart of skeletal joint point information fusion under multiple Kinect, where the joint point data processing process includes four parts: data acquisition, coordinate calibration, information fusion, and dance movement recognition.The human body data is collected in multiple frames by two Kinects and recorded and saved.Coordinate calibration is to solve the spatial position conversion relationship between the two Kinects and complete the coordinate calibration work so as to unify the data information obtained from the two sensors.) Collect

Fixing of joint point occlusion problem
For the obscured joint points, this paper refers to the bone length and restores the joint middle point and the end joint point as the main motion information with the help of analyzing the constraint of human motion.The specific restoration method is described as follows: 1) Repair of intermediate joint point motion information.The right arm is used as an example to illustrate the proposed method of restoring the joint point information.In frame , we know joint point and joint point to find joint point .Based on the structural characteristics of the arm and geometric knowledge, it is known that joint point is contained in ball (ball is centered at and radius at ) and also in ball (ball is centered at and radius at ).
Based on the continuity of human motion, it is determined that the joint point in the first frame and the first frame are moving at the same speed.Let the coordinates of joint in frame be and the time interval of each frame be .The average velocity of this point before frame is calculated from the motion information of joint in the first frames, that is: The average motion velocity of node before frame is calculated by combining the above motion information: Since the average velocity of node in frame and the first frames of frame is the same, combined with the above equation ( 9), we can see that: (10) Let the coordinates of node in frame be , then the following equation ( 11) is satisfied: The above equation shows that there are two cases of the intersection of the ball and the circle: one intersection and two intersections.Let the direction vectors of the three lines be , respectively, and the following are their specific expressions: (12) This leads to the formula for : There are three specific cases of trade-offs between and .If , i.e., , then is discarded and is chosen.If , i.e., , then is discarded and is chosen.If , i.e., , then either or is discarded.
Recovery of motion information of end joint points.The restoration is based on the prediction method of the length and velocity of joint .The velocity of joint is known, and it is assumed that joint moves at a uniform speed in a short period of time.Therefore, we can obtain equation ( 14) based on the velocity of joint : Combining the above equation with equation (11), we can obtain it by simplifying it: The curves and are the trajectories of the joint .According to equations ( 12) and ( 13), we can obtain the following: (16) (17) Where is the angle between line (vector ) and line (vector ), and is the angle between line and line .The angular velocity of the nodal point in frame can be inferred from the angular velocity of the previous frames, which is in the range of velocity.If the angular velocity of the repaired nodal point is in the conforming threshold range, then it is considered credible, and the test can be terminated.If it is not in the threshold range, then it is considered untrustworthy, and then the final verification step of the joint information is substituted.In case the result is not credible, repeat the solving step of the joint information and calculate and .If it is still not credible, repeat the solving step of the joint information and calculate and .If none of the three obtained joints are within the threshold, then select the point closest to the threshold.

Basic movement training effect comparison
One tester was selected to learn the basic dance movement of the horse stance traverse using the information fusion technology dance teaching method.After 10 training sessions, the learning effect of the test subject was evaluated in terms of movement trajectory and joint angle to verify the effectiveness of the information fusion dance teaching strategy.The joint trajectories of the test subjects were evaluated at the hand_right joint point, for example, and the frames 0-300 with large differences between each exercise were selected for viewing, as shown in Figure 3.The four curves represent the hand_right joint point motion trajectory at the 1st exercise, the hand_right joint point motion trajectory at the 5th exercise, the hand_right joint point motion trajectory at the 10th exercise, and the hand_right joint point motion trajectory of the template movement.By observing the curve band, the mean value of the error between this tester's joint point trajectory and the template motion decreased from 10mm to 4mm after several exercises, indicating that the tester's joint trajectory was more and more similar to the template motion trajectory. (

Comparison of the trajectory of the hand_right joint point under different numbers of exercises
The testers' joint angles were evaluated using the elbow_right joint point as an example.By removing the part with large errors between the beginning and the end, frames 150-1000 of each exercise were selected for viewing, as shown in Figure 4.The four curves represent the elbow_right joint point angle at the 1st exercise, the elbow_right joint point angle at the 5th exercise, the elbow_right joint point angle at the 10th exercise and the elbow_right joint point angle for the template movement.By observing the curve bands, the mean error of this tester's joint point joint angle with the template movement decreased from 90° to 35° after several exercises.The tester's joint angle became increasingly similar to the template action joint angle.The analysis of the learning effects of the 10 training sessions of this tester using the dance education practice model with information fusion technology shows that the repeated use of the education model incorporating information fusion technology to train basic dance movements enables the tester's dance movements to become increasingly similar to the template movements.This verifies that the information fusion technology in the dance education practice reform model can effectively guide learners in dance movement learning.
To further verify the superiority of the dance education practice reform strategy, this experimental session will be compared with the effect of basic dance movement training on students who did not use this model.The first is the training of the inner thigh muscle group, which includes three sets of movements.The second is the anterior thigh muscle group training, which includes two sets of movements.The third is the training of the ankle and calf muscle groups, which includes five sets of movements.Choose three dynamic power-type movements to test the ability to support the handle kick front leg, side leg, and ground single medium jump.The first is to kick the front leg.The second is to kick the side leg.The speed presented by these two kicking movements can test the effectiveness of teaching training of the first medial thigh and the second anterior thigh muscle groups.The test method was to count the number of kicks of the front leg and the side leg of the students in the experimental and control groups in one minute.The third movement was the mid-jump in place, and the training effect of the ankle and calf muscle groups was examined by measuring the height of the ground in centimeters.The experimental and control groups were concluded by comparing the data before and after four months of training, as shown in Figure 5. was better.Kicking is one of the technical dance-type strengths, and this strength ability is a must for dance students.The development level of kicking and swinging power can reflect the development level of dancers' strength ability to a certain extent.It is the lower limb strength when the leg space reaches the highest space position.The kicking ability stands in a very important position in dance training, is one of the important basic strengths, and is an important means of speedy strength development.Power generation is mainly the pelvic muscle groups and thigh muscle groups to make the lower limbs at the hip joint, rapid kicking, and swinging power.In the process of fast kicking, due to the inherent weakness of girls' core strength, the waist and back are more prone to swaying and lack stability when starting and dropping the leg.The experimental group could obviously see that the students had more kicks and more stable strength.The students in the control group only practiced the kicking action in the normal basic skills training class without targeted auxiliary training, and it could be clearly seen that the movement completion speed was slower than the experimental group.
The jump height of a single medium jump is also a basic action to test leg strength.In dance training, it belongs to the strong action and also belongs to the technical action.Students who want to jump high off the ground should have the above two abilities.From the data in the figure, after the experiment, the height of the experimental middle jump was increased by 10cm, while the control group was only increased by 7cm, and the experimental group obviously jumped higher than the control group.The students in the control group just did the regular training and did not train for the weaknesses with the assistance of information integration technology, so the improvement was slower.

Comparison of overall dance movement performance
In order to verify the effectiveness of the folk dance teaching strategy, three different technical skills were selected and tested.In order to ensure the authenticity and objectivity of the test results, three non-teaching teachers from the dance teaching and research group were selected as examiners to conduct the test.The students in the experimental and control groups were mixed and crossed together for a uniform test using the double-blind method.The statistical results of the processed tests are shown in Figure 6.From Figure 6 (a) and (b), we can see that the students in both groups improved in all three scores after the experiment than before the experiment.However, the post-experimental dance students' scores in the experimental group showed significant progress and improvement over the control group's scores before the experiment.The average score of point-turning movement of the experimental group was 78, which was 3 points higher than that of the control group.The average score of the flat turn movement was 79, which was 2 points higher than the control group.The average score of the purple gold crown jumping movement was 85, which was 5 points higher than that of the control group.Therefore, it is easy to find that there is a significant difference between the teaching effect of the two groups of students before and after the experiment.The above experimental results show that the teaching effect of folk dance is significantly improved through the use of information integration technology, and the strategy of dance education practice reform has significant advantages over the traditional teaching method.Especially in the teaching of technical skills of flat turn, the teaching effect of the information fusion education model of dance is far beyond the traditional teaching method.

Conclusion
In this paper, we use information fusion technology, combine national aesthetic personality, and refer to multi-factor theory, construction theory, and distillation theory to design the art practice model of national dance education.Using the characteristics of redundancy and real-time multi-frame data from multiple Kinect sensors, the Kalman filter algorithm is selected to establish the human skeletal motion model and fuse the information of the dancer's skeletal joint points to reform the dance education art practice model.Taking the testers' hand_right and elbow_right joints as examples, we selected 0-300 frames and 150-1000 frames to view the first, fifth, tenth, and template movement joints' trajectories, respectively and found that the average error between the testers' joints' trajectories and template movements decreased from 10mm to 4mm, and the average error between the joints' angles and template movements decreased from 90° to 35°, to 35°.Comparing the dance movement training effects and scores of the experimental group and the control group, the experimental group kicked the front and side legs an average of 70 times/minute and increased the mid-jump height by 10cm.The average score of the point turn movement was 78 points, which was 3 points higher than the control group.The average score of flat turn movement was 79, which was 2 points higher than the control group.The average score for the purple gold crown jump was 85, which was 5 points higher than that of the control group.It can be seen that the strategy of dance education practice reform based on information integration technology can better guide the dancers to complete the dance movements.This strategy can help achieve the practical innovation of folk dance education in colleges and universities and improve the comprehensive level of folk dance.

4 )
Distillation theory.The distillation theory session basically consists of two parts: simulation and classroom feedback.The role of this session is to practice and test the first level and application of the concept, multi-factor theory, and construction theory of the course.Distillation theory is a prerequisite for the development of the material and serves as a guide, organizer and standardizer, etc.At the same time, it is an important part of reflection and evaluation, putting the unsatisfactory course content back into the multi-factor theory again to refine and reconstruct the course content.

Figure 1 .
Figure 1.Artistic practice curriculum design for ethnic minority dance education

Figure 4 .)
Figure 4. Comparison of joint angles at the elbow_right joint point for different numbers of exercises

Figure 5 .
Figure 5.Comparison of the dance movement training effect between the experimental group and the control group before and after the experiment

Figure 6 .
Figure 6.Comparison of the overall dance movement performance between the experimental group and the control group