The concept of usability is now widely used in the field of design, and a large body of research has identified usability as critical to the success of interactive systems or products [1]. According to the ISO 9241-11:2018 international standard, the purpose of products and services is to enable users to achieve their goals effectively, efficiently and satisfactorily. Usability is a key component of user-centred design (UCD), and the main task of improving usability is to understand and meet the needs of users. The literature summarises the tools used to improve product usability, including mythological research, user involvement in design, focus groups, research, surveys, heuristic evaluations and usability testing [2].

The Reality-Virtuality Continuum theory considers the transition from the real world to the virtual world (VR) to be continuous [3], with all intermediate states in the process being defined as mixed reality (MR) [4]. The category of an immersive technology depends on the ratio between the real information it conveys to the user from a physical object and the virtual information generated by the computer. Data given by industry analyst IDC in the 2022 V1 edition of the IDC Worldwide Augmented and Virtual Reality Spending Guide show that the total global AR/VR investment was close to US $14.67 billion in 2021 and is expected to increase to US $74.73 billion in 2026, with a 5-year CAGR that will reach 38.5%. As immersive technologies such as virtual reality and augmented reality have matured and become useful in many areas [5–9], researchers have suggested that immersive technologies can improve the ability of users to identify usability problems with products [10]. However, any design approach comes with a cost for use, and a commonly accepted and adopted approach may not necessarily have the highest design benefit, but in some scenarios it is the approach that balances the design benefit with the cost of use and has the best overall value, determining the need for such an approach to be used in practice in the long term.

In the early stages of designing usability improvements for existing products, direct semi-structured interviews with users to uncover usability issues have been widely used in several studies [11], demonstrating the excellent overall value of this method in this scenario. There is no precedent for an immersive design approach that has been shown to have better overall value than the interview method in terms of uncovering usability issues, and there is little focus in the existing literature on the value of the approach, particularly in terms of quantitative analysis of the value of use.

This study takes a usability improvement design for an industrial crane remote control commonly used in industrial production, focuses on the early stages of the design process, builds a design tool based on virtual reality technology, and quantitatively analyses whether the addition of the design tool can bring higher design benefits with a generally acceptable cost of use in the process of obtaining usability issues through the user interview method described above. The value of the design tool is better than that of the user interview method. The results of this study will guide the promotion of immersive technologies in product design and the search for new focus points.

The potential value of usability issues identified by users is usually evaluated in terms of the number and importance of the issues identified. The raw data collected was collated into a list of usability issues, and the importance of each usability issue was scored by product design experts using a 5-point

For interactive products, styling represents the usability of the product in terms of shape, and the role of usability issues obtained by designers for improving the shape of the product is important for usability improvement design work with a focus on styling.

The evaluation indicators used in this study are numerous and interact with each other. Hierarchical analysis and fuzzy integrated evaluation methods can transform this complex problem into a hierarchical evaluation system according to affiliation [12], quantifying the fuzzy factors involved and therefore giving intuitive results with full consideration of such internal correlations. These methods have been shown to be effective for product evaluation [13, 14].

The combined value of a design method includes its design benefits and usage costs; in this study the respondents were the product designers who had to bear these usage costs. As the selected control method is an interview method with apparently very low usage costs, it is necessary to demonstrate that this method has higher design benefits while incurring acceptable usage costs in the same scenario, as evidenced by the positive willingness of designers to use it, which determines the potential value of the method to replace existing interview methods.

The designer’s specific understanding of the usage costs of the virtual reality method relied on thorough discussions with the researcher, culminating in a list of various usage costs, each of which was evaluated on a 7-point

This experiment was a controlled trial consisting of a control group and an experimental group, with the control group going directly to the interview session to ask usability questions and design suggestions, while the experimental group first used the virtual reality tool we constructed and then conducted the same interviews as the control group. The evaluation of the usability questions and improved design solutions in the above experimental method can reflect the level of design benefit of this virtual reality design method, and then combined with the evaluation of the designer’s willingness to use it, determine whether the overall value of the method is higher than that of the interview method.

A total of 32 expert users of an industrial crane remote control were recruited offline as subjects, including 28 men and 4 women. They all had at least 1 year of work experience. They were divided equally into two groups of 16 each, based on their length of service, gender and the company they worked for. None of them had any experience of working in product design and had never received any training related to product design.

Head-mounted virtual reality devices, such as the

The virtual reality-based design tool consists of an

On top of this basic scenario, the design tool also features freehand interaction [15, 16] and 3D sketching [17–19].

The

3D sketching is achieved using the

The design tool is aimed at users with little experience of using virtual reality equipment and participating in product design, so it should be easy to learn and use. In many studies, 3D sketching has been identified as an accessible and flexible method of creation, suitable for the early stages of product design where efficiency and creativity are required [23]. The gesture recognition technology provides intuitive interaction, while the real-time image of the hands also gives the user an important reference when sketching and analysing design problems. In terms of interaction with the design tool, there is no reliance on multi-level menus and all models and panels are placed directly in the virtual space, which minimises the number of steps the user has to take. The availability of scaled-up models makes it easier to show product details and reduces the user’s difficulty in handling them.

Prior to the start of the trial, each subject was informed about the trial, completed the necessary training and signed an information sheet. Once the trial had started each subject in the group was given free access to the virtual reality tool to reflect on usability issues with the selected existing industrial crane remote control product. This process was open-ended and allowed for breaks, but the researcher did not communicate any design-related issues with the subjects and only provided the necessary assistance in using the tool. A semi-structured interview was then conducted with each subject in the test and control groups to record the usability issues collected.

The interview data was collated by eight additional online invited industrial control equipment experts who had extensive experience in using a wide range of industrial control equipment including the remote control selected for this study and had >6 years of experience in industrial production related work. Each expert collated the data individually to form a preliminary coding scheme, and after repeated discussions in the online group meetings all experts reached a consensus and completed the coding of all the data.

Four postgraduate product design students were recruited to form a design team, and after understanding all of the collated usability issues, the two groups were guided through the design of two improved solutions, with a 2-week interval between designs to minimise disruption to each other. The renderings were required to be of similar modelling and rendering quality and the design specification should be in uniform format.

After collating the interview data, a total of 28 usability problems were identified by subjects in the control group, 32 usability problems were identified by subjects in the test group and 22 usability problems were identified jointly by subjects in both groups. The independent sample

Eight industrial control equipment experts scored the importance of each usability issue on a 5-point Likert scale (1 unimportant, 2 relatively unimportant, 3 generally important, 4 relatively important, 5 important) and took the mean value. An independent samples t-test showed that the importance of the usability issues identified by all subjects in the test group was not significantly different from that of the control group (

From the evaluation of the potential value of usability problems, it is clear that the subjects in the test group were slightly more able to identify usability problems than those in the control group, the main difference being that the subjects in the test group were able to identify a greater number of usability problems.

The design team designed improved solutions based on two sets of usability issues, guiding solution 1 for the usability issues identified in the pilot group and solution 2 for the usability issues identified in the control group. In all, 40 product design practitioners with at least 1 year’s experience and varying degrees of involvement in the design of industrial equipment were recruited via the Internet. In this study, they conducted a remote solution evaluation using solution renderings and design specifications.

For equipment products, a comprehensive evaluation method based on evaluation characteristics is usually used to reflect on the elements of product design quality in the process of evaluation to build a judgement tree, which constructs the product design elements into three levels: the target level, the criterion level and the indicator level. The criterion level is the prerequisite principle for generalising the target level, and the indicator level is several relevant refinement elements of the criterion. Referring to the standard DB621/T148-1993 ‘Evaluation method for modelling of mechanical and electrical products’, the product is evaluated in five aspects: form, colour, material, human-machine, and overall relationship, shown in Figure 2.

Set the target level as A. Within the guideline level, morphological properties B1 include structural stability C1, proportional relationship C2, confirmation style C3 and morphological normality C4 of the product; colour properties B2 include colour coordination C5, colour comfort C6, colour matching C7 and colour stability C8 of the whole machine; material properties B3 include material matching C9, process complexity C10, material quality C11, material cost C12; human-machine properties B4 include assembly rationality C13, operational convenience C14, operational standardisation C15, human-machine interaction C16; overall relationship properties B5 include functional coordination C17 volume coordination C18, overall sense of assembly C19 and overall style C20.

Definition of scales: In the hierarchical analysis method, the numbers 1–9 and their reciprocals are cited as the judgement matrix scales, as shown in Table 1.

Judgement matrix templates

Scale | Definition |
---|---|

Compare the two indicators, equal importance | |

Compare the two indicators, the former is slightly more important than the latter | |

Compare the two indicators, the former is more important than the latter | |

Compare the two indicators, the former is more strongly important than the latter | |

Compare the two indicators, the former is extremely more important than the latter | |

Intermediate value of the above adjacent judgement | |

If the ratio of the importance of indicators |

Construct the judgement matrix: According to the above scale, eight industrial control equipment experts scored the elements of each level after discussion and compared them two by two to form the judgement matrix, and the results of the judgement matrix of the criterion level indicators relative to the target level are as follows (Table 2):

Judgement matrix of criteria level indicators relative to target level

A | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

1 | 3 | 1 | 1/5 | 1/2 | |

1/3 | 1 | 1/3 | 1/7 | 1/4 | |

1 | 3 | 1 | 1/5 | 1/2 | |

5 | 7 | 5 | 1 | 3 | |

2 | 4 | 2 | 1/3 | 1 |

Calculating the weight of each indicator in the criterion level and consistency test: Based on the judgement matrix constructed, the weight of each indicator in the criterion level is derived in three steps, as follows.

Step 1: The judgement matrix is normalised by column.

Step 2: Sum by rows.

Step 3: The sum is normalised to give the weights.

After the three steps above, the results are listed below (Table 3).

Level hierarchical weights and consistency tests

Guideline level | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

0.13 | 0.0471 | 0.13 | 0.4797 | 0.2132 |

After calculating the five guideline level index weights of morphological properties B1, colour properties B2, material properties B3, human-machine properties B4 and overall relationship properties B5, a consistency test is required to determine whether the weighting results are reasonable. The consistency test is judged by the value of the consistency ratio CR. If the CR value is <0.1, the consistency test is passed and the resulting weights are reasonable; if the CR value is >0.1, the consistency test is not passed, and the judgement matrix needs to be reconstructed for calculation. CR is calculated as follows.

CI is calculated as follows.

In this equation,

RI criteria values for judgement matrices of different orders

Steps | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0.52 | 0.89 | 1.12 | 1.26 | 1.36 | 1.41 | 1.46 |

The judgement matrix CI = 0.0187, RI = 1.12, CR = 0.0167, which is <0.1, indicating that it passes the consistency test, that is, the weighting results are reasonable.

Calculate the relative weights of indicator-level indicators and consistency test: Repeat the above process, calculate the weights of indicator-level indicators relative to each criterion-level indicators, and conduct consistency test, and obtain the weights of each level indicators as shown below (Table 5).

Weighting of indicators at each level

Guideline level | Weight | Indicator level | Relative weights |
---|---|---|---|

0.13 | Structural stability C1 | 0.1819 | |

Proportional relationship C2 | 0.3636 | ||

Confirmation style C3 | 0.0909 | ||

Morphological normality C4 | 0.3636 | ||

Colour coordination C5 | 0.3844 | ||

Colour comfort C6 | 0.3844 | ||

0.0471 | Colour matching C7 | 0.1432 | |

Colour stability C8 | 0.088 | ||

Material matching C9 | 0.096 | ||

Process complexity C10 | 0.2772 | ||

0.13 | Material quality C11 | 0.1609 | |

Material cost C12 | 0.4659 | ||

Assembly rationality C13 | 0.2857 | ||

Operational convenience C14 | 0.2857 | ||

0.4797 | Operational standardisation C15 | 0.1429 | |

Human-machine interaction C16 | 0.2857 | ||

Functional coordination C17 | 0.522 | ||

Volume coordination C18 | 0.2073 | ||

0.2132 | Overall sense of assembly C19 | 0.2073 | |

Overall style C20 | 0.0634 |

Determine the set of evaluation factors, the set of weights, the set of rubrics and the set of values for the industrial remote-control design. Evaluation factors: according to the industrial remote control design evaluation index system, the set of evaluation factors obtained has 2 levels.

Level 1 A = (B1, B2, B3, B4, B5).

Level 2 B1 = (C1, C2, C3, C4); B2 = (C5, C6, C7, C8); B3 = (C9, C10, C11, C12); B4 = (C13, C14, C15, C16); B5 = (C17, C18, C19, C20)

Weights set: based on the above weights obtained through the level hierarchical analysis, the set of target allocation weights can be obtained as follows.

W = (W1, W2, W3, W4, W5) = (0.13,0.0471,0.13,0.4797,0.2132) W1 = (0.1819,0.3636,0.0909,0.3636)

W2 = (0.3844,0.3844,0.1432,0.088)

W3 = (0.096,0.2772,0.1609,0.4659)

W4 = (0.2857,0.2857,0.1429,0.2857)

W5 = (0.522,0.2073,0.2073,0.0634)

Sets of comments V = (V1 V2 V3 V4 V5) = (Very good. Good. Normal. Poor. Very poor.)

The set of values corresponds to the set of comments, as follows = (N1, N2, N3, N4, N5) = (5, 4, 3, 2, 1)

Forty designers evaluated the quality of the styling design of the two schemes according to each evaluation indicator in the indicator level, and the affiliation of each indicator was obtained according to the number of completed evaluation levels.

Level 1 fuzzy evaluation: According to the affiliation matrix of each scheme, the fuzzy relationship matrix corresponding to each scheme’s criterion-level indicators can be obtained, which is expressed by Ri. Take Scheme 1 as an example, the fuzzy relationship matrix R1 for the criterion level indicator ‘morphological properties’ is shown below. Similarly, the fuzzy relationship matrix for the remaining criteria level indicators of Scheme 1 and the fuzzy relationship matrix for the criteria level indicators of Scheme 2 can be derived.

0.35 | 0.225 | 0.175 | 0.2 | 0.05 |

0.525 | 0.225 | 0.15 | 0.1 | 0 |

0.45 | 0.4 | 0.1 | 0.05 | 0 |

0.475 | 0.2 | 0.225 | 0.075 | 0.025 |

After finding out the fuzzy relationship matrix for each criterion level indicator of the two scenarios, the corresponding judgement matrix can be found by using the formula E = WR. Taking the example of the criterion level indicator ‘morphological properties’ for Scenario 1, the corresponding matrix is as follows.

Similarly, the judgement matrix corresponding to the remaining criterion level indicators for Scenario 1 and the judgement matrix corresponding to the criterion-level indicators for Scenario 2 can be derived, as shown below (Table 6).

Level 1 fuzzy evaluation results

Option | Indicators | Very good | Good | Normal | Poor | Very poor |
---|---|---|---|---|---|---|

0.4682 | 0.2318 | 0.1773 | 0.1046 | 0.0181 | ||

0.4126 | 0.2918 | 0.1838 | 0.0788 | 0.033 | ||

0.2991 | 0.3851 | 0.2695 | 0.0423 | 0.004 | ||

0.4464 | 0.3071 | 0.1787 | 0.0571 | 0.0107 | ||

0.4711 | 0.2789 | 0.1469 | 0.0484 | 0.0547 | ||

0.2955 | 0.1909 | 0.3159 | 0.1477 | 0.05 | ||

0.2904 | 0.3137 | 0.2525 | 0.0978 | 0.0456 | ||

0.228 | 0.3425 | 0.2658 | 0.1079 | 0.0558 | ||

0.2964 | 0.2536 | 0.2322 | 0.1714 | 0.0464 | ||

0.2504 | 0.2323 | 0.2804 | 0.1655 | 0.0714 |

Level 2 fuzzy evaluation: It is known that W = (W1 W2 W3 W4 W5) = (0.13, 0.0471, 0.13, 0.4797, 0.2132). In the first level fuzzy evaluation part, the judgement matrix corresponding to the criterion-level indicators of Scheme 1 and Scheme 2 is obtained, then the integrated fuzzy relationship matrix R of Scheme 1 and Scheme 2 can be obtained as follows.

After finding the comprehensive fuzzy relationship matrix, then find the comprehensive judgement matrix of each scheme. The comprehensive judgement matrix can be obtained by multiplying the weights of the indicators at the criterion level with the comprehensive fuzzy relationship matrix, as follows (Table 7).

Combined judgement results

Option | Very good | Good | Normal | Poor | Very poor |
---|---|---|---|---|---|

0.4338 | 0.3007 | 0.1838 | 0.0605 | 0.0212 | |

0.2773 | 0.2553 | 0.2587 | 0.1553 | 0.0534 | |

The overall score P = E × NT |

Option 1 scoring: P1 = 0.4338 × 5 + 0.3007 × 4 + 0.1838 × 3 + 0.0605 × 2 + 0.0212 × 1 = 4.0654

Option 2 scoring: P2 = 0.2773 × 5 + 0.2553 × 4 + 0.2587 × 3 + 0.1553 × 2 + 0.0534 × 1 = 3.5478

As P1 is greater than P2, Option 1 has better styling design quality. The results show that the usability issues uncovered by the virtual reality design system we built are more effective than the user interview method in improving usability at the product styling level, and are important for usability improvement design work focusing on styling design.

The 40 product design practitioners who completed the styling evaluation of the modified design solution continued to participate in this study. Each person was divided into five groups according to their company, with three groups of eight people each, and two groups of 6 and10 people, respectively. The reason for grouping by company is that there is a high degree of variability in business focus, working methods, staff composition and financial status between companies and it is uncertain in the initial validation to what extent this will affect the judgement of cost of use, therefore the feedback from each designer will be grouped and discussed individually.

The cost of using our virtual reality design system was clearly higher than the user interview method. The researcher conducted online focus group sessions with each group of designers to discuss the details of how to use the system, the caveats, and the costs of using the design system in practice over time and how to categories them. There was general agreement on the types of usage costs included in the design, namely: portability of the device, complexity of operation of the device, difficulty of using the software, time consumption, price of use and overall usage costs. Each designer’s willingness to accept each of these costs was evaluated individually using a 5-point Likert scale (1 not at all, 2 rather unacceptable, 3 average, 4 rather acceptable, 5 completely acceptable) and the average level of acceptance of each of the five groups is shown in Figure 3.

In the early stages of designing usability improvements for existing products, direct semi-structured interviews with users to uncover usability issues is a common method with high overall value. Although there is a long history of using immersion techniques in product design, there is no precedence for using immersion techniques to improve on this traditional approach. This study verifies the combined value of this combined approach over the use of user interviews alone in terms of the number and importance of usability questions mined by users, the level of styling of improved design solutions guided by usability questions, and the willingness of designers to use the approach. It provides a useful reference for the promotion of immersive techniques in the field of product design and the search for new focus points.

The virtual reality design system developed in this study provides additional large-scale models making it unsuitable for analysing large devices. The ability to quickly move and scale the model could be added to the system or special gesture commands could be used to lock on to the target object to improve the accuracy of the user’s manipulation. On the other hand, head-mounted virtual reality devices prevent users from observing the reality of their surroundings, so they need to use a safety measure to avoid accidental injuries and increase their sense of security as they walk through the venue.

0.35 | 0.225 | 0.175 | 0.2 | 0.05 |

0.525 | 0.225 | 0.15 | 0.1 | 0 |

0.45 | 0.4 | 0.1 | 0.05 | 0 |

0.475 | 0.2 | 0.225 | 0.075 | 0.025 |

#### Judgement matrix of criteria level indicators relative to target level

A | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

1 | 3 | 1 | 1/5 | 1/2 | |

1/3 | 1 | 1/3 | 1/7 | 1/4 | |

1 | 3 | 1 | 1/5 | 1/2 | |

5 | 7 | 5 | 1 | 3 | |

2 | 4 | 2 | 1/3 | 1 |

#### Combined judgement results

Option | Very good | Good | Normal | Poor | Very poor |
---|---|---|---|---|---|

0.4338 | 0.3007 | 0.1838 | 0.0605 | 0.0212 | |

0.2773 | 0.2553 | 0.2587 | 0.1553 | 0.0534 | |

The overall score P = E × NT |

#### Judgement matrix templates

Scale | Definition |
---|---|

Compare the two indicators, equal importance | |

Compare the two indicators, the former is slightly more important than the latter | |

Compare the two indicators, the former is more important than the latter | |

Compare the two indicators, the former is more strongly important than the latter | |

Compare the two indicators, the former is extremely more important than the latter | |

Intermediate value of the above adjacent judgement | |

If the ratio of the importance of indicators |

#### Weighting of indicators at each level

Guideline level | Weight | Indicator level | Relative weights |
---|---|---|---|

0.13 | Structural stability C1 | 0.1819 | |

Proportional relationship C2 | 0.3636 | ||

Confirmation style C3 | 0.0909 | ||

Morphological normality C4 | 0.3636 | ||

Colour coordination C5 | 0.3844 | ||

Colour comfort C6 | 0.3844 | ||

0.0471 | Colour matching C7 | 0.1432 | |

Colour stability C8 | 0.088 | ||

Material matching C9 | 0.096 | ||

Process complexity C10 | 0.2772 | ||

0.13 | Material quality C11 | 0.1609 | |

Material cost C12 | 0.4659 | ||

Assembly rationality C13 | 0.2857 | ||

Operational convenience C14 | 0.2857 | ||

0.4797 | Operational standardisation C15 | 0.1429 | |

Human-machine interaction C16 | 0.2857 | ||

Functional coordination C17 | 0.522 | ||

Volume coordination C18 | 0.2073 | ||

0.2132 | Overall sense of assembly C19 | 0.2073 | |

Overall style C20 | 0.0634 |

#### Level hierarchical weights and consistency tests

Guideline level | B1 | B2 | B3 | B4 | B5 |
---|---|---|---|---|---|

0.13 | 0.0471 | 0.13 | 0.4797 | 0.2132 |

#### Level 1 fuzzy evaluation results

Option | Indicators | Very good | Good | Normal | Poor | Very poor |
---|---|---|---|---|---|---|

0.4682 | 0.2318 | 0.1773 | 0.1046 | 0.0181 | ||

0.4126 | 0.2918 | 0.1838 | 0.0788 | 0.033 | ||

0.2991 | 0.3851 | 0.2695 | 0.0423 | 0.004 | ||

0.4464 | 0.3071 | 0.1787 | 0.0571 | 0.0107 | ||

0.4711 | 0.2789 | 0.1469 | 0.0484 | 0.0547 | ||

0.2955 | 0.1909 | 0.3159 | 0.1477 | 0.05 | ||

0.2904 | 0.3137 | 0.2525 | 0.0978 | 0.0456 | ||

0.228 | 0.3425 | 0.2658 | 0.1079 | 0.0558 | ||

0.2964 | 0.2536 | 0.2322 | 0.1714 | 0.0464 | ||

0.2504 | 0.2323 | 0.2804 | 0.1655 | 0.0714 |

#### RI criteria values for judgement matrices of different orders

Steps | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 |
---|---|---|---|---|---|---|---|---|---|

0 | 0 | 0.52 | 0.89 | 1.12 | 1.26 | 1.36 | 1.41 | 1.46 |

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background of artificial intelligence Study on Interactive Relations between Enterprise Social Media and Decision Style Based on a vector Autoregressive Model Research on Dynamics of Flexible Multibody System with Deployable Antenna Based on Static Lagrangian Function The Optimization of Mathematics Teaching Models in Colleges and Universities Based on Nonlinear Differential Equations Study on spatial planning and design of learning commons in university libraries based on fuzzy matrix model The Stability Model of Piano Tone Tuning Based on Ordinary Differential Equations Construction and application of automobile user portrait based on k-mean clustering model The Homework Model of Screening English Teaching Courses Based on Fractional Differential Equations VR-based computer maintenance practical training platform development design and application research Research on innovative human capital for China’s economic development based on STI model In-depth analysis of the artistic 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in Programmable Networks The Complexity of Virtual Reality Technology in the Simulation and Modeling of Civil Mathematical Models University Library Lending System Model Based on Fractional Differential Equations Calculation and Performance Evaluation of Text Similarity Based on Strong Classification Features Intelligent Matching System of Clauses in International Investment Arbitration Cases Based on Big Data Statistical Model Evaluation and Verification of Patent Value Based on Combination Forecasting Model Financial Institution Prevention Financial Risk Monitoring System Under the Fusion of Partial Differential Equations Prediction and Analysis of ChiNext Stock Price Based on Linear and Non-linear Composite Model Calculus Logic Function in Tax Risk Avoidance in Different Stages of Enterprises The Psychological Memory Forgetting Model Based on the Analysis of Linear Differential Equations Optimization Simulation System of University Science Education Based on Finite Differential 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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 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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 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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