The rapid development of national economy and technology is inseparable from the great contribution made by industrialisation. Industry is the strong cornerstone of a nation’s development [1–3]. In the process of industrial development, the most important task in the early stage is the process design of related industrial production. Process design refers to the general term for process specification design and process equipment design, which are determined according to the product characteristics, production properties and functions of industrial production. The process specification is the main process document that is determined by words, charts and other carriers to guide product processing and worker operations. Only by forming a specific process flow can enterprise manufacturing be more intelligent and automated. Process design is the basis for enterprise planning, organisation and control of production and is an important guarantee for enterprises to ensure product quality and improve labour productivity. In machinery manufacturing enterprises, there are three main forms of process regulations: process card, process card, and process card. Process equipment is referred to as ‘tooling’. The general term for tools, fixtures, moulds, measuring tools and station tools required to manufacture products. Process equipment not only is necessary for manufacturing products but also plays an important role as labour materials to ensure product quality, improve production efficiency and achieve safe and civilised production [4–6]. However, in the process of development, craft products have become diversified and refined, and more and more craft products have higher requirements for related parameters and aesthetics. Traditional designs such as CAD have already faced such requirements. It is difficult to deal with [7, 8], which will undoubtedly reduce the sales of industrial products. Therefore, it is very important to find better design methods and optimisation methods for industrial products.

The development of computer networks has led to the rapid development of the corresponding Internet of Things (IoT). The IoT connects objects all over the world through computer networks, can be used to view products located in other regions at any time according to user needs and is not limited by any time and place. The IoT mainly includes three structural components: the perception layer, the network layer and the application layer [9–11]. The IoT first collects object information through a large number of sensing technologies and updates the information to the network in real time. After receiving the collected information, it is transmitted and, finally, after some information data processing, the data are processed into a type that meets the needs of users [12–14]. In the IoT, a large amount of data are processed in real time. In addition, the sensitivity to data is also very high, and the IoT has a high level of intelligence [15–18], which has opened a new way to the research into product process design and optimisation. In recent years, research on the intelligence of the IoT has become more and more popular. There is an increase in the number of articles on the IoT and intelligent computing published in recent years, as shown in Figure 1. We can clearly see that the relevant research is increasing year by year, from <100 articles published around 2005 to >1500 articles published this year, which shows that the intelligent computing of the IoT is more and more recognised by everyone. Haseeb et al. [19], with an aim of providing solutions for energy services that provide secure data transmission for sustainable cities, proposed an intelligent and secure edge computing (ISEC) model for sustainable cities using green IoT, to formulate communication strategies and reduce responsibility for energy management and data security of data transfers. The proposed model uses deep learning to generate optimal features for data routing, which may help train sensors to predict the best route to edge servers [20]. Furthermore, the integration of distributed hashing with on-chain policies simplifies security solutions with efficient computing systems. IoT intelligent computing has shown excellent performance in the field of energy security. In addition, for the optimisation of intelligent deep learning models of the IoT, Zhao et al. [21] proposed Deep Q-Network for automatically learning offloading decisions to optimise system performance, and a neural network (NN) trained to predict offloading actions, where the training data are generated from the environment system. Furthermore, they propose several bandwidth allocation schemes by adopting bandwidth allocation to optimise the wireless spectrum of the link between users and CAPs. Finally, simulation results demonstrate the effectiveness of the proposed reinforcement learning offloading strategy. In particular, the proposed deep reinforcement learning-based algorithm can significantly reduce system latency and energy cost. Kuhn et al. [22] analysed and synthesised all the process designs of building integrated photovoltaics. They found that the early process design is very important for the energy consumption and safety performance of the whole system. In the design of modern process products, the products are becoming more and more complex, and the design requirements are becoming more and more strict. Dong et al. [23] and others optimised the design of complex mechanical products through complex network intelligent computing. Firstly, they constructed a complex network model of CMPs. The model is processed unidirectionally by analysing the constraints and dependencies between parts. Second, all nodes in the network are divided into hierarchies, and all feasible change propagation paths are selected by breadth-first search. Experimental comparisons show that the proposed method is reasonable and can output the list of affected parts and the preferred ordering of propagation paths, which can provide clearer and more direct guidance for DMs. Their research provides new impetus for process product design and optimisation.

Through research and analysis on IoT intelligent computing, product process design and optimisation, we can find that IoT intelligent computing has shown excellent and stable performance in many fields, whether it is security protection, intelligence or parameter optimisation. For product process design, the requirements for detailed parameters of products and related product coordination are getting higher and higher. However, in the process of product process design, for some complex parameters generated, how to match and optimize the sub-parts of related industrial products, and how to improve the quality level of corresponding products and improve the competitiveness of products in the international market. There are still deficiencies; therefore, in this study, we combine the IoT, to intelligently process the data of a large number of design object parameters and process product-related entity parameters, to optimise parameters and the process of products as well as design and to promote the design level and production level of process products.

Process design not only the shape of physical objects generally manufactured by means of industrial production but also the structural connection of the products, and the product as a whole obtains the unity of function and structure from this connection. Craft design actively participates in the interaction of material culture and artistic culture. Nowadays, many physical objects around us become obsolete in function, usage and appearance. Various physical objects require frequent modifications and adaptations of existing various components. Process design is closely related to the objective process of technological development, thereby meeting people’s practical requirements. On the other hand, craft design always maintains a certain relationship with the production and consumer fields, and its objects are often commodities. In this way, craft design affects various social and cultural development mechanisms of society and the formation of aesthetic ideals, standards and hobbies. Craft design, as an aspect of aesthetic activity, aims to humanise the surrounding physical environment.

In the process of product process design, the model theory involves the fuzzy description of process design, the pattern recognition problem of process plan optimisation and the problem of process deviation. In order to improve the core competitiveness of products, process design is the most basic requirement. In this study, we use the intelligent computing of the IoT, which introduces the particle swarm-based algorithm [24, 25] and the XGBoost algorithm [26, 27] to optimise the intelligent computing and product process design process. There are many ambiguities in the formulation of the process plan. Fuzziness refers to an objective attribute with no clear boundaries in quantity. Concepts such as ‘tight process tolerances’ and ‘less margins’ have certain ambiguities, and it is difficult to quantify them in numbers [28, 29]. Also, in the process design, the fuzziness should be considered; the fuzzy factors in the process design should be dealt with through fuzzy mathematics; and the economical and feasible process routes should be formulated to ensure the product accuracy. In the manufacturing process, the main accuracy factors that affect the product are equipment reasons, the structure of parts, operation methods and operator levels. The influencing factors can be expressed as:

By introducing the characteristic function

In the process of production, as long as the product tolerance exceeds

In the process of product process design, taking into account the fuzziness, first through derivation, according to whether the set is a finite set, the fuzzy set is divided into:

When it is a finite set:

The main centralised representation methods of fuzzy sets are as follows:

The first is an ordered description method, referred to as ordinal even representation, which records the membership degree of each element that affects the level of industrial design in order. When it is 0, it will not be ignored.

The second is an expression based on a vector method.

The third is the Zadeh vector representation:

When the factor of the set is an infinite and uncountable set, the characteristic function can be represented as the following formula.

After formulating the technological process plan, it is necessary to review and judge the relevant plans to select the best one. Here, we select by synthesising the fuzzy sets, and the relevant calculation process is as follows:

In the process of process design, addition and subtraction operations are sometimes required. The specific forms are as follows:

Through the aforementioned fuzzy set operation, the parameters of the product can be optimised and matched, thereby improving the accuracy of the product. During the review process, if many parameters are considered in the process design, the corresponding indicators of the Zadeh operator need to be reduced, and then the relevant calculations are carried out, which will easily cause some standard losses and affect the accuracy.

In the process of process design, due to some non-uniqueness of parts, adjustable processing between features and diversity of resources, it is necessary to provide several methods for identifying problems. In order to select the optimal route that can not only realise the design tolerance of the part but also relax the process tolerance during the machining process, it is necessary to comprehensively evaluate the multiple process routes. When comprehensively evaluating multiple process routes, there are two routes to choose from:

Direct calculation: Comprehensive evaluation is carried out through the previous direct fuzzy calculation results, and the optimal scheme is selected according to the results of fuzzy changes.

Indirect calculation: Firstly, optimise the relevant eigenvectors, calculate
the characteristic lines of each line and then calculate the relevant fit. The
common calculation formula is as follows:

Then, the closeness of the two eigenvectors

After a certain process design scheme is determined, the rationality and economically analysis of the overall route of the process should be carried out through various evaluations. The relevant judgement formulas are as follows.

Another fuzzy vector that includes all non-negative real numbers in the evaluation is as follows:

The calculation of the two is as follows. All the evaluation criteria are fuzzy transformed. For the relevant parameter design, the selection of the interface has a good application.

The established fuzzy matrix is shown in Equation (17), which is mainly composed of a membership degree or membership function, which is used to express the matching relationship of the relevant evaluation criteria. The matching relationship is the possibility between them. The elements in the matrix are all in [0, 1].

After particle calculation, the optimisation calculation is further carried out through the XGBoost algorithm. XGBoost is a set of machine learning systems that can improve and expand. It has the effect of gradient enhancement and shows excellent performance in supervised learning data _{i}_{i}_{i}_{i}

Here, _{K}_{i}_{i}

Here,

_{j}_{2} regularisation term of

First of all, for the product process design and optimisation model, there are many influencing factors, and there are many accuracy standards for the algorithm. In our study, we choose the root mean square error and goodness of fit to evaluate the accuracy of intelligent calculation and to determine whether the optimisation model is good or bad. We choose the root mean square error for the objective function; the smaller the root mean square error, the better the intelligent calculation effect of the algorithm and the better the optimisation effect. The root mean square error is as follows:

For the trained optimisation model, apply the product process design of the intelligent computing of the IoT, and use the degree of fit to judge the accuracy of the model. If the error is large, the fitting formula is as follows:

Among them, n represents the number of samples, _{i}_{p}

For the intelligent computing of the IoT combining particle swarm and XGBoost algorithms, the accuracy and stability of the algorithm are very important for the application. In the process of machining, the machining error rate will have a serious impact on the quality of the product. Therefore, it is necessary to reduce the machining error rate when performing machining optimisation. In general, the machining error rate occurs in the primary stage of product processing, which is also the design stage. Therefore, as a designer, we should analyse the problems existing in the design through scientific algorithms and reasonable planning to minimise the generation of error rates. Therefore, we verified its root mean square and goodness of fit, and the specific conclusions are shown in Table 1.

Algorithm root mean square and fit table

Traditional algorithm | Particle swarm algorithm | Particle swarm + XGBoost | |
---|---|---|---|

RMSE | 0.91 | 0.953 | 0.968 |

^{2} | 0.895 | 0.936 | 0.971 |

As shown in Table 1, for the particle swarm algorithm, the root mean square error in the product process design process can be increased from the original 0.91 to 0.953. After further optimisation by XGBoost, the root mean square error can be further increased to 0.968, showing an increase of 5.8%. In terms of product process design fitting and optimisation, the particle swarm algorithm can improve the fitting degree by 4.1%. After further optimisation through XGBoost, the fitting degree is improved to 0.971. In the basic class of the particle swarm algorithm, the fitting degree is further increased by 3.5%, with an increase of 7.6%. This shows that the combination algorithm can further improve the design of the product and provide more excellent choices for the product. As shown in Table 1, for the particle swarm algorithm, the root mean square error in the product process design process can be increased from the original 0.91 to 0.953. After further optimisation by XGBoost, the root mean square error can be further increased to 0.968, an increase of 5.8%. In terms of product process design fitting and optimisation, the particle swarm algorithm can improve the fitting degree by 4.1%. After further optimisation through XGBoost, the fitting degree is improved to 0.971. In the basic class of the particle swarm algorithm, the fitting degree is further increased by 3.5%, an increase of 7.6%. This shows that the combination algorithm can further improve the design of the product and provide more excellent choices for the product.

In our experiment, we selected 8,000 product process design data as the training set and 2,000 product process design data as the test set. The relevant conclusions are shown in Figure 2, which is a graph of the number of iterations and accuracy.

As shown in Figure 2, the training set reaches a stable state after 140 iterations, and the highest accuracy can reach 91.5%. At the same time, the test set has 40 fewer iterations than the training set, and the highest accuracy is 95.6% after 100 iterations. By contrast, the accuracy has increased by 5.1%, and the process design of the product is pushed to the new development process, which greatly promotes the quality of the product. At the same time, after about 50 iterations, the accuracy basically reaches 90%, which greatly saves the calculation time and reduces unnecessary power consumption.

For the production process design of intelligent computing of the IoT, the optimisation of multiple schemes is often involved, and the selection of the optimal scheme is faster, which means that the response speed of intelligent computing is faster and the effect is better. Therefore, we perform a statistical analysis on the response time of the optimal solution selected in the IoT, as shown in Figure 3.

As shown in Figure 3, the optimal solution comparison time chart shows that before optimisation, the optimal solution selection time in 10 different fields ranges from 140 to 170 minutes. After the optimisation model is processed, the selection of the optimal solution time is about 80 minutes, and the optimisation model reduces the selection time of the scheme by 42.85%–52.94%, which greatly improves the selection ability of the scheme.

In addition, after the relevant process design and optimisation, it is necessary to discuss how to improve the production efficiency of mechanical processing equipment. The generation and realisation of the process mainly rely on mechanical equipment. At the same time, machining equipment is also an important process for producing mechanical products. For the rationalisation of mechanical processing equipment, it is necessary to select the equipment according to the actual situation and compare its production efficiency with the optimal design scheme that has been selected. The generated efficiency comparison chart is shown in Figure 4.

As shown in Figure 4, after optimising the process flow through the intelligent computing of the IoT, we selected 50 process products in the IoT to conduct a comparative study of production efficiency. The selected 50 process products cover many fields, including clothing, electronic devices and stationery. We can see that the production efficiency of the products produced by the process production process design without optimisation is 86.59%–92.5%, and the fluctuation range is around 6%. After the particle swarm algorithm performs fuzzy change calculation on its related influencing factors and after further optimisation by XGBoost, the production efficiency of the selected process production design scheme is between 93.6% and 96.5%, and the fluctuation range is 3%. Compared with the monthly optimisation plan, it reduces by 50%, improves the stability and accuracy of the production process and creates more economic value. In addition, after the optimised generative design process, the overall production efficiency has been increased by about 5%, saving a lot of production raw materials, providing impetus for the construction of economical-friendly industrial development.

Before the product is processed, the related process design of the product according to the technical standards and correct parameters is the first step in industrial production. Process product design is an important part of the production process, and it also directly affects the entire production process and the quality of the product. Based on the particle swarm algorithm and XGBoost algorithm, combined with the intelligent computing of the IoT, we transform some uncertain factors in the process of industrial product design through the fuzzy matrix and select the optimal IoT through the optimised intelligent calculation of the IoT. The design scheme and the influence of the scheme before and after optimisation on production efficiency is compared. The relevant specific conclusions are as follows:

Before the algorithm, ensuring the stability and accuracy of the algorithm is the key factor in the subsequent work of the algorithm. The algorithm we optimised has an iterative accuracy of up to 95.6%; in addition, in terms of degree, the root mean square and the fitting degree of the IoT intelligent computing combined with the particle swarm algorithm and the XGBoost algorithm are, respectively, 0.968 and 0.971. This shows that our optimisation scheme has good stability and accuracy and can meet the requirements related to the design and optimisation of process products.

The ultimate purpose of process product design and optimisation is to improve the production efficiency of the product. We conduct research on the optimal solution selection of the optimised model and the improvement of production efficiency. The optimised model can select the optimal solution. The time-consumption reduction is 42.85%–52.94%; in addition, the targeted selection of the best solution in their respective fields can increase the overall production efficiency of the product by about 5%, saving raw materials and creating more economic value assistance.

#### Algorithm root mean square and fit table

Traditional algorithm | Particle swarm algorithm | Particle swarm + XGBoost | |
---|---|---|---|

RMSE | 0.91 | 0.953 | 0.968 |

^{2} |
0.895 | 0.936 | 0.971 |

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