Research on product process design and optimisation model based on IoT intelligent computing

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: 1 X=(X1X2X3⋯Xn)

By introducing the characteristic function G(x) to describe the set of influencing factors, it represents the quality of the process product, and the component tolerances within the range of δ are the products that meet the requirements.

2 G(x)={1,0≤x≤[δ]0,x>[δ] $$G(x) = \left\{ {\matrix{ {1,} \hfill & {0 \le x \le [\delta ]} \hfill \cr {0,} \hfill & {x > [\delta ]} \hfill \cr } } \right.$$

In the process of production, as long as the product tolerance exceeds δ, the product is not qualified and the part cannot be used, which will undoubtedly increase the manufacturing cost. We correspond to the value of G(x) in a general range, which is referred to as a fuzzy subset δg for short, and μδ(x) is the membership function of the tolerance influencing factor.

3 δg={x,μδ(x)∣x∈X}

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: 4 X=(X1X2X3⋯Xn)

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.

5 G=[(μA(x1),x1),(μA(x2),x2),⋯(μA(xn),xn)]

The second is an expression based on a vector method.

6 G=[(μA(x1)),(μA(x2)),⋯(μA(xn))]

The third is the Zadeh vector representation: 7 G=[(μA(x1)),x1(μA(x2)),x2⋯(μA(xn)),xn] $$\matrix{ {G = \left[ {{{({\mu _A}({x_1})),} \over {{x_1}}}{{({\mu _A}({x_2})),} \over {{x_2}}} \cdots {{({\mu _A}({x_n})),} \over {{x_n}}}} \right]} \cr } $$

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

8 G=∫(μA(x))x

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: 9 {μA∪B(x)=μA(x)∪μB(x)=max(μA(x),μB(x))μA∩B(x)=μA(x)∩μB(x)=min(μA(x),μB(x)) $$\left\{ {\matrix{ {{\mu _{A \cup B}}(x) = {\mu _A}(x) \cup {\mu _B}(x) = \max \left( {{\mu _A}(x),{\mu _B}(x)} \right)} \hfill \cr {{\mu _{A \cap B}}(x) = {\mu _A}(x) \cap {\mu _B}(x) = \min \left( {{\mu _A}(x),{\mu _B}(x)} \right)} \hfill \cr } } \right.$$

In the process of process design, addition and subtraction operations are sometimes required. The specific forms are as follows: 10 {a+b=min(1,a+b)a−b=max(0,a+b−1) $$\left\{ {\matrix{ {a + b = \min (1,a + b)} \hfill \cr {a - b = \max (0,a + b - 1)} \hfill \cr } } \right.$$

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.

Then, the closeness of the two eigenvectors A and B is obtained.

13 σ(A⋅B)=12[A⋅B+(1−A⊙B)]

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.

14 R=(rjx)m×n

Another fuzzy vector that includes all non-negative real numbers in the evaluation is as follows: 15 A={a1,a2,a3,⋯an−1,an}

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.

16 A⋅R={b1,b2,b3,⋯bm}

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].

17 R=(rjx)m×n={r11,r12⋯r1mr21,r22⋯r2m⋯rn1,rn2⋯rnm} $$\matrix{ {R = {{({r_{jx}})}_{m \times n}} = \left\{ {\matrix{ {{r_{11}},{r_{12}} \cdots {r_{1m}}} \cr {{r_{21}},{r_{22}} \cdots {r_{2m}}} \cr \cdots \cr {{r_{n1}},{r_{n2}} \cdots {r_{nm}}} \cr } } \right\}} \cr } $$

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 x_i to predict target variable y_i. The model in supervised learning usually means that the predicted result y_i is determined by the input data set x_i, and the predicted value is based on different tasks, that is, classification tasks or regression tasks. Different interpretations are possible. In fact, classification and regression are algorithms of the same nature, except that classification is a discrete result value, and regression algorithm is a continuous result value. The principles and essence of classification and regression are the same, and they are all between features and prediction results. function map. The output of the classification tree is in the form of categories, and the output of the regression tree is in the form of numbers. During regression, information gain, information gain rate and Gini coefficient cannot be effectively used to judge the node splitting of the tree, and then a new method is used to predict the error. Commonly used prediction error methods include mean square error, logarithmic error and other prediction error methods. And the nodes of the tree are values, and not categories. The specific form of XGBoost calculation is as follows: 18 yi=∑K=1KfK(xi)

Here, K is the total number of trees in the algorithm, f_K represents the K-th tree and y_i is the prediction result under sample x_i. From the point of view of process product design, for many factors, the maximum amount of generalisation capability is required, and the optimised objective function is as follows: 19 Obj(θ)=∑i=1nl(yi−y)+∑K=1KΩ(fK)

Here, i represents the i-th sample; l(yi−y) represents the prediction error of the i-th sample, and the smaller the error, the better; Ω(fK) represents the regular term of the K-th tree; and ∑K=1KΩ(fK) $\mathop \sum \limits_{K = 1}^K {\rm{\Omega }}({f_K})$ represents the function of the complexity of the tree, and the smaller the value, the lower the complexity and the stronger the generalisation ability.

20 Ω(fK)=γT+12λ∑j=1Twj2 where T represents the number of leaves and w_j represents the L₂ regularisation term of w.

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: 21 RMSE=1n∑i=1n(yi−yp)2

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: 22 R2(yi−yp)=1−∑i=1n(yi−yp)2∑i=1n(yi−y¯)2 $$\matrix{ {{R^2}({y_i} - {y_p}) = 1 - {{\mathop \sum \limits_{i = 1}^n {{({y_i} - {y_p})}^2}} \over {\mathop \sum \limits_{i = 1}^n {{({y_i} - \bar y)}^2}}}} \cr } $$

Among them, n represents the number of samples, y_i is the actual value, y_p is the predicted value and y¯ is the mean. When the predicted value is equal to the true value, the goodness of fit is equal to 1, and at this time, the model predicts the best. When the predicted value is equal to the mean, the goodness of fit is equal to 0, at which point the model predicts the worst.

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.

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.

Fig. 2

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.

Fig. 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.

Fig. 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.