# Research on the Development Path of Manufacturing Industry and Its Economic Effect Based on Computational Visualization

Authors: Shiyuan Zhou; Zhixiong Liao; Xiaoqin Yang
Journal: Mathematical Problems in Engineering
 (2022)

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## Abstract

In order to improve the analysis effect of the manufacturing development path and improve the economic benefits of the manufacturing industry, this paper combines the computer visualization technology to analyze the manufacturing development path and its economic effect. Moreover, this paper introduces the minimum ill-posedness criterion in the optimal placement criteria of time-domain sensors and the modal guarantee criterion in the optimal placement criteria for frequency-domain sensors. In addition, in this paper, the optimal arrangement of sensors is carried out based on the above two criteria, and the improved monkey swarm algorithm is applied to the optimization problem of the sensor of the visual system, and an intelligent computer visualization system is constructed. The experimental research results show that the research model of the manufacturing development path and its economic effects based on computational visualization proposed in this paper has certain practical effects.


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## Body

## 1. Introduction

At present, China is actively participating in the development path of returning to the manufacturing industry and has put forward the strategic plan of “Made in China 2025” of great significance and hopes to change the status quo that China’s manufacturing industry is large but not strong before 2025 and upgrade from a large manufacturing country to a manufacturing power.In recent years, countries around the world has adopted a series of policy measures such as the establishment of special economic zones, export processing zones, coastal development zones along the river, customs bonded zones, and free trade zones and the adoption of various tariff concessions and exemptions, export tax rebates, and foreign direct investment to penetrate into the international industrial cooperation and economic division system on a large scale and in an all-round way [1]. In particular, manufacturing has become an important part of the world industrial cycle system. The international trade volume, especially the manufacturing processing trade volume, has grown rapidly and has gradually formed a processing trade model with “the three-plus-one trading-mix” as the main form and “both-ends-abroad” as the dominant feature [2]. In this way, manufacturing enterprises are embedded in labor-intensive production links such as processing and assembly in the division of labor in the global value chain by virtue of sufficient labor factors and cheap labor costs and become “world factories.” Although the world-renowned East Asian Miracle has been achieved through high-input and high-output import and export trade, the growth of macro and industrial total factor productivity is an important support for maintaining medium-to-high-speed economic growth and improving the quality of economic growth in the future. Judging from the current situation, it is an undeniable fact that China and developed countries have obvious differences in the international division of labor, and the international division of labor of products further solidifies the status of China and developed countries in the international division of labor. Manufacturing industries in developed countries are generally at the high end of the value chain engaged in high value-added activities such as upstream R&D and downstream brand marketing. However, China’s manufacturing industry is generally “locked” in the low value-added middle- and low-end links in the value chain division of labor, mainly manufacturing and processing [3]. Therefore, how to help local manufacturing companies get rid of the “low-end lock” and “capture” effects of the value chain, change the overall low total factor productivity of the manufacturing industry, and realize the task of climbing from low-end manufacturing and export to medium- and high-end value chain is imminent.This paper combines computer visualization technology to analyze the development path of manufacturing industry and its economic effect, which provides a theoretical reference for the subsequent development of manufacturing industry.


## 2. Related Work

Manufacturing is an important part of industry, an important force driving the development of the national economy, and an important guarantee for the country’s comprehensive national strength. As we all know, the quality of German products is well known all over the world, and the important guarantee for winning these products comes from the long-term prosperity of the German manufacturing industry. The quality of German manufacturing has always maintained a world-leading level [4]. With the support of the government, Japan’s manufacturing industry has maintained a steady growth in the total amount of Japan’s manufacturing industry through a series of measures such as reducing energy consumption, strengthening technological innovation and foreign investment, continuing Japan’s manufacturing industry continued prosperity [5]. Literature [6] pointed out the disparity in the status of developing countries and developed countries in the value chain. When developing countries rely on low-level elements such as resources to embed into the value chain, developed countries will dominate the global value chain with advanced elements such as technology and brand. From the perspective of the integrated development of manufacturing and service industries, literature [7] makes a quantitative analysis of the two using the relevant data of manufacturing and service industries in the United States and points out that the servitization of manufacturing is essentially the integration of manufacturing and service industries developing. Literature [8] believes that there are two ways for multinational enterprises to integrate into the global value chain. Only by embedding the global value chain from the high end of the value chain can the international competitiveness of the enterprise be improved. If it is embedded from the low end of the value chain, the enterprise will face the danger of falling into a poverty-stricken growth trap. Reference [9] analyzes the impact of global value chains on the international division of labor in the manufacturing industry by using the method of export technical complexity. Literature [10] believes that the import of intermediate products is beneficial to the improvement of domestic manufacturing production efficiency.Literature [11] believes that technological progress is an important driving force for the upgrading of manufacturing industries in developing countries. Literature [12] emphasizes the focus on dynamic capabilities, which is the ability of enterprises to develop and innovate by learning new knowledge and mastering new technologies in the long-term learning process. Literature [13] pointed out that enterprises should pay attention to the core competitiveness and the ability to create value for consumers through the research on the transformation and upgrading of the manufacturing industry. Reference [14] pointed out that the essence of the manufacturing upgrade process is the process of manufacturing enterprises from low value-added to high value-added and from labor-intensive to capital-intensive, and in this process, enterprises realize the promotion of their status in the division of labor and trade. Under the pattern of the division of labor in the value chain, technological innovation is the basis for realizing the upgrading of the manufacturing industry. Reference [15] pointed out that when developing countries try to upgrade high value-added links in the value chain division of labor, they will be hindered and controlled by developed countries. Literature [16] found through research on China that although the development of the processing and manufacturing industry has promoted a substantial increase in China’s trade level to a certain extent, this export-oriented and highly competitive industry based on imported technology and foreign-funded enterprises has limited local trade, production, and technological diffusion in China’s domestic industry.Literature [17] conducted a general research and exploration on the dynamic mechanism and governance structure in the theory of global value chain, aiming to explore how manufacturing enterprises can make use of their strengths and avoid weaknesses to realize industrial transformation and upgrading from the perspective of value chain under the background of economic globalization and deepening competition. Literature [18] measured the cost of each link in the enterprise value chain from the perspective of cost and proposed countermeasures and suggestions to improve the competitiveness of enterprises by reducing costs. Literature [19] conducted an empirical analysis and research on the factors affecting the transformation and upgrading of manufacturing enterprises at the microlevel and pointed out that industrial agglomeration, external supporting services, and exports have a significant impact on the transformation and upgrading of the manufacturing industry. Reference [20] starts from the value chain theory and studies the upgrading of the processing and manufacturing industry from the positive and negative effects of the value chain on the processing and manufacturing industry. Literature [21] analyzed the correlation between the processing manufacturing industry and the logistics industry and pointed out that there is a close connection between the logistics industry and the upgrading of the processing manufacturing industry. The development of the modern logistics industry has accelerated the upgrading of the technological structure of the processing manufacturing industry to a certain extent. It is of great significance to the transformation and upgrading of the processing and manufacturing industry.


## 3. The Construction of Computer Visualization Network Based on the Internet of Things

There are many sensor points to be selected for large-scale structures. In order to better reflect the dynamic characteristics of the structure and obtain more sufficient structural information, a good sensor layout scheme is required. The development of sensor optimal layout criteria provides a basis for sensor layout, and different sensor optimal layout criteria enable the structural health monitoring system to obtain different recognition effects. In order to better monitor the health of the structure, this paper selects the minimum ill-posedness criterion and the modal assurance criterion to optimize the arrangement of sensors.


### 3.1. Minimum Ill-Posedness Criterion for a Single Type of Sensor

Any multi-degree-of-freedom linear elastic finite element equation of motion can be expressed by the following formula:(1)Mx¨+Cx˙+Kx=Ft.Among them,M is the mass matrix, C is the damping matrix, and the Rayleigh damping model is used. K is the stiffness matrix, Ft is the external load, and x¨ is the acceleration response.When a structure is damaged, stiffness usually decreases.αi is the local stiffness change rate of the i-th element of the structure, −1≤αi≤0. When αi=−1, it means that the structural stiffness at this time is 0; that is, complete damage has occurred. When αi=0, it means that the stiffness of the structure has not changed. When −1<αi<0, it means that the structure has been damaged to a certain extent, and the stiffness of the structure is reduced. Taking the partial derivative of the local stiffness change rate on both sides of the equation of motion, we can get(2)M∂x¨∂αi+∂M∂αix¨+C∂x˙∂αi+∂C∂αix˙+K∂x∂αi+∂K∂αix˙=∂F∂αi.Among them, the mass matrix isM, and the external load F is independent of the local stiffness change rate. Therefore, its partial derivative to the local stiffness change rate is 0, and (3) can be obtained after arranging (2):(3)M∂x¨∂αi+C∂x˙∂αi+K∂x∂αi=−∂K∂αix−a∂K∂αix˙.Among them,∂x¯/∂αi,∂x˙/∂αi,∂x/∂αi is the sensitivity vector of acceleration, velocity, and displacement, respectively.The form of (3) at this time is exactly the same as that of equation of motion (1), and the sensitivity vectors of acceleration, velocity, and displacement can be solved by the explicit Newmark−β-direct integration method.If it is assumed that the structure hasN units and g is the response of the i-th sensor to be measured, the functional relationship between γi and the local rate of change of all units can be established, as shown in the following formula:(4)γi=fiα1,α2,…,αN.At this time, taking the response of the measuring point as the acceleration, and expanding it according to the multivariate Taylor series, the formula about the acceleration signal can be obtained:(5)Saα+oα2=ΔX¨.Among them,Sa is the total acceleration sensitivity matrix, α is the stiffness change rate vector, and ΔX is the difference between the measured acceleration and the calculated acceleration. Then, the total acceleration sensitivity matrix can be expressed as(6)Sa=Sa1,Sa2…,SaN.When the damage identification (5) is obtained, the multivariate Taylor series method is used, and the second-order and higher-order terms are ignored, there is an error between the stiffness change rate vector α and the real value, and the error needs to be eliminated by an iterative method. After each iteration, the stiffness will be corrected once, and a new stiffness change rate vector α will be obtained. The iteration termination condition is(7)αk+1−αkαk+1<T.Among them,m is a minimum value close to 0, and the final stiffness change rate vector α is obtained by adding the stiffness change rate vectors obtained in each iteration.The correlation coefficient between each column vector of the acceleration sensitivity matrixSa is calculated by the following formula:(8)eai,j=0,i=j,eai,j=saiSajTSaiSaiT⋅|SajSajT,i≠j.By assembling the correlation coefficients, the acceleration correlation coefficient matrixea can be obtained:(9)ea=ea1,1⋯ea1,i⋯ea1,N⋮⋱⋮⋱⋮eai,1⋯eai,i⋯eai,N⋮⋱⋮⋱⋮eaN,1⋯eaN,i⋯eaN,NN×N.There are as many sensor layout schemes as there are acceleration correlation coefficient matricesea. The acceleration arrangement index βa can be obtained by summing all the correlation coefficients in each acceleration correlation coefficient matrix ea. The smaller the acceleration placement index βa is, the smaller the correlation between the column vectors of different elements of the structure is and the better the placement position of the sensor is.(10)βa=∑i=1,j=1Neai,j.


### 3.2. Minimum Ill-Posedness Criterion for Two Types of Sensors

In (3), the displacement sensitivity vector can be solved by the direct integration method of Newmark−β, and then the displacement sensitivity matrix Sd can be solved by the same method. Strain sensitivity and displacement sensitivity are the partial derivatives of strain and displacement with respect to the local rate of stiffness change, respectively. In finite element theory, the strain at a point on the structure can be obtained from the displacement of the nodes at both ends of the element through the transformation matrix. Therefore, the strain sensitivity matrix Sε can also be obtained from the displacement sensitivity matrix Sd, and the calculation formula is as follows:(11)Sε=BRSd.Among them,B is the unit strain transformation matrix, R is the unit rotation axis matrix, and the same strain sensitivity matrix can be divided into N strain sensitivity vectors:(12)Sε=Sε1,Sε2,⋯,SεN.By assembling the obtained acceleration sensitivity matrixSa and strain sensitivity matrix Sε, the dual-signal sensitivity matrix can be obtained. However, the magnitudes of the acceleration sensitivity matrix Sa and the strain sensitivity matrix Sε are inconsistent. If it is directly assembled, it will inevitably cause the calculation information of the smaller order of magnitude to be masked. Therefore, the order of magnitude of the two types of sensitivity matrices can be made consistent with the help of the standardization method. The standardization process is as follows:(13)1X¨cjSajα=1X..cjX..mj−X¨cj⇒Saj∗α=X..mj∗−X..cj∗.In the formula,X..mj is the measured acceleration response at the jth sensor position; X¨cj is the calculated acceleration response at the jth sensor position; X¨mj∗ is the normalized measured acceleration response at the jth sensor position; X¨cj∗ is the normalized calculated acceleration response at the jth sensor placement.(14)Sa∗=Sa11∗⋯Sai1∗⋯SaN1∗⋮⋱⋮⋱⋮Sa1j∗⋯Saij∗⋯SaNj∗⋮⋱⋮⋱⋮Sa1Na∗⋯SaiNa∗⋯SaNNa∗.In the formula,Na is the number of acceleration sensors; Sa∗ is the normalized acceleration sensitivity matrix; N is the number of units of the structure.(15)1εcjSεjα=1εcjεmj−εcj⇒Sεj∗α=εmj∗−εcj∗.In the formula,εmj is the measured strain response at the jth sensor position; εcj is the calculated strain response at the jth sensor position; εmj∗ is the normalized measured strain response at the jth sensor location; εcj∗ is the normalized calculated strain response at the jth deployed sensor location.(16)Sε∗=Sε11∗⋯Sεi1∗⋯SεN1∗⋮⋱⋮⋱⋮Sε1j∗⋯Sεij∗⋯SεNj∗⋮⋱⋮⋱⋮Sε1Nε∗⋯SεiNε∗⋯SεNNε∗.In the formula,Nε is the number of strain sensors; Sε∗ is the normalized strain sensitivity matrix.By assembling the normalized acceleration sensitivity matrixSa∗ and the normalized strain sensitivity matrix Sε∗, the dual-signal sensitivity matrix S∗ can be obtained:(17)S∗=Sa1∗⋯Sai∗⋯SaN∗Sε1∗⋯Sεi∗⋯SεN∗=S1∗⋯Si∗⋯SN∗.By assembling the standardized measured acceleration responseX..m∗, the standardized calculated acceleration response X..c∗, the standardized measured strain response εm∗, and the standardized calculated strain response εc∗ in the same way, the dual-signal damage identification equation can be obtained:(18)S∗α+oα2=Δy∗.Among them,Δy∗ is the difference between the measured response and the calculated response of the dual signal. Similarly, the ill-posedness of the dual-signal damage identification equation is judged by the arrangement index method.The correlation coefficient between each column vector of the dual-signal sensitivity matrixS∗ is calculated by formula (19):(19)ei,j=0,i=j,ei,j=saiSajTSaiSaiT⋅|SajSajT,i≠j,(20)e=e1,1⋯e1,i⋯e1,N⋮⋱⋮⋱⋮ei,1⋯ei,i⋯ei,N⋮⋱⋮⋱⋮eN,1⋯eN,i⋯eN,NN×N.The two-signal arrangement indexe can be obtained by summing all the correlation coefficients in each two-signal correlation coefficient matrix β. The smaller the dual-signal arrangement index β, the smaller the correlation between the column vectors of different elements of the structure, the smaller the ill-posedness of the dual-signal damage identification equation, and the more reasonable the sensor arrangement position.(21)β=∑i=1,j=1Nei,j.The modal guarantee criterion can be used to monitor the magnitude of the angle between two vectors and then evaluate the magnitude of the linear independence between the two vectors. The formula of the modal guarantee criterion is shown in the following formula:(22)MACij=φiTφj2φiTφiφjTφj.The off-diagonal elements in the MAC matrix represent the size of the space angle between the two vectors, that is, the size of the correlation between the two vectors.MACij is an element in the modal guarantee matrix, and the value of MACij have magnitudes between 0 and 1. When MACij is equal to 1, it means that the angle between the two vectors is 0, and the two vectors are completely related. When MACij is equal to 0, it means that the two vectors are orthogonal to each other, and the vectors are independent of each other. Among them, φi,φj denotes a vector of order i and order j.The traditional monkey swarm algorithm is introduced first, and then an improved monkey swarm algorithm is proposed.Algorithm parameters: population size, climbing step length, viewing field width, jumping interval length, number of climbing, looking, and jumping processes, number of iterative cycles, and dimension of the solution problem.Algorithm termination condition:(1)
The algorithm reaches the specified number of iterations.(2)
The optimal solution of the fitness function value reaches a certain limit range.(3)
After the specified number of consecutive iterations, the optimal solution of the fitness function value does not change.The monkey swarm algorithm defines the feasible region of the optimization problem as the overall activity range of the monkey swarm. The specific search process is as follows.


#### 3.2.1. Climbing Process

Each monkey searches in a small local area of its own location, and if it finds a better location, it moves to the better location until it reaches the specified number of climbs. The position of each monkey isxi=xi1,xi2,…xig, where g is the number of elements each monkey contains. The climbing step length is p, and the column vector dxi=dxi1,dxi2,…,dxig is generated in a random manner. The generation rule is shown in the following formula:(23)dxij=p,Probability is0.5−p,Probability is0.5,j=1,2,…,g.Each monkey moves according to the pseudogradient direction at its own position to reach the next positionyi. If yi exceeds the value range of the monkey group, yi takes the boundary value, and the objective function value at yi is compared. If the objective function value at yi is better, then yi is replaced by xi; otherwise, climbing is not performed. The above process is repeated until the specified number of climbs is reached, or the value of the objective function basically does not change. The pseudogradient calculation formula is shown in(24)fij′xi=fxi+dxi−fxi−dxi2dxij.The position reached along the pseudogradient isyi=yi1,yi2,…,yig, and the calculation formula of yi is shown in (25)yj=xij+p⋅signfij′xi.


#### 3.2.2. Looking Process

After the climbing process, the monkeys stood on their local highest peaks and looked around to see if there were higher peaks. If there is, it jumps to the higher peak; otherwise it does not move on the original peak. We set the visual field width to bes, which is the furthest distance the monkey can observe at its own position. At this time, the position of each monkey is xi=xi1,xi2,…,xig, and the position of the foothold of the field of vision is yi=yi1,yi2,…,yig, where the calculation formula of r is shown in (26)yix=rand0,1×xix−s,xix+s.Ifyi exceeds the value range of the monkey group, then yi takes the boundary value. The objective function value at yi is computed. If the objective function value at yi is better, then xi is replaced by yi; otherwise, the position remains unchanged. The above process is repeated until the desired number of times is reached, or the value of the objective function basically does not change.


#### 3.2.3. Jump Process

After the monkey finds the local optimal solution, it goes to find the global optimal solution. It uses a certain position as a support point, jumps at a certain distance, reaches a new area, realizes the escape behavior, and then continues the process of climbing, looking, and jumping in the new area. The length of the jump interval is [b, c], and the length of the flip radius f is any value in the jump interval [b, c]. The calculation formula is shown in(27)f=rand0,1×b,c.The support point is the center of gravityP=p1,p2,…,pg of the monkey group, the population size is N, and the calculation formula of the position of the center of gravity is shown in (28)pj=1N∑i=1Nxij,j=1,2,…,g.The new position after the jump isyi=yi1,yi2,…,yig, and the calculation formula is shown in (29)yij=xij+fpj−xij.Ifyi exceeds the value range of the monkey group, yi takes the boundary value. The objective function value at yi is calculated; if the objective function value at yi is better, xi is replaced with yi; otherwise, the monkey does not jump. The above process is repeated until the specified number of hops is reached, or the value of the objective function basically does not change.The traditional monkey swarm algorithm has three detailed processes of climbing, looking, and jumping, and the specific process of the traditional monkey swarm algorithm can be obtained as shown in Figure1.Figure 1
Flow chart of traditional monkey swarm algorithm.


#### 3.2.4. Accumulation Rule of Sensor Layout

The study found that there is an accumulation rule for the sensor layout scheme, that is, the layout scheme ofn + 1 sensors; in order to search on the basis of the original n sensor layout schemes, the n sensor layout schemes are a subset of n + 1 sensor layout schemes. For example, the optimal layout plan for 2 sensors is {5, 8}, the optimal solution for 3 sensors is {5, 8, 10}, the optimal solution for 4 sensors is {5, 8, 10, 12}, and so on. This accumulation law can effectively overcome the shortcomings of the traditional optimal arrangement of sensors, which greatly increases the calculation time with the increase of the number of sensors. The accumulation law is combined with the traditional monkey group algorithm, which is the cumulative monkey group algorithm. It can significantly improve the computational efficiency of determining the optimal arrangement of sensors of different numbers.


## 3.1. Minimum Ill-Posedness Criterion for a Single Type of Sensor

Any multi-degree-of-freedom linear elastic finite element equation of motion can be expressed by the following formula:(1)Mx¨+Cx˙+Kx=Ft.Among them,M is the mass matrix, C is the damping matrix, and the Rayleigh damping model is used. K is the stiffness matrix, Ft is the external load, and x¨ is the acceleration response.When a structure is damaged, stiffness usually decreases.αi is the local stiffness change rate of the i-th element of the structure, −1≤αi≤0. When αi=−1, it means that the structural stiffness at this time is 0; that is, complete damage has occurred. When αi=0, it means that the stiffness of the structure has not changed. When −1<αi<0, it means that the structure has been damaged to a certain extent, and the stiffness of the structure is reduced. Taking the partial derivative of the local stiffness change rate on both sides of the equation of motion, we can get(2)M∂x¨∂αi+∂M∂αix¨+C∂x˙∂αi+∂C∂αix˙+K∂x∂αi+∂K∂αix˙=∂F∂αi.Among them, the mass matrix isM, and the external load F is independent of the local stiffness change rate. Therefore, its partial derivative to the local stiffness change rate is 0, and (3) can be obtained after arranging (2):(3)M∂x¨∂αi+C∂x˙∂αi+K∂x∂αi=−∂K∂αix−a∂K∂αix˙.Among them,∂x¯/∂αi,∂x˙/∂αi,∂x/∂αi is the sensitivity vector of acceleration, velocity, and displacement, respectively.The form of (3) at this time is exactly the same as that of equation of motion (1), and the sensitivity vectors of acceleration, velocity, and displacement can be solved by the explicit Newmark−β-direct integration method.If it is assumed that the structure hasN units and g is the response of the i-th sensor to be measured, the functional relationship between γi and the local rate of change of all units can be established, as shown in the following formula:(4)γi=fiα1,α2,…,αN.At this time, taking the response of the measuring point as the acceleration, and expanding it according to the multivariate Taylor series, the formula about the acceleration signal can be obtained:(5)Saα+oα2=ΔX¨.Among them,Sa is the total acceleration sensitivity matrix, α is the stiffness change rate vector, and ΔX is the difference between the measured acceleration and the calculated acceleration. Then, the total acceleration sensitivity matrix can be expressed as(6)Sa=Sa1,Sa2…,SaN.When the damage identification (5) is obtained, the multivariate Taylor series method is used, and the second-order and higher-order terms are ignored, there is an error between the stiffness change rate vector α and the real value, and the error needs to be eliminated by an iterative method. After each iteration, the stiffness will be corrected once, and a new stiffness change rate vector α will be obtained. The iteration termination condition is(7)αk+1−αkαk+1<T.Among them,m is a minimum value close to 0, and the final stiffness change rate vector α is obtained by adding the stiffness change rate vectors obtained in each iteration.The correlation coefficient between each column vector of the acceleration sensitivity matrixSa is calculated by the following formula:(8)eai,j=0,i=j,eai,j=saiSajTSaiSaiT⋅|SajSajT,i≠j.By assembling the correlation coefficients, the acceleration correlation coefficient matrixea can be obtained:(9)ea=ea1,1⋯ea1,i⋯ea1,N⋮⋱⋮⋱⋮eai,1⋯eai,i⋯eai,N⋮⋱⋮⋱⋮eaN,1⋯eaN,i⋯eaN,NN×N.There are as many sensor layout schemes as there are acceleration correlation coefficient matricesea. The acceleration arrangement index βa can be obtained by summing all the correlation coefficients in each acceleration correlation coefficient matrix ea. The smaller the acceleration placement index βa is, the smaller the correlation between the column vectors of different elements of the structure is and the better the placement position of the sensor is.(10)βa=∑i=1,j=1Neai,j.


## 3.2. Minimum Ill-Posedness Criterion for Two Types of Sensors

In (3), the displacement sensitivity vector can be solved by the direct integration method of Newmark−β, and then the displacement sensitivity matrix Sd can be solved by the same method. Strain sensitivity and displacement sensitivity are the partial derivatives of strain and displacement with respect to the local rate of stiffness change, respectively. In finite element theory, the strain at a point on the structure can be obtained from the displacement of the nodes at both ends of the element through the transformation matrix. Therefore, the strain sensitivity matrix Sε can also be obtained from the displacement sensitivity matrix Sd, and the calculation formula is as follows:(11)Sε=BRSd.Among them,B is the unit strain transformation matrix, R is the unit rotation axis matrix, and the same strain sensitivity matrix can be divided into N strain sensitivity vectors:(12)Sε=Sε1,Sε2,⋯,SεN.By assembling the obtained acceleration sensitivity matrixSa and strain sensitivity matrix Sε, the dual-signal sensitivity matrix can be obtained. However, the magnitudes of the acceleration sensitivity matrix Sa and the strain sensitivity matrix Sε are inconsistent. If it is directly assembled, it will inevitably cause the calculation information of the smaller order of magnitude to be masked. Therefore, the order of magnitude of the two types of sensitivity matrices can be made consistent with the help of the standardization method. The standardization process is as follows:(13)1X¨cjSajα=1X..cjX..mj−X¨cj⇒Saj∗α=X..mj∗−X..cj∗.In the formula,X..mj is the measured acceleration response at the jth sensor position; X¨cj is the calculated acceleration response at the jth sensor position; X¨mj∗ is the normalized measured acceleration response at the jth sensor position; X¨cj∗ is the normalized calculated acceleration response at the jth sensor placement.(14)Sa∗=Sa11∗⋯Sai1∗⋯SaN1∗⋮⋱⋮⋱⋮Sa1j∗⋯Saij∗⋯SaNj∗⋮⋱⋮⋱⋮Sa1Na∗⋯SaiNa∗⋯SaNNa∗.In the formula,Na is the number of acceleration sensors; Sa∗ is the normalized acceleration sensitivity matrix; N is the number of units of the structure.(15)1εcjSεjα=1εcjεmj−εcj⇒Sεj∗α=εmj∗−εcj∗.In the formula,εmj is the measured strain response at the jth sensor position; εcj is the calculated strain response at the jth sensor position; εmj∗ is the normalized measured strain response at the jth sensor location; εcj∗ is the normalized calculated strain response at the jth deployed sensor location.(16)Sε∗=Sε11∗⋯Sεi1∗⋯SεN1∗⋮⋱⋮⋱⋮Sε1j∗⋯Sεij∗⋯SεNj∗⋮⋱⋮⋱⋮Sε1Nε∗⋯SεiNε∗⋯SεNNε∗.In the formula,Nε is the number of strain sensors; Sε∗ is the normalized strain sensitivity matrix.By assembling the normalized acceleration sensitivity matrixSa∗ and the normalized strain sensitivity matrix Sε∗, the dual-signal sensitivity matrix S∗ can be obtained:(17)S∗=Sa1∗⋯Sai∗⋯SaN∗Sε1∗⋯Sεi∗⋯SεN∗=S1∗⋯Si∗⋯SN∗.By assembling the standardized measured acceleration responseX..m∗, the standardized calculated acceleration response X..c∗, the standardized measured strain response εm∗, and the standardized calculated strain response εc∗ in the same way, the dual-signal damage identification equation can be obtained:(18)S∗α+oα2=Δy∗.Among them,Δy∗ is the difference between the measured response and the calculated response of the dual signal. Similarly, the ill-posedness of the dual-signal damage identification equation is judged by the arrangement index method.The correlation coefficient between each column vector of the dual-signal sensitivity matrixS∗ is calculated by formula (19):(19)ei,j=0,i=j,ei,j=saiSajTSaiSaiT⋅|SajSajT,i≠j,(20)e=e1,1⋯e1,i⋯e1,N⋮⋱⋮⋱⋮ei,1⋯ei,i⋯ei,N⋮⋱⋮⋱⋮eN,1⋯eN,i⋯eN,NN×N.The two-signal arrangement indexe can be obtained by summing all the correlation coefficients in each two-signal correlation coefficient matrix β. The smaller the dual-signal arrangement index β, the smaller the correlation between the column vectors of different elements of the structure, the smaller the ill-posedness of the dual-signal damage identification equation, and the more reasonable the sensor arrangement position.(21)β=∑i=1,j=1Nei,j.The modal guarantee criterion can be used to monitor the magnitude of the angle between two vectors and then evaluate the magnitude of the linear independence between the two vectors. The formula of the modal guarantee criterion is shown in the following formula:(22)MACij=φiTφj2φiTφiφjTφj.The off-diagonal elements in the MAC matrix represent the size of the space angle between the two vectors, that is, the size of the correlation between the two vectors.MACij is an element in the modal guarantee matrix, and the value of MACij have magnitudes between 0 and 1. When MACij is equal to 1, it means that the angle between the two vectors is 0, and the two vectors are completely related. When MACij is equal to 0, it means that the two vectors are orthogonal to each other, and the vectors are independent of each other. Among them, φi,φj denotes a vector of order i and order j.The traditional monkey swarm algorithm is introduced first, and then an improved monkey swarm algorithm is proposed.Algorithm parameters: population size, climbing step length, viewing field width, jumping interval length, number of climbing, looking, and jumping processes, number of iterative cycles, and dimension of the solution problem.Algorithm termination condition:(1)
The algorithm reaches the specified number of iterations.(2)
The optimal solution of the fitness function value reaches a certain limit range.(3)
After the specified number of consecutive iterations, the optimal solution of the fitness function value does not change.The monkey swarm algorithm defines the feasible region of the optimization problem as the overall activity range of the monkey swarm. The specific search process is as follows.


### 3.2.1. Climbing Process

Each monkey searches in a small local area of its own location, and if it finds a better location, it moves to the better location until it reaches the specified number of climbs. The position of each monkey isxi=xi1,xi2,…xig, where g is the number of elements each monkey contains. The climbing step length is p, and the column vector dxi=dxi1,dxi2,…,dxig is generated in a random manner. The generation rule is shown in the following formula:(23)dxij=p,Probability is0.5−p,Probability is0.5,j=1,2,…,g.Each monkey moves according to the pseudogradient direction at its own position to reach the next positionyi. If yi exceeds the value range of the monkey group, yi takes the boundary value, and the objective function value at yi is compared. If the objective function value at yi is better, then yi is replaced by xi; otherwise, climbing is not performed. The above process is repeated until the specified number of climbs is reached, or the value of the objective function basically does not change. The pseudogradient calculation formula is shown in(24)fij′xi=fxi+dxi−fxi−dxi2dxij.The position reached along the pseudogradient isyi=yi1,yi2,…,yig, and the calculation formula of yi is shown in (25)yj=xij+p⋅signfij′xi.


### 3.2.2. Looking Process

After the climbing process, the monkeys stood on their local highest peaks and looked around to see if there were higher peaks. If there is, it jumps to the higher peak; otherwise it does not move on the original peak. We set the visual field width to bes, which is the furthest distance the monkey can observe at its own position. At this time, the position of each monkey is xi=xi1,xi2,…,xig, and the position of the foothold of the field of vision is yi=yi1,yi2,…,yig, where the calculation formula of r is shown in (26)yix=rand0,1×xix−s,xix+s.Ifyi exceeds the value range of the monkey group, then yi takes the boundary value. The objective function value at yi is computed. If the objective function value at yi is better, then xi is replaced by yi; otherwise, the position remains unchanged. The above process is repeated until the desired number of times is reached, or the value of the objective function basically does not change.


### 3.2.3. Jump Process

After the monkey finds the local optimal solution, it goes to find the global optimal solution. It uses a certain position as a support point, jumps at a certain distance, reaches a new area, realizes the escape behavior, and then continues the process of climbing, looking, and jumping in the new area. The length of the jump interval is [b, c], and the length of the flip radius f is any value in the jump interval [b, c]. The calculation formula is shown in(27)f=rand0,1×b,c.The support point is the center of gravityP=p1,p2,…,pg of the monkey group, the population size is N, and the calculation formula of the position of the center of gravity is shown in (28)pj=1N∑i=1Nxij,j=1,2,…,g.The new position after the jump isyi=yi1,yi2,…,yig, and the calculation formula is shown in (29)yij=xij+fpj−xij.Ifyi exceeds the value range of the monkey group, yi takes the boundary value. The objective function value at yi is calculated; if the objective function value at yi is better, xi is replaced with yi; otherwise, the monkey does not jump. The above process is repeated until the specified number of hops is reached, or the value of the objective function basically does not change.The traditional monkey swarm algorithm has three detailed processes of climbing, looking, and jumping, and the specific process of the traditional monkey swarm algorithm can be obtained as shown in Figure1.Figure 1
Flow chart of traditional monkey swarm algorithm.


### 3.2.4. Accumulation Rule of Sensor Layout

The study found that there is an accumulation rule for the sensor layout scheme, that is, the layout scheme ofn + 1 sensors; in order to search on the basis of the original n sensor layout schemes, the n sensor layout schemes are a subset of n + 1 sensor layout schemes. For example, the optimal layout plan for 2 sensors is {5, 8}, the optimal solution for 3 sensors is {5, 8, 10}, the optimal solution for 4 sensors is {5, 8, 10, 12}, and so on. This accumulation law can effectively overcome the shortcomings of the traditional optimal arrangement of sensors, which greatly increases the calculation time with the increase of the number of sensors. The accumulation law is combined with the traditional monkey group algorithm, which is the cumulative monkey group algorithm. It can significantly improve the computational efficiency of determining the optimal arrangement of sensors of different numbers.


## 3.2.1. Climbing Process

Each monkey searches in a small local area of its own location, and if it finds a better location, it moves to the better location until it reaches the specified number of climbs. The position of each monkey isxi=xi1,xi2,…xig, where g is the number of elements each monkey contains. The climbing step length is p, and the column vector dxi=dxi1,dxi2,…,dxig is generated in a random manner. The generation rule is shown in the following formula:(23)dxij=p,Probability is0.5−p,Probability is0.5,j=1,2,…,g.Each monkey moves according to the pseudogradient direction at its own position to reach the next positionyi. If yi exceeds the value range of the monkey group, yi takes the boundary value, and the objective function value at yi is compared. If the objective function value at yi is better, then yi is replaced by xi; otherwise, climbing is not performed. The above process is repeated until the specified number of climbs is reached, or the value of the objective function basically does not change. The pseudogradient calculation formula is shown in(24)fij′xi=fxi+dxi−fxi−dxi2dxij.The position reached along the pseudogradient isyi=yi1,yi2,…,yig, and the calculation formula of yi is shown in (25)yj=xij+p⋅signfij′xi.


## 3.2.2. Looking Process

After the climbing process, the monkeys stood on their local highest peaks and looked around to see if there were higher peaks. If there is, it jumps to the higher peak; otherwise it does not move on the original peak. We set the visual field width to bes, which is the furthest distance the monkey can observe at its own position. At this time, the position of each monkey is xi=xi1,xi2,…,xig, and the position of the foothold of the field of vision is yi=yi1,yi2,…,yig, where the calculation formula of r is shown in (26)yix=rand0,1×xix−s,xix+s.Ifyi exceeds the value range of the monkey group, then yi takes the boundary value. The objective function value at yi is computed. If the objective function value at yi is better, then xi is replaced by yi; otherwise, the position remains unchanged. The above process is repeated until the desired number of times is reached, or the value of the objective function basically does not change.


## 3.2.3. Jump Process

After the monkey finds the local optimal solution, it goes to find the global optimal solution. It uses a certain position as a support point, jumps at a certain distance, reaches a new area, realizes the escape behavior, and then continues the process of climbing, looking, and jumping in the new area. The length of the jump interval is [b, c], and the length of the flip radius f is any value in the jump interval [b, c]. The calculation formula is shown in(27)f=rand0,1×b,c.The support point is the center of gravityP=p1,p2,…,pg of the monkey group, the population size is N, and the calculation formula of the position of the center of gravity is shown in (28)pj=1N∑i=1Nxij,j=1,2,…,g.The new position after the jump isyi=yi1,yi2,…,yig, and the calculation formula is shown in (29)yij=xij+fpj−xij.Ifyi exceeds the value range of the monkey group, yi takes the boundary value. The objective function value at yi is calculated; if the objective function value at yi is better, xi is replaced with yi; otherwise, the monkey does not jump. The above process is repeated until the specified number of hops is reached, or the value of the objective function basically does not change.The traditional monkey swarm algorithm has three detailed processes of climbing, looking, and jumping, and the specific process of the traditional monkey swarm algorithm can be obtained as shown in Figure1.Figure 1
Flow chart of traditional monkey swarm algorithm.


## 3.2.4. Accumulation Rule of Sensor Layout

The study found that there is an accumulation rule for the sensor layout scheme, that is, the layout scheme ofn + 1 sensors; in order to search on the basis of the original n sensor layout schemes, the n sensor layout schemes are a subset of n + 1 sensor layout schemes. For example, the optimal layout plan for 2 sensors is {5, 8}, the optimal solution for 3 sensors is {5, 8, 10}, the optimal solution for 4 sensors is {5, 8, 10, 12}, and so on. This accumulation law can effectively overcome the shortcomings of the traditional optimal arrangement of sensors, which greatly increases the calculation time with the increase of the number of sensors. The accumulation law is combined with the traditional monkey group algorithm, which is the cumulative monkey group algorithm. It can significantly improve the computational efficiency of determining the optimal arrangement of sensors of different numbers.


## 4. Research on the Development Path and Economic Effect of Manufacturing Industry Based on Computer Visualization

The modeling in this paper has the following points: upper-level ontology establishment, relational schema extraction, schema mapping, and data transformation, as shown in Figure2.Figure 2
Semantic modeling flowchart.Based on the semantic model, this paper establishes a visualization platform to visualize the semantic model established above and, at the same time, browse the instance data of the semantic model. On the one hand, it is convenient for users to view the semantic model to further improve the modeling. On the other hand, as a prototype system of data management system, it provides data browsing and data query, which provides strong support for cross-platform data integration and cross-enterprise data sharing. The platform adopts B/S mode and J2EE technology development framework, and its structure is shown in Figure3.Figure 3
Visualization system architecture diagram.The visual simulation platform is designed in the form of a browser/server (B/S) structure and consists of three parts: the interface layer, the compilation and interpretation layer, and the control layer, as shown in Figure4.Figure 4
System structure of the simulation platform.The overall structure of the integrated monitoring and management system platform is shown in Figure5.Figure 5
Architecture design of monitoring management platform.Different monitoring platforms correspond to different 3D scene files and only need to replace the corresponding scene files. After the program is packaged, a page link is added to the main page of the monitoring platform. As long as the user clicks on the page, the browser will jump to the 3D visualization platform page. The data analysis and processing of the 3D visual alarm system is shown in Figure6.Figure 6
System data analysis and processing.It is also possible to introduce RFID technology to realize the physical structure of the actual collection of data, as shown in Figure7:Figure 7
Physical architecture diagram of RFID data acquisition system.The mapping relationship of the ontology extracted from the relational database can be determined, as shown in Figure8.Figure 8
Mapping relationship from relational database to ontology.On the basis of the above research, this paper analyzes the development path of the manufacturing industry based on computer visualization and its economic effect, counts the research effect of the model in this paper, and obtains the model effect evaluation results shown in Table1 and Figure 9.Table 1
Model evaluation data.
NumberModel effectNumberModel effectNumberModel effect184.682686.855189.28286.482780.125282.44382.782881.785382.60485.472984.705482.20585.263088.175581.49688.643189.915688.40785.213288.705779.07884.153385.445879.78979.643485.455985.851085.603583.156079.341181.903681.796183.841289.473780.146279.201380.043885.816379.061483.683979.146479.841579.994085.666588.101681.364183.256682.551784.234289.686783.211882.654389.076882.661987.414484.226980.332079.624584.297090.502187.604679.397180.162281.324787.027289.952390.084882.727389.362479.804989.777487.362585.365086.667585.32Figure 9
Statistical results of model evaluation.From the above research, it can be seen that the research model of the manufacturing development path and its economic effects based on computational visualization proposed in this paper has certain practical effects.From the perspective of the enterprise, the level of cost management directly affects the performance of the enterprise, which in turn affects the level of service-oriented development. Therefore, enterprises should strive to improve the management level of cost control and cost optimization and continuously optimize their capital structure according to market changes, so as to serve the manufacturing industry and provide a good development environment. In addition, it is necessary to improve the internal governance mechanism of the enterprise and properly solve the problems of talents and funds in the process of servitization. From the government’s point of view, first, the government should provide an environment for integrated development of manufacturing services and support corresponding development strategies. In terms of investment and financing environment, tax environment, and policy environment, it will facilitate the manufacturing service-oriented development. At the same time, efforts will be made to build a manufacturing service-oriented demonstration zone, build an information platform for manufacturing service-oriented development, and conduct a nationwide strategy from the level of manufacturing development strategy and regional strategic planning. Second, the government should further improve the regulatory policy system for the servitization of the manufacturing industry and strive to promote the transformation and upgrading of the manufacturing industry to high-end servitization. In terms of policy regulation, the government should carry out the top-level design of the servitization of the manufacturing industry, create a series of supporting frameworks for the selection of the servitization direction of the manufacturing industry, formulate models and optimize development, and promote the upgrading of the servitization of the manufacturing industry. From a social point of view, it should be committed to cultivating manufacturing service-oriented talents with professional service level. The healthy development of manufacturing servitization is inseparable from professional service talents. All walks of life, especially various intermediary training institutions and human resource management institutions, should consciously cultivate specialized talents for manufacturing servitization, so as to provide services for the process of manufacturing servitization—the right talent team.


## 5. Conclusion

At present, China’s labor-intensive manufacturing industry accounts for a large proportion. With the gradual deepening of economic globalization and the increasingly refined international division of labor, the development of international division of labor has been refined from the division of labor between industries to the division of labor for different production processes on the same product. At the same time, countries around the world are actively integrating into the global value chain to make efforts to realize the value-added of different production links in the value chain. For many years, China’s manufacturing industry has mainly undertaken the transfer of low-end links in the value chain of developed countries and carried out production processes such as processing and assembly with low technical content. This paper combines computer visualization technology to analyze the development path of manufacturing industry and its economic effects. The experimental research results show that the research model of the manufacturing development path and its economic effects based on computational visualization proposed in this paper has certain practical effects.



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*Source: 1762561-2022-05-17.xml*