A real-time identification and mitigation solution generation method of random disturbance in a manufacturing system

Abstract

In order to timely identify and mitigate the adverse effect of the random disturbance in the manufacturing system, a method of identifying and mitigating the random disturbance is proposed. In the method, the disturbance is structured into several categories, and each is subdivided into several events. The disturbance data detected by the hardware system are normalized to 10 scales for more accurate monitoring. An evaluation model is built and it has a bi-layer criteria system, which can evaluate every category disturbance and the whole system at the same time. The fuzzy analytic hierarchy process is utilized to calculate the criteria weights and evaluate the impacts of the disturbance. Time and cost used as constraints are combined into the adjustment solution. The BP neural network is used to generate adjustment solution for the disturbance, and then the resource and task scheduler are adjusted to mitigate the loss caused by the disturbance. Finally, the proposed method is illustrated by an example, and the validity of the method is verified.

Keywords

Manufacturing system disturbance BP neural network fuzzy analytic hierarchy process

Introduction

Disturbance in the manufacturing system

In the complex manufacturing system, there are various kinds of disturbances, such as order change, insufficient supply of raw materials, delay or shortage of goods, change in the production process, change of equipment status and quantity, and so on. These disturbances often result in the failure of the production plan.¹ Therefore, it is very important to study the disturbance and the real-time identifying and mitigating method.

Balasubram² defined random disturbance as a lack of accurate knowledge or prediction of a process. Zhu³ deemed that the random disturbance is caused by inaccurate information, unknown information, inherent model, subjective judgment, and so on. Wu⁴ deemed that the disturbance randomness rooted in manufacturing resources and the external environment. Liu et al.⁵ divided disturbances into the task disturbance, production process disturbance, material resource disturbance, and production executive disturbance. The above-described method of random disturbance mainly includes probability distribution description, fuzzy mathematical description, interval description, and discrete value description.⁶ On this basis, Bokrantz et al.⁷ proposed 21 production disturbance factors.

Related research

In recent years, the identifying method of disturbance has been studied. Li et al.⁸ studied the operating status identifying system of the digital production workshop. Chang et al.⁹ established a workshop production process monitoring system and developed the related software and hardware. Liu et al.¹⁰ constructed a production information monitoring model. Sun et al.¹¹ communicated programmable logic controller (PLC) with Ethernet to collect production site data and developed control software. Li et al.¹² designed a real-time monitoring system to monitor and respond quickly to the manufacturing workshop. The above systems mainly focus on the data collection and disturbance alarm of the manufacturing system.

For mitigating the adverse effect of the disturbance, some models or methods are introduced. Roy et al.¹³ developed a knowledge model for managing disturbances in steel-making. Li and Shan¹⁴ established a disturbance response model based on binary information for quantitatively evaluating solutions and realizing adjustment quickly. Leng et al.¹⁵ proposed a contextual self-organizing method for disturbance recognition and response. Felea et al.¹⁶ proposed a decision support model for production disturbance estimation in manufacturing systems, which can implement a dynamic evaluation of some disturbances. Abdelhamied et al.¹⁷ introduced an agent-based method to automatically deal with different disturbances in flexible manufacturing systems. Abid et al.¹⁸ proposed a method to model the sources of disturbance and its management in manufacturing systems. McLean et al.¹⁹ proposed a decision-making system based on an artificial neural network, which can mitigate the manufacturing disturbance in reconfigurable systems.

Most of the above research assume that the factors causing the disturbance are known in advance, such as orders, equipment, other production resources, and so on. The developed system or proposed methods rely on precise task, environmental information, and mathematical model. Therefore, a method for real-time identification of random disturbances and generation of mitigation methods is proposed in this article.

In the proposed method, first the status information of the manufacturing system is monitored and the disturbance is identified timely. Second, the adverse effect of the disturbance is evaluated timely by the evaluation system based on the evaluation model and fuzzy analytic hierarchy process (FAHP). Third, for the disturbance that exceeds the threshold, the adjustment solutions will be generated automatically. The detailed steps are described in the following paragraphs.

Identification of disturbance

The random disturbances of the manufacturing system are structured into several categories, and each is used as evaluation criteria and described by $A t_{1}, A t_{2}, \dots, A t_{m}$ . Each category of disturbance includes $n$ events, so each disturbance is described by the vector as follows

A t_{i} = [A t_{i 1}, A t_{i 2}, \dots, A t_{i j}, \dots, A t_{i n}], i = 1, 2, \dots, m

(1)

The normal value of detected items is in a database, and it is described as follows

v'_{i} = [v'_{i 1}, v'_{i 2}, \dots, v'_{ij}, \dots, v'_{in}], i = 1, 2, \dots, m

(2)

where $v'_{i}$ is the normal value vector, $v'_{i 1} \dots v'_{in}$ are the values of the criteria, and they are between 0 and 1.

The monitoring data detected and collected by the hardware monitoring system real-timely are normalized into values of 10 scales between 0 and 1. They are described as

v_{i} = [v_{i 1}, v_{i 2}, \dots, v_{ij}, \dots, v_{in}], i = 1, 2, \dots, m

(3)

where $v_{i}$ is the monitoring value vector, $v_{i 1} \dots v_{in}$ are the monitoring values, which between 0 and 1.

Detected values will be matched with the data in the database, and the disturbance is generated if there is a difference, as shown in Figure 1.

Figure 1.

Identification of the disturbance.

Evaluation of the adverse effect

First, an evaluation model is constructed, and second the FAHP is utilized to calculate the weight of each criterion and its event. Third, the evaluation value of each criterion is obtained by multiplying and adding the events’ value and the events’ weight. Finally, the evaluation index of the manufacturing system is calculated by multiplying and adding the criteria’s values and its weight.

Evaluation model

An example of the evaluation model is shown in Figure 2. There are five criteria, such as planning task, material resource, manufacturing process, manufacturing resource, and personnel change.

Figure 2.

Evaluation model.

In Figure 2, the criteria are described by a vector shown as follows

At = [A t_{IT}, A t_{IR}, A t_{IP}, A t_{IM}, A t_{IW}]

(4)

Each criterion includes several events, which are shown as follows

A t_{IT} = [A t_{IT 1}, A t_{IT 2}, A t_{IT 3}, A t_{IT 4}, A t_{IT 5}]

(5)

A t_{IR} = [A t_{IR 1}, A t_{IR 2}, A t_{IR 3}, A t_{IR 4}]

(6)

A t_{IP} = [A t_{IP 1}, A t_{IP 2}, A t_{IP 3}]

(7)

A t_{IM} = [A t_{IM 1}, A t_{IM 2}, A t_{IM 3}, A t_{IM 4}, A t_{IM 5}]

(8)

A t_{IW} = [A t_{IW 1}, A t_{IW 2}, A t_{IW 3}]

(9)

Calculation of the weight

The theory of fuzzy mathematics is applied to the analytic hierarchy process, so it can be used as a basis for evaluation and decision-making through quantitative analysis.¹⁶ For the complementary fuzzy judgment matrix $A = (a_{ij})_{n \times n}$ , the matrix $\bar{A} = ({\bar{a}}_{ij})_{n \times n}$ is called the synthesis matrix of the matrix $A$ . It is calculated by $\bar{A} = λ_{1} A_{1} \oplus λ_{2} A_{2} \oplus \dots \oplus λ_{s} A_{s}$ . $r_{i} = \sum_{k = 1}^{n} a_{ik}, (i = 1, 2, \dots, n)$ is used to calculate the sum of each row in the matrix $\bar{A} = ({\bar{a}}_{ij})_{n \times n}$ , and according to the equation $r_{ij} = ((r_{i} - r_{j}) / 2 (n - 1)) + 0.5$ , then get consistent fuzzy matrix $R = (r_{ij})_{n \times n}$ . Finally, the unit eigenvectors of this consistent fuzzy matrix are obtained by the normalizing rank aggregation (NRA), and it is calculated by $ω_{i} = ((\sum_{j = 1}^{n} a_{ij} + (n / 2) - 1) / (n (n - 1))), i = 1, 2, \dots, n$ . Then the sorted vector is a weight vector.

Calculation of the evaluation value of each criterion

The evaluation value of each criterion is described by $f_{i}$ calculated by the following equation

f_{i} = | A t_{i} | \cdot ω_{Bi} = \sum_{j = 1}^{n} | A t_{ij} | \times ω_{Bij}, i \in [1, 2, \dots, m]

(10)

where $f_{i}$ indicates the index of the $i$ criterion. $ω_{Bij}$ is the weight of each event of the $i$ criterion. $m$ is the quantity of evaluation criteria.

Calculation of the evaluation index of the whole manufacturing system

The weight vector of criteria is expressed as

ω_{A} = [ω_{1}, \dots, ω_{i}, \dots, ω_{m}]^{T}

(11)

where $\sum_{i = 1}^{m} ω_{i} = 1$ , $ω_{i}$ is the weight of $i$ criterion.

$f = (f_{1}, f_{2}, \dots, f_{m})$ is defined to describe the evaluation index vector. The index $E_{T}$ is the evaluation value of the whole system, which is calculated by the following equation

E_{T} = f \cdot ω_{A} = \sum_{i = 1}^{m} f_{i} \times ω_{i}

(12)

The smaller the value of $E_{T}$ , the smaller the disturbance. The greater its value, the greater the damage of the system.

Generation of mitigation solution based on BP neural network

Adjustment method of the disturbance

When the disturbance emerges, one or more methods are selected as adjustment methods to mitigate the impact of disturbance. Different methods are developed according to the experience of experts. Some methods are presented in Table 1.

Table 1.

Adjustment methods for the disturbance.

Methods	Description
1	Replace the current manufacturing unit
2	Replace the original processing technology by one or more techniques
3	Increase production capacity
4	Change the priority of production tasks
5	Add the equipment or outsource
6	Urgently purchase some raw materials
7	Train the staff
8	Assign some workers to work overtime or temporarily replacement

Different disturbance has different adverse effects on the system, and has different mitigating methods. Some disturbance events and mitigation methods are shown in Table 2.

Table 2.

Disturbance events and adjustment methods.

Disturbance events	Impact of disturbance	High priority methods	Low priority methods
Emergency order	Task conflict for the manufacturing unit	4	3
Order cancel	A manufacturing unit is hided	4	1
Order in advance	Task conflict or manufacturing unit is hided	4	3
Order delay	A manufacturing unit is hided	4	1
Order priority changes	Task conflict or disorder of the manufacturing unit	4	2
Raw material shortage	Production delay or failure	6	7
Outsourcing component shortage	Production delay or failure	6	7
Auxiliary material shortage	Production delay or failure	6	7
Material disqualification	Production delay or failure	6	7
Process sequence change	New logistics path emerged	4	1
Process reduction	Original logistics path disappearance	4	2
Process increase	New logistics path emerged	4	1
Device fault	Production task is aborted or delayed	4	2
Device repair	Production task is aborted or delayed	4	1
Device increase	New logistics path emerged	4	1
Device reduction	Task conflict or abort	2	1
Tooling time delay	Production delay	4	1
Operators absenteeism	Production task is aborted or delayed	1	8
Operation error	Production delay	4	7
Operators’ skill level is poor	Production delay	4	7

Definition of mitigation solution

There is more than one method to mitigate a disturbance, and one method may have an effect on more than one disturbance. In order to select the appropriate solution for each disturbance, there are two constraints used to select a method, and they are time and cost. The time or cost of the same method may differ for different workshops. By adjusting time and cost, we have more flexibility in choosing methods. Therefore, time and cost are integrated with two alternative approaches to constitute a solution for one category of disturbance, which can be defined as

A d_{i} = [A d_{i 1}, A d_{i 2}, A d_{i 3}, A d_{i 4}]

(13)

where $A d_{i 1}, A d_{i 2}$ are the time and the cost, respectively. $A d_{i 3}, A d_{i 4}$ represent the approach, respectively.

Generation of the mitigation solution

The disturbance is randomness and complexity, and it is difficult to establish a very accurate mathematical model. A neural network is a kind of intelligent methods and can implement the most nonlinear mapping after learning. According to the characteristics of the disturbance, a neural network–based approach is used to deal with the random disturbance. The mitigation method of the unacquainted disturbance is generated by the proposed method after training based on the data already existing in the database. The generated appropriate approach will be continuously added to the database. The steps of the algorithm are as follows:

Step 1: When the adverse effect of one category disturbance or the whole manufacturing system exceeds the threshold, the anti-disturbance system will operate automatically. The detected disturbance is matched first to the disturbance in the database, and if there is the same disturbance, the anti-disturbance system goes to step 2, otherwise, it goes to step 3.

Step 2: According to the disturbance, search the corresponding method from the method database. If it can execute automatically, it will be executed automatically. Otherwise, it goes to step 4 and submits the solutions to the operator.

Step 3: Based on the disturbance, the neural network is started to generate the new mitigation method, and the generated method is submitted to the operator and the system goes to step 4.

Step 4: The method is judged and modified by the operator, and executed according to the modified method to eliminate the effect of the disturbance, and the modified new method is stored in the database.

Step 5: Judge whether the effect of the disturbance is eliminated, if yes, the program ends, otherwise goes to step 2.

Application example

The example mentioned in section “Evaluation model” is used to illustrate the proposed methods. There are five categories disturbance described in section “Evaluation model,” and the evaluation model is presented in Figure 2. The monitoring data are acquired by the digital twin-driven manufacturing cyber-physical system.²⁰ So, we’ve got the disturbance data as shown from equations (14)–(18). Then, the weight of each category of disturbance and each event in the disturbance is calculated first. Second, the adverse effect value of each type of disturbance and all disturbances on the system are calculated. Third, it is determined whether the value of the adverse effect exceeds the threshold. Fourth, for the disturbance that exceeds the threshold, the mitigation method is solved. Finally, on the basis of the generated method, the adverse effect of the disturbance is eliminated automatically or manually. The detailed steps are outlined in the following paragraphs.

Disturbance identification

By comparing the variation of evaluation criteria with the normal data, the disturbance is identified as mentioned in section “Identification of disturbance.” In this case, the values of planned task events are changed and these are quantified by the operator to compare with the normal value, so the disturbance of the planned task is generated as shown in Table 3.

Table 3.

Disturbance and changes of the production task in a workshop.

	Rush order	Order cancel	Order in advance	Order delay	Order priority changes
Changes in planned tasks	Six rush orders have been issued	Eight orders canceled	Five orders need to be made in advance	Seven orders need to be delayed	The priority of seven orders has changed
Quantification of change	0.6	−0.8	0.5	−0.7	0.7
Normal data	0	0	0	0	0
Disturbance	0.6	−0.8	0.5	−0.7	0.7

The identified disturbance of the planned task is described with vector as follows

\begin{matrix} A t_{IT} = [A t_{IT 1}, A t_{IT 2}, A t_{IT 3}, A t_{IT 4}, A t_{IT 5}] \\ = [0.6, - 0.8, 0.5, - 0.7, 0.7] \end{matrix}

(14)

By the same way, the disturbances of other criteria are described with vector as follows

A t_{IR} = [A t_{IR 1}, A t_{IR 2}, A t_{IR 3}, A t_{IR 4}] = [0, 0.3, 0, 0]

(15)

A t_{IP} = [A t_{IP 1}, A t_{IP 2}, A t_{IP 3}] = [0.2, 0, 0.1]

(16)

\begin{matrix} A t_{IM} = [A t_{IM 1}, A t_{IM 2}, A t_{IM 3}, A t_{IM 4}, A t_{IM 5}] \\ = [0.2, 0, - 0.1, 0.1, 0.1] \end{matrix}

(17)

A t_{IW} = [A t_{IW 1}, A t_{IW 2}, A t_{IW 3}] = [0.2, 0, 0.1]

(18)

Calculation of the weight

As mentioned in section “Calculation of the weight,” FAHP is used to calculate the weight of each criterion and its event. Two manufacturing experts are hired to construct the complementary fuzzy matrix. They have equal weight and each is 0.5. Therefore, two complementary fuzzy matrices are obtained as follows

A_{1} = \begin{matrix} \begin{matrix} IT \\ IR \\ IP \\ IM \\ IW \end{matrix} & [\begin{matrix} IT & IR & IP & IM & IW \\ 0.5 & 0.3 & 0.2 & 0.4 & 0.5 \\ 0.7 & 0.5 & 0.7 & 0.4 & 0.5 \\ 0.8 & 0.3 & 0.5 & 0.7 & 0.6 \\ 0.6 & 0.6 & 0.3 & 0.5 & 0.4 \\ 0.5 & 0.5 & 0.4 & 0.6 & 0.5 \end{matrix}] \end{matrix}

(19)

A_{2} = \begin{matrix} \begin{matrix} IT \\ IR \\ IP \\ IM \\ IW \end{matrix} & [\begin{matrix} IT & IR & IP & IM & IW \\ 0.5 & 0.6 & 0.7 & 0.5 & 0.7 \\ 0.4 & 0.5 & 0.4 & 0.5 & 0.4 \\ 0.3 & 0.6 & 0.5 & 0.3 & 0.5 \\ 0.5 & 0.5 & 0.7 & 0.5 & 0.4 \\ 0.3 & 0.6 & 0.5 & 0.6 & 0.5 \end{matrix}] \end{matrix}

(20)

$A_{1}$ and $A_{2}$ are, respectively, transformed into the consistent fuzzy matrix $R_{1}$ and $R_{2}$ . Then, the fuzzy uniform judgment matrix $\bar{R} = λ_{1} R_{1} \oplus λ_{2} R_{2}$ is acquired and shown as follows

\begin{matrix} \bar{R} = 0.5 R_{1} \oplus 0.5 R_{2} \\ = \begin{matrix} \begin{matrix} IT \\ IR \\ IP \\ IM \\ IW \end{matrix} & [\begin{matrix} IT & IR & IP & IM & IW \\ 0.5000 & 0.49375 & 0.4875 & 0.49375 & 0.49375 \\ 0.50625 & 0.5000 & 0.49375 & 0.5000 & 0.5000 \\ 0.5125 & 0.50625 & 0.5000 & 0.50625 & 0.50625 \\ 0.50625 & 0.5000 & 0.49375 & 0.5000 & 0.5000 \\ 0.50625 & 0.5000 & 0.49375 & 0.5000 & 0.5000 \end{matrix}] \end{matrix} \end{matrix}

(21)

The weight of each criterion is obtained using the NRA in the $\bar{R}$ , and it is

\begin{matrix} ω_{A} = [ω_{IT}, ω_{IR}, ω_{IP}, ω_{IM}, ω_{IW}] \\ = [0.19843, 0.2, 0.20157, 0.2, 0.2] \end{matrix}

(22)

By the same way, the weight of each event for every criterion is acquired and shown as follows

ω_{BIT} = [0.2375 0.2275 0.2215 0.1685 0 {. 145]}^{T}

(23)

ω_{BIR} = [0.1325 0.3225 0.1208 0.4242]^{T}

(24)

ω_{BIP} = [0.2432 0.525 0.2318]^{T}

(25)

ω_{BIM} = [0.12 0.2195 0.3125 0.221 0 {. 127]}^{T}

(26)

ω_{BIW} = [0.237 0.337 0.426]^{T}

(27)

where $ω_{BIT}$ , $ω_{BIR}$ , $ω_{BIP}$ , $ω_{BIM}$ , $ω_{BIW}$ represent the weight vector of each event, respectively.

Calculation of evaluation index

The disturbance evaluation value of the plan task criterion can be calculated by

\begin{matrix} f_{IT} = | A t_{IT} | \times ω_{BIT} = [0.6, | - 0.8 |, 0.5, | - 0.7 |, 0.7] \\ \times [\begin{matrix} 0.2375 \\ 0.2275 \\ 0.2215 \\ 0.1685 \\ 0.145 \end{matrix}] = 0.6547 \end{matrix}

(28)

Similarly, we can calculate the evaluation value of other criteria. Therefore, the evaluation index vector is

\begin{matrix} f = (f_{IT}, f_{IR}, f_{IP}, f_{IM}, f_{IW}) \\ = [0.6547, 0.09675, 0.07182, 0.09005, 0.09] \end{matrix}

(29)

The evaluation index vector $f$ is multiplied by its weight $ω_{A}$ and then added together to get the system index $E_{T}$ , and the equation is

\begin{matrix} E_{T} = f \cdot ω_{A} = [0.6547, 0.09675, 0.07182, 0.09005, 0.09] \\ \times [\begin{matrix} 0.19843 \\ 0.2 \\ 0.20157 \\ 0.2 \\ 0.2 \end{matrix}] = 0.199747 \end{matrix}

(30)

In order to more clearly describe the relationship between the disturbance, the status values of each disturbance are summarized in Table 4.

Table 4.

Weight and value of the disturbance.

Disturbance category	Weight ( $ω_{A}$ )	Evaluation value	Events	Weight ( $ω_{B}$ )	Identified value
Plan task ( $A t_{IT}$ )	0.1984	0.6547	IT1: emergency order	0.2375	0.6
			IT2: order cancel	0.2275	0.8
			IT3: order in advance	0.2215	−0.5
			IT4: order delay	0.1685	0.7
			IT5: order priority changes	0.145	0.7
Material resource ( $A t_{IR}$ )	0.2	0.09675	IR1: raw material shortage	0.1325	0
			IR2: outsourcing component shortage	0.3225	0.3
			IR3: auxiliary material shortage	0.1208	0
			IR4: material disqualification	0.4242	0
Production process ( $A t_{IP}$ )	0.20157	0.07182	IP1: process sequence change	0.2432	0.2
			IP2: process reduction	0.525	0
			IP3: process increase	0.2318	0.1
Manufacturing resource ( $A t_{IM}$ )	0.2	0.09005	IM1: device fault	0.12	0.2
			IM2: device repair	0.2195	0
			IM3: device increase	0.3125	−0.1
			IM4: device reduction	0.221	0.1
			IM5: tooling time delay	0.127	0.1
Personnel change ( $A t_{IW}$ )	0.2	0.09	IW1: operators absenteeism	0.237	0.2
			IW2: operation error	0.337	0
			IW3: operators’ skill level is poor	0.426	0.1

Judgment of the adverse effect

The threshold is used to judge the adverse effect. If the values of the system index and single category disturbance exceed the threshold, this indicates that the system is seriously disturbed and needs to be adjusted. In this case, the system index threshold $T_{E}$ is set to $0.2$ , and the disturbance threshold $T_{f}$ is set to $0.4$ . Although $E_{T} < T_{E}$ indicate the whole system isn’t adjusted, but $f_{IT} > T_{f}$ indicates the planned task disturbance has serious adverse effects and should be adjusted.

Generation of the mitigation solution

Based on the adjustment solution defined in section “Definition of mitigation solution,” a three-layer BP neural network is used to generate the adjustment solution for the disturbance. In this case, the planned task disturbance should be adjusted. Some training samples are shown in Table 5.

Table 5.

Adjustment solution of the planned task disturbance.

Disturbance of the planned task (At_IT)	Adjustment solution
	Time	Cost	Higher priority methods	Lower priority methods
[0.1 0.1 0.2 0.1 0.9]	2	9	4	2
[–0.2 0.1 0.1 1 0.1]	9	4	4	1
[0.1 0.1 0.9 0.1 0.1]	4	10	4	3
[0.1 0.8 0.1 0.2 0.1]	12	6	4	1
[0.8 0.1 0.1 0.1 0.1]	3	12	4	3
[0.9 −0.1 −0.2 −0.3 1]	6	20	4	3
[0.1 0.1 0.9 0.9 −0.2]	12	14	4	1
[–0.1 0.9 0.1 0.2 1]	15	14	4	1
[0.1 1 0.1 0.9 0.2]	21	11	4	2
[0.1 0.1 0.8 −0.2 0.9]	7	18	4	3
[0.9 0.1 0.8 0.1 −0.1]	6	22	4	3
[–0.1 0.9 0.8 0.2 0.9]	18	24	4	2
[0.8 −0.1 0.2 0.9 0.9]	16	24	4	3
[0.1 0.9 0.9 0.8 −0.1]	24	20	4	1
[0.6 0.8 −0.5 0.7 0 0.7]	9	32	4	3

The planned task disturbance consists of five events. Therefore, the BP neural network input layer node number is five. The data range of the input vector is −1 to 1. The hidden layer node selects the S-type tangent function Tansig. The adjustment solution has four parameters. Therefore, the output layer consists of four nodes. The output layer node can select the S-type logarithmic function Logsig.

Because the BP neural network of a single hidden layer can approach an arbitrary continuous nonlinear function, so it is adopted. The number of nodes in the hidden layer directly affects the nonlinear predictive ability of the network, so more nodes are utilized here. The number of nodes in the hidden layer is set to 20, and the neural network module in MATLAB is used for analysis. The BP network structure to generate the adjustment solutions is constructed, as shown in Figure 3.

Figure 3.

BP neural network structure.

In Table 5, the last disturbance is the same disturbance that we’re going to calculate. Therefore, the first 14 rows of data in Table 5 are selected as training samples, and the last row data are used as the verified data. The training variation curve of the neural network is given in Figure 4.

Figure 4.

Training variation curve.

After the training, the disturbance data $A t_{IT} = [0.6, 0.8, - 0.5, 0.7, 0.7]$ is inputted, and the output is [8.81, 31.45, 4.02, 2.78], which is similar to the mitigation solution $[9, 32, 4, 3]$ in the last row of Table 4. So, the result is effective.

Conclusion

In the article, a method for identifying real-timely disturbance and generating an adjustment solution is offered. The detected data are described by 10 scales to improve the detection accuracy. The evaluation model realized bi-layer monitor. It can not only monitor the adverse effect of a single category disturbance, but also monitor the health status of the whole system. Time and cost are combined into the adjustment solution, and this makes the choice of solution more rational and flexible. Depending on the proposed method, the disturbance can be disposed in advance, so as to make the healthy operation of the manufacturing system.

But, the implementation of the method requires a manufacturing cyber-physical system. Therefore, in the subsequent work, the hardware and software should be developed and the real-time data detected by the hardware should be processed to 10 scales. Current research to further work is underway.

Footnotes

Handling Editor: James Baldwin

Declaration of conflicting interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This research was supported by the Natural Science Foundation of Shandong Province (No. ZR2016EEM47), Higher Educational Science and Technology Program of Shandong Province (No. JB18B018), and Doctor Research Foundation of Linyi University (No. LYDX2015BS014).

ORCID iD

Yuyun Kang

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