[1] Liu Jinsong. Research and application of key technology of digital twin of high-end CNC machine tools [D]. University of Chinese Academy of Sciences (Shenyang Institute of Computing Technology, Chinese Academy of Sciences), 2022. DOI: 10.27587/d.cnki.gksjs.2022.000005.

Experimental verification

Convolutional Neural Networks for Fault Diagnosis

The experiment uses a convolutional neural network structure as shown in the figure below, including three convolutional layers, three pooling layers, one fully connected hidden layer, and one Softmax layer. The fault data passes through the first convolutional layer and the ReLU activation function, outputs a set of feature maps (Feature Maps), and then undergoes maximum pooling for downsampling. Repeat the operation more than two times, connect the feature map output by the last pooling layer to the fully connected hidden layer, and pass it to the last Softmax layer after being activated by the ReLU function.

The number of convolution kernels in the first convolution layer is 16, the size of the convolution kernel is 62×1, and the step size is 16×1; the number of convolution kernels in the second and third convolution layers is 64, and the size of the convolution kernel is is 3×1, and the step size is 1×1. The sliding window size of the first pooling layer is 2×1, and the step size is 1×1; the sliding window size of the second and third pooling layers is 2×1, and the step size is 2×1. The number of neurons in the fully connected layer is 64, and the number of categories output by the Softmax layer is 10.

Construction and verification of fault knowledge graph

I haven't touched it, I don't understand it...just look at the meaning ┗( ▔, ▔ )┛

Research on production rescheduling decision-making method of digital twin of high-end CNC machine tool

Motivation

When the fault information of the CNC machine tool is detected, the maintenance knowledge of the fault is obtained according to the fault knowledge map retrieval reasoning, and these knowledge are used as constraints, and the re-scheduling decision-making algorithm is used to assist in updating the production plan, providing a dynamic adjustment and execution of the production plan. policy support. Aiming at the production rescheduling decision-making problem of digital twins of high-end CNC machine tools, an integrated decision-making architecture for fault diagnosis and production rescheduling is proposed, aiming at realizing intelligent fault maintenance and production rescheduling decisions.

Integrated Decision-Making Architecture of Fault Diagnosis and Production Rescheduling

(1) Fault diagnosis layer . Based on the previously proposed data perception method, this layer builds a high-end CNC machine tool all-element perception data acquisition network, realizes real-time acquisition of all-element perception data of the CNC machine tool, maps the real-time operating status data of the CNC machine tool to the information space, and maintains physical entities and digital twins The consistency of the model provides rich information for the fault diagnosis of CNC machine tools. The fault diagnosis technology proposed before realizes the intelligent diagnosis of CNC machine tool faults.

(2) Knowledge application layer. Based on the constructed fault knowledge map of CNC machine tools, knowledge map retrieval and reasoning technology are applied to realize multi-level analysis of faults, fast and efficient fault maintenance, knowledge transfer and sharing, and also provide knowledge support for intelligent decision-making.
(3) Intelligent decision-making layer. When the fault diagnosis result is made at the fault diagnosis layer, the maintenance knowledge provided by the knowledge application layer (such as maintenance reasons, maintenance measures, and estimated maintenance time, etc.) can provide guidance for CNC machine tool fault maintenance at the intelligent decision-making layer. The fault maintenance strategy updates the original maintenance knowledge.

Rescheduling Decision Algorithm Model

The rescheduling decision model is established using the following symbols:

$J=\left \{ J_{i} \right \},1\leq i\leq n$ , J represents n jobs that have completed the initial scheduling.
$M=\left \{ M_{k} \right \},1\leq k\leq m$ , M represents m machine tools.
Each job $J_{i}$ has an ordered sequence of tasks, i.e. $J_{i}=\left \{ O_{i,h} \right \},1\leq h\leq q_{i}$ , $O_{i,h}$ denote $J_{i}$ the hth task of the job, $q_{i}$ denote $J_{i}$ the total number of tasks of the job.
$p_{i,h,m}$ Indicates the time spent processing tasks on the machine tool $J_{i}$ in the job. $O_{i,h}$ $M_{k}$

The production rescheduling decision-making problem driven by digital twins can be regarded as a constrained scheduling problem, and its main goal is to achieve the efficiency of the scheduling scheme and minimize the deviation of the original scheduling scheme. Therefore, two important performance indicators, efficiency performance and stability, are considered, and the maximum completion time (expressed as ) that can reflect the efficiency of the rescheduling decision-making scheme $C_{max}$ and the starting time deviation (expressed as SI ) and sequence deviation (expressed as F) to evaluate the performance of the rescheduling decision-making scheme, the calculation methods are as follows:

$\begin{array}{c} C_{\max }=\max _{1 \leq i \leq n} c_{i} \\\\ S I=\frac{\sum_{i=1}^{n} \sum_{j=1}^{q_{j}}\left|S T_{i j, \text { new }}-S T_{i j, \text { ori }}\right|}{\sum_{i=1}^{n} q_{i}} \\\\ F=1-\frac{\sum_{i=1}^{n} \sum_{h=1}^{q_{i}} \sum_{k=1}^{m} x_{i, h, m}}{\sum_{i=1}^{n} q_{i}} \end{array}$

Algorithm framework

Monte Carlo tree search method introduction reference: https://www.bilibili.com/video/BV1JD4y1Q7mV/?spm_id_from=333.337.search-card.all.click&vd_source=0ef0e3dcc699e4536466b007ec6c95cf
uses the Monte Carlo tree search method to construct a rescheduling decision algorithm, The overall algorithm framework is as follows:

Each state node in the Monte Carlo search tree represents a state of the current scheduling. State nodes are divided into two types: terminal nodes and non-terminal nodes. side. Non-terminal nodes are opposite to terminating nodes. There are unscheduled tasks in the current scheduling state, including a set of edges (s, a). Each edge corresponds to a behavior a in the legal behavior space A(s) in the current state s. Behaviors in the behavior space are composed of scheduling rules according to the current scheduling state, and statistics are stored in each edge:

$\{N(s, a), Q(s, a), P(s, a)\}$

Where N(s, a) is the number of visits to the edge, Q(s, a) is the global behavior value of the edge, and P(s, a) is the selection probability of the edge. In the search of each state, if the node is not a terminal state node, the algorithm constructs a search tree with the current state node as the root node, which contains all actions in the legal action space in this state, and selects one of them Actions are expanded, and finally a complete rescheduling sequence is constructed through multiple expansions, and the rescheduling sequence is evaluated and backpropagated to optimize the next round of search. Therefore, the algorithm is divided into four stages: selection, expansion, evaluation, and backpropagation. The four stages are described in detail below.

selection stage

When the visited state node st is an explored non-terminal node, select the behavior in the legal behavior space in the current state. The behavior at of the current state St is selected using the upper bound confidence interval algorithm:

$\begin{array}{c} a_{t}=\underset{a}{\arg \max }\left(Q\left(s_{t}, a\right)+U\left(s_{t}, a\right)\right) \\\\ U\left(s_{t}, a\right)=c_{p u c t} P\left(s_{t}, a\right) \frac{\sqrt{\sum_{a} N\left(s_{t}, a^{\prime}\right)}}{1+N\left(s_{t}, a\right)} \end{array}$

where is $c_{puct}$ a constant that determines the degree of exploration. When the visited state node st is an unexplored non-terminal node, the algorithm enters the expansion stage to explore the behavior of the node state.

expansion stage

When st is an unexplored non-terminal node, expand it:

$\left\{N\left(s_{t}, a_{i}\right)=0, Q\left(s_{t}, a_{i}\right)=0, P\left(s_{t}, a_{i}\right)=P_{a_{i}}\right\}$

Among them, Paj is the selection probability of behavior ai when the legal behavior space under the current state node is A(s)={a1,a2,...,an}, the calculation formula of Paj is as follows:

$P_{a_{i}}=\frac{\sum_{i=1}^{n} v_{i}}{v_{i} \sum_{i=1}^{n} \frac{\sum_{i=1}^{n} v_{i}}{v_{i}}}$

Where vi represents the local behavior value of the state node obtained by executing behavior ai in the current state. In summary, the calculation method of Unit Index Value (UIV) is as follows:

$v_{i}=\sum_{j=1}^{3} w_{j} \frac{q_{i j}-q_{\min }^{j}}{q_{\max }^{j}-q_{\min }^{j}}$

Among them, w={w1,w2,w3} respectively represent the user preference weights of Cmax, SI and F in the scheduling strategy, and $\sum_{j=1}^{3} w_{j}=1$ qi1, qi2 and qi3 respectively represent the Cmax, SI and F of the state node after executing behavior ai value, $q_{max}^{j}$ and $q_{min}^{j}$ represent the maximum value and minimum value of index j in the state node obtained by all behaviors respectively.

evaluation stage

If the state node currently visited in this round is a terminal state node, it enters the evaluation phase. In the evaluation phase, the index value of the scheduling sequence is obtained according to this round, and the feedback value of this round is calculated, which is used to update the path in the backpropagation process Q-values in each behavior.

backpropagation stage

Backpropagation is used to implement the backtracking of the estimated value, thereby updating the Q value. First, add 1 to the count of the edges passed in all search paths, that is $N\left(s_{t}, a_{t}\right)=\mathrm{N}\left(s_{t}, a_{t}\right)+1$ , and update the Q value of the edge using the following formula:

$Q\left(s_{t}, a_{t}\right)=\frac{N\left(s_{t}, a_{t}\right)-1}{N\left(s_{t}, a_{t}\right)}+\frac{R}{N\left(s_{t}, a_{t}\right)}$

Digital twin paper reading notes [1.2]