A Condition Monitoring Strategy of Looms Based on DSmT Theory and Genetic Multiobjective Optimization Improves the Rough Set Method

In order to improve the effect of intelligent monitoring and condition analysis of textile machinery, some solutions have been proposed to mitigate incomplete monitoring positions, insufficient decision accuracy, uncertainty reasoning and generalization of the current loom monitoring system. Firstly, a model of the weaving machine spindle dynamics was constructed, and the types and sources of monitoring data were specified. Secondly, an improved rough set method is proposed for processing the collected loom attribute data. A genetic multi-objective optimization method combined with a genetic algorithm is proposed to improve the problem of too many reduction results of the rough set method and improve the monitoring system’s reliability. In order to solve the problem that new objects do not have unique matching rules in the constructed rule base, a fusion of Dezert-Smarandache Theory (DSmT) for uncertainty inference is proposed, which increases the distinguishability of decision support probabilities. Experiments show that the improved rough set method based on DSmT and genetic multi-objective optimization has higher classification accuracy and better recognition than the traditional rough set method for weaving machine condition monitoring.


I. INTRODUCTION
Condition monitoring and identification of textile machinery is the basis for the digitalization and intelligence of textile machinery. With the continuous development of textile machinery functions and structures, traditional equipment condition monitoring technology cannot meet the needs of intelligent weaving equipment. Therefore, a particular loom condition monitoring method is studied. It is an inevitable choice and an essential direction for the current development of textile machinery. Equipment maintenance technology has gone through four stages: post-event maintenance, preventive planned maintenance, maintenance considering economic goals, and condition maintenance. The innovation of each generation of equipment maintenance technology is actually the innovation of equipment condition monitoring technology. With the development of deep learning and multi-source The associate editor coordinating the review of this manuscript and approving it for publication was Hisao Ishibuchi . data fusion, the current equipment condition monitoring technology is no longer limited to equipment maintenance. It is based on the hidden state information inside the equipment so as to realize intelligent manufacturing applications such as intelligent fault warning, intelligent efficiency optimization, and CPS model mapping of equipment.

A. DEVELOPMENT STATUS OF LOOM MONITORING SYSTEM
DORNIER's loom control system adopts industrial interconnection technology, which can precisely control and monitor the critical quality parameters of the loom. The Picanol BlueBox, an electronic platform for looms from Picanol, Belgium, integrates on-board diagnostic systems, intelligent production efficiency optimization systems, user interfaces, device browsers, and remote fault diagnosis systems. It better realizes the loom's innovative management and online fault diagnosis [1]. Vladimir et al. built a fabric visual inspection VOLUME 10, 2022 This work is licensed under a Creative Commons Attribution 4.0 License. For more information, see https://creativecommons.org/licenses/by/4.0/ system through a web camera and a microcomputer and designed a feasible scheme for automatic online monitoring of fabric quality [2]. P. P. J designed a shuttle loom control module with the peripheral interface and microcontroller, which can monitor and measure errors in warp and weft [3]. Dong and Shi adopted the redundant structure of dual-bus and dual-region processors to realize the self-diagnosis of the loom system, the automatic loading of working parameters, and the automatic shielding and recovery of loom interface faults. This system has high reliability and maintainability, but the degree of intelligence is insufficient [4]. Sun et al. used the fault tree to judge the real-time data, which improved the data transmission and processing performance of the realtime information detection system of the loom [5]. The above works have designed the control and monitoring system of the loom, but these systems have the problem of insufficient intelligence. The focus of these researches does not involve data fusion and feature extraction of loom attributes, loom status recognition and loom data sharing. In order to realize the condition monitoring of the loom, it is necessary to analyze the entire mechanical structure of the loom, establish a dynamic model of the core components of the loom, and determine the data source and data type of the loom monitoring data according to the model. It is also necessary to analyze a large amount of data collected by combining intelligent condition monitoring methods and fault diagnosis methods to support the system in making correct decisions.

B. DEVELOPMENT STATUS OF CONDITION MONITORING AND FAULT DETECTION TECHNOLOGY
The new state monitoring system typically includes data acquisition, analysis; diagnosis and output; data transmission; and communication [6]- [10]. Existing condition monitoring systems typically replace single-sensor signal monitoring with multisensor data fusion monitoring. Caporuscio et al. analyzed troubleshooting solutions for many heterogeneous connected devices and summarized the effect evaluation criteria of status detection and fault diagnosis systems from different perspectives [11]. Reference [12] comprehensively used multiple sensor signals to construct a health monitoring and fault diagnosis system for hydromechanical transmission. Experiments proved that the condition monitoring method based on multisensor data fusion has lower hysteresis and a more accurate condition recognition effect than the traditional ferrography analysis and vibration monitoring methods. In power systems, condition monitoring technology has matured in many applications, and there is a separate online condition monitoring method for each device in the system [13]- [15]. It can be seen that the specificity of the condition monitoring technology is very high, the condition monitoring of different manufacturing equipment needs to be studied in a targeted manner, and the monitoring points and data volume of the condition monitoring task are massive. A more efficient data processing method is needed. The set and data sharing requirements are higher [16], [17].
In the field of condition monitoring systems, the research on algorithms for mining deep hidden information combined with deep learning methods has become a hot topic. Reference [18] proposed using the fuzzy threshold method to classify the state data of wind turbines and then using the fuzzy neural network (FNN) and fast Fourier transform to evaluate and make decisions about monitoring data. Reference [19] proposed using likelihood learning to process the warpage feature of the wind turbine gearbox vibration signal. These cases show that algorithms such as deep learning can effectively mine deeply hidden information in state data but are strongly dependent on the dataset.
How to quickly obtain high-quality condition monitoring data sets and improve the generalization performance of control decisions is a practical problem that needs to be faced. Chen constructed a wavelet neural network algorithm based on the niche genetic algorithm for fault diagnosis of rapier loom bearings [20]. Zhang et al. proposed a grid fault localization and fault type identification method that combines Variational Mode Decomposition (VMD) and Convolutional Neural Networks (CNN) [21]. Zhang et al. proposed using a multi-group quantum genetic algorithm (MQGA) to optimize the combination of quality factor parameters for fault detection of aero-engine bearings [22]. Zhang et al. proposed using deep convolution generative adversarial network (DCGAN) to generate virtual fault data, expand the training samples, and then use the residual connected convolutional neural network (RCCNN) model to extract and classify stator current data to achieve fault diagnosis [23]. The above works have proposed different fault diagnosis and condition monitoring methods. However, the above work has a general effect of dealing with uncertain information with complex data sources. It is not suitable for the loom system in which each institution's data is relatively independent, and a consistent interpretation and description of the equipment status cannot be obtained. In order to improve the processing effect of multi-source uncertain information, it is necessary to introduce multisource data fusion technology, such as rough set theory, grey system theory, Bayesian reasoning, etc.
Rough set theory (RST) has been successfully applied to machine learning, decision analysis, process control, approximate reasoning, pattern recognition, data mining and other intelligent information processing fields. Zhang et al. discussed the methods and applications of multisource information fusion based on rough set theory, reporting that rough sets are suitable for classifying noisy, inaccurate, or incomplete data [24]. RST does not rely on prior information. It can make full use of available information to identify basic knowledge and rules of target problems from sample data to keep the classification ability of the information system unchanged [25]. Muralidharan et al. proposed using a discrete wavelet transform (DWT) to calculate wavelet features from vibration signals and then using rough set generation rules to achieve fault diagnosis of single-body centrifugal pumps [26]. Wang et al. proposed a fault diagnosis scheme combining rough set theory and fuzzy logic [27].
These examples show that using the rough set method to process data can extract effective decision-making rules from data with complex sources and ambiguous relationships. However, the rules extracted by the simple rough set method may have new objects that cannot be matched. Therefore, it is necessary to integrate other suitable algorithms to improve the accuracy and adaptability of the constructed decision rule base. The steps of the rough set method include attribute reduction, rule extraction, and rule matching. Some scholars propose integrating other algorithms to improve the results of these steps to improve decision-making using the rough set method. For example, Suo et al. proposed using a datadriven loss function matrix to design a neighbourhood decision theory rough set model to improve the results of attribute reduction [28]. Rajeswari et al. proposed using a genetic algorithm (GA) and a rough set-based method to select the best input features to improve the reduction efficiency [29]. Hu et al. introduce different weights into neighbourhood relations and construct a Weighted Neighborhood Rough Set (WNRS) model based on weighted neighbourhood relations. The experimental results show that WNRS has higher classification accuracy and compression ratio [30]. Xie et al. propose a new weighted neighbourhood probabilistic rough set model based on data binning [31]. Although the above work improves the rough set method, it is not entirely suitable for processing loom attribute data. The state data of the loom is continuous in the time domain, which cannot be processed by the rough set method. In addition, the above work mainly improves the attribute reduction step of the rough set method, and the rule extraction step and the rule matching step of the rough set method are less improved. When the rough set method processes the loom state data, there are many reduction results, and the new object cannot match the unique rule in the rule base. In order to solve these two problems, this paper proposes to use the genetic algorithm to improve the attribute reduction step of the rough set method so as to improve the classification accuracy of decision-making, and to use Dezert-Smarandache Theory (DSmT) theory for uncertainty reasoning so as to increase the discrimination degree of decision support probability.
To sum up, the main contributions of this paper are as follows.
1) According to the analysis of the loom mechanical equipment and weaving principle, the dynamic model of the main shaft of the rapier loom is established, and the monitoring data collection position and type of the loom state monitoring are clarified through the model. In addition, this paper proposes that the loom state analysis can be based on the warp tension of the loom and the commonly used vibration data. 2) Aiming at the problem of many reduction results when the rough set method is directly applied to loom attribute data processing, this paper proposes a genetic multiobjective optimization method fused with the genetic algorithm. The method uses the genetic algorithm to improve the reduction step in the rough set method to optimize the reduction result and improve the classification accuracy of the system decision. 3) Aiming at the problem of matching multiple rules for new objects in the rough set method, this paper proposes to use DSmT theory combined with rough set theory to carry out uncertainty reasoning and increase the distinguishability of decision support probability. In order to verify the feasibility and effect of the method proposed in this paper, a step-by-step comparison experiment and a system experiment on an actual rapier loom are carried out in this paper. The loom condition monitoring mapping network can obtain a better identification effect and improve the performance of the loom condition monitoring system.

II. DYNAMIC MODEL OF LOOM SPINDLE
In this section, the structure and weaving process of the loom are analyzed, the dynamic model of the loom is constructed, and the monitoring data source of the condition monitoring system is determined accordingly.

A. WEAVING PRINCIPLE OF LOOM
A rapier loom can be divided into five significant mechanisms: opening, weft insertion, beating-up, let-off and coiling. The mechanical structure of the rapier loom is shown in Fig. 1. Different angles of the weaving machine spindle correspond to different weaving process processes, which is the core of the weaving machine operation. Fig. 2 shows a table of the spindle position angles of the weaving machine when performing different processes.  The mechanical transmission relationship of the rapier loom spindle is shown in Fig. 3. The primary motor transmits the power to the weaving machine spindle through the belt pulley, brake clutch system, and reduction gear to drive the weaving machine spindle movement. The primary shaft drives the wefting cam to complete the wefting process.

B. SPINDLE DYNAMICS MODEL
The main shaft of the loom is formed by a series of mass elements, beam elements, and support elements connected one after another in the form of a chain-like structure. It is convenient and practical to use the transfer matrix method to analyze and calculate the vibration system of this form [32]. The dynamic model diagram of the spindle of the rapier loom is shown in Fig. 4. As shown in Fig. 4, the loom spindle system is decomposed into several relatively simple subsystems with a single degree of freedom. The state vectors represent the generalized forces and generalized displacements on the connected end faces of each subsystem, and the transfer matrix is used to represent the relationship from the input end of the system to the output end. The primary shaft system of the loom is calculated according to the concentrated mass point, beam and support point separately.
When the system performs simple harmonic motion since m i is a rigid body, its left and right lateral displacements y are equal, which can be expressed as: The rotation angle θ on the left and right sides of m i is equal, which is expressed as: m i is a large volume part whose rotational inertia cannot be neglected. Thus, the bending moment of the subsystem can be expressed as: The sheer force transfer relationship between the left and right sides of the subsystem can be expressed as: In these equations, the R and L superscripts indicate the location of the parameters (i.e., the right or left side of the subsystem), M is the bending moment received by the subsystem, J is its moment of inertia, ω is the angular frequency of system motion, and Q is the shear force experienced by the subsystem. Therefore, the state transfer relationship between the left and right sides of m i can be expressed as: which can be abbreviated as: where [P] i is called the point transfer matrix of the concentrated mass point m i . Denote beams with l i . Separating l i from the system and ignoring the mass of the beam itself, the transfer relationship of the bending moment on the beam is as follows based on a balance of forces: The shear force transfer relationship of the beam is: The force analysis of beam l i uses the left end point of the beam as the coordinate origin, the radial direction of the beam is the x direction, and the tangential direction is the y direction. According to the mechanics of materials, we know: where E is the elastic modulus of the beam, and I is the moment of inertia of the beam. From the set relation, we know: Therefore, the angle transfer relationship between the left and right ends of the beam is: The lateral displacement transfer relationship between the left and right ends of the beam is: 59726 VOLUME 10, 2022 The left end rotation angle of the middle beam on the right side of (12) is represented by the rotation angle of the right endpoint of its adjacent subsystem, and it is substituted into (11) to obtain: The rotation angle of the left end of the beam is expressed by the lateral displacement of the right end point of its adjacent subsystem and is substituted into (12) to obtain: Equations (7), (8), (13), and (14) can be represented in matrix form as: which can be abbreviated as: where [F] i is the field transfer matrix of massless beam segment l i . Using (5) for ideal rigid points and (15) for ideal massless beams, the state vector relationship model of each point from the left end to the right end of the system can be established.
Assuming that the equivalent stiffness of the support point m i is k, the equivalent viscous damping coefficient is ζ , and the concentrated mass of the support is m i , the displacement relationship between the left and right sides of the support point is: Therefore, the transfer relationship of the state vectors on the left and right sides of the support point of m i is: The bending moment relationship is expressed as: The shear force relationship is expressed as: Therefore, the transfer relationship of the state vectors on the left and right sides of the support point is: which can be abbreviated as: where [T ] i is the transfer matrix of the state vectors on both sides of the support point.
According to the structure of the main shaft of the rapier loom and the working principle of the loom, using the parameters listed in Table 1, the dynamic model of the main shaft of the rapier loom is established.
Thus, the input from one end of the primary shaft can be transmitted to any position of the primary shaft, and the VOLUME 10, 2022 natural frequency and primary vibration shape of the primary shaft of the loom can be calculated.

III. DATA PROCESSING AND FUSION OF THE STATE DETECTION SYSTEM
Because many of the data collected on the loom are incomplete and uncertain, these data cannot be directly used for decision-making on the loom status [33], [34]. The collected data must be preprocessed before the data are fused to construct a rough set decision table.

A. LOOM STATE FEATURE DESCRIPTION AND DATA PREPROCESSING
The fluctuation characteristics of the warp tension of the loom can describe the working state of the opening mechanism, the beating-up mechanism, and the roll feeding system. The primary vibration of the loom mechanical equipment can systematically reflect the overall operation state of the equipment. Therefore, this system focuses on the fluctuation of the warp tension. Data and body vibration data are processed as source data, and a decision table is constructed.

1) CHARACTERISTIC DESCRIPTION OF THE WARP TENSION FLUCTUATION OF LOOMS
The warp yarn tension data of the loom sampled by the sensor is represented only by the function y i = f(t i ) (i = 0, 1, . . . , n) of a series of points t i in the corresponding time interval. In order to evaluate the fluctuation characteristics of warp tension, it is necessary to estimate the function value corresponding to any time node. This system selects the cubic spline interpolation method to solve the approximation function of the warp tension fluctuation curve of the loom. Because all the weaving actions of the loom are performed based on the spindle position angle, the spindle position angle is selected as the independent variable of the warp tension fluctuation function of the loom, and the definition domain is [0, 360).
The interpolation curve of the warp tension fluctuation composed of the warp tension of the loom in one cycle is shown in Fig. 5, which indicates that the interpolation effect of 49 interpolation nodes is better than that of 24 interpolation nodes. Also, the cubic spline interpolation curve using 49 interpolation nodes can more accurately describe the measured fluctuation of warp tension on the loom and the nature of the curve. Therefore, in the onboard condition monitoring system of the loom, six attributes of the three extreme point positions of the 49-point interpolation curve, the relative stability interval of the tension, and the mean value of the tension sampling points are selected to describe the warp tension fluctuation of the loom.

2) CHARACTERISTIC DESCRIPTION OF THE VIBRATION SIGNAL OF THE LOOM SPINDLE
From the analysis of the weaving principle of the loom above, we can see that the main shaft of the loom is the power source of the weaving mechanism, and its vibration can reflect the condition of the entire loom. The vibration of the main shaft of the loom can be obtained by measuring the vibration of the journals at both ends of the main shaft. The sensor used in this paper is an IEPE acceleration sensor. The physical diagram of the journals and the sensor at both ends is shown in Fig. 6.  The operating speed of the main shaft is generally below 10 r/s, that is, below 10 Hz. Therefore, the fundamental frequency of vibration of the main shaft of the loom is below 10 Hz. The operating speed of the spindle is called the fundamental frequency of the spindle, denoted as X. Taking the spindle fundamental frequency X as the unit, the vibration generated by the spindle has multiple harmonics in addition to 1 times the spindle fundamental frequency 1X. The failure of the loom is often reflected in the multiple harmonics. Below 1X is the sub-low-frequency area, 1X to 10X is the lowfrequency area, and above 10X is the high-frequency area. If the amplitude in the sub-low-frequency region is high, the fault types include oil swirl and so on. If the amplitude in the low-frequency region is high, the fault types are unbalance, misalignment, looseness, etc. If the amplitude in the highfrequency region is high, the gear bearing is often faulty, such as wear, cracks, etc. In this paper, the vibration signal of the main shaft is divided into six attributes according to the amplitude: 0∼0.4X, 0.4∼0.6X, 0.6∼1X, 1X, 2X and greater than 2X. Since there are two measurement points of the spindle vibration, the left journal and the right journal, there are 12 attributes to describe the spindle vibration signal. The vibration attribute table of the main shaft of the loom is shown in Table 2.

1) CONSTRUCTION OF THE ROUGH SET DECISION TABLE
Assuming that the loom state feature monitoring system contains five first-generation attribute items, denoted as A = {a 1 , a 2 , a 3 , a 4 , a 5 }, the definition set can be denoted V = {V 1 , V 2 , V 3 , V 4 , V 5 }, where V i is the attribute A set of values for a i , i = 1, 2, . . . , 5. The function f : ai −−> Vi represents the relationship between the attribute a i and its value. The existing state instance set U is collected according to the first-generation attribute items. According to rough set theory, the loom state monitoring information system can be expressed as IS = U, A, V, f .
Considering the identification of the spindle wear degree as an example, we let the attribute a 1 represent the wear degree of the loom spindle, where V 1 = {severe, slight, normal}; the attribute a 2 represents the measured value of the weft yarn tension in a certain weaving cycle, which is divided into five levels as V 2 = {2, 1, 0, −1, −2}; attribute a 3 represents the weaving performance of the loom at a certain stage, and the weaving performance of the loom is divided into four types, where V 3 = {excellent, good, medium, poor}; and attributes a 4 and a 5 are other parameter attributes of the loom. The resulting decision table is shown in Table 3. For the loom parameter monitoring problem, the loom weft tension monitoring decision table is constructed as shown in Table 4.

2) REDUCTION OF ROUGH SET DECISION TABLES
After the rough set decision table is constructed, the attribute reduction of the information system can be carried out. The core idea of attribute reduction is to reduce redundant attributes and obtain attribute reduction subsets according to the size of attribute dependence or importance without affecting the classification and decision-making ability of the decision information table. Attribute reduction of VOLUME 10, 2022 information systems can maintain the classification ability of the information system and simplify the system's expression and optimize the system's operational performance. This paper adopts a heuristic attribute reduction algorithm based on attribute importance. The algorithm first finds the kernel of the decision-making system, then calculates the importance of each conditional attribute and adds it to the attribute set according to specific requirements until the set is a reduction. In the information system IS = U, A, V, f , if the indistinguishable relation induced by attribute set A is equal to the indistinguishable relation induced by its subset, then IND(A) = IND(A − {a}). Then, attribute a is a redundant attribute of attribute set A, and the process of eliminating redundant attributes in the attribute set is called knowledge reduction. An information system can have multiple attribute reductions, and the intersection of all reductions is called the core of the information system. Attribute reduction of information systems can maintain the classification ability of the information system and simplify the system's expression and optimize the system's operational performance.
In the onboard condition monitoring system of the loom, some attributes make only small contributions to the loom state decision and can even lead to the wrong state decision; thus, these irrelevant and misleading attributes must be eliminated. In the information system IS = U, C, D, V, f , the importance of attribute a relative to decision attribute D based on attribute set B can be determined by the following equation: where SIGr(a, B, D) describes the contribution of attribute a to decision attribute set D based on conditional attribute set B: the larger the value is, the more important attribute a is to decision-making. The heuristic attribute reduction algorithm flow based on attribute importance is shown in Fig. 8. The reduction algorithm based on attribute importance is applied to decision table 3, and the reduction result is: 1) Attribute set C a11 = {a 3 , a 4 , a 5 }; 2) Attribute set C a12 = {a 2 , a 4 }; 3) Attribute set C a13 = {a 2 , a 3 , a 5 }; Similarly, the reduction result of decision Table 4 is: 1) Attribute set C a21 = {a 1 , a 3 , a 5 }; 2) Attribute set C a22 = {a 1 , a 4 }; 3) Attribute set C a23 = {a 3 , a 4 , a 5 };

C. MACHINE LEARNING GENERALIZATION PERFORMANCE CONTROL
Because an industrial site where data are collected is typically noisy, this decision-making algorithm may lead to overfitting.
In order to ensure more reliable state monitoring results, the reduction results of rough set methods need to be improved. According to the structural risk minimization (SRM) principle, to reduce the structural risk of the rough set method, both empirical risk and confidence range must be minimized concurrently. However, empirical risk minimization and confidence range minimization are often contradictory. Therefore, the structural risk control of the rough set method is a typical multiobjective optimization problem, and there are multiple relative optimal solutions. Under the premise of not deteriorating other goals, these solutions can only ensure that one or a few core goals that are most concerned are optimal.

1) EMPIRICAL RISK CONTROL ALGORITHM BASED ON GENETIC MULTIOBJECTIVE OPTIMIZATION
A genetic algorithm is a computational model of an optimization problem that simulates Darwin's natural evolution process. It has been widely used in machine learning, neural network, optimal control and other fields. It has the characteristics of a flexible search process, wide application range, global optimization ability and high optimization process efficiency. In this paper, the genetic multi-objective optimization method is used to optimize the reduction steps of the rough set method. The application steps of the genetic algorithm can be summarized as follows: 1) Determination of the initial population: we encode the candidate solutions in the feasible domain, randomly select a part as the first generation encoding group, and then calculate the fitness of each encoding concurrently; 2) Selection operation: Similar to natural evolution, the selection mechanism of the genetic algorithm should ensure that individuals with high fitness are more easily selected. Usually, the probability of an individual being 59730 VOLUME 10, 2022 selected can be described as: 3) Crossover and mutation operation: The crossover operator selects some bits of the two individual samples of the population to generate the next generation of individuals by random exchange, and the mutation operator randomly reverses a specific bit in the individual samples. Typically, crossover and mutation should be applied concurrently to avoid prematurely trapping the algorithm into a local optimum. 4) Optimal population output: We repeat this process of selection, mutation, and crossover until the end condition is met, and the new generation of the population obtained is the optimal solution set found by the algorithm. When applying the genetic algorithm, selection, inheritance, and mutation operations are standard processes, but the coding process and fitness evaluation must be designed according to different applications. When using the genetic algorithm to evaluate the structural risk of the attribute subset of the decision table, each condition attribute subset is regarded as a candidate solution and coded. The coding rule is as follows: when the ith condition attribute in the decision table is included in the subset condition attribute subset, the ith bit of the code is 1; otherwise, it is 0.
Fitness describes the individual's contribution to the optimization goal, and a suitable fitness evaluation mechanism is the key to the success of the genetic algorithm. When using the genetic algorithm to control the structural risk of the rough set method, the empirical risk corresponding to the conditional attribute subset is defined as: The algorithm flow for obtaining the fitness of the candidate solution is shown in Fig. 9.

2) PERFORMANCE TEST OF THE GENETIC OPTIMIZATION ROUGH SET METHOD
In order to verify the effectiveness of the empirical risk control algorithm based on multiobjective genetic optimization, 10 UCI datasets were used for testing. Table 5 shows the classification accuracy of the conventional rough set method for each UCI dataset when the threshold is 0.95, the attribute importance index parameter is 0.5, as well as the classification accuracy of the algorithm using the multiobjective genetic optimization empirical control method.
The experimental results show that the rough set method optimized by the genetic algorithm more easily obtains high classification accuracy with different datasets.

3) EXAMPLE OF ATTRIBUTE REDUCTION BASED ON GENETIC MULTIOBJECTIVE OPTIMIZATION
The reduction with the smallest number of attributes is typically considered the best reduction. However, not all the  reductions of decision tables have only a unique reduction result with the smallest number of attributes. In order to choose the best reduction result of the decision table, the empirical risk control algorithm based on multiobjective genetic optimization is used to evaluate the fitness of Tables 3 and 4, and the results are shown in the following  table. 1) The selection basis of the attribute reduction results of decision Table 3 is shown in Table 6.
2) The selection basis of the attribute reduction results of decision Table 4 is shown in Table 7. VOLUME 10, 2022  After evaluation, the best-reduced attribute set of decision Table 3 is C a12 = {a 2 , a 4 }, and the best-reduced attribute set of decision Table 4 is C a22 = {a 1 , a 4 }. In addition, if the risk of taking an attribute value is relatively high, the order of the decision attribute rule set can be appropriately adjusted according to the dominant order value.

IV. JUDGMENT AND DECISION-MAKING METHOD OF MONITORING SYSTEM STATUS A. EXTRACTION METHOD OF DECISION RULES BASED ON ROUGH SET THEORY
After attribute reduction is completed, decision rules can be constructed by reducing attribute sets and attribute values. After processing by the rough set rule extraction algorithm, the corresponding relationship between the condition attribute and the decision attribute of the information system is shown in Fig. 10.
For information system IS = U, C, D, V, f , we let its attribute reduction result B be the proper subset of attribute set C, U/B means classify U according to B set, U/D means that U is classified according to D set, X belongs to U/B, and Y belongs to U/D. Thus, the decision rule of the information system can be expressed as: where DES(X, B) is called the rule antecedents, which is the condition part of the rule; DES(Y, D) is called the rule consequences, which is the decision part of the rule; and DES(X, B) is defined as: where a = f(x, a) represents the essential elements of the class description. Due to data inconsistency and uncertainty, there may be a deterministic or possible relationship between rule antecedents and rule posteriors. According to generalization decision theory, the objects with the same generalization decision value in the universe are divided into the same set K. If the generalization decision of an object subset K is |δB(x)| = 1, then all objects in K can be accurately classified under the knowledge level given by B. If the generalization decision of the object subset K is |δB(x)| > 1, then all objects in K cannot be accurately classified under the knowledge level given by B. The generalization decision of object x in U concerning attribute set B is defined as: where v i is the decision attribute. Therefore, the rough set method's minimum rule set extraction algorithm flow is shown in Fig. 11. In order to obtain the best classification accuracy, it should be ensured that a smaller set of rules is obtained when the decision rules are extracted. The following takes the spindle wear identification and weft tension parameter monitoring as examples to extract the minimum ruleset.
1) The rule set extracted from decision Table 3 is shown in Table 8.
2) The rule set extracted from decision Table 4 is shown in Table 9.

B. UNCERTAINTY REASONING
When there is a new object for rule matching, three situations may occur: (1) The new object matches only one rule.
(2) The new object matches multiple rules.
(3) The new object does not match any rules.   Case (1) can directly determine decision-making attributes, and case (3) can typically be converted into the case (1) or (2) using the partial rule matching method. In case (2), the most common method is to score the support of each matching rule for the new object and then select the rule with the most considerable support for the decision of the new object.

1) UNCERTAINTY REASONING METHOD BASED ON DSmT THEORY
The new object can infer the decision attribute value by matching the rules in the rule base. However, when the new instance matches a nondeterministic rule with credibility lower than 1, the unique decision attribute value cannot be obtained. In order to deal with the uncertainty of system rule matching, this paper incorporates the DSmT uncertainty inference method. In this application, the recognition framework of DSmT is a collection of new object matching rules, defined as: The superpower set DU generated by the union and intersection of elements in the identification frame satisfies the following conditions: 1) φ, θ 1 , θ 2 , . . . , θ n ∈ D U .
2) If sets A and B belong to the superpower set DU, then the intersection and union of A and B also belong to DU; 3) Only if the elements satisfy conditions (1) and (2) Then, m(A) is called the basic probability assignment of A, which represents the exact degree of confidence in proposition A. The trust function on U is defined as: The function BEL(A) represents the total trust of A. The likelihood function that defines the recognition frame U is: where PL(A) represents the degree of trust of A. When three rules are initially matched, the description of the implementation process of the DSmT-based rule uncertainty inference method is shown in Fig. 12.

2) EXAMPLE OF UNCERTAINTY REASONING FOR LOOM CONDITION MONITORING
Taking the uncertainty rules 6 and 8 in Table 8 as examples, the decision rule matching reasoning is carried out. 1) We let the new instance be as shown in Table 10.
2) According to the rule matching method, instance x k matches rules 6 and 8 in table 8, and its corresponding decision attributes may be d 1 = 1 and d 2 = 2; thus, the identification framework for determining the target is U = {d 1 , d 2 }. Then, the superpower set is: In the information table, the proportion of support of the rule, the prior probability of the value of the decision attribute, and the proportion of the value of attributes a 3 VOLUME 10, 2022   These calculations indicate that various rule evaluation methods can be integrated through fusion, which can markedly increase the discrimination of decision support probability. If a threshold is introduced, the decision value of the newly added objects listed above can be determined to be d 2 .

V. TEST OF THE ON-BOARD CONDITION MONITORING SYSTEM OF LOOMS A. LOOM STATE DATA COLLECTION TEST
The onboard condition monitoring platform of the loom collects data according to the characteristics of the first generation and simultaneously displays data of different sampling frequencies. After analyzing the data collected by the loom's analog quantity, the loom's average spindle speed is 330.01 RPM, which is near the actual system setting. Also, the maximum deviation is 1.01 RPM, and the relative error is less than 0.31%, which meets the measurement requirements of the spindle speed of the loom. Similarly, the relative errors of other analog acquisition parameters of the system are calculated, and the relative errors can be lower than 0.35%.
The set values of the loom parameters and the calculation results of the relative error are shown in Table 11.  According to the index of the attribute data in the table, it can be known that the data sampling results of each attribute item of the monitoring system can genuinely reflect the actual situation of the loom parameters. The system can also realize real-time synchronization of loom state characteristic data, providing data support for state reasoning.

B. RECOGNITION RATE TEST OF THE ONBOARD CONDITION MONITORING SYSTEM OF LOOMS
In order to test the effect of the proposed loom on-board condition monitoring method, taking the identification of main shaft system wear as an example, the system was installed on two looms of the same model with different degrees of wear. The loom state data were collected for 1000 seconds, respectively. The 2000 data instances are randomly divided into ten groups, each containing 200 data instances. Table 12 compares recognition rates between the decision network constructed by the traditional rough set method and the decision network constructed by the improved rough set method.
The above test experiments on the recognition rate of spindle wear show that the average recognition rate of the loom state mapping network constructed by the traditional rough set method for spindle wear is 99.955%; after improvement, the average recognition rate can reach 99.998%. Compared with the traditional rough set method, the genetic multiobjective optimization and DSmT improved rough set method have a better recognition effect on the loom state decision.

VI. CONCLUSION
This paper presents a decision method for condition monitoring of high-speed rapier loom systems, mainly improving the attribute reduction step and the decision matching step of the traditional rough set method. A spindle dynamics model is developed for the spindle, the core of the weaving process, and a table of weaving machine spindle parameters are summarised to identify the sources of weaving machine monitoring data. The addition of warp vibration monitoring is proposed to improve the monitoring system's decision accuracy and compensate for the lack of data sources for conventional weaving machine monitoring. The data is analyzed using the rough set method. For discontinuous data types in the time domain, the data are first pre-processed using interpolation methods, which give a complete picture of warp tension fluctuations. For the problem of complex loom attribute data and the unclear association between data content and decision making, the rough set method is used for processing. Experiments show that the loom attribute data can be effectively extracted using the rough set method from the loom state decision rules. However, the pure rough set method suffers from weak machine generalization and uncertain rules for matching new objects. In order to improve the generalization performance of machine learning, this paper proposes a genetic multi-objective optimization method incorporating the rough set method with a genetic algorithm, in which each conditional attribute subset of the decision table is treated as a candidate solution encoded. The genetic algorithm is applied to evaluate the structural risk of the attribute subset of the decision table to construct a weaving machine state decision rule base with a good recognition effect and high decision accuracy. In order to reduce the uncertainty of matching rules for new objects, this paper proposes a rough set method incorporating the uncertainty derivation method of DSmT to assign basic probabilities and two-level source combinations to the rules that may match so as to derive the decision with the highest accuracy, and experiments show that this method increases the discrimination of decision support probabilities. Finally, the condition monitoring system is tested on a actual loom. The experimental test shows that the average recognition rate of the spindle wear problem is 99.955% with the loom state mapping network constructed by the traditional rough set method. After the rough set method is improved by genetic algorithm and DSmT theory, the average recognition rate of spindle wear identification is 99.998%. Compared with the traditional rough set method, the improved rough set method can achieve better recognition results for the weaving machine monitoring mapping network. Overall, this paper proposes a series of improvements and implementations for condition monitoring of high-speed rapier weaving machines, hopefully providing some reference for researchers in this field.
WEILING LIU received the bachelor's and master's degrees in mechanical engineering from the Hebei University of Technology, in 1995 and 1998, respectively, and the Ph.D. degree from Tianjin University, in 2006.
From 2009 to 2011, she conducted postdoctoral research with Bao Jingling at the Tianjin Academy of Environmental Sciences. She is currently an Associate Professor with the Hebei University of Technology. Her main research interests include artificial intelligence and automation control.
PING LIU received the graduate degree from the Hebei University of Technology, in 2020, where she is currently pursuing the master's degree. Her research interests include intelligent control and health management.
XIAOLIANG WANG is currently pursuing the master's degree in electronic information with the Hebei University of Technology. His research interests include embedded technology and intelligent control.