A numerical control machine tool space-time fault propagation and diffusion analysis method based on multiple factors

Abstract

The application discloses a kind of based on multi-factor influence under numerical control machine tool space-time fault propagation diffusion analysis method, belongs to numerical control machine tool technical field, including the following steps: based on numerical control machine tool historical fault data, establish time dimension fault probability model;Establish space dimension fault propagation hierarchical topology directed graph model;Establish numerical control machine tool function component node comprehensive importance degree model;Based on PageRank method, calculate the fault influence degree in space dimension hierarchical topology model;While considering the fault tolerance ability and the most likely probability of failure mode of function component itself and other factors, propose space-time fault propagation diffusion model;By analysis method, reduce the fault location range, determine key function component and key fault propagation diffusion path;The application fully considers the influence ability of fault propagation characteristics in time-space dimension and node itself on fault propagation diffusion, compared with traditional fault propagation analysis method, more in line with engineering practice.

Description

Technical Field

[0001] This invention belongs to the field of CNC machine tool technology and relates to a method for analyzing the spatiotemporal fault propagation and diffusion of CNC machine tools based on the influence of multiple factors. Specifically, it involves a fault propagation analysis method for establishing a time-dimensional fault probability model, a spatial-dimensional hierarchical topological directed graph model, a functional component node comprehensive importance model, and a node fault tolerance and spatiotemporal fault propagation and diffusion model. Background Technology

[0002] CNC machine tools are indispensable components in precision machining processes. They are complex systems integrating multiple functional components such as mechanical, electrical, and hydraulic systems. The high degree of coupling between these internal components makes them prone to various unforeseen failures. In most cases, these unexpected failures originate from a single functional component. If these failures are not addressed promptly, even small malfunctions accumulate within the system and gradually propagate to other related functional components, eventually affecting the entire machine tool and leading to downtime. This can cause incalculable losses to the company. Therefore, fault propagation analysis of CNC machine tools is crucial for improving their reliability.

[0003] Currently, research on fault propagation analysis methods for CNC machine tools mainly revolves around theoretical methods based on Petri nets, complex networks, cellular automata, and graph theory to study the fault propagation mechanism of machine tool systems. Traditional Petri nets, due to the non-reusable nature of resources in their models, struggle to clearly describe concurrent phenomena in CNC fault propagation. Furthermore, Petri nets can only establish relatively simple models; their modeling efficiency drops significantly when the system encounters complex and difficult-to-understand fault modes at system nodes. Cellular automata models are discrete-time and discrete-space dynamic models, but they tend to overlook the influence of the overall system structure on the changes in unit states. They also stipulate that systems composed of units following the same evolutionary law evolve according to an equal-length discrete-time distribution. However, CNC machine tool systems have complex structures; the states of each component do not change at equal times and cannot follow the same laws, making this model unsuitable for describing the fault propagation process of CNC machine tool systems. Fault propagation models based on complex topological networks are often used to describe the cascading failure process caused by overload in systems with complex fault transmission structures. However, the modeling and simulation processes of topological network models are cumbersome and time-consuming, and the accuracy of the results is closely related to the modeling process. Graph theory-based fault propagation analysis methods are mainly used for complex systems with clear logic and well-defined fault mechanisms. However, when the system is large in scale and the relationships between factors within the system are highly complex, building the corresponding model is a large and tedious task.

[0004] From the practical perspective of CNC machine tools, most current research on fault propagation models only considers fault mechanisms qualitatively, using graph theory or topological network methods to construct fault propagation models. These methods only provide a preliminary description of the propagation process between components of a CNC machine tool system. However, in actual machine tool service, functional components are affected by a complex interplay of factors such as time, space, critical components, and fault modes. Relying on a single method is insufficient to accurately characterize the propagation and diffusion mechanism of faults within the machine tool system, leading to deviations in fault path identification. Summary of the Invention

[0005] Current fault propagation analysis methods only provide a preliminary description of the propagation process between components of CNC machine tool systems, lacking consideration of the interplay of multiple factors such as time, space, critical components, and fault modes affecting machine tool functional components, leading to inaccurate identification of critical fault paths. This invention provides a spatiotemporal fault propagation and diffusion analysis method for CNC machine tools based on the influence of multiple factors. Starting from both time and space dimensions, it constructs a spatiotemporal fault propagation and diffusion model for CNC machine tools under the influence of multiple factors, clarifies the spatiotemporal fault propagation and diffusion mechanism, identifies critical propagation paths, determines key system nodes, improves the service life of CNC machine tools, reduces enterprise maintenance costs, and ensures the safety and reliability of machine tools during operation.

[0006] To solve the above-mentioned technical problems, the present invention is implemented using the following technical solution, which is described below in conjunction with the accompanying drawings:

[0007] A method for analyzing the spatiotemporal propagation and diffusion of CNC machine tool faults under the influence of multiple factors includes the following steps:

[0008] Step 1: Divide the CNC machine tool into several functional components according to the structural and functional mapping relationship of the product. Based on the failure interval time of the CNC machine tool, establish a time-dimensional failure probability model for each functional component using the least squares method.

[0009] Step 2: Using Failure Mode and Effects Analysis (FMEA) to conduct correlation analysis on the functional components of the CNC machine tool, obtain the direct influence matrix of the functional components of the CNC machine tool, and establish a spatial layered topological directed graph model of the CNC machine tool through matrix decomposition and reconstruction.

[0010] Step 3: Consider the centrality index of functional component nodes in the hierarchical topological directed graph model, and establish a comprehensive function degree model of functional component nodes through the analytic hierarchy process (AHP).

[0011] Step 4: Calculate the fault impact value of each functional component node and each connecting edge in the hierarchical topological directed graph model based on the PageRank algorithm, and sort the importance of each functional component node and each edge.

[0012] Step 5: Taking into account factors such as the fault tolerance capability of the functional components themselves and the probability of the most likely occurrence of the failure mode, calculate the fault propagation intensity of the hierarchical topological directed graph model through the spatiotemporal fault propagation model.

[0013] Step 6: Narrow down the fault location range of the CNC machine tool by measuring the fault propagation intensity, and determine the key functional component nodes and key fault propagation paths.

[0014] The specific method for constructing the time-dimensional fault probability model in step one is as follows:

[0015] Based on the functional structure mapping relationship of CNC machine tools, CNC machine tools are divided into several functional components according to the structural function mapping relationship of the product, and the failure interval time of each functional component is statistically analyzed.

[0016] (1) Establishment of the empirical distribution function;

[0017] Based on formula (1), an empirical distribution function F is established based on the fault interval time. s (t);

[0018]

[0019] In the formula, i = 1, 2, ..., N; N represents the number of fault intervals;

[0020] (2) Parameter estimation of the failure probability model for each functional component node;

[0021] Assuming that the fault data of the functional component nodes of the CNC machine tool follow a two-parameter Weibull distribution, the cumulative fault probability distribution function is calculated using formula (2);

[0022]

[0023] In the formula, t represents the time variable, t≥0; η represents the scale parameter, η≥0; α represents the shape parameter, α≥0;

[0024] The parameters of the assumed distribution model are estimated and solved using the least squares method. The specific solution steps are as follows: After rearranging the terms of formula (2), we can obtain... Taking the logarithm of both sides of the equation twice yields the following result. make X l =lnt i This leads to the univariate linear regression equation Y. l =αX l -αlnη, we can calculate α=b1,

[0025] (3) Correction of parameters estimated by the failure probability model;

[0026] Because the amount of machine tool fault data is relatively small, the parameter estimation results may have some bias. For any sample size n ≥ 3, the unbiased correction coefficient G(n) for the estimated parameters always has G(n) < 1, and...

[0027] When n = 3, the unbiased correction coefficient G(n) of parameter α is calculated using formula (3);

[0028]

[0029] When n is an even number greater than or equal to 4, the unbiased correction coefficient G(n) of parameter α is calculated using formula (4);

[0030]

[0031] When n is an even number greater than or equal to 5, the unbiased correction coefficient G(n) of parameter α is calculated using formula (5);

[0032]

[0033] The unbiased correction of the shape parameter α is calculated using formula (6);

[0034]

[0035] The unbiased correction coefficient G(n,α) of the scale parameter η is calculated using formula (7). * );

[0036]

[0037] The unbiased correction of parameter η is calculated using formula (8);

[0038]

[0039] (4) Hypothesis distribution model testing;

[0040] Considering the machine tool failure as a small sample case, at a significance level of γ = 0.05, the goodness of fit of the hypothetical distribution model is tested using the test formula (9), D. n This can be obtained by looking up the relevant table, if D n <D n,γ If the result is positive, the null hypothesis is accepted; otherwise, the null hypothesis is rejected.

[0041] D = max|F s (t)-F(t)| (9)

[0042] In the formula, F(t) represents the calculated distribution function;

[0043] The parameters of the hypothetical distribution model were estimated using the least squares method, and unbiased corrections and hypothesis testing were performed on the estimated parameters. Thus, the time-dimensional failure probability model was completed. The establishment of.

[0044] The specific modeling steps for the spatial dimension hierarchical topological directed graph model of the CNC machine tool in step two are as follows:

[0045] (1) Construct a direct impact matrix based on the associated fault data, and construct a standardized direct impact matrix;

[0046] After dividing the CNC machine tool into several functional components, the correlation analysis of the functional components of the CNC machine tool is carried out using the failure model and the impact analysis method (FMEA). The direct influence matrix Y of the CNC machine tool functional components is obtained using formula (10), and the standardized direct influence matrix X is constructed using formula (11).

[0047]

[0048]

[0049] In the formula, y ij Represents the functional component node v i The functional component node v was affected by a fault. j Frequency of failures; n represents the number of nodes in the functional component;

[0050] (2) Construct the comprehensive impact matrix of the fault;

[0051] Taking into account the direct or indirect fault impact relationships and the degree of impact between functional components, a comprehensive fault impact matrix is ​​constructed using formula (12);

[0052]

[0053] In the formula, E d Represents an n-order identity matrix;

[0054] (3) Considering the factors of the functional components themselves, construct the overall influence matrix using formula (13);

[0055] H z =T+E d (13)

[0056] (4) Construct the reachability matrix M using formula (14). s ;

[0057]

[0058] In the formula, λ represents the set threshold used to simplify the system. Considering that the number of divisions in the machine tool system is small, λ = 0 is taken.

[0059] (5) Deconstruct the reachability matrix and partition the hierarchy;

[0060] Using formula (15), the reachability matrix M s The set of functional components corresponding to all columns with a value of 1 in the i-th row is called the functional component node v. i The reachable set R i The set of functional components corresponding to all rows in the i-th column that are 1 is called the antecedent set S. i If the common set C i =R i ∩S i =R i If true, then in the reachability matrix M s Remove row i and column i from the middle, and the functional component node v i It belongs to the terminated functional component and is located at the top level L1. Repeat step (5) until all functional component nodes are removed to realize the hierarchical division of functional component nodes.

[0061]

[0062] (6) Construct the skeleton matrix and initially establish a hierarchical topological directed graph model;

[0063] Construction principle 1: Form a lower triangular matrix based on the order of removal;

[0064] Construction Principle 2: Remove parameters that have cross-level binary relations or that have binary relations themselves (i.e., m). ij =0);

[0065] (7) Add virtual nodes to eliminate direct impact relationships in leaps and establish a hierarchical topological directed graph model for fault propagation. It should be noted that virtual nodes do not exist in the actual system.

[0066] Thus, the establishment of the spatial-dimensional fault hierarchical topological directed graph model of CNC machine tools was completed.

[0067] The specific modeling steps for the comprehensive importance model of the CNC machine tool functional components in step three are as follows:

[0068] The overall importance I of the functional component node is calculated using formula (16);

[0069] I i =w1DC i +w2BC i +w3CC i (16)

[0070] In the formula, w 1,2,3 The weights representing the centrality of each functional component node are obtained through the analytic hierarchy process (AHP); DCi Represents the functional component node v i Degree centrality; BC i Indicates the betweenness centrality of functional component nodes; CC i Indicates proximity centrality;

[0071] The degree centrality DC of the functional component nodes is calculated using formula (17). i index;

[0072]

[0073] In the formula, i represents the target functional component node v i j represents any functional component node v in the network. j ; n represents the number of functional component nodes in the hierarchical topological directed graph model; a ij Represents the reachability matrix M s Elements in;

[0074] The betweenness centrality BC of the functional component nodes is calculated using formula (18). i index;

[0075]

[0076] In the formula, N(j,k) represents the functional component node v j and v k The number of shortest paths between nodes; N(j,i,k) represents the edge betweenness number, and represents the number of nodes v. j and v k Between v i The number of shortest paths;

[0077] The proximity centrality CC of the functional component nodes is calculated using formula (19). i index;

[0078]

[0079] In the formula, d ij Represents the functional component node v i and v j The shortest distance between them.

[0080] In step four, the fault impact values ​​of each functional component node and each connecting edge of the CNC machine tool are calculated. The specific steps are as follows:

[0081] (1) Fault impact of functional component nodes Pr(v) i );

[0082] The failure impact degree of functional component nodes in a hierarchical topological directed graph model is calculated based on the PageRank algorithm. The initial state transition matrix Q = [q] is obtained by transposing the standardized direct impact matrix X. ij ] n×n The influence values ​​of all functional component nodes are obtained by iteratively solving formula (20).

[0083]

[0084] In the formula, pr x+1 ,pr x d represents the failure impact vector of each functional component node obtained in the (x+1)th and xth iterations, respectively; d is the damping factor, d = 0.3;

[0085] Assign initial value to pr Its initial value will not affect the convergence effect and final result of formula (20). When the iteration convergence threshold ε = 0.0001, and the iteration calculation satisfies |pr x+1 -pr x When | < ε, the iteration ends, and the failure impact value Pr(v) of all functional component nodes is obtained. i );

[0086] (2) Functional component node v i and v j The influence of the directed edge failure between them, Pr(e) i→j );

[0087] Calculate the functional component node v using formula (21) i and v j The influence of the directed edge failure between them, Pr(e) i→j );

[0088]

[0089] In the formula, Pr(v i ) and Pr(v j ) represents the functional component node v i and v j The degree of impact of the fault;

[0090] The spatiotemporal fault propagation and diffusion model in step five integrates the influence of the temporal fault probability of functional components, the spatial directed graph model, the fault tolerance capability of functional component nodes, the comprehensive importance of functional component nodes, and the probability of the most likely occurrence of functional component fault modes on the spatiotemporal propagation intensity of faults. This establishes a spatiotemporal fault propagation and diffusion model for CNC machine tools, and the calculation result of the model is the fault propagation intensity. The specific steps are as follows:

[0091] Establish a set V = {v1, v2, ..., v} based on functional component nodes. n}, establish a set e based on the edges connecting the functional component nodes. ij ,i≠j, establish a set FM based on the failure modes of functional component nodes. ij (f), i = 1, 2, ..., n, j = 1, 2, ..., n, n represents the number of functional component nodes; different functional components have different fault tolerance capabilities. The larger the Tor value, the stronger the fault tolerance capability of the functional component node. The Tor value is usually given by experiments and expert experience, Tor ∈ [0, 1].

[0092] The fault propagation intensity in the spatiotemporal dimension of the CNC machine tool is calculated using formula (22);

[0093]

[0094] In the formula, w A,B The weight of the functional component node is represented by w, which is obtained through the analytic hierarchy process. A and w B Weighting coefficients; This represents the functional component node v after k-1 steps of propagation. i The probability of failure in the current time dimension Similarly; I i Represents the functional component node v i The comprehensive importance model, I j Similarly; Pr(e i→j ) represents a directed edge e i→j The degree of failure impact; Tor represents the functional component node v i and functional component node v j The product of fault tolerance capabilities; This indicates that during the k-th step of fault propagation, the functional component node v i The r-th failure mode f ir This leads to the functional component node v j The probability value of the most likely failure mode.

[0095] The specific steps in step six to narrow down the fault location range of the CNC machine tool and determine the key functional component nodes and key fault propagation paths are as follows:

[0096] (1) Identification of key propagation paths;

[0097] In the propagation path of CNC machine tool system, there are series propagation and series-parallel propagation. When there is a series relationship between multiple nodes, the fault propagation intensity value between two nodes is calculated using formula (23) as the product of the fault propagation intensity of all passing nodes. When there is both a series relationship and a parallel relationship between multiple nodes, based on the fault propagation intensity of the series part of the path between two nodes, the parallel part is summed using formula (24), and all propagation paths are arranged in descending order.

[0098]

[0099]

[0100] In the formula, k represents the functional component node v i Propagate to functional component node v j The fault propagation strength at the k-th step;

[0101] (2) Determination of key functional component nodes in the propagation path;

[0102] The key functional components are ultimately determined based on the overall importance of key functional component nodes, key propagation paths, the impact of failures of key functional components, and the intensity of path propagation.

[0103] Thus, by considering both time and space dimensions, the spatiotemporal fault propagation mechanism of CNC machine tools has been clarified, the critical path of fault propagation has been identified, and the critical fault nodes of the system have been determined.

[0104] Compared with the prior art, the beneficial effects of the present invention are:

[0105] The fault propagation analysis method provided by this invention considers the structural characteristics of fault propagation from both qualitative and quantitative perspectives. It also analyzes the propagation and diffusion mechanism of faults in the temporal and spatial dimensions from both temporal and spatial dimensions. It considers the impact of various factors on fault propagation from the perspective of distribution and diffusion, thereby reducing enterprise maintenance costs and providing a guarantee for the safety and reliability of machine tools during operation. Attached Figure Description

[0106] Figure 1 This is a flowchart of the spatiotemporal fault propagation and diffusion analysis method for CNC machine tools described in this invention;

[0107] Figure 2 This is the hierarchical topological directed graph model of CNC machine tools described in this invention;

[0108] Figure 3 This is the spatiotemporal fault propagation and diffusion model for CNC machine tools described in this invention;

[0109] Figure 4 This is the critical fault path and critical node identification diagram of the CNC machine tool described in this invention. Detailed Implementation

[0110] The present invention will now be described in detail with reference to the accompanying drawings:

[0111] Please see Figure 1 The present invention provides a method for analyzing the spatiotemporal fault propagation and diffusion of CNC machine tools under the influence of multiple factors, which specifically includes the following steps: establishing a time-dimensional fault probability model; establishing a spatial-dimensional hierarchical topological directed graph model; calculating the comprehensive importance model of functional component nodes; establishing a spatiotemporal fault propagation and diffusion model under the influence of multiple factors; and identifying key fault paths and key nodes.

[0112] Step 1: Divide the CNC machine tool into several functional components according to the structural and functional mapping relationship of the product. Based on the failure interval time of the CNC machine tool, establish a time-dimensional failure probability model for each functional component using the least squares method.

[0113] Step 2: Using Failure Mode and Effects Analysis (FMEA) to conduct correlation analysis on the functional components of the CNC machine tool, obtain the direct influence matrix of the functional components of the CNC machine tool, and establish a spatial layered topological directed graph model of the CNC machine tool through matrix decomposition and reconstruction.

[0114] Step 3: Consider the centrality index of functional component nodes in the hierarchical topological directed graph model, and establish a comprehensive importance model of functional component nodes through the analytic hierarchy process (AHP).

[0115] Step 4: Calculate the fault impact value of each functional component node and each connecting edge in the hierarchical topological directed graph model based on the PageRank algorithm, and sort the importance of each functional component node and each edge.

[0116] Step 5: Taking into account factors such as the fault tolerance capability of the functional components themselves and the probability of the most likely occurrence of the failure mode, calculate the fault propagation intensity of the hierarchical topological directed graph model through the spatiotemporal fault propagation and diffusion model.

[0117] Step 6: Narrow down the fault location range of the CNC machine tool by analyzing the fault propagation intensity, and determine the key functional component nodes and key fault propagation paths;

[0118] I. Establishing a Time-Dimensional Fault Probability Model

[0119] Based on the functional structure mapping relationship of CNC machine tools, the CNC machine tool is divided into several functional components according to the structural function mapping relationship of the product. The actual fault interval of each functional component is statistically analyzed and substituted into F. s (t) = i - 0.3 / N + 0.4, obtaining the empirical distribution function of each functional component; assuming that each functional component follows a two-parameter Weibull distribution, its failure probability function can be expressed as F(t) = 1 - exp[-(t / η)] α], t≥0, where t represents the time variable, t≥0; η represents the scale parameter, η≥0; α represents the shape parameter, α≥0; the parameters of the assumed distribution model are estimated and solved using the least squares method. First, after rearranging the fault probability function, we can obtain 1 / (1-F(t) i ))=exp(t / η) α Taking the logarithm twice on both sides of the equation yields lnln(1 / (1-F(t)))=αlnt-αlnη. Let Y l =lnln(1 / (1-F(t))),X l =lnt, further yielding the univariate linear regression equation Y l =αX l Substituting -αlnη into the data yields the estimated parameters of the Weibull distribution. Because the amount of machine tool fault data is relatively small, the parameter estimation results may have some deviation. Therefore, an appropriate unbiased correction coefficient G(n) should be selected based on the actual number of fault intervals and substituted into the equation. Obtain the unbiased correction for the shape parameter α; substitute the corrected shape parameter into... Unbiased correction for the scaling parameter η; at a significance level of γ = 0.05, using the test formula D = max|F s The goodness of fit of the hypothetical distribution model is tested using (t)-F(t)|, D. n This can be obtained by looking up the relevant table, if D n <D n,γ If the result is positive, the null hypothesis is accepted; otherwise, the null hypothesis is rejected.

[0120] II. Spatial Dimensional Hierarchical Topological Directed Graph Model for CNC Machine Tools

[0121] After dividing the CNC machine tool into several functional components, a correlation analysis of the functional components is conducted using a failure model and the Factorization Effects Analysis (FMEA) method to obtain the direct influence matrix Y of the CNC machine tool functional components. A standardized direct influence matrix X is constructed by solving for the maximum value in each row of the matrix; and then, using T = X(E... d -X) -1 Construct a comprehensive fault impact matrix T, while also considering its own factors, through H z =T+E d Construct the overall influence matrix; then construct the reachability matrix M. s Based on principle 1: remove the order of precedence to form a lower triangular matrix and principle 2: remove parameters with skip-level binary relationships and those with binary relationships to construct a skeleton matrix; finally, add virtual nodes to eliminate skip-type direct propagation relationships and establish a hierarchical topological directed graph model for fault propagation.

[0122] III. Establishing a comprehensive importance model for functional component nodes

[0123] Through I i =w1DC i +w2BC i +w3CC i Calculate the overall importance of the functional component nodes, w 1,2,3 The weights representing the centrality of each functional component node are obtained through the analytic hierarchy process (AHP); DC i Represents the functional component node v i Degree centrality, through The calculation shows that i represents the target functional component node v. i j represents any functional component node v in the network. j ; n represents the number of functional component nodes in the hierarchical topological directed graph model; a ij Represents the reachability matrix M s Elements in BC; i The betweenness centrality of functional component nodes is represented by calculation. We obtain N(j,k) as the functional component node v. j and v k The number of shortest paths between nodes; N(j,i,k) represents the edge betweenness number, and represents the number of nodes v. j and v k Between v i Number of shortest paths; CC i To represent proximity centrality, by Calculations show that d ij Represents the functional component node v i and v j The shortest distance between them;

[0124] IV. Fault Influence Values ​​of Each Functional Component Node and Edge of CNC Machine Tool

[0125] The PageRank algorithm is used to calculate the fault impact Pr(v) of functional component nodes in a hierarchical topological directed graph model. i The calculation is performed, and the initial state transition matrix Q = [q] is obtained by transposing the standardized direct influence matrix X. ij ] n×n ; Assign an initial value to pr use Iteratively solve for the influence value of all functional component nodes, pr x+1 ,pr x Let represent the fault impact vectors of each functional component node obtained in the (x+1)th and xth iterations, respectively; d is the damping factor, d = 0.3; when the iteration convergence threshold ε = 0.0001, and the iterative calculation satisfies |pr x+1 -pr xWhen | < ε, the iteration ends, and the failure impact value Pr(v) of all functional component nodes is obtained. i ).pass Computational functional component node v i and v j The influence of the directed edge failure between them, Pr(e) i→j ), Pr(v i ) and Pr(v j ) represents the functional component node v i and v j The failure impact value.

[0126] V. Establishing a spatiotemporal fault propagation and diffusion model

[0127] Establish a set V = {v1, v2, ..., v} based on functional component nodes. n}, establish a set e based on the edges connecting the functional component nodes. ij ,i≠j, establish a set FM based on the failure modes of functional component nodes. ij (f), i = 1, 2, ..., n, j = 1, 2, ..., n, n represents the number of functional component nodes; different functional components have different fault tolerance capabilities. The larger the Tor value, the stronger the fault tolerance capability of the functional component node. The Tor value is usually given by experiments and expert experience, Tor ∈ [0, 1]; the time dimension failure probability F(t) of the functional component, the spatial dimension directed graph model, the fault tolerance capability Tor of the functional component itself, the comprehensive importance I of the functional component, and the probability of the most likely occurrence of the failure mode of the functional component FM are considered together. ij (f) The impact on the intensity of fault propagation in the spatiotemporal dimension, through... Calculate the fault propagation intensity in the spatiotemporal dimensions of CNC machine tools.

[0128] VI. Identify key functional component nodes and critical fault propagation paths

[0129] In the propagation path of a CNC machine tool system, there are series propagation and series-parallel propagation scenarios. When multiple nodes are in series, the propagation path is determined by... The fault propagation strength between two nodes is the product of the fault propagation strengths of all traversing nodes. When multiple nodes are connected in both series and parallel relationships, the fault propagation strength of the series path between the two nodes is calculated, and then... The parallel parts are summed, where k is the functional component node v. i Propagate to functional component node v j The fault propagation strength at the k-th step is determined, and all propagation paths are then sorted in descending order. Based on the overall importance of key functional component nodes, key propagation paths, the fault impact of key functional components, and the propagation strength of each path, the critical fault propagation paths and key functional components are ultimately determined.

[0130] Example

[0131] Fault information, including causes, locations, times, and durations of failures, was collected and statistically analyzed for a certain type of CNC machine tool from January to July. Correlation analysis was conducted on the machine tool system using the Fault Analysis Method (FMEA), resulting in 56 related fault information entries for 9 functional components of the CNC machine tool, as shown in Table 1.

[0132] Table 1 Actual Fault Intervals of Functional Components in CNC Machine Tools

[0133]

[0134]

[0135] Based on the time-dimensional failure probability model established in step one, the initial estimated parameters are first obtained using the least squares method. Then, an unbiased correction method is applied to the estimated parameters of each functional component to reduce the risk of parameter deviations due to the small sample size of failures in each functional component. Next, the KS test is used to verify whether the corrected parameter distribution model conforms to the assumed distribution. Finally, the failure probability function distribution and cumulative failure distribution of each functional component of the CNC machine tool are obtained. The estimated parameter correction values, hypothesis tests, and failure probabilities of each functional component distribution model are shown in Table 2.

[0136] Table 2 shows the revised estimated parameters, hypothesis tests, and failure probabilities for each functional component's distribution model.

[0137]

[0138]

[0139] Based on step two, a spatial layered topological directed graph model of the CNC machine tool is established. Correlation analysis is performed on the functional components of the CNC machine tool using failure modes and effects analysis methods to obtain the direct influence matrix Y of the functional components. A standardized direct influence matrix X is constructed by solving for the maximum value in each row of this matrix. Furthermore, a comprehensive failure influence matrix T is constructed, and the overall influence matrix H is obtained by considering its own factors. z .

[0140]

[0141] Then construct the reachability matrix M. s Based on principle 1: Following the order of removal, a lower triangular matrix is ​​formed; and based on principle 2: Parameters with skip-level binary relationships and those with their own binary relationships are removed to construct a skeleton matrix; finally, virtual nodes are added to eliminate skip-type direct influence relationships, establishing a hierarchical topological directed graph model for fault propagation. Please refer to [link to relevant documentation]. Figure 2 .

[0142]

[0143] Based on the comprehensive importance influence model of functional component nodes established in step three, the node centrality DC, betweenness centrality BC, and proximity centrality CC are solved. Furthermore, based on the weight matrix of the three as [10.21; 513; 10.3331], the weight coefficients are solved by the analytic hierarchy process, and finally the comprehensive importance I of functional component nodes is obtained, as shown in Table 3.

[0144] Table 3. Node Centrality and Overall Importance of Functional Components

[0145]

[0146] Based on step four, the fault impact values ​​of each functional component node and each connecting edge are calculated using the PageRank algorithm, as shown in Table 4.

[0147] Table 4. Fault impact values ​​for each functional component node and each connection edge.

[0148]

[0149]

[0150] Based on the spatiotemporal fault propagation and diffusion model established in step five, step one calculates the fault probability of each functional component under 1500 hours; step two obtains the spatial dimension hierarchical topological directed graph model; step three calculates the comprehensive importance of each functional component node; step four calculates the fault impact value of each functional component node and each connecting edge; then, based on historical fault information and expert judgment, the fault tolerance coefficient of each functional component is obtained, and the maximum probability of occurrence of each functional component's fault mode is obtained through fault analysis methods, as shown in Table 5. The fault propagation intensity is calculated by substituting the above data into the spatiotemporal fault propagation and diffusion model; please refer to [reference needed]. Figure 3 .

[0151] Table 5. Relevant fault data for each functional component

[0152]

[0153] Based on step six, identify critical functional component nodes and critical fault propagation paths. Please refer to [link / reference]. Figure 3As can be seen, there are four long paths for the fault to propagate from layer L1 to layer L5: path (a) EH-NC-SM; path (b) EHCSM; path (c) EHFSM; and path (d) EHLA. Furthermore, it can be observed that the fault propagates from functional component node E to functional component node S not only through a single path, but also through both series and parallel propagation links. Please refer to [link to relevant documentation]. Figure 4 Based on the spatiotemporal fault propagation model, the propagation intensity of the four paths was calculated: Path (b): 3.88e-8 > Path (c): 3.503e-8 > Path (a): 3.424e-8 > Path (d): 8.460e-9.

[0154] The product safety manual defines a fault propagation threshold; when a fault spreads from one node to another, the propagation threshold is below 10. -8 When the fault propagation is considered to have terminated, the failure is considered to have terminated. Comparing the four paths, it was found that fault propagation can occur between L1 to L5 in paths (a), (b), and (c), with path (c) having the highest failure probability. In path (d), the fault only occurs between L1 and L4. Compared to other functional components, the spindle system S, lubrication system L, and hydraulic system H have a higher probability of failure, a conclusion consistent with expert experience. Therefore, maintenance measures for these three functional components should be given special consideration when developing maintenance plans.

[0155] Based on the functional structure mapping relationship, this invention divides the functional components of CNC machine tools and establishes a time-dimensional fault probability model based on correlation analysis. According to the direct influence relationship matrix, a spatial-dimensional hierarchical topological directed graph model is obtained through matrix transformation and decomposition. In addition, considering the comprehensive importance of each functional component, the comprehensive influence of each functional component node and edge, the fault tolerance capability of each functional component, and the fault mode of each functional component, a spatiotemporal fault propagation and diffusion model is established to identify key fault nodes and key propagation paths, and to clarify the spatiotemporal fault propagation and diffusion mechanism.

Claims

1. A method for analyzing the spatiotemporal propagation and diffusion of CNC machine tool faults under the influence of multiple factors, characterized in that, Includes the following steps: Step 1: Divide the CNC machine tool into several functional components according to the structural and functional mapping relationship of the product. Based on the failure interval time of the CNC machine tool, establish a time-dimensional failure probability model for each functional component using the least squares method. Step 2: Using Failure Mode and Effects Analysis (FMEA) to conduct correlation analysis on the functional components of the CNC machine tool, obtain the direct influence matrix of the functional components of the CNC machine tool, and establish a spatial layered topological directed graph model of the CNC machine tool through matrix decomposition and reconstruction. Step 3: Consider the centrality index of functional component nodes in the hierarchical topological directed graph model, and establish a comprehensive importance model of functional component nodes through the analytic hierarchy process (AHP). Step 4: Calculate the fault impact of each functional component node and each connecting edge in the hierarchical topological directed graph model based on the PageRank algorithm, and sort the importance of each functional component node and each edge. Step 5: Taking into account factors such as the fault tolerance capability of the functional components themselves and the probability of the most likely occurrence of the failure mode, calculate the fault propagation intensity of the hierarchical topological directed graph model through the spatiotemporal fault propagation and diffusion model. Step 6: Narrow down the fault location range of the CNC machine tool by analyzing the fault propagation intensity, and determine the key functional component nodes and key fault propagation paths; The spatiotemporal fault propagation and diffusion model in step five integrates the influence of the temporal fault probability of functional components, the spatial directed graph model, the fault tolerance capability of the functional components themselves, the overall importance of the functional components, and the probability of the most likely occurrence of the functional component's fault mode on the intensity of fault propagation in the spatiotemporal dimension. The specific steps are as follows: Establish a set V = {v1, v2, ..., v} based on functional component nodes. n }, establish a set e based on the edges connecting the functional component nodes. ij ,i≠j, establish the set FM based on the failure modes of functional component nodes. ij (f), i = 1, 2, ..., n, j = 1, 2, ..., n, n represents the number of functional component nodes; different functional components have different fault tolerance capabilities. The larger the Tor value, the stronger the fault tolerance capability of the functional component node. The Tor value is usually given by experiments and expert experience, Tor ∈ [0, 1]. The following formula is used to calculate the fault propagation intensity in the spatiotemporal dimensions of a CNC machine tool; In the formula, w A,B The weight of the functional component node is represented by w, which is obtained through the analytic hierarchy process. A and w B Weighting coefficient; P i k-1 This represents the functional component node v after k-1 steps of propagation. i The probability of failure in the current time dimension, P i k-1 =F i k-1 (t), i = 1, 2, ..., n, Similarly; I i Represents the functional component node v i The comprehensive importance model, I j Similarly; Pr(e i→j ) represents a directed edge e i→j The degree of impact of the failure; Tor represents the functional component node v i and functional component node v j The product of fault tolerance capabilities; This indicates that during the k-th step of fault propagation, the functional component node v i The r-th failure mode f ir This leads to the functional component node v j The probability value of the most likely failure mode.

2. The method for analyzing the spatiotemporal fault propagation and diffusion of CNC machine tools based on the influence of multiple factors, as described in claim 1, is characterized in that: The specific method for constructing the time-dimensional failure probability model of each functional component in step one is as follows: Based on the functional structure mapping relationship of CNC machine tools, CNC machine tools are divided into several functional components according to the structural function mapping relationship of the product, and the failure interval time of each functional component is statistically analyzed. (1) Establishment of the empirical distribution function; Based on formula (1), an empirical distribution function F is established based on the fault interval time. s (t); In the formula, i = 1, 2, ..., N; N represents the number of fault intervals; (2) Parameter estimation of the failure probability model for each functional component node; Assuming that the fault data of the functional component nodes of the CNC machine tool follow a two-parameter Weibull distribution, the cumulative fault probability distribution function is calculated using formula (2); In the formula, t represents the time variable, and t≥0; η represents the scale parameter, η≥0; α represents the shape parameter, α≥0; The parameters of the assumed distribution model are estimated and solved using the least squares method. The specific solution steps are as follows: After rearranging the terms of formula (2), we obtain... Taking the logarithm twice on both sides of the equation yields make The univariate linear regression equation Y is obtained l =αX l -αlnη, calculated to obtain (3) Correction of parameters estimated by the failure probability model; Because the amount of machine tool fault data is relatively small, the parameter estimation results may have some bias. For any sample size n ≥ 3, the unbiased correction coefficient G(n) for the estimated parameters always has G(n) < 1, and... When n = 3, the unbiased correction coefficient G(n) of parameter α is calculated using formula (3); When n is an even number greater than or equal to 4, the unbiased correction coefficient G(n) of parameter α is calculated using formula (4); When n is an even number greater than or equal to 5, the unbiased correction coefficient G(n) of parameter α is calculated using formula (5); The unbiased correction of the shape parameter α is calculated using formula (6); The unbiased correction coefficient G(n,α) of the scale parameter η is calculated using formula (7). * ); The unbiased correction of parameter η is calculated using formula (8); (4) Hypothesis distribution model testing; Considering the machine tool failure as a small sample case, at a significance level of γ = 0.05, the goodness of fit of the hypothetical distribution model is tested using the test formula (9), D. n This is obtained by looking up the relevant tables, if D n <D n,γ If the result is positive, the null hypothesis is accepted; otherwise, the null hypothesis is rejected. D=max|F s (t)-F(t)| (9) In the formula, F(t) represents the calculated distribution function.

3. The method for analyzing the spatiotemporal fault propagation and diffusion of CNC machine tools based on the influence of multiple factors, as described in claim 1, is characterized in that: The specific modeling steps for the spatial dimension hierarchical topological directed graph model of the CNC machine tool in step two are as follows: (1) Construct a direct impact matrix based on the associated fault data, and construct a standardized direct impact matrix; After dividing the CNC machine tool into several functional components, the correlation analysis of the functional components of the CNC machine tool is carried out using the failure model and the impact analysis method FMEA. The direct influence matrix Y of the CNC machine tool functional components is obtained by formula (10), and the standardized direct influence matrix X is constructed by formula (11). In the formula, y ij Represents the functional component node v i The functional component node v was affected by a fault. j Frequency of failures; n represents the number of nodes in the functional component; (2) Construct the comprehensive impact matrix of the fault; Taking into account the direct and indirect fault impact relationships and degree of impact among functional components, a comprehensive fault impact matrix is ​​constructed using formula (12); In the formula, E d Represents an n-order identity matrix; (3) Considering the factors of the functional components themselves, construct the overall influence matrix using formula (13); H z =T+E d (13) (4) Construct the reachability matrix M using formula (14). s ; In the formula, λ represents the set threshold used to simplify the system. Considering that the number of divisions in the machine tool system is small, λ = 0 is taken. (5) Deconstruct the reachability matrix and partition the hierarchy; Using formula (15), the reachability matrix M is... s The set of functional components corresponding to all columns with a value of 1 in the i-th row is called the functional component node v. i The reachable set R i The set of functional components corresponding to all rows in the i-th column that are 1 is called the antecedent set S. i If the common set C i =R i ∩S i =R i If true, then in the reachability matrix M s Remove row i and column i from the middle, and the functional component node v i It belongs to the terminated functional component and is located at the top level L1. Repeat step (5) until all functional component nodes are removed to realize the hierarchical division of functional component nodes. (6) Construct the skeleton matrix and initially establish a hierarchical topological directed graph model; Construction principle 1: Form a lower triangular matrix based on the order of removal; Construction principle 2: Remove parameters m that have hierarchical binary relations or that have binary relations themselves. ij =0; (7) Add virtual nodes to eliminate direct impact relationships in leaps and establish a hierarchical topological directed graph model for fault propagation. Virtual nodes do not exist in the actual system.

4. The method for analyzing the spatiotemporal fault propagation and diffusion of CNC machine tools based on the influence of multiple factors, as described in claim 1, is characterized in that: The specific modeling steps for the comprehensive importance model of CNC machine tool functional component nodes in step three are as follows: The overall importance I of the functional component node is calculated using formula (16); I i =w1DC i +w2BC i +w3CC i (16) In the formula, w 1,2,3 The weights representing the centrality of each functional component node are obtained through the analytic hierarchy process (AHP); DC i Represents the functional component node v i Degree centrality; BC i Indicates the betweenness centrality of functional component nodes; CC i Indicates proximity centrality; The degree centrality DC of the functional component nodes is calculated using formula (17). i index; In the formula, i represents the target functional component node v i j represents any functional component node v in the network. j ; n represents the number of functional component nodes in the hierarchical topological directed graph model; a ij Represents the reachability matrix M s Elements in; The betweenness centrality BC of the functional component nodes is calculated using formula (18). i index; In the formula, N(j,k) represents the functional component node v j and v k The number of shortest paths between nodes; N(j,i,k) represents the edge betweenness number, and represents the number of nodes v. j and v k Between v i The number of shortest paths; The proximity centrality CC of the functional component nodes is calculated using formula (19). i index; In the formula, d ij Represents the functional component node v i and v j The shortest distance between them.

5. The method for analyzing the spatiotemporal fault propagation and diffusion of CNC machine tools based on the influence of multiple factors, as described in claim 1, is characterized in that: In step four, the fault impact values ​​of each functional component node and each connecting edge of the CNC machine tool are calculated. The specific steps are as follows: (1) Fault impact of functional component nodes Pr(v) i ); The failure impact degree of functional component nodes in a hierarchical topological directed graph model is calculated based on the PageRank algorithm. The initial state transition matrix Q = [q] is obtained by transposing the standardized direct impact matrix. ij ] n×n The influence values ​​of all functional component nodes are obtained by iteratively solving formula (20). In the formula, represent the fault impact vectors of each functional component node obtained in the (x+1)th and xth iterations, respectively; d is the damping factor, d = 0.3; Assign initial value to pr Its initial value will not affect the convergence effect and final result of formula (20). When the iteration convergence threshold ε = 0.0001, and the iteration calculation satisfies |pr x+1 -pr x When | < ε, the iteration ends, and the failure impact value Pr(v) of all functional component nodes is obtained. i ); (2) Functional component node v i and v j The influence of the directed edge failure between them, Pr(e) i→j ); Calculate the functional component node v using formula (21) i and v j The influence of the directed edge failure between them, Pr(e) i→j ); In the formula, Pr(v j ) and Pr(v j ) represents the functional component node v i and v j The failure impact value.

6. The method for analyzing the spatiotemporal propagation and diffusion of CNC machine tool faults under the influence of multiple factors as described in claim 1, characterized in that: The specific steps in step six to narrow down the fault location range of the CNC machine tool and determine the key functional component nodes and key fault propagation paths are as follows: (1) Identification of key propagation paths; In the propagation path of CNC machine tool system, there are series propagation and series-parallel propagation. When there is a series relationship between multiple nodes, the fault propagation intensity value between two nodes is calculated using formula (22) as the product of the fault propagation intensity of all passing nodes. When there is both a series relationship and a parallel relationship between multiple nodes, based on the fault propagation intensity of the series part of the path between two nodes, the parallel part is summed using formula (23), and all propagation paths are arranged in descending order. In the formula, k represents the functional component node v i Propagate to functional component node v j The fault propagation strength at the k-th step; (2) Determination of key functional component nodes in the propagation path; The critical fault propagation path is finally determined based on the overall importance of key functional component nodes, critical propagation paths, the impact of critical functional component failures, and the propagation strength of the paths.

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