CN114719962A - Mechanical vibration digital twin model construction method based on machine learning - Google Patents
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Abstract
The invention discloses a mechanical vibration digital twin model construction method based on machine learning, wherein dynamic characteristic vectors of all nodes in a digital twin grid model are sent into a plurality of parallel nonlinear dynamic processing modules, so that an explicit form of a specified PDE equation and a complex time-consuming numerical solving process can be abandoned, and nonlinear differential dynamic characteristics of mechanical vibration propagation are automatically extracted through the nonlinear dynamic processing modules, so that the model can be continuously optimized and approximated to a real physical system, the model can be finally learned to the implicit dynamic behavior of mechanical vibration propagation under the condition of infinitely fitting a real scene, and forward operation can be accelerated through a large-scale GPU, so that the real fixed vibration propagation speed is greatly improved and even followed, and real-time optimization is carried out according to historical behaviors; therefore, the mechanical vibration digital twin model constructed by the method can be used for quickly and accurately simulating and predicting the mechanical vibration propagation.
Description
Technical Field
The invention belongs to the technical field of engineering numerical calculation analysis, and particularly relates to a mechanical vibration digital twin model construction method based on machine learning.
Background
Mechanical vibration is widely existed in a plurality of engineering problems, the vibration dynamics characteristic of a specific object is accurately grasped, and particularly, the mechanical vibration dynamics characteristic under high-speed high-frequency disturbance is the core and key for solving the complex engineering problems. For example, complex coupled vibration behavior of a tool under high-speed cutting in the advanced manufacturing field, flutter behavior of a composite material part under high-speed cruising of an aircraft and the like have urgent needs on a mechanical vibration numerical calculation theory and a method which are rapid, accurate and even capable of being optimized in real time.
At present, Finite Element Method (FEM) is mostly adopted for analyzing and calculating mechanical vibration propagation in actual engineering. The finite element method is a simulation calculation method for numerically solving a physical object specific Partial Differential Equation (PDE). Although the finite element method is widely applied in various engineering fields, the finite element method has obvious limitations: firstly, the finite element method needs to appoint the constitutive equation of the physical object in advance, and the constitutive equation inevitably has certain deviation with the real action rule between the physical objects; secondly, the finite element method needs to solve the weak solution of the field function on the projection of the shape function space by a Gaussian product-solving equal numerical integration method (such as the Galerkin method), the GPU parallel computing architecture of a modern computer is difficult to be efficiently utilized, the consumed computing time is long, and the real-time prediction cannot be realized only by off-line analysis and computation; moreover, once the finite element method is specified, the finite element method cannot be self-optimized, and the development requirement of the next-generation intelligent numerical calculation model based on the digital twin under the background of the current industrial big data and artificial intelligence is difficult to meet.
Disclosure of Invention
In view of the above, the present invention provides a mechanical vibration digital twin model construction method based on machine learning, and the constructed mechanical vibration digital twin model can be used for rapid and accurate simulation and prediction of mechanical vibration propagation.
In order to achieve the purpose, the invention provides the following technical scheme:
a mechanical vibration digital twin model construction method based on machine learning comprises the following steps:
1) measuring the vibration displacement of each vibration measurement point on the surface of the physical entity at the current moment;
2) inserting the vibration displacement of each vibration measurement point into a corresponding node of the digital twin model corresponding to the physical entity, and taking the displacement of the node at the last moment from the displacement of the node which does not correspond to the vibration measurement point to obtain the current digital twin grid model; calculating the vibration velocity, the first-order acceleration and the second-order acceleration of each node at the current moment, and combining the vibration displacement of the corresponding node and the object attribute digital mark to jointly form a feature vector of the node;
3) coding the characteristic vector of each node in the digital twin grid model into a dynamic characteristic vector;
4) sending the dynamic characteristic vectors of all nodes in the digital twin grid model into a plurality of parallel nonlinear dynamic processing modules, wherein each nonlinear dynamic processing module comprises a nonlinear discrete differential operator processing layer and a nonlinear activation function layer which are alternately superposed and act on the digital twin grid model; the nonlinear discrete differential operator is approximated by a high-order Chebyshev polynomial, the coefficient of the high-order Chebyshev polynomial is taken as a parameter to be learned and optimized of the nonlinear dynamics processing module of the digital twin model, and a linear discrete Laplacian operator is taken as a primitive operator; integrating multiple eigenvectors output by the multiple nonlinear dynamics processing modules into a single dynamics eigenvector through a linear network layer;
5) decoding the kinetic characteristic vector output in the step 4) into a displacement vector of a node;
6) superposing the node displacement vector to the position coordinate of the node at the previous moment, and updating the position coordinate information of the node;
7) and (5) circulating the step 1) to the step 6), and performing forward calculation on a time step in an iteration mode to simulate the dynamic evolution of the mechanical vibration in time.
Further, in the step 1), the vibration measuring points are sparsely distributed on the surface of the physical entity.
Further, in the step 2), the vibration displacement of each vibration measurement point is inserted into a corresponding node of the digital twin model by adopting a k-nearest neighbor algorithm.
Further, in the step 3), a multilayer neural network is constructed as a kinetic information Encoder, which is expressed as an Encoder; encoding the feature vector of each current node in the digital twin mesh model into a dynamic parameter hidden space vector h through a dynamic information encoderiNamely:
hi＝Encoder(Fi)
wherein ,FiA feature vector representing a node i in the digital twin mesh model, and: fi∈RmI.e. FiIs an m-dimensional real vector.
Further, in the step 4), a triangle formed by connecting lines between the node i and any adjacent node j and node k is defined as Δi-jk(ii) a The laplacian at node i is:
wherein, (Deltaf)iThe Laplace operator of the node i represents the gain caused by the change of any node j connected with the node i to the node i; f. ofiA function value representing the function f at node i; f. ofjA function value representing the function f at the node j; w is aijRepresenting a node edge e between node i and node jijThe edge weight of (c); a isiRepresents the total weight of node i; and:
ai＝∑ai-jk
wherein ,lijRepresenting the length of a node edge obtained by connecting the node i and the node j; likRepresenting the length of a node edge obtained by connecting the node i and the node k; ljkRepresenting the length of a node edge obtained by connecting the node j and the node k; si-jkRepresents a triangle deltai-jkThe area of (d); a isi-jkIndicates node i is at Δi-jkThe weight in (1);
integrating Laplacian operators of all nodes into a matrix form, and constructing an edge weight wijA matrix W of n × n elements; if the node i is not adjacent to the node j, the node i is not connected with the node j, and the element w at the corresponding position in the matrixij＝0；
Constructing a node weight aiIs a diagonal matrix of elements
Element a in the matrixiRepresenting the node weight of the node i, and the rest positions are 0;
construct a structure ofiFor a matrix F of column vectors, the laplacian of all nodes can be expressed as:
ΔL＝A-1(D-W)F
wherein Δ L represents the laplacian of all nodes; d represents a degree matrix of a graph network formed by all nodes;
adopting a linear discrete Laplace operator as a primitive operator delta L, and constructing the primitive operator delta L into a nonlinear discrete differential operator through an m-order Chebyshev polynomial, namely:
where θ is the coefficient vector of the chebyshev polynomial, and θ ∈ RmIs an m-dimensional real vector; delta L represents Laplacian operators of all nodes, is an m-order matrix, and is the number of all nodes in the digital twin grid model; and:
at the moment, an m-order Chebyshev polynomial coefficient vector theta is an optimized parameter to be learned of the digital twin model nonlinear dynamics processing module;
further, the nonlinear dynamics processing module comprises a nonlinear discrete differential operator processing layer and a nonlinear activation function layer, namely:
ΔL(l+1)＝σ[A-1(D-W)ΔL(l)]
wherein ,A-1(D-W)ΔL(l)A processing layer for a nonlinear discrete differential operator; Δ L(l)Is the Laplace matrix of the L-th layer, and Δ L(0)F; sigma being non-linear activationA function layer.
Further, in the step 5), a multilayer neural network is constructed to serve as a dynamic information Decoder, and is represented as a Decoder; hiding the final dynamic parameter of each node in the current digital twin mesh model into a space vector through a dynamic information decoder
Decoding into a displacement vector uiNamely:
further, in step 6), the updated node position coordinate information:
wherein ,
representing the position coordinate information of the node i after updating at the current moment t;
representing the position coordinate information of the node i at the last moment t-1;
representing a displacement vector obtained by decoding the node i at the current moment t; mask represents an operator matrix and is used for shielding displacement updating of nodes meeting boundary conditions, corresponding coefficients of all nodes under the boundary conditions in the Mask operator matrix are 0, and corresponding coefficients of all nodes under non-boundary conditions are 1.
Further, in the execution process of the step 7), comparing the historical predicted vibration displacement with the actual measured displacement, taking the average difference value of the L2 norm as a loss function target, and using a random gradient descent optimizer to perform offline or real-time optimization on the loss function, so that the vibration behavior of the digital twin model is continuously approximated to a physical entity.
The invention has the beneficial effects that:
the mechanical vibration digital twin model construction method based on machine learning is characterized in that dynamic characteristic vectors of all nodes in a digital twin grid model are sent into a plurality of parallel nonlinear dynamics processing modules, so that an explicit form and a complex time-consuming numerical solving process of a specified PDE equation can be abandoned, nonlinear differential dynamics characteristics of mechanical vibration propagation can be automatically extracted through the nonlinear dynamics processing modules, the model can be continuously optimized and approximated to a real physical system, the model can be finally learned to the implicit dynamics behavior of mechanical vibration propagation under the condition of infinite fitting to the real scene, forward operation can be accelerated through a large-scale GPU, the real fixed vibration propagation speed is greatly improved and even followed, and real-time optimization is carried out according to historical behaviors; therefore, the mechanical vibration digital twin model constructed by the method can be used for quickly and accurately simulating and predicting the mechanical vibration propagation.
Drawings
In order to make the object, technical scheme and beneficial effect of the invention more clear, the invention provides the following drawings for explanation:
FIG. 1 is a schematic diagram of a mechanical vibration digital twin model construction method based on machine learning, taking machining of an engine blade as an example;
FIG. 2 is a schematic diagram of a plurality of parallel nonlinear dynamics processing modules;
fig. 3 is a schematic diagram of calculating laplacian matrix parameters using nonlinear discrete differential operators.
Detailed Description
The present invention is further described with reference to the following drawings and specific examples so that those skilled in the art can better understand the present invention and can practice the present invention, but the examples are not intended to limit the present invention.
As shown in fig. 1, a schematic diagram of an engine blade machining as an example of the mechanical vibration digital twin model construction method based on machine learning according to the present invention is shown. Firstly, a three-dimensional digital twin model of a physical entity needs to be constructed, wherein the digital twin model comprises a motion constraint point position of the physical entity and a contact three-dimensional model of the physical entity influenced by an external force; and secondly, carrying out grid discrete division on the digital twin model, wherein grid intersection points are nodes of the digital twin model, and obtaining the digital twin grid model which is used as a geometric digital twin body of the physical entity. Specifically, the method for constructing the mechanical vibration digital twin model based on machine learning in the embodiment includes the following steps:
1) measuring the vibration displacement of each vibration measurement point on the surface of the physical entity at the current moment; specifically, the vibration displacement of the vibration measuring points on the surface of the physical entity at the current moment is measured by using the multipoint laser scanning vibration measuring equipment, the vibration measuring points comprise a force-applying object and a force-applying object contacting with the force-applying object, the vibration measuring points can be selected at will, but in order that the digital twin model can be converged more quickly, the vibration measuring points are sparsely distributed on the surface of the physical entity as much as possible.
2) Inserting the vibration displacement of each vibration measurement point into a corresponding node of the digital twin model corresponding to the physical entity, and taking the displacement of the node at the last moment from the displacement of the node which does not correspond to the vibration measurement point to obtain the current digital twin grid model; and calculating the vibration velocity, the first-order acceleration and the second-order acceleration of each node at the current moment according to the current and necessary historical measurement data, and combining the vibration displacement of the corresponding node and the object attribute digital mark to jointly form the feature vector of the node. Specifically, the vibration displacement of each vibration measurement point is inserted into the corresponding node of the digital twin model by using a k-nearest neighbor algorithm.
3) And coding the characteristic vector of each node in the digital twin mesh model into a dynamic characteristic vector. Specifically, a multilayer neural network is constructed to be used as a kinetic information Encoder, which is expressed as an Encoder; encoding the feature vector of each current node in the digital twin mesh model into a dynamic parameter hidden space vector h through a dynamic information encoderiNamely:
hi＝Encoder(Fi)
wherein ,FiRepresenting nodes i in a digital twin mesh modelA feature vector, and: fi∈RmI.e. FiIs an m-dimensional real vector.
4) Sending the dynamic characteristic vectors of all nodes in the digital twin grid model into a plurality of parallel nonlinear dynamic processing modules, wherein each nonlinear dynamic processing module comprises a nonlinear discrete differential operator processing layer and a nonlinear activation function layer which are alternately superposed on the digital twin grid model, and the nonlinear discrete differential operator processing layer and the nonlinear activation function layer are shown in figure 2; the nonlinear discrete differential operator is approximated by a high-order Chebyshev polynomial, the coefficient of the high-order Chebyshev polynomial is taken as a parameter to be learned and optimized of the nonlinear dynamics processing module of the digital twin model, and a linear discrete Laplacian operator is taken as a primitive operator; and integrating the multiple eigenvectors output by the multiple nonlinear dynamics processing modules into a single dynamics eigenvector through a linear network layer.
Specifically, a triangle formed by connecting lines between the node i and any adjacent node j and point k is defined as Δi-jk(ii) a The laplacian at node i is:
wherein, (Deltaf)iThe Laplace operator of the node i represents the gain caused by the change of any node j connected with the node i to the node i; f. ofiA function value representing the function f at node i; f. ofjA function value representing the function f at the node j; w is aijRepresenting a node edge e between node i and node jijThe edge weight of (c); a isiRepresents the total weight of node i; and:
ai＝∑ai-jk
wherein ,lijRepresenting the length of a node edge obtained by connecting the node i and the node j; l. theikRepresenting the length of a node edge obtained by connecting the node i and the node k; ljkRepresenting the length of a node edge obtained by connecting the node j and the node k; si-jkRepresents a triangle deltai-jkThe area of (d); a isi-jkIndicates node i is at Δi-jkThe weight in (1);
integrating Laplacian operators of all nodes into a matrix form, and constructing an edge weight wijA matrix W of n × n elements; if the node i is not adjacent to the node j, the node i is not connected with the node j, and the element w at the corresponding position in the matrixij＝0；
Constructing a node weight aiIs a diagonal matrix of elements
Element a in the matrixiRepresenting the node weight of the node i, and the rest positions are 0;
construct a structure ofiFor a matrix F of column vectors, the laplacian of all nodes can be expressed as:
ΔL＝A-1(D-W)F
wherein Δ L represents the laplacian of all nodes; d represents a degree matrix of a graph network formed by all nodes;
adopting a linear discrete Laplace operator as a primitive operator delta L, and constructing the primitive operator delta L into a nonlinear discrete differential operator through an m-order Chebyshev polynomial, namely:
where θ is the coefficient vector of the chebyshev polynomial, and θ ∈ RmIs an m-dimensional real vector; delta L represents Laplacian operators of all nodes, is an m-order matrix, and is the number of all nodes in the digital twin grid model; and:
at the moment, an m-order Chebyshev polynomial coefficient vector theta is an optimized parameter to be learned of the digital twin model nonlinear dynamics processing module;
specifically, the nonlinear dynamics processing module comprises a nonlinear discrete differential operator processing layer and a nonlinear activation function layer, namely:
ΔL(l+1)＝σ[A-1(D-W)AL(l)]
wherein ,A-1(D-W)ΔL(l)A processing layer for a nonlinear discrete differential operator; Δ L(l)Is the Laplace matrix of the L-th layer, and Δ L(0)F; σ is a nonlinear activation function layer, and the nonlinear activation function layer in this embodiment selects ReLU.
5) Decoding the dynamic characteristic vector output in the step 4) into a displacement vector of the node. Specifically, a multilayer neural network is constructed to be used as a dynamic information Decoder, and is expressed as a Decoder; hiding the final dynamic parameter of each node in the current digital twin mesh model into a space vector through a dynamic information decoder
Decoding into a displacement vector uiNamely:
6) and superposing the node displacement vector to the position coordinate of the node at the previous moment, and updating the position coordinate information of the node. The updated node position coordinate information is as follows:
wherein ,
representing the position coordinate information of the node i after updating at the current moment t;
representing the position coordinate information of the node i at the last moment t-1;
representing a displacement vector obtained by decoding the node i at the current moment t; mask represents an operator matrix and is used for shielding displacement updating of nodes meeting boundary conditions, corresponding coefficients of all nodes under the boundary conditions in the Mask operator matrix are 0, and corresponding coefficients of all nodes under non-boundary conditions are 1.
7) And (5) circulating the step 1) to the step 6), and performing forward calculation on a time step in an iteration mode to simulate the dynamic evolution of the mechanical vibration in time.
Specifically, in the step 7) cyclic execution process, historical predicted vibration displacement and actual measured displacement are compared, the average difference value of the L2 norm is used as a loss function target, and a random gradient descent optimizer is used for performing offline or real-time optimization on the loss function, so that the vibration behavior of the digital twin model is continuously approximated into a physical entity.
The above-mentioned embodiments are merely preferred embodiments for fully illustrating the present invention, and the scope of the present invention is not limited thereto. The equivalent substitution or change made by the technical personnel in the technical field on the basis of the invention is all within the protection scope of the invention. The protection scope of the invention is subject to the claims.
Claims (9)
1. A mechanical vibration digital twin model construction method based on machine learning is characterized in that: the method comprises the following steps:
1) measuring the vibration displacement of each vibration measurement point on the surface of the physical entity at the current moment;
2) inserting the vibration displacement of each vibration measurement point into a corresponding node of the digital twin model corresponding to the physical entity, and taking the displacement of the node at the last moment from the displacement of the node which does not correspond to the vibration measurement point to obtain the current digital twin grid model; calculating the vibration speed, the first-order acceleration and the second-order acceleration of each node at the current moment, and combining the vibration displacement of the corresponding node and the object attribute digital mark to jointly form a feature vector of the node;
3) coding the characteristic vector of each node in the digital twin grid model into a dynamic characteristic vector;
4) sending the dynamic characteristic vectors of all nodes in the digital twin grid model into a plurality of parallel nonlinear dynamic processing modules, wherein each nonlinear dynamic processing module comprises a nonlinear discrete differential operator processing layer and a nonlinear activation function layer which are alternately superposed and act on the digital twin grid model; the nonlinear discrete differential operator is approximated by a high-order Chebyshev polynomial, the coefficient of the high-order Chebyshev polynomial is taken as a parameter to be learned and optimized of the nonlinear dynamics processing module of the digital twin model, and a linear discrete Laplacian operator is taken as a primitive operator; integrating multiple eigenvectors output by the multiple nonlinear dynamics processing modules into a single dynamics eigenvector through a linear network layer;
5) decoding the kinetic characteristic vector output in the step 4) into a displacement vector of a node;
6) superposing the node displacement vector to the position coordinate of the node at the previous moment, and updating the position coordinate information of the node;
7) and (5) circulating the step 1) to the step 6), and performing forward calculation on a time step in an iteration mode to simulate the dynamic evolution of the mechanical vibration in time.
2. The machine learning-based mechanical vibration digital twin model construction method according to claim 1, characterized in that: in the step 1), the vibration measuring points are sparsely distributed on the surface of the physical entity.
3. The machine learning-based mechanical vibration digital twin model construction method according to claim 1, characterized in that: in the step 2), the vibration displacement of each vibration measurement point is inserted into a corresponding node of the digital twin model by adopting a k-nearest neighbor algorithm.
4. The machine learning-based mechanical vibration digital twin model construction method according to claim 1, characterized in that: in the step 3), a multilayer neural network is constructed to serve as a kinetic information Encoder, and is expressed as an Encoder; encoding the feature vector of each current node in the digital twin mesh model into a dynamic parameter hidden space vector h through a dynamic information encoderiNamely:
hi＝Encoder(Fi)
wherein ,FiA feature vector representing a node i in the digital twin mesh model, and: fi∈RmI.e. FiIs an m-dimensional real vector.
5. The machine learning-based mechanical vibration digital twin model construction method according to claim 1, characterized in that: in the step 4), a triangle formed by connecting lines between the node i and any adjacent node j and node k is defined as deltai-jk(ii) a The laplacian at node i is:
wherein, (Deltaf)iThe Laplace operator of the node i represents the gain caused by the change of any node j connected with the node i to the node i; f. ofiA function value representing the function f at node i; f. ofjA function value representing the function f at the node j; w is aijRepresenting a node edge e between node i and node jijThe edge weight of (c); a isiRepresents the total weight of node i; and:
ai＝Σai-jk
wherein ,lijRepresenting the length of a node edge obtained by connecting the node i and the node j; likRepresenting the length of a node edge obtained by connecting the node i and the node k; ljkRepresenting the length of a node edge obtained by connecting the node j and the node k; si-jkRepresents a triangle deltai-jkThe area of (d); a is ai-jkIndicates node i is at Δi-jkThe weight in (1);
integrating Laplacian operators of all nodes into a matrix form, and constructing an edge weight wijA matrix W of n x n elements; if the node i is not adjacent to the node j, the node i is not connected with the node j, and the element w at the corresponding position in the matrixij＝0；
Constructing a node weight aiIs a diagonal matrix of elements
Element a in the matrixiRepresenting the node weight of the node i, and the rest positions are 0;
construct a structure ofiFor a matrix F of column vectors, the laplacian of all nodes can be expressed as:
ΔL＝A-1(D-W)F
wherein Δ L represents the laplacian of all nodes; d represents a degree matrix of a graph network formed by all nodes;
adopting a linear discrete Laplace operator as a primitive operator delta L, and constructing the primitive operator delta L into a nonlinear discrete differential operator through an m-order Chebyshev polynomial, namely:
where θ is the coefficient vector of the chebyshev polynomial, and θ ∈ RmIs an m-dimensional real vector; Δ L represents Laplacian of all nodes, Δ L is m-order momentM is the number of all nodes in the digital twin grid model; and:
at the moment, the coefficient vector theta of the chebyshev polynomial of the order m is a parameter to be learned and optimized of the nonlinear dynamics processing module of the digital twin model.
6. The mechanical vibration digital twin model building method based on machine learning according to claim 5, characterized in that: the nonlinear dynamics processing module comprises a nonlinear discrete differential operator processing layer and a nonlinear activation function layer, namely:
ΔL(l+1)＝σ[A-1(D-W)ΔL(l)]
wherein ,A-1(D-W)ΔL(l)A processing layer for a nonlinear discrete differential operator; Δ L(l)Is the Laplace matrix of the L-th layer, and Δ L(0)F; σ is the nonlinear activation function layer.
7. The machine learning-based mechanical vibration digital twin model construction method according to claim 1, characterized in that: in the step 5), a multilayer neural network is constructed to serve as a dynamic information Decoder, and is expressed as a Decoder; hiding the final dynamic parameter of each node in the current digital twin mesh model into a space vector through a dynamic information decoder
Decoding into a displacement vector uiNamely:
8. the mechanical vibration digital twin model building method based on machine learning according to claim 1, characterized in that: in the step 6), the updated node position coordinate information:
wherein ,
representing the position coordinate information of the node i after updating at the current moment t;
representing the position coordinate information of the node i at the last moment t-1;
representing a displacement vector obtained by decoding the node i at the current moment t; mask represents an operator matrix and is used for shielding displacement updating of nodes meeting boundary conditions, corresponding coefficients of all nodes under the boundary conditions in the Mask operator matrix are 0, and corresponding coefficients of all nodes under non-boundary conditions are 1.
9. The machine learning-based mechanical vibration digital twin model construction method according to any one of claims 1-8, characterized by: in the step 7) executing process, comparing the historical predicted vibration displacement with the actual measurement displacement, taking the average difference value of L2 norms as a loss function target, and using a random gradient descent optimizer to perform offline or real-time optimization on the loss function, so that the vibration behavior of the digital twin model can be continuously forced into a physical entity.
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