技术领域technical field
本发明属于工程数值计算分析技术领域，具体的为一种基于机器学习的机械振动数字孪生模型构建方法。The invention belongs to the technical field of engineering numerical calculation and analysis, in particular to a method for constructing a mechanical vibration digital twin model based on machine learning.
背景技术Background technique
机械振动广泛存在于众多工程问题中，准确把握特定对象的振动动力学特性，特别是在高速高频激扰下机械振动动力学特性是解决复杂工程问题的核心和关键。如先进制造领域中刀具高速切削下的复杂耦合振动行为，航空器高速巡航下复合材料件的颤振行为等，均对快速、准确甚至可实时优化的机械振动数值计算理论和方法具有迫切需求。Mechanical vibration widely exists in many engineering problems. Accurately grasping the vibration dynamic characteristics of specific objects, especially under high-speed and high-frequency excitation, is the core and key to solve complex engineering problems. For example, in the field of advanced manufacturing, the complex coupled vibration behavior of cutting tools under high-speed cutting, and the flutter behavior of composite parts under high-speed aircraft cruise, etc., all have urgent needs for fast, accurate and even real-time optimized mechanical vibration numerical calculation theories and methods.
当前实际工程中对机械振动传播的分析计算大多采用有限元法(FEM)。有限元法是一种对物理对象特定偏微分方程(PDE)进行数值求解的一种仿真计算方法。有限元法虽在各种工程领域都得到了广泛的应用，但其具有明显局限性：首先有限元法需要事先指定物理对象的本构方程，本构方程难免与物理对象间的真实作用规律存在一定偏差；其次有限元法需通过高斯求积等数值积分方法求解场函数在形函数空间投影上的PDE弱解(如伽辽金法)，难以高效利用现代计算机的GPU并行计算架构，花费的计算时间较长，导致其只能离线分析计算无法做到实时预测；再则，有限元法一经指定无法进行自优化，难以满足当前工业大数据及人工智能背景下基于数字孪生的下一代智能数值计算模型的发展需求。Most of the analysis and calculation of mechanical vibration propagation in current actual engineering adopts the finite element method (FEM). The finite element method is a simulation calculation method for numerically solving a specific partial differential equation (PDE) of a physical object. Although the finite element method has been widely used in various engineering fields, it has obvious limitations: firstly, the finite element method needs to specify the constitutive equation of the physical object in advance, and the constitutive equation inevitably exists with the real interaction law between the physical object. A certain deviation; Secondly, the finite element method needs to solve the PDE weak solution of the field function on the projection of the shape function space (such as the Galerkin method) through numerical integration methods such as Gaussian quadrature, which is difficult to efficiently use the GPU parallel computing architecture of modern computers, and the cost of The calculation time is long, so it can only be analyzed and calculated offline and cannot be predicted in real time; moreover, once the finite element method is specified, it cannot be self-optimized, and it is difficult to meet the needs of the next generation of intelligent numerical values based on digital twins under the background of current industrial big data and artificial intelligence. Computational Model Development Requirements.
发明内容Contents of the invention
有鉴于此，本发明的目的在于提供一种基于机器学习的机械振动数字孪生模型构建方法，构建得到的机械振动数字孪生模型能够用于对机械振动传播的快速精确模拟和预测。In view of this, the object of the present invention is to provide a method for constructing a mechanical vibration digital twin model based on machine learning, and the constructed mechanical vibration digital twin model can be used for fast and accurate simulation and prediction of mechanical vibration propagation.
为达到上述目的，本发明提供如下技术方案：To achieve the above object, the present invention provides the following technical solutions:
一种基于机器学习的机械振动数字孪生模型构建方法，包括如下步骤：A method for constructing a mechanical vibration digital twin model based on machine learning, comprising the following steps:
1)测量当前时刻物理实体表面各测振点的振动位移；1) Measure the vibration displacement of each vibration measurement point on the surface of the physical entity at the current moment;
2)将各测振点的振动位移插入与物理实体对应的数字孪生模型的对应节点中，未对应有测振点的节点的位移取该节点在上一时刻的位移，得到当前的数字孪生网格模型；计算当前时刻各节点的振动速度、一阶加速度和二阶加速度，并结合对应节点的振动位移和物体属性数字标示，共同构成该节点的特征向量；2) Insert the vibration displacement of each vibration measurement point into the corresponding node of the digital twin model corresponding to the physical entity, and the displacement of the node not corresponding to the vibration measurement point takes the displacement of the node at the previous moment to obtain the current digital twin network Grid model; calculate the vibration velocity, first-order acceleration and second-order acceleration of each node at the current moment, and combine the vibration displacement of the corresponding node and the digital label of the object attribute to form the eigenvector of the node;
3)将数字孪生网格模型中各节点的特征向量编码为动力学特征向量；3) Encode the eigenvectors of each node in the digital twin grid model into dynamic eigenvectors;
4)将数字孪生网格模型中所有节点的动力学特征向量送入并行的多个非线性动力学处理模块中，所述非线性动力学处理模块包括交替叠加作用于数字孪生网格模型上的非线性离散微分算子处理层和非线性激活函数层；所述非线性离散微分算子通过高阶契比雪夫多项式，以高阶契比雪夫多项式系数为数字孪生模型非线性动力学处理模块的待学习优化参数，采用线性离散拉普拉斯算子作为基元算子进行逼进；通过一层线性网络层将多个非线性动力学处理模块输出的多份特征向量整合为单份动力学特征向量；4) Send the dynamic eigenvectors of all nodes in the digital twin grid model to multiple parallel nonlinear dynamic processing modules, the nonlinear dynamic processing modules include alternately superimposed on the digital twin grid model A nonlinear discrete differential operator processing layer and a nonlinear activation function layer; the nonlinear discrete differential operator uses high-order Chebyshev polynomials as the coefficients of the high-order Chebyshev polynomials as the nonlinear dynamics processing module of the digital twin model To optimize the parameters to be learned, the linear discrete Laplacian operator is used as the primitive operator for approximation; through a linear network layer, multiple feature vectors output by multiple nonlinear dynamic processing modules are integrated into a single dynamic Feature vector;
5)将步骤4)中输出的动力学特征向量解码为节点的位移向量；5) decoding the dynamic feature vector output in step 4) into the displacement vector of the node;
6)将节点位移向量叠加到上一时刻的节点位置坐标中，并更新节点的位置坐标信息；6) Superimpose the node displacement vector into the node position coordinates at the previous moment, and update the node position coordinate information;
7)循环步骤1)至步骤6)，在时间步上迭代进行前向计算，以模拟机械振动在时间上的动力学演化。7) Step 1) to step 6) are looped, and forward calculation is performed iteratively on the time step to simulate the dynamic evolution of mechanical vibration over time.
进一步，所述步骤1)中，测振点稀疏分布于物理实体表面。Further, in the step 1), the vibration measuring points are sparsely distributed on the surface of the physical entity.
进一步，所述步骤2)中，采用k近邻算法将各测振点的振动位移插入数字孪生模型的对应节点中。Further, in the step 2), the k-nearest neighbor algorithm is used to insert the vibration displacement of each vibration measurement point into the corresponding node of the digital twin model.
进一步，所述步骤3)中，构建多层神经网络作为动力学信息编码器，表示为Encoder；通过动力学信息编码器将数字孪生网格模型中当前各节点的特征向量编码为动力参数隐空间向量hi，即：Further, in the step 3), a multi-layer neural network is constructed as a dynamic information encoder, represented as Encoder; the eigenvectors of each current node in the digital twin grid model are encoded into a dynamic parameter hidden space through the dynamic information encoder Vector hi , namely:
hi＝Encoder(Fi)hi ＝Encoder(Fi )
其中，Fi表示数字孪生网格模型中的节点i的特征向量，且：Fi∈Rm，即Fi为m维实向量。Among them, Fi represents the feature vector of node i in the digital twin grid model, and: Fi ∈ Rm , that is, Fi is an m-dimensional real vector.
进一步，所述步骤4)中，定义节点i与任意相邻的节点j和节点k之间的连线组成的三角形为Δi-jk；则节点i处的拉普拉斯算子为：Further, in the step 4), the triangle formed by the connection between the definition node i and any adjacent node j and node k is Δi-jk ; then the Laplacian at the node i is:
其中，(Δf)i是节点i的拉普拉斯算子，表示任意一个与节点i相连的节点j变化到节点i所带来的增益；fi表示函数f在节点i处的函数值；fj表示函数f在节点j处的函数值；wij表示节点i与节点j之间的节点边eij的边权重；ai表示节点i的总权重；且：Among them, (Δf)i is the Laplacian operator of node i, which represents the gain brought by any node j connected to node i changing to node i; fi represents the function value of function f at node i; fj represents the function value of function f at node j; wij represents the edge weight of node edge eij between node i and node j; ai represents the total weight of node i; and:
ai＝∑ai-jkai =∑ai-jk
其中，lij表示节点i与节点j之间相连得到的节点边长度；lik表示节点i与节点k之间相连得到的节点边长度；ljk表示节点j与节点k之间相连得到的节点边长度；Si-jk表示三角形Δi-jk的面积；ai-jk表示节点i在Δi-jk中的权重；Among them, lij represents the node edge length obtained by the connection between node i and node j; lik represents the node edge length obtained by the connection between node i and node k; ljk represents the node obtained by the connection between node j and node k side length; Si-jk represents the area of triangle Δi-jk ; ai-jk represents the weight of node i in Δi-jk ;
将所有节点的拉普拉斯算子整合成矩阵的形式，构造一个以边权重wij为元素的n×n的矩阵W；若节点i与节点j之间不相邻，则节点i与节点j之间不连接，矩阵中对应位置的元素wij＝0；Integrate the Laplacian operators of all nodes into a matrix form, and construct an n×n matrix W with edge weight wij as an element; if node i and node j are not adjacent, then node i and node j There is no connection between j, the element wij of the corresponding position in the matrix = 0;
构造一个以节点权重ai为元素的对角矩阵矩阵中元素ai表示节点i的节点权重，其余位置均为0；Construct a diagonal matrix with node weights ai as elements The element ai in the matrix represents the node weight of node i, and the rest of the positions are all 0;
构造一个以fi为列向量的矩阵F，则所有节点的拉普拉斯算子可以表示为：Construct a matrix F with fi as the column vector, then the Laplacian operator of all nodes can be expressed as:
ΔL＝A-1(D-W)FΔL＝A-1 (DW)F
其中，ΔL表示所有节点的拉普拉斯算子；D表示所有节点组成的图网络的度矩阵；Among them, ΔL represents the Laplacian operator of all nodes; D represents the degree matrix of the graph network composed of all nodes;
采用线性离散拉普拉斯算子作为基元算子ΔL，通过m阶契比雪夫多项式将基元算子ΔL构建成非线性离散微分算子，即：The linear discrete Laplacian operator is used as the primitive operator ΔL, and the primitive operator ΔL is constructed into a nonlinear discrete differential operator through the m-order Chebyshev polynomial, namely:
其中，θ是契比雪夫多项式的系数向量，且θ∈Rm为m维实向量；ΔL表示所有节点的拉普拉斯算子，ΔL为m阶矩阵，m为数字孪生网格模型中所有节点的数量；且：Among them, θ is the coefficient vector of the Chebyshev polynomial, and θ∈Rm is the m-dimensional real vector; ΔL represents the Laplacian operator of all nodes, ΔL is the m-order matrix, and m is all the number of nodes; and:
此时，m阶契比雪夫多项式系数向量θ为数字孪生模型非线性动力学处理模块的待学习优化参数；At this time, the m-order Chebyshev polynomial coefficient vector θ is the parameter to be learned and optimized for the nonlinear dynamics processing module of the digital twin model;
进一步，非线性动力学处理模块包含非线性离散微分算子处理层和非线性激活函数层，即：Further, the nonlinear dynamics processing module includes a nonlinear discrete differential operator processing layer and a nonlinear activation function layer, namely:
ΔL(l+1)＝σ[A-1(D-W)ΔL(l)]ΔL(l+1) = σ[A-1 (DW)ΔL(l) ]
其中，A-1(D-W)ΔL(l)为非线性离散微分算子处理层；ΔL(l)是第l层的拉普拉斯矩阵，且ΔL(0)＝F；σ为非线性激活函数层。Among them, A-1 (DW)ΔL(l) is the nonlinear discrete differential operator processing layer; ΔL(l) is the Laplacian matrix of layer l, and ΔL(0) = F; σ is the nonlinear activation function layer.
进一步，所述步骤5)中，构建多层神经网络作为动力学信息解码器，表示为Decoder；通过动力学信息解码器将当前数字孪生网格模型中各节点的最终动力参数隐空间向量解码为位移向量ui，即：Further, in the step 5), a multi-layer neural network is constructed as a dynamic information decoder, represented as Decoder; the final dynamic parameter hidden space vector of each node in the current digital twin grid model is obtained by the dynamic information decoder Decoded to a displacement vector ui , that is:
进一步，所述步骤6)中，更新后的节点位置坐标信息：Further, in the step 6), the updated node position coordinate information:
其中，表示节点i在当前时刻t更新后的位置坐标信息；/>表示节点i在上一时刻t-1的位置坐标信息；/>表示节点i在当前时刻t解码得到的位移向量；Mask表示算子矩阵，用于对满足边界条件的节点的位移更新进行屏蔽，且Mask算子矩阵中所有处于边界条件的节点的对应系数0，所有处于非边界条件的节点的对应系数为1。in, Indicates the updated position coordinate information of node i at the current moment t;/> Indicates the position coordinate information of node i at the last moment t-1; /> Represents the displacement vector decoded by node i at the current moment t; Mask represents the operator matrix, which is used to shield the displacement updates of nodes satisfying the boundary conditions, and the corresponding coefficients of all nodes under the boundary conditions in the Mask operator matrix are 0, All nodes in non-boundary conditions have a corresponding coefficient of 1.
进一步，在所述步骤7)执行过程中，对历史预测振动位移和实际测量位移进行对比，以L2范数的平均差值作为损失函数目标，使用随机梯度下降优化器对损失函数进行离线或实时优化，使数字孪生模型的振动行为得以不断逼进物理实体。Further, during the execution of step 7), the historical predicted vibration displacement is compared with the actual measured displacement, and the average difference of the L2 norm is used as the loss function target, and the stochastic gradient descent optimizer is used to perform offline or real-time optimization of the loss function. Optimization, so that the vibration behavior of the digital twin model can continuously approximate the physical entity.
本发明的有益效果在于：The beneficial effects of the present invention are:
本发明基于机器学习的机械振动数字孪生模型构建方法，通过将数字孪生网格模型中所有节点的动力学特征向量送入并行的多个非线性动力学处理模块中，则可摈弃指定PDE方程的显式形式和复杂耗时的数值求解过程，通过非线性动力学处理模块自动提取机械振动传播的非线性微分动力学特征，使模型得以向真实物理系统进行不断优化和逼近，使模型最终学习到无限贴合真实场景下机械振动传播的隐式动力学行为，且可通过大规模GPU加速进行前向运算，极大提高甚至跟进真实固定振动传播速度并不断根据历史行为进行实时优化；因此，通过本发明方法构建得到的机械振动数字孪生模型能够用于对机械振动传播的快速精确模拟和预测。The method for constructing a digital twin model of mechanical vibration based on machine learning in the present invention sends the dynamic feature vectors of all nodes in the digital twin grid model to a plurality of parallel nonlinear dynamic processing modules, so that the specified PDE equation can be discarded The explicit form and complex and time-consuming numerical solution process automatically extract the nonlinear differential dynamics characteristics of mechanical vibration propagation through the nonlinear dynamics processing module, so that the model can be continuously optimized and approximated to the real physical system, so that the model can finally learn Infinitely fits the implicit dynamic behavior of mechanical vibration propagation in real scenes, and can perform forward calculations through large-scale GPU acceleration, greatly improving or even following up the real fixed vibration propagation speed and continuously optimizing in real time based on historical behavior; therefore, The mechanical vibration digital twin model constructed by the method of the present invention can be used for fast and accurate simulation and prediction of mechanical vibration propagation.
附图说明Description of drawings
为了使本发明的目的、技术方案和有益效果更加清楚，本发明提供如下附图进行说明：In order to make the purpose, technical scheme and beneficial effect of the present invention clearer, the present invention provides the following drawings for illustration:
图1为本发明基于机器学习的机械振动数字孪生模型构建方法以发动机叶片加工为例的原理图；Fig. 1 is the schematic diagram of the machine learning-based mechanical vibration digital twin model construction method of the present invention taking engine blade processing as an example;
图2为多个并行非线性动力学处理模块的结构示意图；Fig. 2 is a structural schematic diagram of multiple parallel nonlinear dynamics processing modules;
图3为利用非线性离散微分算子计算拉普拉斯算子矩阵参数的示意图。Fig. 3 is a schematic diagram of calculating Laplacian matrix parameters by using a nonlinear discrete differential operator.
具体实施方式Detailed ways
下面结合附图和具体实施例对本发明作进一步说明，以使本领域的技术人员可以更好的理解本发明并能予以实施，但所举实施例不作为对本发明的限定。The present invention will be further described below in conjunction with the accompanying drawings and specific embodiments, so that those skilled in the art can better understand the present invention and implement it, but the examples given are not intended to limit the present invention.
如图1所示，为本发明基于机器学习的机械振动数字孪生模型构建方法以发动机叶片加工为例的原理图。首先，需要构建物理实体的三维数字孪生模型，数字孪生模型包括物理实体的运动约束点位置和受外力影响物理体的接触三维模型；其次，对数字孪生模型进行网格离散划分，网格相交点即为数字孪生模型的节点，得到数字孪生网格模型，以此作为物理实体的几何数字孪生体。具体的，本实施例基于机器学习的机械振动数字孪生模型构建方法，包括如下步骤：As shown in FIG. 1 , it is a schematic diagram of the method for constructing a digital twin model of mechanical vibration based on machine learning in the present invention, taking engine blade processing as an example. First of all, it is necessary to construct a 3D digital twin model of the physical entity. The digital twin model includes the position of the motion constraint point of the physical entity and the contact 3D model of the physical body affected by external forces; secondly, the digital twin model is divided into discrete grids, and the intersection points It is the node of the digital twin model, and the digital twin grid model is obtained, which is used as the geometric digital twin of the physical entity. Specifically, the method for constructing a digital twin model of mechanical vibration based on machine learning in this embodiment includes the following steps:
1)测量当前时刻物理实体表面各测振点的振动位移；具体的，使用多点激光扫描测振设备对当前时刻物理实体表面的测振点的振动位移进行测量，包括受力物体和接触受力物体部分的施力物体，测振点可任意选择，但为了数字孪生模型能够收敛更加快速，测振点应尽量稀疏分布于物理实体表面。1) Measure the vibration displacement of each vibration measurement point on the surface of the physical entity at the current moment; specifically, use a multi-point laser scanning vibration measurement device to measure the vibration displacement of the vibration measurement points on the surface of the physical entity at the current moment, including the force-bearing object and the contact object For the force-applying object of the force object, the vibration measurement points can be selected arbitrarily, but in order to make the digital twin model converge faster, the vibration measurement points should be distributed as sparsely as possible on the surface of the physical entity.
2)将各测振点的振动位移插入与物理实体对应的数字孪生模型的对应节点中，未对应有测振点的节点的位移取该节点在上一时刻的位移，得到当前的数字孪生网格模型；根据当前及必要历史测量数据，计算当前时刻各节点的振动速度、一阶加速度和二阶加速度，并结合对应节点的振动位移和物体属性数字标示，共同构成该节点的特征向量。具体的，本实施例采用k近邻算法将各测振点的振动位移插入数字孪生模型的对应节点中。2) Insert the vibration displacement of each vibration measurement point into the corresponding node of the digital twin model corresponding to the physical entity, and the displacement of the node not corresponding to the vibration measurement point takes the displacement of the node at the previous moment to obtain the current digital twin network According to the current and necessary historical measurement data, calculate the vibration velocity, first-order acceleration and second-order acceleration of each node at the current moment, and combine the vibration displacement of the corresponding node and the digital label of the object attribute to form the eigenvector of the node. Specifically, in this embodiment, the k-nearest neighbor algorithm is used to insert the vibration displacement of each vibration measurement point into the corresponding node of the digital twin model.
3)将数字孪生网格模型中各节点的特征向量编码为动力学特征向量。具体的，构建多层神经网络作为动力学信息编码器，表示为Encoder；通过动力学信息编码器将数字孪生网格模型中当前各节点的特征向量编码为动力参数隐空间向量hi，即：3) Encode the eigenvectors of each node in the digital twin grid model into dynamic eigenvectors. Specifically, a multi-layer neural network is constructed as a dynamic information encoder, denoted as Encoder; through the dynamic information encoder, the current feature vectors of each node in the digital twin grid model are encoded into the dynamic parameter hidden space vector hi , namely:
hi＝Encoder(Fi)hi ＝Encoder(Fi )
其中，Fi表示数字孪生网格模型中的节点i的特征向量，且：Fi∈Rm，即Fi为m维实向量。Among them, Fi represents the feature vector of node i in the digital twin grid model, and: Fi ∈ Rm , that is, Fi is an m-dimensional real vector.
4)将数字孪生网格模型中所有节点的动力学特征向量送入并行的多个非线性动力学处理模块中，所述非线性动力学处理模块包括交替叠加作用于数字孪生网格模型上的非线性离散微分算子处理层和非线性激活函数层，如图2所示；所述非线性离散微分算子通过高阶契比雪夫多项式，以高阶契比雪夫多项式系数为数字孪生模型非线性动力学处理模块的待学习优化参数，采用线性离散拉普拉斯算子作为基元算子进行逼进；通过一层线性网络层将多个非线性动力学处理模块输出的多份特征向量整合为单份动力学特征向量。4) Send the dynamic eigenvectors of all nodes in the digital twin grid model to multiple parallel nonlinear dynamic processing modules, the nonlinear dynamic processing modules include alternately superimposed on the digital twin grid model The nonlinear discrete differential operator processing layer and the nonlinear activation function layer, as shown in Figure 2; the nonlinear discrete differential operator passes through the high-order Chebyshev polynomial, and uses the high-order Chebyshev polynomial coefficient as the digital twin model non- The parameters to be learned and optimized of the linear dynamics processing module are approximated by using the linear discrete Laplacian operator as the primitive operator; multiple eigenvectors output by multiple nonlinear dynamics processing modules are passed through a linear network layer Integrate into a single kinetic eigenvector.
具体的，定义节点i与任意相邻的节点j和点k之间连线组成的三角形为Δi-jk；则节点i处的拉普拉斯算子为：Specifically, define the triangle formed by the connection between node i and any adjacent node j and point k as Δi-jk ; then the Laplacian operator at node i is:
其中，(Δf)i是节点i的拉普拉斯算子，表示任意一个与节点i相连的节点j变化到节点i所带来的增益；fi表示函数f在节点i处的函数值；fj表示函数f在节点j处的函数值；wij表示节点i与节点j之间的节点边eij的边权重；ai表示节点i的总权重；且：Among them, (Δf)i is the Laplacian operator of node i, which represents the gain brought by any node j connected to node i changing to node i; fi represents the function value of function f at node i; fj represents the function value of function f at node j; wij represents the edge weight of node edge eij between node i and node j; ai represents the total weight of node i; and:
ai＝∑ai-jkai =∑ai-jk
其中，lij表示节点i与节点j之间相连得到的节点边长度；lik表示节点i与节点k之间相连得到的节点边长度；ljk表示节点j与节点k之间相连得到的节点边长度；Si-jk表示三角形Δi-jk的面积；ai-jk表示节点i在Δi-jk中的权重；Among them, lij represents the node edge length obtained by the connection between node i and node j; lik represents the node edge length obtained by the connection between node i and node k; ljk represents the node obtained by the connection between node j and node k side length; Si-jk represents the area of triangle Δi-jk ; ai-jk represents the weight of node i in Δi-jk ;
将所有节点的拉普拉斯算子整合成矩阵的形式，构造一个以边权重wij为元素的n×n的矩阵W；若节点i与节点j之间不相邻，则节点i与节点j之间不连接，矩阵中对应位置的元素wij＝0；Integrate the Laplacian operators of all nodes into a matrix form, and construct an n×n matrix W with edge weight wij as an element; if node i and node j are not adjacent, then node i and node j There is no connection between j, the element wij of the corresponding position in the matrix = 0;
构造一个以节点权重ai为元素的对角矩阵矩阵中元素ai表示节点i的节点权重，其余位置均为0；Construct a diagonal matrix with node weights ai as elements The element ai in the matrix represents the node weight of node i, and the rest of the positions are all 0;
构造一个以fi为列向量的矩阵F，则所有节点的拉普拉斯算子可以表示为：Construct a matrix F with fi as the column vector, then the Laplacian operator of all nodes can be expressed as:
ΔL＝A-1(D-W)FΔL＝A-1 (DW)F
其中，ΔL表示所有节点的拉普拉斯算子；D表示所有节点组成的图网络的度矩阵；Among them, ΔL represents the Laplacian operator of all nodes; D represents the degree matrix of the graph network composed of all nodes;
采用线性离散拉普拉斯算子作为基元算子ΔL，通过m阶契比雪夫多项式将基元算子ΔL构建成非线性离散微分算子，即：The linear discrete Laplacian operator is used as the primitive operator ΔL, and the primitive operator ΔL is constructed into a nonlinear discrete differential operator through the m-order Chebyshev polynomial, namely:
其中，θ是契比雪夫多项式的系数向量，且θ∈Rm为m维实向量；ΔL表示所有节点的拉普拉斯算子，ΔL为m阶矩阵，m为数字孪生网格模型中所有节点的数量；且：Among them, θ is the coefficient vector of the Chebyshev polynomial, and θ∈Rm is the m-dimensional real vector; ΔL represents the Laplacian operator of all nodes, ΔL is the m-order matrix, and m is all the number of nodes; and:
此时，m阶契比雪夫多项式系数向量θ为数字孪生模型非线性动力学处理模块的待学习优化参数；At this time, the m-order Chebyshev polynomial coefficient vector θ is the parameter to be learned and optimized for the nonlinear dynamics processing module of the digital twin model;
具体的，非线性动力学处理模块包含非线性离散微分算子处理层和非线性激活函数层，即：Specifically, the nonlinear dynamics processing module includes a nonlinear discrete differential operator processing layer and a nonlinear activation function layer, namely:
ΔL(l+1)＝σ[A-1(D-W)AL(l)]ΔL(l+1) = σ[A-1 (DW)AL(l) ]
其中，A-1(D-W)ΔL(l)为非线性离散微分算子处理层；ΔL(l)是第l层的拉普拉斯矩阵，且ΔL(0)＝F；σ为非线性激活函数层，本实施例的非线性激活函数层选用ReLU。Among them, A-1 (DW)ΔL(l) is the nonlinear discrete differential operator processing layer; ΔL(l) is the Laplacian matrix of layer l, and ΔL(0) = F; σ is the nonlinear activation Function layer, the nonlinear activation function layer in this embodiment selects ReLU.
5)将步骤4)中输出的动力学特征向量解码为节点的位移向量。具体的，构建多层神经网络作为动力学信息解码器，表示为Decoder；通过动力学信息解码器将当前数字孪生网格模型中各节点的最终动力参数隐空间向量解码为位移向量ui，即：5) Decode the dynamic feature vector output in step 4) into the displacement vector of the node. Specifically, a multi-layer neural network is constructed as a dynamic information decoder, expressed as Decoder; through the dynamic information decoder, the final dynamic parameter latent space vector of each node in the current digital twin grid model Decodes to displacement vector ui , that is:
6)将节点位移向量叠加到上一时刻的节点位置坐标中，并更新节点的位置坐标信息。更新后的节点位置坐标信息为：6) Add the node displacement vector to the node position coordinates at the previous moment, and update the node position coordinate information. The updated node position coordinate information is:
其中，表示节点i在当前时刻t更新后的位置坐标信息；/>表示节点i在上一时刻t-1的位置坐标信息；/>表示节点i在当前时刻t解码得到的位移向量；Mask表示算子矩阵，用于对满足边界条件的节点的位移更新进行屏蔽，且Mask算子矩阵中所有处于边界条件的节点的对应系数0，所有处于非边界条件的节点的对应系数为1。in, Indicates the updated position coordinate information of node i at the current moment t;/> Indicates the position coordinate information of node i at the last moment t-1; /> Represents the displacement vector decoded by node i at the current moment t; Mask represents the operator matrix, which is used to shield the displacement updates of nodes satisfying the boundary conditions, and the corresponding coefficients of all nodes under the boundary conditions in the Mask operator matrix are 0, All nodes in non-boundary conditions have a corresponding coefficient of 1.
7)循环步骤1)至步骤6)，在时间步上迭代进行前向计算，以模拟机械振动在时间上的动力学演化。7) Step 1) to step 6) are looped, and forward calculation is performed iteratively on the time step to simulate the dynamic evolution of mechanical vibration over time.
具体的，在所述步骤7)循环执行过程中，对历史预测振动位移和实际测量位移进行对比，以L2范数的平均差值作为损失函数目标，使用随机梯度下降优化器对损失函数进行离线或实时优化，使数字孪生模型的振动行为得以不断逼进物理实体。Specifically, during the cyclic execution of step 7), the historical predicted vibration displacement is compared with the actual measured displacement, and the average difference of the L2 norm is used as the loss function target, and the loss function is performed offline by using the stochastic gradient descent optimizer. Or real-time optimization, so that the vibration behavior of the digital twin model can continuously approximate the physical entity.
以上所述实施例仅是为充分说明本发明而所举的较佳的实施例，本发明的保护范围不限于此。本技术领域的技术人员在本发明基础上所作的等同替代或变换，均在本发明的保护范围之内。本发明的保护范围以权利要求书为准。The above-mentioned embodiments are only preferred embodiments for fully illustrating the present invention, and the protection scope of the present invention is not limited thereto. Equivalent substitutions or transformations made by those skilled in the art on the basis of the present invention are all within the protection scope of the present invention. The protection scope of the present invention shall be determined by the claims.
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN116992624B (en)* | 2022-08-08 | 2024-02-13 | 重庆大学 | New energy automobile motor heat management method |
| CN115310227B (en)* | 2022-08-09 | 2023-06-16 | 重庆大学 | Construction method of digital twin model of gear power transmission |
| CN115310228B (en)* | 2022-08-09 | 2023-06-27 | 重庆大学 | Gear modification design method based on digital twin |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2021036671A1 (en)* | 2019-08-29 | 2021-03-04 | 深圳市广宁股份有限公司 | Digital twin-based intelligent vibration detection method and device |
| CN112487584A (en)* | 2020-12-03 | 2021-03-12 | 天津工业大学 | Dynamics-based rolling bearing digital twin modeling method |
| CN112800660A (en)* | 2019-11-14 | 2021-05-14 | 通用电气公司 | Core friction diagnostics in an engine fleet |
| CN112904805A (en)* | 2021-01-15 | 2021-06-04 | 天津商业大学 | Digital twin modeling and virtual-real synchronization method for multi-axis numerical control machine tool |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20210157312A1 (en)* | 2016-05-09 | 2021-05-27 | Strong Force Iot Portfolio 2016, Llc | Intelligent vibration digital twin systems and methods for industrial environments |
| KR102338159B1 (en)* | 2020-02-17 | 2021-12-10 | 경희대학교 산학협력단 | Virtual sensing apparatus of structural vibration and operating method thereof |
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| WO2021036671A1 (en)* | 2019-08-29 | 2021-03-04 | 深圳市广宁股份有限公司 | Digital twin-based intelligent vibration detection method and device |
| CN112800660A (en)* | 2019-11-14 | 2021-05-14 | 通用电气公司 | Core friction diagnostics in an engine fleet |
| CN112487584A (en)* | 2020-12-03 | 2021-03-12 | 天津工业大学 | Dynamics-based rolling bearing digital twin modeling method |
| CN112904805A (en)* | 2021-01-15 | 2021-06-04 | 天津商业大学 | Digital twin modeling and virtual-real synchronization method for multi-axis numerical control machine tool |
| Title |
|---|
| 基于数字孪生的多轴数控机床轮廓误差抑制方法;张雷 等;计算机集成制造系统;第27卷(第12期);全文* |
| Publication number | Publication date |
|---|---|
| CN114719962A (en) | 2022-07-08 |
| Publication | Publication Date | Title |
|---|---|---|
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