Running state monitoring method for plate shell parts

Abstract

The invention relates to the technical field of state evaluation of electromechanical equipment, and discloses a running state monitoring method for plate shell parts, which comprises the following steps of: 1) constructing a physical simplified model of the plate shell parts, and dispersing the simplified model by using a finite element method to obtain a finite element model; 2) performing order reduction on the finite element model of the plate shell part by using eigen-orthogonal decomposition, analyzing the precision of order reduction models with different orders, and selecting the order reduction model with the minimum order reduction order as a final order reduction model on the premise that the precision meets the actual engineering requirements; 3) compiling upper computer software in a computer, deploying the reduced-order model into the upper computer software, building a test device at the same time, and performing online monitoring on physical entity strain by using the reduced-order model; the order reduction model constructed by using the method can effectively calculate the physical quantity of a physical entity in real time, and high precision is achieved, so that the running state of the plate shell type part is monitored on line.

Description

Technical Field

[0001] The present invention relates to the technical field of status assessment of electromechanical equipment, and in particular to a method for monitoring the operating status of plate and shell components. Background Art

[0002] Plate and shell parts are important parts with distinct geometric features, and are widely used in various industries, such as solar panels, wind turbine blades, and plate and shell parts. Since plate and shell parts generally play the role of bearing and capturing energy, the stress conditions are complex and changeable, and they are prone to failure. Therefore, it is necessary to monitor the status of plate and shell parts.

[0003] Traditional methods for monitoring the condition of electromechanical equipment parts or components as a whole are generally divided into two types, namely data-driven and physical model-based. The data-driven method can quickly obtain the operating status of the equipment, but it relies on high-quality data and has problems such as poor interpretability; the physical model-based method has high computational costs, but can better reflect the operating status of the monitored object. In view of the high computational cost of physical models, the present invention proposes an operating status monitoring method for plate and shell components based on intrinsic orthogonal decomposition.

[0004] Using physical model methods to monitor the condition of complex physical entities requires solving the physical field differential equations and has high requirements on the speed of solving the differential equations. Traditional numerical methods (such as finite element method, finite volume method, and finite difference method) have high computational costs when solving physical field differential equations due to the high number of degrees of freedom in the discretized equations. They are difficult to be directly used to construct condition monitoring of plate and shell components. Therefore, it is necessary to reduce the order of the constructed physical model.

[0005] The model reduction method obtains a low-dimensional reduced-order model from a high-dimensional finite element model through numerical fitting, physical simplification, mathematical projection and other methods. It is an effective method to reduce the computational cost. Using the model reduction method to construct a reduced-order model of plate and shell components can realize real-time calculation and analysis of the physical quantities of plate and shell components (such as overall displacement, etc.), and then realize online perception of the operating status of plate and shell components, which is beneficial to ensure the safe and efficient operation of mechanical equipment. Summary of the invention

[0006] In view of the problems existing in the prior art, the purpose of the present invention is to provide a method for monitoring the operating status of plate and shell components, and an overall implementation process.

[0007] The technical solution of the present invention is as follows:

[0008] A method for monitoring the operating status of plate and shell components comprises the following steps:

[0009] Step 1: Obtain a simplified physical model of plate and shell components based on their geometric features, analyze the actual stress conditions of plate and shell components, and construct a finite element model of plate and shell components;

[0010] Step 2: Use Proper Orthogonal Decomposition (POD) to perform order reduction analysis on the finite element model constructed in step 1, compare the accuracy of the reduced-order models with different orders, and determine the final reduced-order. The final reduced-order should satisfy the engineering requirements of the reduced-order model at this order. The present invention requires that the relative error between the predicted value of the final reduced-order model and the calculated value of the finite element model is less than 1×10 -4 ;

[0011] Step 3: Design and build the host computer software in the computer, and deploy the reduced-order model of the plate and shell components to the host computer software; build the physical entities of the plate and shell components and install strain sensors and inclination sensors, use the microcontroller to read the sensor data and upload the data to the host computer to convert it into boundary conditions, and then input the boundary conditions into the reduced-order model for calculation;

[0012] Step 4: Determine the accuracy of the constructed reduced-order model by calculating the error between the strain measurement value of the strain sensor and the strain calculation value of the reduced-order model in the host computer.

[0013] Furthermore, the process described in step 1 is as follows: firstly, a simplified physical model based on plate and shell components is constructed and a finite element model is divided. The simplified finite element model of plate and shell components and the schematic diagram of their bending deformation are shown in FIG. Figure 2 As shown in the figure, the origin O of the coordinate system XYZ is the intersection of the axis of the plate and shell parts before bending and deformation and the lower boundary of the plate and shell parts; n0 and n1 are the normal vectors of the top end face of the plate and shell parts before and after bending and deformation, respectively, and the angle between the two vectors is the inclination angle θ of the end face at the top of the plate and shell parts. The expression of the deflection w at the top of the plate and shell parts and the end face inclination angle θ is:

[0014]

[0015] Where F is the concentrated load applied to the top of the plate and shell parts, in N; E is the elastic modulus of the plate and shell parts material, in Pa; I is the section inertia moment of the plate and shell parts, in m 4 ; L is the length of plate and shell components, and L is set to 220mm in the present invention.

[0016] The deflection w at the top of the plate and shell components is converted into a displacement boundary condition. The transient equilibrium equation of the finite element model of the plate and shell components under the displacement boundary condition is shown in formula (2):

[0017]

[0018] Where M a , C a , K a M is the mass matrix, damping matrix and stiffness matrix corresponding to the nodes without displacement constraints in the finite element model; ab , C ab , K ab is the coupling matrix between the displacement constraint nodes and the non-displacement constraint nodes of the finite element model; q a , is the node displacement vector, node velocity vector and node acceleration vector of the node without displacement constraint in the finite element model; q a , is the node displacement vector, node velocity vector and node acceleration vector of the displacement constraint node of the finite element model; g a is the nodal gravity load vector corresponding to the finite element model without displacement constraint.

[0019] Furthermore, the process described in step 2 is: combining the intrinsic orthogonal decomposition with the finite element method to construct a reduced-order model of the displacement field of plate and shell components, including:

[0020] Solve the finite element model of step 1 to obtain the node displacement solution set, and select m samples from the set to form a matrix X = [q1, q2, ..., q m ]; where q i =[u1,u2,...,u z ] T is the displacement solution of the node, z is the number of degrees of freedom of the finite element model; let {ζ1,ζ2,...,ζ n} is a set of n standard orthogonal bases of X, which are written in matrix form and recorded as Φ; for the finite element model of plate and shell components, the node displacement value qt at any time can be expressed by {ζ1,ζ2,...,ζ n}express:

[0021]

[0022] In the formula,

[0023] Choose {ζ1,ζ2,...,ζ n}The first k standard orthogonal basis vectors in qt are:

[0024]

[0025] In the formula, Φ k =[ζ1,ζ2,...,ζ k ], k<n; bt(k) =[b t1 ,b t1 ,...,b tk ] T .

[0026] Let the error function be:

[0027]

[0028] To obtain the error function under the constraints {ζ1,ζ2,…,ζ n} is the optimal solution under the standard orthogonal basis, and the Lagrange factor u is introduced ij (i, j = k+1, k+2,…, n), construct a Lagrange function, and find the standard orthogonal basis corresponding to the optimal solution.

[0029]

[0030] In the formula, δ ij is the Kronecker function.

[0031] Put the two ends of equation (6) to ζ j Taking partial derivatives, we get:

[0032]

[0033] In the formula, Φ n-k =[ζ k+1 ,ζ k+2 ,...,ζ n ] T ,u j =[u k+1,j ,u k+2,j ,...,u n,j ] T . Writing the above equation in matrix form gives the following equation:

[0034]

[0035] Where U n-k =[u k+1 ,u k+2 ,...,u n ] T To find the optimal solution, set equation (8) equal to 0 and multiply it by Since the matrix Φ n The interior vectors are orthogonal, so we have

[0036] Yizhi, U n-k is a semi-positive definite matrix, so there exists an orthogonal matrix P that can convert U n-k Diagonalize to get Multiply both ends of the above equation by Φ n-k P, we get the following formula:

[0037]

[0038] Where Λ is U n-k The diagonal matrix of Λ. Arrange the diagonal elements of Λ in descending order. From equation (9), we can see that the i-th diagonal element of Λ is XX T The eigenvalue λ i , and the matrix Φ n-k The i-th column of P is XX T Corresponding to λ i Considering that the orthogonal matrix has the Frobenius norm The following is norm-preserving, so equation (5) can be rewritten as:

[0039]

[0040] Take the left singular value vectors corresponding to the first n singular values ​​of X to form the transformation matrix Φ n , at this time Φ n is the error function under the constraints {ζ1,ζ2,…,ζ n} is the optimal solution under the standard orthogonal basis, and the error function has a minimum value of the matrix XX T The sum of the last nk eigenvalues. Define the following formula:

[0041]

[0042] In the formula, λ i For XX T The eigenvalues ​​are arranged in descending order. If I(k)≥d%, the k-dimensional basis vector is said to retain d% of the characteristic information of the original sample. Construct reduced-order models at different orders, and calculate the accuracy of the reduced-order models at different reduced-order orders respectively, determine the appropriate reduced-order order and obtain the reduced-order model, and the final reduced-order order should satisfy the reduced-order model at this order to meet the actual engineering needs.

[0043] Furthermore, for step 3, build the physical entity of plate and shell parts, build a simplified model of plate and shell parts, install strain sensors and inclination sensors on the physical entity of plate and shell parts; write a single-chip computer program to read the sensor measurement data and upload the data to the computer; design and build the host computer software on the computer, and deploy the reduced-order model to the host computer software; the host computer reads the sensor data uploaded by the single-chip computer, converts the data into displacement boundary conditions, and inputs them into the reduced-order model to realize fast calculation, and obtain the strain and stress calculation values ​​of the current physical entity of plate and shell parts, as well as the displacement solution of the node. After the reduced-order model completes the calculation, the calculation results are processed in the host computer, that is, the physical entity deformation of plate and shell parts is quickly quantified based on the node displacement solution and displayed in the host computer.

[0044] Furthermore, for step 4, the test results show that the proposed method can effectively calculate the physical quantities of physical entities in real time with high accuracy, thereby realizing online monitoring of the operating status of plate and shell components.

[0045] The design ideas of the present invention are as follows:

[0046] 1) Construct a simplified physical model of plate and shell components, and use the finite element method to discretize the simplified model to obtain a finite element model; 2) Use proper orthogonal decomposition to reduce the order of the finite element model of plate and shell components, analyze the accuracy of reduced-order models with different orders, and select the reduced-order model with the smallest order when the accuracy meets the actual engineering requirements as the final reduced-order model; 3) Write the host computer software in the computer, deploy the reduced-order model to the host computer software, and build an experimental device at the same time, and use the reduced-order model to monitor the strain of the physical entity online; the reduced-order model constructed by this method can effectively calculate the physical quantities of the physical entity in real time, and achieve high accuracy, thereby monitoring the operating status of plate and shell components online.

[0047] The beneficial effects of the present invention are as follows:

[0048] The present invention provides a method for monitoring the operating status of plate and shell components. By establishing a high-precision reduced-order model of the physical entity, the physical quantity (displacement, strain) of the physical entity is quickly calculated, and the calculated data and sensor measurement data are displayed in real time. The experimental results show that compared with the existing technology (such as the data-driven status monitoring method), the method proposed in the present invention has better real-time performance and higher accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0049] Figure 1 It is a roadmap for the technical implementation scheme of the present invention;

[0050] Figure 2It is a schematic diagram of deformation of plate and shell parts;

[0051] Figure 3 It is the impact response curve of plate and shell components;

[0052] Figure 4 is the characteristic value curve graph;

[0053] Figure 5 Each order of transformation matrix does not retain the characteristic information graph of the original sample;

[0054] Figure 6 is the error logarithm plot of the 6th-order reduced-order model at time;

[0055] Figure 7 is a diagram of the test apparatus;

[0056] Figure 8 It is a simplified calculation diagram for online monitoring of strain of plate and shell components. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with the accompanying drawings and embodiments.

[0058] like Figure 1 As shown, a method for monitoring the operating status of plate and shell components, the specific steps are as follows:

[0059] Step 1: Establish a simplified physical model of plate and shell components, approximate the plate and shell components into a slender beam with a flange structure at one end, the beam cross-section is a circular ring shape, and the material is 304 stainless steel; use four-node and twenty-four-degree-of-freedom shell elements to divide the simplified model into grids, and obtain a grid model with 70 nodes and 420 degrees of freedom.

[0060] To calculate the node displacement vector q of the node without displacement constraint of plate and shell components a , use the direct integration method to construct the solution equation for formula (2):

[0061]

[0062] In the formula, Δt is the time step of integration, which is 0.01s in the present invention, and α and δ are the control parameters of the Newmark method, where α=0.25 and δ=0.5.

[0063] Solving the above equations can obtain the node displacement solution, node velocity solution, and node acceleration solution. The physical quantity that is ultimately monitored online in the present invention is strain. In the Kirchhoff plate theory, the physical quantity in the plate can be represented by displacement. In the present invention, the node displacement solution is used to refer to equation (13) to calculate the strain in the unit along the length direction of the plate:

[0064]

[0065] In the formula, q z represents the displacement of the point along the thickness direction of the plate; z represents the z-coordinate of the point.

[0066] Step 2: Apply impact load to the top of the model and solve the finite element model. The calculation results are as follows: Figure 3 As shown in the figure, the calculated node displacement solutions are sorted according to the sampling point numbers to form a matrix V = [v1,v1,…,v 20 ], use singular value decomposition on the matrix V to obtain the singular value matrix Σ and the left singular value vector matrix W. Plot the first 20 singular values ​​on the diagonal of the singular value matrix Σ on Figure 4 In the example, the singular values ​​are numbered according to their positions in the matrix Σ. The first singular value on the diagonal is numbered 1, and so on. Figure 4 From the results obtained in , we can know that the singular values ​​from sequence number 6 to 20 are similar in size. Select the left singular value vectors corresponding to the first k singular values ​​to construct the transformation matrix, use the transformation matrix to construct the reduced-order model, and calculate the feature information retained by the reduced-order model through formula (11). When k is less than or equal to 10, the transformation matrix retains the feature information of the original sample, such as Figure 5 As shown. Figure 4 It can be seen that when the value of k is greater than or equal to 6, the characteristic information of the original sample retained by the transformation matrix changes little; through calculation, it can be seen that when the reduction order is 6, the transformation matrix retains 99.98% of the characteristic information of the original sample, so the reduction order is preliminarily determined to be 6.

[0067] The first five columns of the left singular value vector matrix W are selected to construct the change matrix Φ6. The change matrix is ​​used to reduce the order of the finite element model to obtain a 6-order reduced-order model. Substitute equation (4) into equation (12) and multiply both ends of equation (12) by The following formula is obtained:

[0068]

[0069] In the formula, b is the coefficient vector, and the length is the reduced order. The displacement vector can be reconstructed according to formula (4).

[0070] Under the same displacement boundary conditions, the reduced-order model and the finite element model are used to calculate the displacement solutions of the nodes. The errors of the displacement solutions of the nodes of the reduced-order model at all times are calculated. The definition of the error of the degradation model at time t is as follows:

[0071] err t =log 10 (||q t -q t(6) || / ||q t ||) (15)

[0072] In the formula, err t is the error of the reduced-order model on the i-th degree of freedom; q t is the displacement solution of the node at time t calculated by the finite element model, q t(6) is the displacement solution of the node at time t calculated by the 6th-order reduced-order model. The error of all degrees of freedom in the displacement solution of the node is calculated and the calculation results are plotted on Figure 6 ,from Figure 6 It can be seen that the error values ​​are concentrated around 10 -10 ~10 -8 Nearby, the maximum error is no more than 10 -4 , to meet the needs of practical engineering applications, the order reduction number of the plate and shell components is determined to be 6.

[0073] Step 3: Test the actual plate and shell components Figure 7 As shown in the figure, the total length of the physical entity is 220mm, and a tilt sensor WT61C is installed at the top of the plate and shell parts. The tilt sensor can detect the tilt angle of the top end face of the plate and shell parts; a strain sensor BF350-3EB is installed on the tower body at a position 50mm away from the fixture. The strain sensor can measure the average strain at the installation position of the plate and shell parts and output voltage; the STM32 microcontroller is used to collect data from the strain sensor and the tilt sensor, and the collected data is uploaded to the computer through the serial communication port of the microcontroller. The computer processes the data and calculates the stress and strain of the plate and shell parts.

[0074] The inclination angle of the top end face of the plate and shell components is detected by using an inclination sensor and converted into a displacement boundary condition. The voltage value of the strain sensor is sampled and read using an analog-to-digital converter (ADC). The average strain of the physical entity at the installation position of the strain sensor can be calculated according to formula (16).

[0075]

[0076] Where, e0 is the output voltage of the strain sensor, in V; E is the supply voltage of the strain sensor, in V; R1, R2, R3, R4 are the bridge resistances of the strain sensor, in Ω; K s is the sensitivity coefficient of the strain sensor, which is related to the material used by the strain sensor. The sensitivity coefficient of the BF350-3EB strain sensor is 2.1; ε is the average strain of the physical entity at the installation position of the strain sensor.

[0077] When analyzing the interaction between the physical entities of plate and shell parts and the reduced-order model on the computer, the STM32 microcontroller is first used to read the data of the inclination sensor and the strain sensor; after obtaining the data, the STM32 microcontroller is used to upload the data to the computer; the inclination data is processed and converted into displacement boundary conditions in the computer host software, and the displacement boundary conditions are substituted into the 5th-order reduced-order model deployed on the host computer to obtain the displacement solution of the node; the 3D cloud map is used in the host software to draw the displacement calculation results in the 3D model display area, and the strain calculation value and measurement value are displayed in real time in the function area. The results are as follows: Figure 8 As shown;

[0078] from Figure 8 It can be seen that although there is a certain error between the strain calculation value of the reduced-order model and the strain measurement value of the strain sensor, the change law of the strain calculation value is consistent with the change law of the strain measurement value.

[0079] In summary, the online condition monitoring method based on intrinsic orthogonal decomposition can effectively obtain the operating status of plate and shell components.

[0080] The above embodiments are only preferred embodiments of the present invention and are not limitations of the technical solutions of the present invention. Any technical solution that can be implemented on the basis of the above embodiments without creative work should be deemed to fall within the scope of protection of the patent of the present invention.

Claims

1. A method for monitoring the operating status of plate and shell components, characterized in that: The steps include: Step 1: Obtain a simplified physical model of plate and shell components based on their geometric features, analyze the stress conditions of the components, and construct a finite element model; Step 2: Use the proper orthogonal decomposition method to perform order reduction analysis on the finite element model constructed in step 1, construct a reduced-order model, and compare the accuracy of the reduced-order models with different orders to determine the final reduced-order number; Step 3: Deploy the reduced-order model constructed in step 2 to the host computer; build the physical entities of the components and install strain sensors and inclination sensors, use the microcontroller to read the sensor data and upload the data to the host computer to convert it into displacement boundary conditions, and then input the displacement boundary conditions into the reduced-order model for calculation; Step 4: Determine the accuracy of the constructed reduced-order model by calculating the error between the strain measurement value of the strain sensor and the strain calculation value of the reduced-order model in the host computer.

2. The method for monitoring the operating status of plate and shell components according to claim 1, characterized in that: The specific process of step 1 is as follows: Considering the geometric characteristics and stress conditions of plate and shell parts, the finite element model of thin plate parts is constructed based on Kirchhoff plate theory; The thin plate parts are constructed using four-node elastic shell elements. The elastic shell elements have six degrees of freedom at each node, including three rotational degrees of freedom. An angular displacement constraint is applied at the top of the model, and an angular velocity constraint and an angular acceleration constraint are additionally added at the same position. The dynamic equation of the finite element model finally constructed is shown in formula (1): Where M a , C a , K a M is the mass matrix, damping matrix and stiffness matrix corresponding to the nodes without displacement constraints in the finite element model; ab , C ab , K ab is the coupling matrix between the displacement constraint nodes and the non-displacement constraint nodes of the finite element model; q a , is the node displacement vector, node velocity vector and node acceleration vector of the node without displacement constraint in the finite element model; q a , is the node displacement vector, node velocity vector and node acceleration vector of the displacement constraint node of the finite element model; g a is the nodal gravity load vector corresponding to the finite element model without displacement constraint.

3. The method for monitoring the operating status of plate and shell components according to claim 1, characterized in that: The specific process of step 2 is: The intrinsic orthogonal decomposition is combined with the finite element method to construct a reduced-order model of the displacement field of the component, including: solving the finite element model in step 1, obtaining a set of displacement solutions of the nodes, selecting m samples from the set to form a matrix X = [q1, q2, ..., q m ]; where q i =[u1,u2,…,u z ] T is the displacement solution of the node, z is the number of degrees of freedom of the finite element model; let {ζ1,ζ2,...,ζ n } is a set of n standard orthogonal bases of X, which are written in matrix form and recorded as Φ; for the finite element model of plate and shell components, the node displacement value q at any time t By {ζ1,ζ2,...,ζ n }express: In the formula, Choose {ζ1,ζ2,...,ζ n }The first k standard orthogonal basis vectors in qt are: where Φ k = [ζ1, ζ2,..., ζ k , k < n; b t(k) = [b t1 , b t1 ,..., b tk T ;​ Let the error function be: To obtain the error function under the constraints {ζ1,ζ2,…,ζ n } is the optimal solution under the standard orthogonal basis, and the Lagrange factor u is introduced ij (i, j = k+1, k+2, ..., n), construct the Lagrange function and find the standard orthogonal basis corresponding to the optimal solution; In the formula, δ ij is the Kronecker function; Put both ends of equation (7) to ζ j Taking partial derivatives, we get: where Φ n-k = [ζ k+1 , ζ k+2 , …, ζ n T , u j = [u k+1,j , u k+2,j , …, u n,j T ;​​ Writing the above formula in matrix form gives the following formula: In the formula, U n-k =[u k+1 ,u k+2 ,...,u n ] T ; To find the optimal solution, let equation (9) equal to 0 and multiply it by Since the matrix Φ n The interior vectors are orthogonal, so we have U n-k is a semi-positive definite matrix, so there exists an orthogonal matrix P that can convert U n-k Diagonalize to get Multiply both ends of the above equation by Φ n-k P, we get the following formula: Where Λ is U n-k The diagonal matrix of ; Arrange the diagonal elements of Λ in descending order. From equation (10), we can see that the i-th diagonal element of Λ is XX T The eigenvalue λ i , and the matrix Φ n-k The i-th column of P is XX T Corresponding to λ i The eigenvector of Considering that the orthogonal matrix has a Frobenius norm The following is norm-preserving, so equation (6) can be rewritten as: Take the left singular value vectors corresponding to the first n singular values ​​of X to form the transformation matrix Φ n , at this time Φ n is the error function under the constraints {ζ1,ζ2,...,ζ n } is the optimal solution under the standard orthogonal basis, and the error function has a minimum value of the matrix XX T The sum of the last nk eigenvalues; Define the following formula: In the formula, λ i For XX T Eigenvalues ​​in descending order; If I(k)≥d%, the k-dimensional basis vector is said to retain d% of the characteristic information of the original sample; construct reduced-order models at different orders, and calculate the accuracy of the reduced-order models at different reduced-order orders respectively, determine the appropriate reduced-order order and obtain the reduced-order model, and the final reduced-order order should satisfy that the reduced-order model at this order meets the actual engineering needs.

4. The method for monitoring the operating status of plate and shell components according to claim 1, characterized in that: In the step 3, the host computer reads the measurement data of the inclination sensor and the strain sensor uploaded by the single-chip computer, inputs the inclination sensor data into the reduced-order model to realize fast calculation, and obtains the strain calculation value of the physical entity of the current component and the displacement solution of the node; after the reduced-order model completes the calculation, the calculation results are processed in the host computer, that is, the deformation of the physical entity of the component is quickly quantified based on the node displacement solution and displayed in the host computer; and the model calculation results and the calculation results of the strain sensor are plotted in the form of dynamic curves.

Images