Member state real-time sensing method based on parameterized load

Abstract

The invention belongs to the field of intelligent manufacturing, and discloses a component state real-time sensing method based on parameterized loads. According to the method, parameterized representation is carried out on the load, an overall stiffness matrix is obtained in combination with finite element analysis, and a displacement data set of a component under the parameterized load is constructed through Monte Carlo statics simulation. On the basis of POD, in combination with parameterized loads, a parameterized intrinsic orthogonal decomposition method is provided, then a projection base vector used for expressing a component displacement deformation mode is obtained, sensor layout optimization is conducted on a component deformation sensitive area through QR decomposition, and finally a real-time and accurate displacement state sensing result is obtained. The calculation amount of real-time sensing of the displacement state of the component can be effectively reduced, and the operation efficiency is improved; and by optimizing the layout of the sensor, the displacement sensing precision of the component is improved.

Description

Technical Field

[0001] The present invention belongs to the field of intelligent manufacturing and relates to a real-time component status perception method based on parameterized loads. Technical Background

[0002] Aerospace components are typically large and weak in rigidity, often incurring dimensional errors and deformation during the manufacturing process. This can lead to deviations between the actual component and the theoretical model during assembly, necessitating repeated adjustments and even forced assembly. To improve the assembly performance of aviation components, accurate sensing of the component's current state is essential. However, due to their large size and complex structure, coupled with the effects of time-varying temperature and gravity, accurate real-time sensing is difficult. Therefore, a method for accurately sensing component status in real time during the assembly process is needed.

[0003] To monitor and perceive component status, Li Tengteng, Wu Zhanjun, and others have developed a patented method for structural status monitoring and load identification based on inverse finite element and finite element methods (CN113468667A). This method uses Mindlin plate theory to discretize plate-shell structures, measures strain with strain sensors, calculates the structural displacement field using the least squares method, and ultimately uses finite element and regularization techniques to achieve structural status monitoring and load identification. This method can reduce errors to a certain extent, but the sensor layout does not consider the deformation characteristics of the structure, and the sensor data quality and perception accuracy cannot be guaranteed.

[0004] The patented method, "A Displacement Field Reconstruction Method for Cylindrical Thin-Walled Structures" (Patent No. CN118627360B), invented by Zhang Meng, Sun Lianghui, and others, combines a cyclic optimization algorithm to select measurement point locations. It then establishes a strain-to-node displacement mapping relationship based on the least squares functional and variational principle, ultimately deriving the global displacement through overall matrix assembly. This method can reduce computational complexity to a certain extent, but when dealing with large, complex structures, it requires processing a large amount of strain data, resulting in low computational efficiency and difficulty in real-time perception. Summary of the Invention

[0005] To address the challenges of high real-time computational complexity and low precision in sensing displacement states during aviation component assembly, this paper proposes a method for accurate, real-time component state sensing based on parameterized loads. This method first establishes a component displacement dataset under parameterized loads by parametrically defining the loads. Next, a component displacement state sensing equation is established based on proper orthogonal decomposition (POD). Furthermore, sensor layout is optimized by analyzing displacement-sensitive areas, ultimately achieving high-precision, real-time sensing of component displacement states under the optimal sensor arrangement.

[0006] Specifically, the method parametrically characterizes the loads, combines it with finite element analysis to obtain the component's global stiffness matrix, and uses Monte Carlo statics simulation to construct a displacement dataset under the parametric loads. Based on this, the method innovatively proposes a parameterized proper orthogonal decomposition (PPOD) method to extract projected basis vectors that characterize the component's displacement deformation patterns. Furthermore, QR decomposition is used to optimize sensor placement in deformation-sensitive areas of the component, enabling real-time and accurate perception of the component's displacement state.

[0007] The technical solution of the present invention:

[0008] A real-time component status perception method based on parameterized loads, the steps are as follows:

[0009] The first step is to construct a data set based on parameterized loads;

[0010] According to the stress of components under different working conditions, a parameterized load equation is established, and the load f is expressed as:

[0011] f(x;p,ω,r,t) (1)

[0012] Where x is the coordinate of the load location; t is the load distribution type; ω is the load application area; r is a subset of ω that shows the load distribution and local strength changes; p is the maximum load value;

[0013] After obtaining the parameterized load, the overall stiffness matrix of the component needs to be obtained to construct the displacement data set. In the actual assembly process, the component mainly behaves in a low-frequency quasi-static form. The mass and damping characteristics of the component are ignored, and only the component stiffness is considered. The component dynamic equation under the action of load f is simplified to:

[0014] Ku=f(x;p,ω,r,t)) (2)

[0015] Among them, u represents the displacement state of the component, and K represents the overall stiffness matrix of the component;

[0016] Finite element discretization is performed on the component to obtain n nodes. During the discretization process, only the three displacement degrees of freedom along the x, y, and z axes are considered, and the rotational degrees of freedom around the x, y, and z axes are ignored. K -1 It is the inverse of the component's overall stiffness matrix K, with a dimension of 3n×3n;

[0017] Combined with the results of finite element discretization of the component, the overall stiffness matrix K of the component is obtained:

[0018]

[0019] Where l = 3n, which represents the displacement degrees of freedom of n nodes along the x, y, and z axes;

[0020] Apply loads f of different sizes and positions through m Monte Carlo static simulations sim =[f1 f2...f m ] T , load f sim The corresponding displacement vector u sim =[u1 u2...u m ] T , forming the displacement data set X, which is expressed as:

[0021] X=[u1 u2...u m ]=[K -1 f1 K -1 f2…K -1 f m ] (4)

[0022] The dimension of the displacement dataset X is l×m, and m is specified to be less than l.

[0023] The second step is to obtain the component deformation mode based on the intrinsic orthogonal decomposition;

[0024] First, perform singular value decomposition on the displacement dataset X:

[0025] X=UΣV T (5)

[0026] Among them, U is a left singular vector matrix that represents the deformation mode of the component. Each column is the displacement projection basis vector generated by the component under different loads. The dimension is l×l and the expression is as follows:

[0027]

[0028] Σ is a diagonal matrix containing all singular values ​​σ1≥σ2≥…≥σ m , all non-diagonal elements are zero, the dimension is l×m, and the size of each singular value represents the weight or contribution of the displacement or load in the data under different load simulations. The expression is as follows:

[0029]

[0030] V T is a matrix composed of right singular vectors with dimension m×m;

[0031] In order to perceive the global displacement state of the component in real time, the computational complexity is reduced by using the order reduction method to retain the main feature information in the displacement dataset, which is expressed as:

[0032] X r =Ur Σ r V r T (8)

[0033] Among them, U r is the first r columns of data in U, with a dimension of l×r, expressed as:

[0034]

[0035] Σ r represents the first r singular values ​​of Σ, with dimension r×r, expressed as:

[0036]

[0037] V r T The dimensions of X are r×m, r It is represented as an approximate matrix of X with dimensions of l×m;

[0038] r is determined by calculating the ratio of the energy retained after reduction to the original energy. The retained energy ratio E r Expressed as:

[0039]

[0040] Among them, the numerator represents the sum of the squares of the first r singular values, which represents the energy retained by the reduced-order data matrix; the denominator represents the sum of the squares of all singular values, that is, the total energy of the original data matrix; the first r projection basis vectors U are selected by POD reduction r , retain the most important deformation mode of the component;

[0041] The third step is to establish the component displacement state perception equation

[0042] Based on the Galerkin method, the component displacement response u is described by the system response equation:

[0043] u=Us (12)

[0044] Where U is the l-order displacement projection basis vector obtained by POD decomposition of formula (5), and s represents the projection coefficient of the displacement basis vector;

[0045] Furthermore, based on the displacement projection basis vector U r ,have to The expression:

[0046]

[0047] in, is the component displacement vector, which represents the approximation of the true u; represents the approximate projection coefficient;

[0048] After placing k measuring point sensors on the component, the displacement data of the nodes are measured by the sensors. The observation matrix C is the position of the measuring point in the reference system with the degree of freedom of the component node as the reference system, which is expressed as:

[0049]

[0050] Among them, the i-th row, 1≤i≤k, contains only one non-zero element And j1≠j2≠j3≠…≠j k , the dimension is k×l;

[0051] Based on the measurement matrix C, the measurement equation of the sensor is expressed as:

[0052] y=Cu+δ (15)

[0053] Where y represents the displacement value measured by the sensor at k measurement points, with a dimension of k×1; u is the displacement response of the component expressed by formula (12), with a dimension of l×1; δ represents the displacement response with a mean of 0 and a variance of σ 2 Normal distribution measurement error; in order to improve numerical stability and focus on the main features of the system during state perception reconstruction, the measurement error δ is ignored and the approximate displacement is introduced The sensor measurement equation is expressed as follows:

[0054]

[0055] Approximate projection coefficients It is expressed as follows:

[0056]

[0057] Further substituting formula (17) into (13), we get the component displacement state perception equation: The expression:

[0058]

[0059] Among them, (CU r ) + Unified Representation CU r The inverse of , when m = r, represents CU r is a square matrix, (CU r ) + =(CU r ) -1 ; When m>r, it is pseudo-inverse, The fourth step is perception error analysis and optimization of measurement point layout in sensitive areas;

[0060] In order to improve the accuracy of component state perception, that is, to perceive displacement Closer to the real displacement u, in order to improve the robustness of the perception method in the measurement point layout optimization, it is necessary to consider the impact of measurement error on perception accuracy. r In certain cases, the perceptual error comes from the difference between the true projection coefficient s and the approximate projection coefficient The difference, projection coefficient error and its variance are expressed as follows:

[0061]

[0062] Where, e is the error of the projection coefficient, is the variance, Z=(CU r ) T CU r ;

[0063] By optimizing the layout of the observation matrix C in the sensitive area, the error is further reduced and the most critical information is captured. First, the deformation sensitivity index U is calculated by normalized weighted summation. w [i], calculate U r The absolute value of each mode of and normalized

[0064]

[0065] Through U r (norm) Each mode of the τ Get U w [τ], where 1≤τ≤r, and w1>w2>…>w r :

[0066]

[0067] Set the threshold T to filter out U w The nodes where [τ] ≥ T are regarded as deformation sensitive areas Ω:

[0068] Ω={τ|U w [τ]>T} (23)

[0069] From U r The modes corresponding to the nodes in the sensitive area Ω are retained to obtain the sensitive area mode U s :

[0070] U s =U r [Ω,:] (24)

[0071] Pair matrix U s Performing QR decomposition with column pivoting can obtain the optimal configuration of the measurement point layout:

[0072] U s ·P=Q·R (25)

[0073] After the QR decomposition with column pivots, Q is an orthogonal matrix, R is an upper triangular matrix, and P is a column permutation matrix. The column order indicates the importance of the node. The candidate nodes corresponding to the first k pivot elements are selected in descending order of the diagonal elements of the R matrix as the final measurement points, and are placed at the positions corresponding to the n nodes divided by the finite element of the component to reconstruct the optimal observation matrix C. * ;

[0074] Step 5: Real-time perception of component status based on binocular vision;

[0075] Based on the optimal observation matrix C * , the component displacement perception equation is expressed as:

[0076]

[0077] K measuring points are pasted on the corresponding nodes of the component. The load is applied by the robotic arm to cause the component to displace. The binocular camera measures the displacement of the pasted measuring points to obtain the actual displacement value y of each measuring point. This is then substituted into the component displacement perception equation to obtain the global displacement state of the component in real time.

[0078] The beneficial effects of the present invention are as follows: Compared with existing component state perception methods, the present invention adopts a parameterized intrinsic orthogonal decomposition method to perceive global displacement, parameterizes the applied load in advance, constructs a displacement data set based on the parameterized load, and then obtains the projection basis vector through POD, which can effectively reduce the amount of calculation for real-time perception of component displacement state and improve computational efficiency; and by defining deformation-sensitive areas and QR decomposition, the optimal measurement point sensor layout is obtained, thereby improving displacement perception accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0079] Figure 1 Schematic diagram of parameterized load when the load on the component is Gaussian distribution.

[0080] Figure 2 This is the logic diagram of the component surface shape rapid perception and reconstruction method based on parametric loads and optimal measurement point layout.

[0081] Figure 3 Schematic diagram of the case device.

[0082] In the figure: 1 left camera, 2 right camera, 3 component under test, 4 experimental bench, 5 sensor measurement point, 6 robotic arm. DETAILED DESCRIPTION

[0083] The specific implementation of the present invention is described in detail below in conjunction with the technical solutions and drawings.

[0084] The component 3 used in the experiment is a curved thin-walled aluminum plate with a radius of 1200 mm, a width of 800 mm, an arc length of 850 mm, and a thickness of 2 mm. It is fixed on the experimental bench 4 with a clamp, and the robotic arm 5 applies a load to the component 3.

[0085] The measurement sensor is an industrial camera, and the 3D displacement information of the measuring point is measured by a binocular vision measurement system consisting of left camera 1 and right camera 2. The 3D displacement data of the measuring point can be obtained through binocular positioning, binocular measurement, and coordinate system conversion.

[0086] The specific steps of this method are as follows:

[0087] The first step is to build a data set based on parameterized loads

[0088] First, component 3 is discretized into 3444 nodes, and the stiffness matrix K is obtained using finite element analysis software. The load applied in the Monte Carlo simulation is defined as a random load. A coordinate system is established at the geometric center of the component. The load on the component is specified to be applied within the range of 200mm-400mm in the y-axis direction. The magnitude of the random load is 0N to 10N in the x-axis direction and -5N to 5N in the y-axis direction. The above conditions are entered into the Monte Carlo simulation, and the displacement data set X can be obtained according to formulas (3) and (4).

[0089] The second step is to obtain the component deformation mode based on POD

[0090] Perform singular value decomposition (SVD) on the data set X and obtain the left singular matrix U according to formula (5). When the energy retention ratio is defined as 99.8%, the truncation order r = 7 is calculated according to formula (11). The matrix U is further truncated and the first 7 columns are retained to obtain the POD projection basis vector U r , which is the main deformation mode of the component.

[0091] The third step is to establish the component displacement state perception equation

[0092] Based on the system response equation (12), substitute the POD projection basis vector U r To U, we get the expression (13) of the displacement approximation. Paste the measuring point on the component 3, and obtain the observation matrix C according to the position of the node where the measuring point is located. The manipulator 6 applies a load to the component 3 and generates deformation. The displacement y generated by the measuring point can be obtained through the binocular measurement system. Substitute it into the sensor measurement equation (15), ignore the measurement error, and substitute formula (13) into (15) to obtain the approximate projection coefficient The expression (17) of the displacement approximation of formula (17) is used to obtain the component displacement state perception equation (18).

[0093] Step 4: Perception error analysis and optimization of measurement point layout in sensitive areas

[0094] The error calculation of the component displacement state perception equation (18) is performed to obtain the mean difference expression (20), and U is calculated according to formula (21): r The absolute value of the r-order mode is normalized, and then the normalized mode is weighted by formula (22) and the threshold T is set. The sensitive area mode U is obtained by formula (23): s Then put U s Substitute into formula (25) and use QR decomposition to calculate the optimal layout C of sensor observation points * .

[0095] Step 5: Real-time perception of component status based on binocular vision

[0096] Based on the optimal observation matrix C * , paste the measuring points at the corresponding nodes, and apply random loads to component 3 through the force of the robot arm 6 to meet the load range set by the Monte Carlo simulation. The load size and position are controlled by the force sensor and the robot arm respectively. The binocular measurement system measures the displacement of the component measuring point and obtains the measurement value y. Substituting it into formula (26) can obtain the global displacement state By measuring the actual displacement values ​​of other nodes using a binocular camera and calculating the average error between the measured displacement and the perceived displacement, we can obtain the results shown in the following table:

[0097]

[0098] It can be concluded from the above table that the method used in the present invention has sufficient accuracy, with a maximum error of 0.2532 mm, and can achieve real-time and accurate perception of the displacement state of the component.

[0099] This method addresses the challenges of high computational complexity and low precision in sensing the state of aviation components during assembly. Compared to existing research methods, it achieves accurate real-time sensing of component displacements using optimal sensor placement. Furthermore, this method is easy to deploy and can be expanded to other sensing areas within intelligent manufacturing.

Claims

1. A real-time component status perception method based on parameterized loads, characterized in that: Here are the steps: The first step is to construct a data set based on parameterized loads; The second step is to obtain the component deformation mode based on the intrinsic orthogonal decomposition; The third step is to establish the component displacement state perception equation; The fourth step is perception error analysis and optimization of measurement point layout in sensitive areas; The fifth step is real-time perception of component status based on binocular vision.

2. The method for real-time component status perception based on parameterized load according to claim 1 is characterized in that: The specific process of the first step of constructing a data set based on parameterized loads is as follows: According to the stress of components under different working conditions, a parameterized load equation is established, and the load f is expressed as: f(x;p,ω,r,t) (1) Where x is the coordinate of the load location; t is the load distribution type; ω is the load application area; r is a subset of ω that shows the load distribution and local strength changes; p is the maximum load value; After obtaining the parameterized load, the overall stiffness matrix of the component needs to be obtained to construct the displacement data set. In the actual assembly process, the component mainly behaves in a low-frequency quasi-static form. The mass and damping characteristics of the component are ignored, and only the component stiffness is considered. The component dynamic equation under the action of load f is simplified to: Ku=f(x;p,ω,r,t)) (2) Among them, u represents the displacement state of the component, and K represents the overall stiffness matrix of the component; Finite element discretization is performed on the component to obtain n nodes. During the discretization process, only the three displacement degrees of freedom along the x, y, and z axes are considered, and the rotational degrees of freedom around the x, y, and z axes are ignored. K -1 is the inverse of the component's overall stiffness matrix K, with a dimension of 3n×3n; Combined with the results of finite element discretization of the component, the overall stiffness matrix K of the component is obtained: Where l = 3n, which represents the displacement degrees of freedom of n nodes along the x, y, and z axes; Apply loads f of different sizes and positions through m Monte Carlo static simulations sim =[f1 f2...f m ] T , load f sim The corresponding displacement vector u sim =[u1 u2...u m ] T , forming the displacement data set X, which is expressed as: X=[u1 u2...u m ]=[K -1 f1 K -1 f2…K -1 f m ] (4) The dimension of the displacement dataset X is l×m, and m is specified to be less than l.

3. The method for real-time component status perception based on parameterized load according to claim 2 is characterized in that: The specific implementation process of the second step of obtaining the component deformation mode based on intrinsic orthogonal decomposition is as follows: First, perform singular value decomposition on the displacement dataset X: X=UΣV T (5) Among them, U is a left singular vector matrix that represents the deformation mode of the component. Each column is the displacement projection basis vector generated by the component under different loads. The dimension is l×l and the expression is as follows: Σ is a diagonal matrix containing all singular values ​​σ1≥σ2≥…≥σ m , all non-diagonal elements are zero, the dimension is l×m, and the size of each singular value represents the weight or contribution of the displacement or load in the data under different load simulations. The expression is as follows: V T is a matrix composed of right singular vectors with dimension m×m; In order to perceive the global displacement state of the component in real time, the computational complexity is reduced by using the order reduction method to retain the main feature information in the displacement dataset, which is expressed as: X r =U r S r V r T (8) Among them, U r is the first r columns of data in U, with a dimension of l×r, expressed as: Σ r represents the first r singular values ​​of Σ, with dimension r×r, expressed as: V r T The dimensions of X are r×m, r It is represented as an approximate matrix of X with dimensions of l×m; r is determined by calculating the ratio of the energy retained after reduction to the original energy. The retained energy ratio E r Expressed as: Among them, the numerator represents the sum of the squares of the first r singular values, which represents the energy retained by the reduced-order data matrix; the denominator represents the sum of the squares of all singular values, that is, the total energy of the original data matrix; the first r projection basis vectors U are selected by POD reduction r , retaining the most important deformation mode of the component.

4. The method for real-time component status perception based on parameterized load according to claim 3 is characterized in that: The specific implementation process of the third step of establishing the component displacement state perception equation is as follows: Based on the Galerkin method, the component displacement response u is described by the system response equation: u=Us (12) Where U is the l-order displacement projection basis vector obtained by POD decomposition of formula (5), and s represents the projection coefficient of the displacement basis vector; Furthermore, based on the displacement projection basis vector U r ,have to The expression: in, is the component displacement vector, which represents the approximation of the true u; represents the approximate projection coefficient; After placing k measuring point sensors on the component, the displacement data of the nodes are measured by the sensors. The observation matrix C is the position of the measuring point in the reference system with the degree of freedom of the component node as the reference system, which is expressed as: Among them, the i-th row, 1≤i≤k, contains only one non-zero element And j1≠j2≠j3≠…≠j k , the dimension is k×l; Based on the measurement matrix C, the measurement equation of the sensor is expressed as: y=Cu+δ (15) Where y represents the displacement value measured by the sensor at k measurement points, with a dimension of k×1; u is the displacement response of the component expressed by formula (12), with a dimension of l×1; δ represents the displacement response with a mean of 0 and a variance of σ 2 Normal distribution measurement error; in order to improve numerical stability and focus on the main features of the system during state perception reconstruction, the measurement error δ is ignored and the approximate displacement is introduced The sensor measurement equation is expressed as follows: Approximate projection coefficients It is expressed as follows: Further substituting formula (17) into (13), we get the component displacement state perception equation: The expression: Among them, (CU r ) + Unified Representation CU r The inverse of , when m = r, represents CU r is a square matrix, (CU r ) + =(CU r ) -1 ; When m>r, it is pseudo-inverse, 5. The method for real-time component status perception based on parameterized load according to claim 4 is characterized in that: The specific implementation process of the fourth step, perception error analysis and optimization of sensitive area measurement point layout, is as follows: In order to improve the accuracy of component state perception, that is, to perceive displacement Closer to the real displacement u, in order to improve the robustness of the perception method in the measurement point layout optimization, it is necessary to consider the impact of measurement error on perception accuracy. r In certain cases, the perceptual error comes from the difference between the true projection coefficient s and the approximate projection coefficient The difference, projection coefficient error and its variance are expressed as follows: Where, e is the error of the projection coefficient, is the variance, Z=(CU r ) T CU r ; By optimizing the layout of the observation matrix C in the sensitive area, the error is further reduced and the most critical information is captured. First, the deformation sensitivity index U is calculated by normalized weighted summation. w [i], calculate U r The absolute value of each mode of and normalized Through U r (norm) Each mode of the τ Get U w [τ], where 1≤τ≤r, and w1>w2>…>w r : Set the threshold T to filter out U w The nodes where [τ] ≥ T are regarded as deformation sensitive areas Ω: Ω={τ|U w [τ]>T} (23) From U r The modes corresponding to the nodes in the sensitive area Ω are retained to obtain the sensitive area mode U s : IN s =U r [Ω,:] (24) Pair matrix U s Performing QR decomposition with column pivoting can obtain the optimal configuration of the measurement point layout: U s ·P=Q·R (25) After the QR decomposition with column pivots, Q is an orthogonal matrix, R is an upper triangular matrix, and P is a column permutation matrix. The column order indicates the importance of the node. The candidate nodes corresponding to the first k pivot elements are selected in descending order of the diagonal elements of the R matrix as the final measurement points, and are placed at the positions corresponding to the n nodes divided by the finite element of the component to reconstruct the optimal observation matrix C. * .

6. The method for real-time component status perception based on parameterized load according to claim 5 is characterized in that: The specific implementation process of the fifth step of real-time perception of component status based on binocular vision is as follows: Based on the optimal observation matrix C * , the component displacement perception equation is expressed as: K measuring points are pasted on the corresponding nodes of the component. The load is applied by the robotic arm to cause the component to displace. The binocular camera measures the displacement of the pasted measuring points to obtain the actual displacement value y of each measuring point. This is then substituted into the component displacement perception equation to obtain the global displacement state of the component in real time.

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