Composite material patching and repairing interface temperature field estimation method based on Kalman filtering
By using a temperature field estimation method based on Kalman filtering, the problem of accurately measuring the bonding interface temperature in composite material repair was solved, enabling online and real-time temperature control and improving repair quality.
Patent Information
- Application Number
- CN202510914468.X
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- Filing Date
- 2025-07-03
- Publication Date
- 2025-11-14
AI Technical Summary
Existing technologies make it difficult to accurately measure and control the temperature field at the bonding interface in multilayer structures during composite material repair, leading to temperature control deviations that affect repair quality.
A Kalman filter-based method was used to construct a temperature field estimation model for the interface of composite material patch repair. By integrating multi-point temperature acquisition data through state estimation and noise suppression techniques, online and real-time temperature field estimation was achieved.
It enables accurate estimation of the bonding interface temperature of the patch, providing a reliable temperature control basis for the temperature control system of the thermal patching instrument and improving the repair quality.
Smart Images
Figure CN120951523A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of composite material repair and intelligent monitoring technology, specifically a method for estimating the temperature field at the interface of composite material patch repair based on Kalman filtering. Background Technology
[0002] Composite materials are widely used in high-end aerospace manufacturing, and their damage repair technology has always been a crucial aspect of ensuring structural safety and extending service life. Among these methods, scarf repair, a mature composite material repair technique, places high demands on the precise control of the temperature field during the repair process. Temperature control directly affects the bonding quality and repair outcome; therefore, accurately measuring and controlling the temperature at the patch bonding interface is key to technological success. Currently, thermal patching instruments primarily use thermocouple sensors for temperature measurement. Thermocouples, due to their simple structure and fast response, have high application value in industrial temperature measurement. However, their principle dictates that they can only collect surface or near-surface temperatures, and cannot directly measure the temperature at the bonding interface in multilayer structures. This makes it difficult to accurately grasp the actual temperature field distribution during composite material scarf repair, potentially leading to temperature control deviations and affecting repair quality.
[0003] The main reasons for the above problems lie in the presence of multiple layers of materials, complex heat conduction paths, and fluctuations in process parameters in composite material repair structures. This results in a non-homogeneous and non-linear temperature distribution. Furthermore, traditional temperature sensing and data processing technologies struggle to balance high precision, real-time performance, and system complexity, becoming a bottleneck in current technological development. Summary of the Invention
[0004] To address the aforementioned technical problems, this invention proposes a method for estimating the temperature field at the interface of composite material patching and repair based on Kalman filtering.
[0005] The technical problem to be solved by this invention is achieved by the following technical solution:
[0006] A method for estimating the interface temperature field of composite material patch repair based on Kalman filtering includes the following steps:
[0007] Step 1: Based on the heat transfer mechanism in the aircraft patching and bonding process, construct the heat transfer control equation for the curing of aircraft composite material patching and repair.
[0008] Step 2: Based on the heat transfer control equation established in Step 1, establish a one-dimensional space model of the heat transfer state of the patch repair solidification. Establish a node every Δz in the thickness direction to obtain the discretized heat control equation and give the boundary points.
[0009] Step 3: Based on the one-dimensional space model established in Step 2, establish a nonlinear Kalman filter model for heat transfer during the patching and repair curing process, derive the Kalman filter coefficients K, input the initial state values, and estimate the bonding interface temperature.
[0010] As a further improvement to the present invention, the construction process in step 1 is as follows:
[0011] The transient nonlinear heat conduction equation is established based on Fourier's heat transfer theorem:
[0012]
[0013] Where T(z,t) is the temperature field (K), ρ(z),c p (z) and λ(z) are the densities of each layer of material (kg / m³) respectively. 3 ), specific heat capacity (J / (kg·K)), thermal conductivity (W / (m·K)), q heater (z,t) represents the heat source of the electric blanket (W / m²). 2 ), located in the electric blanket layer, q cure (z,t) represents the heat source of heat release during solidification (W / m²). 2 It acts on the patch layer and the adhesive layer.
[0014] As a further improvement to the present invention, the heating equation for the electric blanket is as follows:
[0015]
[0016] Where P(t) is the heating power of the electric blanket, A is the heating area, and δ(z-z1) is the Dirac function.
[0017] As a further improvement to the present invention, the curing exothermic reaction equation is as follows:
[0018]
[0019] Where, ρ resin Let Z be the resin density, ΔH be the curing enthalpy (J / kg), and χ(z) be the characteristic function, which is 1 when Z is in the patch layer and adhesive layer, and 0 otherwise.
[0020]
[0021] Where k0 is the reaction rate constant, E is the activation energy (J / mol), R is the gas constant 8.314 (J / (mol·K)), and m,n are the reaction orders.
[0022] As a further improvement to the present invention, the specific process in step 2 is as follows:
[0023] In the thickness direction, a node is established every Δz, numbered i = 0, 1, 2…n. For time derivatives, forward differencing is used; for spatial second derivatives, central differencing is used. This yields the results for internal nodes i = 0, 1, 2…n.
[0024] The time derivative is:
[0025]
[0026] The spatial derivative is:
[0027]
[0028] Local constant parameters can be used at each node, then ρ i , k i Let be the parameters of the layer corresponding to node i, and let the thermal conductivity be continuous between nodes. Then the discretized heat conduction equation is:
[0029]
[0030] After sorting, we get:
[0031]
[0032] in, The diffusion factor is obtained for discrete heat transfer. is the scale factor for the exothermic term;
[0033] The temperature at the upper boundary point is T0 = T ￥ +ct, where t is the heating time of the electric blanket and c is the heating rate of the electric blanket;
[0034] The temperature at the lower boundary point is Where h is the convective heat transfer coefficient, T ￥ For ambient temperature, The formula is as follows:
[0035]
[0036] As a further improvement to the present invention, the specific process in step 3 is as follows:
[0037] The governing equations contain nonlinear terms. Extended Kalman filtering is used for internal interface node temperature estimation; the state vector is defined as follows:
[0038]
[0039] The state transition function f(×) is constructed according to the discretization formula (8), and for i = 1, 2, ..., n, we have:
[0040]
[0041] in, For boundary nodes:
[0042]
[0043] In summary, the state equation is:
[0044] X t+1 =f(X) t ,u t )+w t (13)
[0045] Where, f(X) t ,u t ) is a nonlinear vector function, and its i-th component is the above f. i , w t For process noise, parameter α i ,β i The observation vector in this model is defined as the real-time temperature feedback from the thermocouples at nodes i and j, which is related to the material parameters and the distance step size at node i.
[0046] The observation equation is:
[0047] Y t =h(X) t )+v t (14)
[0048] in, v t To measure noise, the observation matrix H in the extended Kalman filter linearization is:
[0049]
[0050] The prediction error covariance in Kalman filtering is:
[0051]
[0052] Among them, P t|t-1 For the prior covariance, Q t-1 The process noise covariance is calculated as follows:
[0053]
[0054] In summary, the Kalman coefficients K are:
[0055]
[0056] The status is then updated to:
[0057]
[0058] The co-writing difference has been updated to:
[0059] P t|t =(IK t H t )P t|t-1 (20).
[0060] The beneficial effects of this invention are:
[0061] This invention provides a method for estimating the temperature field at the interface of composite material patch repair based on Kalman filtering. By introducing state estimation and noise suppression techniques, it effectively integrates multi-point temperature acquisition data to accurately estimate the temperature of the patch bonding interface online and in real time. This provides a reliable temperature control basis for the temperature control system of the heat repair instrument, thus overcoming the problem of inaccurate temperature control in the prior art. Attached Figure Description
[0062] The present invention will be further described below with reference to the accompanying drawings and embodiments:
[0063] Figure 1 This is a flowchart of the present invention;
[0064] Figure 2 This is a schematic diagram of a typical aircraft panel structure patching and repair model.
[0065] Figure 3 A schematic diagram showing the location of thermocouples for repairing composite materials in aircraft.
[0066] Figure 4 To repair and solidify the one-dimensional space model of the heat transfer state;
[0067] Figure 5 Here is a flowchart of the nonlinear Kalman filter algorithm;
[0068] Figure 6 A comparison chart of the predicted temperature and the measured temperature at the interface point P1.
[0069] Figure 7 A comparison chart of the predicted temperature and the measured temperature at the interface at point P2.
[0070] Figure 8 A comparison chart of the predicted temperature and the measured temperature at the interface (point P3).
[0071] Figure 9 A comparison chart of the predicted temperature and the measured temperature at the interface (point P4).
[0072] Figure 10 This is a comparison chart of the predicted temperature and the measured temperature at the interface shown at point P5. Detailed Implementation
[0073] To make the technical means, creative features, objectives and effects of this invention easier to understand, the invention will be further described below in conjunction with the accompanying drawings and embodiments.
[0074] In this embodiment, the research object is a typical aircraft wing panel component with a 50mm crack on the skin. The damaged area is circled, and patching is performed within a circle with a radius of 55mm centered on the center of the damaged area. The patching geometry is as follows. Figure 2 As shown, from top to bottom, the components are the electric blanket, patch, adhesive layer, skin and ribs, and stringer, with thicknesses of 5mm, 1.5mm, 0.2mm, 3mm, 2mm, and 2mm, respectively. Five thermocouples are distributed on the contact surface between the electric blanket and the patch to measure the real-time heating temperature of the electric blanket. Figure 3 As shown, five thermocouples are placed vertically on the lower surface of the rib.
[0075] like Figure 1 As shown, the method for estimating the temperature field at the interface of composite material patch repair based on Kalman filtering includes the following steps:
[0076] Step 1: Based on the heat transfer mechanism in the aircraft patching and bonding process, construct the heat transfer control equation for the curing of aircraft composite material patching and repair.
[0077] The transient nonlinear heat conduction equation is established based on Fourier's heat transfer theorem:
[0078]
[0079] Where T(z,t) is the temperature field (K), ρ(z),c p (z) and λ(z) are the densities of each layer of material (kg / m³) respectively. 3 ), specific heat capacity (J / (kg·K)), thermal conductivity (W / (m·K)), q heater (z,t) represents the heat source of the electric blanket (W / m²). 2 ), located in the electric blanket layer, q cure (z,t) represents the heat source of heat release during solidification (W / m²). 2 It acts on the patch layer and the adhesive layer. The heating equation for the electric blanket is:
[0080]
[0081] Where P(t) is the heating power of the electric blanket, A is the heating area, and δ(z-z1) is the Dirac function.
[0082] The curing exothermic reaction equation is:
[0083]
[0084] Where, ρ resin Let Z be the resin density, ΔH be the curing enthalpy (J / kg), and χ(z) be the characteristic function, which is 1 when Z is in the patch layer and adhesive layer, and 0 otherwise.
[0085]
[0086] Where k0 is the reaction rate constant, E is the activation energy (J / mol), R is the gas constant 8.314 (J / (mol·K)), and m,n are the reaction orders.
[0087] In this embodiment, the physical properties of the composite material, adhesive, electric blanket and aluminum alloy material used are shown in Table 1 below, and the curing kinetic model parameters of the ZT7H / QY9611 prepreg used are shown in Table 2 below.
[0088] Table 1 Physical properties of materials used
[0089]
[0090]
[0091] Table 2 Curing kinetic model parameters of ZT7H / QY9611 prepreg
[0092]
[0093] Step 2: Based on the heat transfer control equations established in Step 1, establish a one-dimensional spatial model of the heat transfer state during patch repair and solidification. Establish a node every Δz along the thickness direction to obtain the discretized heat control equations, and specify boundary conditions. The model is as follows: Figure 3 As shown.
[0094] In this embodiment, a node is established every ρZ = 0.1 mm, numbered i = 0, 1, 2…n. Forward difference is used for time derivative, and central difference is used for spatial second derivative, resulting in the following for internal nodes i = 0, 1, 2…n; where the time derivative is:
[0095]
[0096] The spatial derivative is:
[0097]
[0098] Local constant parameters can be used at each node, then ρ i , k i Let be the parameters of the layer corresponding to node i, and let the thermal conductivity be continuous between nodes. Then the discretized heat conduction equation is:
[0099]
[0100] After sorting, we get:
[0101]
[0102] in, The diffusion factor is obtained for discrete heat transfer. is the scale factor for the exothermic term;
[0103] The temperature at the upper boundary point is T0 = T ￥ +ct, where t is the heating time of the electric blanket and c is the heating rate of the electric blanket;
[0104] The temperature at the lower boundary point is Where h is the convective heat transfer coefficient, T ￥ For ambient temperature, The formula is as follows:
[0105]
[0106] Step 3: Based on the one-dimensional spatial model established in Step 2, establish a nonlinear Kalman filter model for heat transfer during the patching and repair curing process. Derive the Kalman filter coefficients K, input the initial state values, and estimate the adhesive interface temperature. (Example:...) Figure 4 As shown. The main process is as follows:
[0107] The state vector is defined as follows:
[0108]
[0109] The state transition function f(×) is constructed according to the discretization formula (8), and for i = 1, 2, ..., n, we have:
[0110]
[0111] in, For boundary nodes:
[0112]
[0113] In summary, the state equation is:
[0114] X t+1 =f(X) t ,u t )+w t (13)
[0115] Where, f(X) t ,u t ) is a nonlinear vector function, and its i-th component is the above f. i , w tFor process noise, parameter α i ,β i The observation vector in this model is defined as the real-time temperature feedback from the thermocouples at nodes i and j, which is related to the material parameters and the distance step size at node i.
[0116] The observation equation is:
[0117] Y t =h(X) t )+v t (14)
[0118] in, v t To measure noise, the observation matrix H in the extended Kalman filter linearization is:
[0119]
[0120] The prediction error covariance in Kalman filtering is:
[0121]
[0122] Among them, P t|t-1 For the prior covariance, Q t-1 The process noise covariance is calculated as follows:
[0123]
[0124] In summary, the Kalman coefficients K are:
[0125]
[0126] The status is then updated to:
[0127]
[0128] The co-writing difference has been updated to:
[0129] P t|t =(IK t H t )P t|t-1 (20).
[0130] according to Figure 3 The positions of the thermocouples are determined using the method described in this embodiment, and the points at the interface between the patch and the adhesive layer are predicted. Figure 3 The temperature (in orange) is estimated as follows: Figure 6-10 As shown.
[0131] The foregoing has shown and described the basic principles, main features, and advantages of the present invention. Those skilled in the art should understand that the present invention is not limited to the above embodiments. The embodiments and descriptions in the specification are merely prisms of the invention. Various changes and modifications can be made to the invention without departing from its spirit and scope, and all such changes and modifications fall within the scope of the present invention as claimed. The scope of protection of this invention is defined by the appended claims and their equivalents.
Claims
1. A method for estimating the temperature field at the interface of composite material patching repair based on Kalman filtering, characterized in that: Includes the following steps: Step 1: Based on the heat transfer mechanism in the aircraft patching and bonding process, construct the heat transfer control equation for the curing of aircraft composite material patching and repair. Step 2: Based on the heat transfer control equation established in Step 1, establish a one-dimensional space model of the heat transfer state of the patch repair solidification. Establish a node every Δz in the thickness direction to obtain the discretized heat control equation and give the boundary conditions. Step 3: Based on the one-dimensional space model established in Step 2, establish a nonlinear Kalman filter model for heat transfer during the patching and repair curing process, derive the Kalman filter coefficients K, input the initial state values, and estimate the bonding interface temperature.
2. The method for estimating the interface temperature field of composite material patching and repair based on Kalman filtering according to claim 1, characterized in that: The specific construction process in step 1 is as follows: The transient nonlinear heat conduction equation is established based on Fourier's heat transfer theorem: Where T(z,t) is the temperature field (K), ρ(z),c p (z) and λ(z) are the densities of each layer of material (kg / m³) respectively. 3 ), specific heat capacity (J / (kg·K)), thermal conductivity (W / (m·K)), q heater (z,t) represents the heat source of the electric blanket (W / m²). 2 ), located in the electric blanket layer, q cure (z,t) represents the heat source of heat release during solidification (W / m²). 2 It acts on the patch layer and the adhesive layer.
3. The method for estimating the interface temperature field of composite material patching and repair based on Kalman filtering according to claim 2, characterized in that: The heating equation for an electric blanket is: Where P(t) is the heating power of the electric blanket, A is the heating area, and δ(z-z1) is the Dirac function.
4. The method for estimating the temperature field at the interface of composite material patching and repair based on Kalman filtering according to claim 2, characterized in that: The curing exothermic reaction equation is: Where, ρ resin Let Z be the resin density, ΔH be the curing enthalpy (J / kg), and χ(z) be the characteristic function, which is 1 when Z is in the patch layer and adhesive layer, and 0 otherwise. Where k0 is the reaction rate constant, E is the activation energy (J / mol), R is the gas constant 8.314 (J / (mol·K)), and m,n are the reaction orders.
5. The method for estimating the temperature field at the interface of composite material patching and repair based on Kalman filtering according to claim 1, characterized in that: The specific process for step 2 is as follows: In the thickness direction, a node is established every Δz, numbered i = 0, 1, 2…n. For time derivatives, forward differencing is used; for spatial second derivatives, central differencing is used. This yields the results for internal nodes i = 0, 1, 2…n. The time derivative is: The spatial derivative is: Local constant parameters can be used at each node, then ρ i , k i Let be the parameters of the layer corresponding to node i, and let the thermal conductivity be continuous between nodes. Then the discretized heat conduction equation is: After sorting, we get: in, The diffusion factor is obtained for discrete heat transfer. is the scale factor for the exothermic term; The temperature at the upper boundary point is T0 = T ￥ +ct, where t is the heating time of the electric blanket and c is the heating rate of the electric blanket; The temperature at the lower boundary point is Where h is the convective heat transfer coefficient, T ￥ For ambient temperature, The formula is as follows:
6. The method for estimating the temperature field at the interface of composite material patching and repair based on Kalman filtering according to claim 1, characterized in that: The specific process for step 3 is as follows: The governing equations contain nonlinear terms. Extended Kalman filtering is used for internal interface node temperature estimation; the state vector is defined as follows: The state transition function f(×) is constructed according to the discretization formula (8), and for i = 1, 2, ..., n, we have: in, For boundary nodes: In summary, the state equation is: X t+1 =f(X t ,u t )+w t (13) Where, f(X) t ,u t ) is a nonlinear vector function, and its i-th component is the above f. i , w t For process noise, parameter α i ,β i The observation vector in this model is defined as the real-time temperature feedback from the thermocouples at nodes i and j, which is related to the material parameters and the distance step size at node i. The observation equation is: Y t =h(X t )+v t (14) in, v t To measure noise, the observation matrix H in the extended Kalman filter linearization is: The prediction error covariance in Kalman filtering is: Among them, P t|t-1 For the prior covariance, Q t-1 The process noise covariance is calculated as follows: In summary, the Kalman coefficients K are: The status is then updated to: The co-writing difference has been updated to: P t|t =(I-K t H t )P t|t-1 (20)。