Method for synchronously estimating thermal growth oxide thickness and defect thickness of thermal barrier coating

Abstract

The invention discloses a method for synchronously estimating thermal growth oxide thickness and defect thickness of a thermal barrier coating. The method comprises the following steps: establishing a one-dimensional, unsteady-state and heat conduction-radiation multi-layer coupling heat transfer equation set for describing an internal heat transfer mechanism of a thermal barrier coating system comprising a semitransparent coating, a defect layer, a thermal growth oxide layer, a bonding layer and a matrix layer in a high-temperature environment; adopting a finite volume method to solve the heat transfer equation set, and combining the determined boundary condition expression to obtain information of observed quantities represented by temperature inside and on the surface of the thermal barrier coating system; determining an observed quantity and an inversion interval; based on the observed quantity, determining an objective function required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; obtaining a measured value of an observed quantity of a real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, and synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect based on a reverse method; the method provides theoretical and technical support for nondestructive testing of internal defects and the like of the thermal barrier coating material in engineering practice.

Description

Technical Field

[0001] The present invention belongs to the field of methods for measuring the thickness of thermally grown oxides and defects, and particularly relates to a method for synchronously estimating the thickness of thermally grown oxides and the thickness of defects in a thermal barrier coating. Background Art

[0002] A thermal barrier coating system generally consists of a semi-transparent coating, a bond coat, and a substrate layer. The working environment of core components of an aero-engine, represented by turbine blades, is in a high-temperature state. Under high-temperature conditions, oxygen elements in the external environment will penetrate through the semi-transparent coating and chemically react with metal elements in the bond coat, and thermally grown oxides will be generated at the interface between the bond coat and the semi-transparent coating. The thickness of the thermally grown oxides will increase with the working time of the coating, resulting in continuous accumulation of stress at the interface. When the stress exceeds the critical value, microcracks will form at the interface. Along with the continuous progress of the thermal cycle, the cracks will continuously expand, eventually forming defects and leading to coating detachment. Given that the growth of thermally grown oxides and the formation of defects are the main reasons for coating failure, developing a method for estimating the thickness of thermally grown oxides and the thickness of defects in a thermal barrier coating system is of crucial significance for evaluating the performance and damage degree of the thermal barrier coating system and ensuring the efficient and safe operation of aero-engines.

[0003] Regarding the problem of synchronous estimation of the thickness of thermally grown oxides and defect thickness in a thermal barrier coating system, methods such as scanning electron microscopy, ultrasonic testing, and active infrared thermography are generally used at present. Among them, scanning electron microscopy can visually observe the structure and morphology of thermally grown oxides and defects in the thermal barrier coating sample. However, in order to obtain a clear image, sample preparation processes such as cutting, grinding, polishing, and coating are required, which will cause a certain degree of damage to the object being detected. Ultrasonic testing uses the propagation and reflection characteristics of ultrasonic waves inside an object to estimate the thickness. For example, ultrasonic waves propagate at a certain speed within the thermal barrier coating system and will reflect when encountering the outer surface of the thermally grown oxide layer and the interface between the thermally grown oxide layer and the bond coat or substrate layer. By measuring the time interval of the reflected signal and the propagation speed of ultrasonic waves within the thermally grown oxide layer, the thickness of the thermally grown oxide layer can be estimated. However, when there are many pores and defects inside the thermal barrier coating system, it may affect the propagation and reflection of ultrasonic waves, resulting in an increase in the error of synchronous estimation. Compared with the first two technologies, active infrared thermography has the advantages of a large single detection area, intuitive detection results, fast detection speed, non-contact, less affected by the external environment, and being suitable for detecting debonding defects in layered structures and coated materials. It is a technical means with great application value in the field of non-destructive testing of thermal barrier coating systems. The principle of active infrared thermography is to actively emit heat to the object being measured through a thermal excitation source (such as a flash lamp, an infrared heating lamp, etc.), causing temperature changes on the surface or inside of the object. For example, when detecting internal defects in a material, the surface of the material is uniformly heated through infrared thermal excitation. Since the defects (such as pores, debonding, etc.) existing inside the material will cause abnormalities in the heat transfer process, different temperature distributions will be formed on the surface. By analyzing the surface temperature distribution information, qualitative and quantitative estimation of the internal defects of the material can be carried out.

[0004] To achieve the synchronous estimation of the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system under high-temperature environments, it is necessary to establish an unsteady forward numerical model that describes the heat transfer process of the thermal barrier coating system. In this context, for the overall heat transfer problem of a multi-layer structure including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer, the prior art ignores the thermal radiation effect inside the semi-transparent coating and replaces it with a simple heat conduction model. Considering the working environment of the thermal barrier coating system, the intensity of radiative heat flux inside the semi-transparent coating under high-temperature environments will increase rapidly in the form of an exponential function of temperature. At this time, ignoring the thermal radiation effect inside the semi-transparent coating will inevitably have a greater impact on the heat transfer simulation inside the system with a complex structure (such as the presence of defects and thermally grown oxides), and then lead to calculation errors in the system output represented by the temperature field, ultimately reducing the synchronous estimation accuracy of the thickness of thermally grown oxide and the thickness of defects based on the inverse method. In addition, the measurement errors caused by the strong thermal interference noise existing in high-temperature environments will also lead to a reduction in the accuracy of thickness synchronous estimation. All of the above factors make it extremely difficult to synchronously estimate the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system under high-temperature and strong thermal interference noise environments. Summary of the Invention

[0005] To solve the problem of synchronous estimation of the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system under high-temperature and strong thermal interference noise environments, compared with the prior art that approximates the internal heat transfer of a thermal barrier coating system with defects and thermally grown oxides under high-temperature environments as a single heat conduction, the present invention takes into account the thermal radiation effect inside the semi-transparent coating at the top of the thermal barrier coating system, establishes a one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer model of the thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer, which is more suitable for high-temperature environments, and realizes the accurate simulation of the internal heat transfer of the thermal barrier coating system with defects and thermally grown oxides under high-temperature environments. On this basis, combining the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system and the influence mechanism of the thermal radiation effect inside the semi-transparent coating on the other layers, by setting temperature terms related to the thermal radiation effect of the semi-transparent coating in the objective function, the objective function is reconstructed, improving the accuracy and robustness of the estimation method under strong thermal interference noise, and realizing the synchronous accurate estimation of the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating system based on the inverse method under high-temperature and strong thermal interference noise environments.

[0006] The present invention adopts the following technical solutions: A method for synchronous estimation of the thickness of thermally grown oxide and the thickness of defects in a thermal barrier coating, the method comprising the following steps: Establish a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature environments; determine the boundary condition expressions for each layer of the thermal barrier coating system; the multi-layer coupled heat transfer equation set and the boundary condition expressions constitute a numerical heat transfer model of the thermal barrier coating system; among them, considering the influence of high-temperature environments on the internal heat transfer of the semi-transparent coating, a description of the thermal radiation effect is added to the equation corresponding to the semi-transparent coating; Use the finite volume method to solve the established one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set, and obtain information on observables represented by temperature at the interior and surface of the thermal barrier coating system in combination with the determined boundary condition expressions; Determine the observables and inversion intervals required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; Based on the observables required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, determine the objective function required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; Obtain the measured values of the observables of the real system required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, and synchronously estimate the thickness of the thermally grown oxide and the thickness of the defect based on the inverse method.

[0007] Furthermore, the method for establishing a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature environments is as follows: Couple the one-dimensional, unsteady radiation transfer equation that describes the internal thermal radiation effect of the semi-transparent coating with the one-dimensional, unsteady, heat conduction differential equation with an internal heat source that describes its internal heat conduction, where the radiation transfer equation is obtained through the PN approximation method, and the internal heat source term in the heat conduction differential equation is the opposite of the divergence of the radiation heat flux density obtained based on the PN approximation method. The above coupled equation can be expressed as: , , Among them, are the temperature and radiation power of the semi-transparent coating respectively, is the time, are the density, specific heat capacity, thermal conductivity, attenuation coefficient, and refractive index of the semi-transparent coating respectively, is the Stefan-Boltzmann constant, and are the divergence and gradient respectively.

[0008] Furthermore, the method for establishing a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bond coat, and a substrate layer under high-temperature conditions further includes: Use the one-dimensional, unsteady, conduction differential equation without internal heat source to describe the heat transfer in the defect layer, thermally grown oxide layer, bond coat, and substrate layer of the thermal barrier coating system respectively.

[0009] Furthermore, for determining the boundary condition expressions of each layer of the thermal barrier coating system, by considering the radiative heat flux density originating from the interior of the semi-transparent coating in the boundary condition at the interface between the semi-transparent coating and the defect layer, the quantitative manifestation of the influence of the thermal radiation effect in the semi-transparent coating on the internal heat transfer of the remaining layers is realized. The specific approach is as follows: For the interface between the semi-transparent coating and the defect layer, based on the conservation of heat flux density at the boundary, the sum of all heat flux densities entering this interface is equal to the sum of all heat flux densities leaving this interface. Among them, all heat flux densities entering this interface include the conductive heat flux density and radiative heat flux density inside the semi-transparent coating, and all heat flux densities leaving this interface include the conductive heat flux density of the air inside the defect layer and the net radiative heat flux density at the interface between the defect layer and the semi-transparent coating; For the interfaces of the remaining layers, the interface between the semi-transparent coating and the external environment, and the interface between the substrate layer and the external environment, the sum of all heat flux densities entering the interface at any moment is equal to the sum of all heat flux densities leaving the interface.

[0010] Furthermore, the method for solving the established one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equation set using the finite volume method and obtaining the information of observables represented by temperature inside and on the surface of the thermal barrier coating system in combination with the determined boundary condition expressions is as follows: In view of the fact that the thermal radiation effect in the semi-transparent coating is transmitted layer by layer to the remaining adjacent layers through the radiative heat flux density in the boundary condition, when discretizing each layer region using the finite volume method, local refinement technology is used to encrypt the grids in the regions near the boundaries of each layer, so as to better capture the change of the heat flux density at the boundary caused by the thermal radiation effect of the semi-transparent coating; on this basis, the control equations in each layer are integrated over volume, simplified to obtain the corresponding discrete equations and solved, and finally the information of observables represented by temperature inside and on the surface of the thermal barrier coating system is obtained.

[0011] Furthermore, when determining the observables and inversion intervals required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, Combined with the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system, the influence mechanism of the internal thermal radiation effect of the semi-transparent coating on the remaining layers, and the parameter sensitivity analysis, the temperature at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment are selected as the observables required for estimation. After determining the observables required for estimation, the inversion intervals required for estimating the thickness of the thermally grown oxide and the defect thickness are determined according to the sensitivity curves of the observables.

[0012] Furthermore, based on the observables required for simultaneously estimating the thickness of the thermally grown oxide and the defect thickness, when determining the objective function required for simultaneously estimating the thickness of the thermally grown oxide and the defect thickness, to enhance the robustness of the estimation method and reduce the estimation error caused by the measurement error of the observables due to environmental thermal interference noise during the simultaneous thickness estimation process, a temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function; The objective function is: the measured value of the observables of the real system corresponding to the true values of the thickness of the thermally grown oxide and the defect thickness and the measured value of the observables of the numerical heat transfer model of the thermal barrier coating system corresponding to a certain value of the parameter to be estimated during the estimation process The gap between them, and the expression is: , where, is the true value of the thickness of the thermally grown oxide and the defect thickness, is the value of the thickness of the thermally grown oxide and the defect thickness during the estimation process; and are the temperatures at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment at The value, that is, the measured value of the observables of the real system; and are and at The value, that is, the measured value of the observables of the numerical heat transfer model of the thermal barrier coating system.

[0013] Furthermore, when obtaining the measured value of the observables of the real system required for simultaneously estimating the thickness of the thermally grown oxide and the defect thickness and performing the simultaneous estimation of the thickness of the thermally grown oxide and the defect thickness based on the inverse method, The measured value of the observables of the real system , is the measured value of the observables of the numerical heat transfer model of the thermal barrier coating system established , This is achieved by adding noise that conforms to the law of random distribution. By changing the intensity of random noise, the different degrees of observation measurement errors caused by environmental thermal interference noise in real situations can be simulated. The estimation based on the inverse method is to find the minimum value of the objective function with the help of particle swarm optimization algorithm. This minimum value is recorded as , is an estimate of the thermally grown oxide thickness and defect thickness.

[0014] The beneficial technical effects of the present invention are: 1. In order to achieve the simultaneous estimation of the thickness of thermally grown oxide and defect thickness of thermal barrier coating system under high temperature environment based on the inverse method, it is first necessary to establish a non-steady-state forward numerical model describing the heat transfer process of thermal barrier coating system. For the overall heat transfer problem of multi-layer structure containing translucent coating, defect layer, thermally grown oxide layer, bonding layer and substrate layer, the prior art ignores the thermal radiation effect inside the translucent coating and replaces it with a simple heat conduction model. Compared with this approach, the present invention considers the thermal radiation effect inside the top translucent coating of the thermal barrier coating system under high temperature environment, and establishes a one-dimensional, non-steady-state, thermally conductive-radiative multi-layer coupled heat transfer model of the thermal barrier coating system containing translucent coating, defect layer, thermally grown oxide layer, bonding layer and substrate layer, which is more suitable for high temperature environment, and realizes the accurate simulation of the internal heat transfer of the thermal barrier coating system containing defects and thermally grown oxide under high temperature environment; 2. The present invention relies on the one-dimensional, non-steady-state, thermal conduction-radiation multilayer coupled heat transfer model that describes the internal heat transfer mechanism of the thermal barrier coating system under high temperature environment, and realizes the synchronous and accurate estimation of the thickness of the thermally grown oxide and the thickness of the defect under high temperature and strong thermal interference noise based on the inverse method: for the general amplitude of the observation measurement error caused by the environmental thermal interference noise, such as the order of magnitude The temperature measurement error and magnitude are [50 W / m 2 , 60000 W / m 2 ], the relative error of the average estimated value of the thermally grown oxide thickness under different thickness combinations is maintained at 0.677% to 2.088%, and the relative error of the average estimated value of the defect thickness is maintained at 0.001% to 0.052%; for the large-scale observation measurement error caused by the environmental thermal interference noise, such as the order of magnitude The temperature measurement error and magnitude are [100 W / m 2 , 120000 W / m 2For the radiation power measurement error of [], the relative errors of the average estimated values of the thickness of thermally grown oxides under different thickness combinations remain within the range of 1.369% to 2.199%, and the relative errors of the average estimated values of the defect thickness remain within the range of 0.031% to 0.321%. Both are within a relatively small range, demonstrating the strong robustness of the estimation method proposed in the present invention. Especially when the thickness of the thermally grown oxides and the defect thickness are relatively thin, even in an environment with strong thermal interference noise, the relative estimation errors of the two still remain at 2.199% and 0.321% respectively. Therefore, the estimation method proposed in the present invention can accurately capture the thermally grown oxides and early defects in the initial growth stage, providing technical support for timely warning and accurate intervention; 3. In addition, compared with a class of methods based on wave transmission and reflection represented by ultrasonic detection technology and active infrared thermal wave technology, this method does not have the problem of overlapping and mutual influence of wave reflection information in complex structures, and has great advantages in the synchronous estimation of multiple thicknesses in complex structures represented by thermal barrier coating systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0015] Figure 1 is a schematic flow chart of a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating in Embodiment 1 of the present invention; Figure 2 is a schematic structural diagram and boundary condition diagram of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer, and a substrate layer in Embodiment 2 of the present invention; Figure 3 is a schematic technical principle diagram of the reverse method part in a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating in an embodiment of the present invention. DETAILED DESCRIPTION OF THE INVENTION Embodiment 1

[0016] The following further clearly and completely describes a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating system proposed by the present invention with reference to the accompanying drawings: As Figure 1 shown, a method for synchronously estimating the thickness of thermally grown oxides and defect thickness in a thermal barrier coating includes the following steps: S1. Establish a one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer equation set that describes the internal heat transfer mechanism of a thermal barrier coating system including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer, and a substrate layer under high-temperature conditions; Given that the thickness of the thermal barrier coating system is much smaller than its dimensions in other directions, when the local curvature change is small, the heat transfer inside it can be approximated as a one-dimensional case. For the semi-transparent coating located at the top of the thermal barrier coating system, in this embodiment, the internal thermal radiation effect is considered on the basis of the prior art. First, the radiative transfer equation describing the internal thermal radiation of the semi-transparent coating is obtained based on the PN approximation method. Subsequently, the internal heat source term in the heat conduction differential equation is replaced by the negative of the divergence of the radiative heat flux density obtained based on the PN approximation method. Finally, a one-dimensional, unsteady, heat conduction-radiation coupling equation describing the internal heat transfer law of the semi-transparent coating is obtained: , , where, are the temperature and radiation power of the semi-transparent coating respectively, is time, are the density, specific heat capacity, thermal conductivity, attenuation coefficient and refractive index of the semi-transparent coating respectively, is the Stefan-Boltzmann constant, and are divergence and gradient respectively.

[0017] Different from the semi-transparent coating, the bond coat and the substrate layer are usually alloy materials, and the thermally grown oxide layer is mainly composed of metal oxides. Compared with the semi-transparent coating, the radiative heat transfer in the thermally grown oxide layer, the bond coat and the substrate layer can be ignored. Therefore, a single heat conduction differential equation is used to describe the one-dimensional, unsteady, heat transfer process without internal heat source inside them: , where, are the density, specific heat capacity and thermal conductivity of the thermally grown oxide layer respectively, are the density, specific heat capacity and thermal conductivity of the bond coat respectively, are the density, specific heat capacity and thermal conductivity of the substrate layer respectively, are the temperatures of the thermally grown oxide layer, the bond coat and the substrate layer respectively.

[0018] For the defect layer inside the thermal barrier coating system, since the defects at the interface are mainly debonding defects, the medium inside the defect layer can be approximated as dry air. The water vapor content in dry air is extremely low and can be approximated as a transparent medium. The radiative heat flux density emitted from the defect layer wall will not be lost when passing through the defect. In addition, the emissivity of dry air is extremely low, and the internal thermal radiation of the air itself can be ignored. Therefore, only the heat conduction differential equation is used to describe the one-dimensional, unsteady, heat transfer process without internal heat source inside it: , where, They are respectively the density, specific heat capacity, thermal conductivity and temperature of the defect layer.

[0019] The radiative heat flux density emitted by the defect wall It can be calculated using the Stefan-Boltzmann formula: , where is the Stefan-Boltzmann constant, is the temperature of the defect wall.

[0020] S2. Determine the expressions for the boundary conditions of each layer of the thermal barrier coating system; For the interfaces between the semi-transparent coating, defect layer, thermally grown oxide layer, bond coat, and substrate layer, the boundary conditions are established by conserving the heat flux density, that is, the sum of all heat flux densities entering the interface at any moment is equal to the sum of all heat flux densities leaving the interface: at the interface between the semi-transparent coating and the defect layer, the sum of the conductive and radiative heat flux densities on the semi-transparent coating side is equal to the sum of the conductive heat flux density on the defect layer side and the net radiative heat flux density at the interface between the defect layer and the semi-transparent coating; at the interface between the defect layer and the thermally grown oxide layer, the sum of the conductive heat flux density on the defect layer side and the net radiative heat flux density at the interface between the defect layer and the thermally grown oxide layer is equal to the conductive heat flux density on the thermally grown oxide layer side; at the interface between the thermally grown oxide layer and the bond coat, the conductive heat flux density on the thermally grown oxide layer side is equal to the conductive heat flux density on the bond coat side; at the interface between the bond coat and the substrate layer, the conductive heat flux density on the bond coat side is equal to the conductive heat flux density on the substrate layer side.

[0021] For the boundary sides of the semi-transparent coating and the substrate layer in contact with the external environment, considering the radiative heat transfer and convective heat transfer between them and the external environment, the boundary conditions are also established by conserving the heat flux density: at the boundary where the semi-transparent coating is in contact with the external environment, the sum of the conductive and radiative heat flux densities on the semi-transparent coating side is equal to the sum of the net heat flux densities exchanged through convective heat transfer and thermal radiation between this side and the external environment; at the boundary where the substrate layer is in contact with the external environment, the conductive heat flux density on the substrate layer side is equal to the sum of the net heat flux densities exchanged through convective heat transfer and thermal radiation between this side and the external environment.

[0022] The above one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer equations describing the internal heat transfer mechanism of the thermal barrier coating system containing a semi-transparent coating, defect layer, thermally grown oxide layer, bond coat, and substrate layer at high temperature, together with the boundary conditions of each layer of the thermal barrier coating system, constitute the numerical heat transfer model of the thermal barrier coating system.

[0023] S3. Use the finite volume method to solve the established one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer equations, and combine the determined boundary condition expressions to obtain the information of the observables represented by temperature inside and on the surface of the thermal barrier coating system; The solution process based on the finite volume method will sequentially traverse the semi-transparent coating, defect layer, thermally grown oxide layer, bond coat, and substrate layer. Taking the semi-transparent coating as an example, the description is as follows: First, discretize the solution domain to determine the temperature nodes and control volumes. Given that the thermal radiation effect in the semi-transparent coating is transmitted layer by layer to the remaining adjacent layers through the radiative heat flux density in the boundary conditions, when using the finite volume method to discretize each layer region, local refinement technology is used to encrypt the grids in the regions near the boundaries of each layer to better capture the changes in the heat flux density at the boundaries caused by the thermal radiation effect of the semi-transparent coating. Subsequently, perform volume integration on the control equation in the semi-transparent coating, that is, the heat conduction-radiation coupling equation, and simplify it to obtain the discrete equations for temperature and radiation power. Solve the above discrete equations to obtain the temperature and radiation power inside the semi-transparent coating.

[0024] For the heat conduction differential equations describing heat transfer in the defect layer, thermally grown oxide layer, bond coat, and substrate layer, the finite volume method is also used for solution. The basic idea is the same as that for solving the heat conduction-radiation coupling equation in the semi-transparent coating, and finally, the temperatures inside the defect layer, thermally grown oxide layer, bond coat, and substrate layer can be obtained.

[0025] S4. Determine the observables and inversion intervals required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; Combining the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system, the influence mechanism of the thermal radiation effect in the semi-transparent coating on the remaining layers, and the parameter sensitivity analysis, the temperature at the contact surface between the semi-transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment are selected as the observables required for estimation.

[0026] The sensitivity is the derivative of the observable with respect to the thickness of the thermally grown oxide and the thickness of the defect to be estimated. Since the observable changes with time, connecting the derivative values of the observable with respect to the parameter to be estimated at each moment can obtain the sensitivity curve that changes with time. For the problem of synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, after determining the observables required for estimation, according to the sensitivity curve of the above observables, determine the inversion interval required for parameter estimation.

[0027] S5. Based on the observables required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect, determine the objective function required for synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect; The objective function is the measured value of the observable of the real system corresponding to the true values of the parameters to be estimated (thermal growth oxide thickness and defect thickness). and the difference (two - norm) between the measured value of the observable of the real system corresponding to the true values of the parameters to be estimated and the value of the observable of the numerical heat transfer model of the thermal barrier coating system corresponding to a certain value of the parameter to be estimated during the estimation process is generally in the form of: , To enhance the robustness of the estimation method and reduce the estimation error caused by the measurement error of the observable due to environmental thermal interference noise during the synchronous thickness estimation process, a temperature term related to the thermal radiation effect of the semi - transparent coating is set in the objective function to reconstruct the objective function. Since there are multiple observables in the current problem, the objective function is in the form of the sum of multiple two - norms: where is the true value of the thermal growth oxide thickness and defect thickness, is the value of the thermal growth oxide thickness and defect thickness during the estimation process; and are the temperatures at the contact surface between the semi - transparent coating and the external environment and the temperature at the contact surface between the substrate layer and the external environment at , that is, the measured value of the observable of the real system; and are and at , that is, the value of the observable of the numerical heat transfer model of the thermal barrier coating system.

[0028] S6. Obtain the measured value of the observable of the real system required for synchronously estimating the thermal growth oxide thickness and defect thickness, and synchronously estimate the thermal growth oxide thickness and defect thickness based on the inverse method; The synchronous estimation of the thermal growth oxide thickness and defect thickness belongs to an inverse problem, and its essence is to invert the unknown input of the system related to the output from the known output of the system. Specifically, it is to invert the unknown input of the real system (i.e., the thermal growth oxide thickness and defect thickness to be estimated) related to these observables from the known output of the real system (i.e., the measured value of the determined observable ), and the inversion method is the inverse method, and its principle is as Figure 3 shown: First, establish a one - dimensional, unsteady, multi - layer coupled heat conduction - radiation heat transfer model that describes the internal heat transfer process of the real thermal barrier coating system. Subsequently, select the parameter to be estimated as the input of the model and the determined observable as the output. When the output value of the model​​ When it is close enough to the output value of the real system the model input value corresponding to the current model output value can be regarded as the input value of the real system approximate value (also called estimated value, denoted as: ). Finally, synchronize the output value of the real system required for estimation, that is, the measured value of the observable is the observable value of the numerical heat transfer model of the established thermal barrier coating system by adding noise that conforms to the random distribution law to achieve. By changing the intensity of the random noise, different degrees of measurement errors of the observable caused by environmental thermal interference noise in the real situation can be simulated.

[0029] According to the principle of the inverse method, the essence of parameter inversion is the process of finding the model input value that makes the gap between the model output value and the real system output value small enough. From a mathematical point of view, the gap between the model output value and the real system output value can be quantitatively represented by the established objective function. The essence of the synchronous estimation process of the thickness of thermally grown oxide and the thickness of defects is to find the objective function to take the minimum value. In this embodiment, the above process of minimizing the objective function is realized by means of the particle swarm optimization algorithm. It can be considered that the number of particles is set to 15 and the maximum number of iterations is set to 80. Embodiment 2

[0030] As an example, in this embodiment, a one-dimensional, unsteady, conduction-radiation multi-layer coupled heat transfer model of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer, and a substrate layer is established, and based on this model, the thickness of thermally grown oxide and the thickness of defects in the thermal barrier coating system are synchronously estimated.

[0031] As Figure 2 shown, considering the convective heat transfer and radiative heat transfer between the thermal barrier coating system and the external environment, where the external environment temperature outside the semi-transparent coating is 2000 K, the convective heat transfer coefficient is 250 W / m 2 / K, the external environment temperature outside the substrate layer is 300 K, the convective heat transfer coefficient is 110 W / m 2 / K, and the initial temperature of the thermal barrier coating system is 300 K. The thermal conductivities of the semi-transparent coating, the defect layer, the thermally grown oxide layer, the bonding layer, and the substrate layer are 0.62 W / m / K, 0.026 W / m / K, 21 W / m / K, 17 W / m / K, and 33 W / m / K respectively, and the volume heat capacities are 3.5×10 6 J / m 3 / K, 1690 J / m 3 / K, 5.2668×10 6 J / m3 / K, 9.45310 6 J / m 3 / K, 4.2510 6 J / m 3 / K. The thicknesses of the semi-transparent coating, the bonding layer, and the substrate layer are 150, 50, and 1.4 mm respectively, and the spatial step sizes of the semi-transparent coating, the bonding layer, and the substrate layer are 10 -6 m, and the spatial step sizes of the defect layer and the thermally grown oxide layer are 10 -7 m. The simulation duration is 20 s, and the time step size is 0.005 s. The absorption coefficient of the semi-transparent coating is 30 m -1 , and the scattering coefficient is 10 4 m -1 , the refractive index is 1.58, the emissivity of the surface of the semi-transparent coating exposed to the environment side is 0.97, the emissivity of the surface of the semi-transparent coating at the junction with the defect layer is 0.92, the emissivity of the surface of the thermally grown oxide layer at the junction with the defect layer is 0.35, and the emissivity of the surface of the substrate layer exposed to the environment side is 0.6; The finite volume method is used to solve the one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer model of the above thermal barrier coating system, and the temperature field and radiation power field inside the thermal barrier coating system are obtained.

[0032] Based on the inspiration of parameter sensitivity, combined with the mutual influence mechanism of heat transfer between layers of the thermal barrier coating system and the influence mechanism of the thermal radiation effect in the semi-transparent coating on the other layers, a temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function, and the temperature at the contact surface of the semi-transparent coating with the external environment and the temperature at the contact surface of the substrate layer with the external environment are selected as the observables required for estimation. Specifically, since 0 to 20 s covers the key information in the region above 50% of the peak of the sensitivity curve, [0, 20 s] is selected as the inversion interval. Use to represent the true values of the thermally grown oxide thickness and the defect thickness, and use to represent a certain value of the thermally grown oxide thickness and the defect thickness during the estimation process, and define the objective function as: , where, is the true value of the thermally grown oxide thickness and the defect thickness, is the value of the thermally grown oxide thickness and the defect thickness during the estimation process. and are the temperatures at the contact surface of the semi-transparent coating with the external environment and the temperature at the contact surface of the substrate layer with the external environment at The value under, i.e., the measured value of the real system observable. and is and the value under i.e., the observable value of the numerical heat transfer model of the thermal barrier coating system.

[0033] The essence of the process of synchronously estimating the thickness of the thermally grown oxide and the thickness of the defect is to find the process that minimizes the objective function This process is implemented by the particle swarm optimization algorithm. The inversion boundaries of the thickness of the thermally grown oxide and the thickness of the defect are respectively set as and , the number of particles is 15, the maximum number of iterations is 80, the maximum number of stagnant iterations is 15, and the function tolerance is 10 -8 , and both the individual learning factor and the social learning factor are 1.49.

[0034] Table 1 shows the results of the synchronous estimation of the thickness of the thermally grown oxide and the thickness of the defect based on the above idea for different degrees of measurement errors of observables caused by environmental thermal interference noise when considering the thermal radiation effect inside the semi-transparent coating. Specifically, two combinations of the thickness of the thermally grown oxide and the thickness of the defect are considered, namely thickness combination 1: , thickness combination 2: and two cases of different degrees of measurement errors of observables caused by environmental thermal interference noise.

[0035] For the general magnitude of measurement errors of observables caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the radiation power measurement error of the order of [50 W / m 2 , 60000 W / m 2 (Case 1), the relative errors of the average estimated values of the thickness of the thermally grown oxide under different thickness combinations remain between 0.677% and 2.088% (the relative error is the percentage of the absolute value of the difference between the average estimated value of the thickness and the true value to the true value), and the relative errors of the average estimated values of the thickness of the defect remain between 0.001% and 0.052%.

[0036] For the large magnitude of measurement errors of observables caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the radiation power measurement error of the order of [100 W / m 2 , 120000 W / m 2The relative error of the average estimated value of the thickness of the thermally grown oxide under different thickness combinations for the measurement error of the radiation power (Case 2) remains between 1.369% and 2.199%, and the relative error of the average estimated value of the defect thickness remains between 0.031% and 0.321%.

[0037] Table 1

[0038] Table 2 shows the estimation results when the internal thermal radiation effect of the semi-transparent coating is ignored under the same conditions. By comparing with the results in Table 1, it can be seen that when the internal thermal radiation effect of the semi-transparent coating is ignored in a high-temperature environment, the errors of the synchronous estimation of the thickness of the thermally grown oxide and the defect thickness based on the inverse method become larger, verifying the necessity of considering the thermal radiation effect.

[0039] Table 2

[0040] In addition, even for the case of strong environmental thermal interference noise (Case 2), the estimation method of the present invention still controls the estimation errors of the thickness of the thermally grown oxide and the defect thickness at an extremely low level (2.199% and 0.321% respectively). With this advantage, the method proposed by the present invention can accurately capture the thermally grown oxide in the initial growth stage and early defects, providing technical support for timely warning and intervention.

[0041] In summary, for the problem of synchronous estimation of the thickness of the thermally grown oxide and the defect thickness in the thermal barrier coating system based on the inverse method, compared with the existing method of ignoring the internal thermal radiation effect of the semi-transparent coating, the present invention incorporates the internal thermal radiation effect of the semi-transparent coating into the thermal barrier coating system containing defects and thermally grown oxides, and establishes a one-dimensional, unsteady, heat conduction-radiation multi-layer coupled heat transfer model of the thermal barrier coating system suitable for high-temperature environments, including a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer, and a substrate layer, realizing the synchronous estimation of the thickness of the thermally grown oxide and the defect thickness in the thermal barrier coating system under high-temperature environments based on the inverse method, and having better accuracy. Specifically: For the measurement error of the observed quantity with a general magnitude caused by environmental thermal interference noise, such as the temperature measurement error of the order of and the radiation power measurement error of the order of [50 W / m 2 , 60000 W / m 2 , the relative error of the average estimated value of the thickness of the thermally grown oxide under different thickness combinations remains between 0.677% and 2.088%, and the relative error of the average estimated value of the defect thickness remains between 0.001% and 0.052%. For the measurement error of the observed quantity with a large magnitude caused by environmental thermal interference noise, such as the order of The temperature measurement error and order of magnitude are [100 W / m 2 , 120000 W / m 2 , and for the radiation power measurement error, the relative errors of the average estimated values of the thickness of thermally grown oxides under different thickness combinations are maintained within 1.369% to 2.199%, and the relative errors of the average estimated values of the defect thickness are maintained within 0.031% to 0.321%. Both are maintained within a small range, demonstrating the strong robustness of the estimation method proposed by the present invention. Especially when the thickness of the thermally grown oxide and the defect thickness are relatively thin, even in an environment with strong thermal interference noise, the relative estimation errors of the two still remain at 2.199% and 0.321% respectively. Therefore, the estimation method proposed by the present invention can accurately capture the thermally grown oxide and early defects in the initial growth stage, providing technical support for timely warning and accurate intervention.

[0042] In addition, compared with a class of methods based on wave transmission and reflection represented by ultrasonic detection technology and active infrared thermal wave technology, this method does not have the problem of overlapping and mutual influence of wave reflection information in complex structures, and has great advantages in the synchronous estimation of multiple thicknesses in complex structures represented by thermal barrier coating systems.

[0043] So far, the technical solution of the present invention has been described in combination with the preferred embodiments shown in the drawings. However, it is easy for those skilled in the art to understand that the protection scope of the present invention is obviously not limited to these specific embodiments. Without departing from the principle of the present invention, those skilled in the art can make equivalent changes or substitutions to relevant technical features, and the technical solutions after these changes or substitutions will fall within the protection scope of the present invention.

Claims

1. A method for synchronously estimating the thickness of thermally grown oxide and defect thickness of a thermal barrier coating, characterized in that: The method comprises the following steps: A one-dimensional, non-steady-state, heat conduction-radiation multilayer coupled heat transfer equation group is established to describe the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer and a substrate layer under a high temperature environment; the boundary condition expressions of each layer of the thermal barrier coating system are determined; the multilayer coupled heat transfer equation group and the boundary condition expressions constitute a numerical heat transfer model of the thermal barrier coating system; wherein, considering the influence of the high temperature environment on the internal heat transfer of the semi-transparent coating, a description of the thermal radiation effect is added to the equation corresponding to the semi-transparent coating; The finite volume method is used to solve the established one-dimensional, non-steady-state, conductive-radiative multilayer coupled heat transfer equations, and the information of the observed quantity represented by temperature inside and on the surface of the thermal barrier coating system is obtained in combination with the determined boundary condition expressions; Determine the observations and inversion intervals required for simultaneous estimation of thermally grown oxide thickness and defect thickness; Determining an objective function required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect based on the observed quantities required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect; The measured values ​​of the real system observation quantities required for synchronous estimation of the thermally grown oxide thickness and the defect thickness are obtained, and the thermally grown oxide thickness and the defect thickness are synchronously estimated based on the inverse method.

2. The method for synchronously estimating the thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 1, characterized in that: The method for establishing a one-dimensional, non-steady-state, conductive-radiative multilayer coupled heat transfer equation group to describe the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer and a substrate layer under high temperature conditions is as follows: The one-dimensional, non-steady-state radiation transfer equation describing the internal thermal radiation effect of the semi-transparent coating is coupled with the one-dimensional, non-steady-state heat conduction differential equation describing its internal heat conduction with an internal heat source. The radiation transfer equation is obtained by the PN approximation method. The internal heat source term in the heat conduction differential equation is the opposite of the divergence of the radiation heat flux density obtained based on the PN approximation method. The above coupling equation can be expressed as: ， ， in, are the temperature and radiation power of the semi-transparent coating, For time, are the density, specific heat capacity, thermal conductivity, attenuation coefficient and refractive index of the semi-transparent coating, is the Stefan-Boltzmann constant, and are the divergence and gradient respectively.

3. The method for synchronously estimating the thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 2, characterized in that: The method of establishing a one-dimensional, non-steady-state, heat conduction-radiation multilayer coupled heat transfer equation group describing the internal heat transfer mechanism of a thermal barrier coating system containing a semi-transparent coating, a defect layer, a thermally grown oxide layer, a bonding layer and a substrate layer under a high temperature environment also includes: One-dimensional, non-steady-state heat conduction differential equation without internal heat source is used to describe the heat transfer in the defect layer, thermally grown oxide layer, bonding layer and substrate layer of the thermal barrier coating system.

4. The method for synchronously estimating the thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 1, characterized in that: For the boundary condition expressions for determining each layer of the thermal barrier coating system, the radiant heat flux density originating from the interior of the semi-transparent coating is considered in the boundary conditions at the interface between the semi-transparent coating and the defective layer, so as to quantitatively express the influence of the thermal radiation effect in the semi-transparent coating on the internal heat transfer of the remaining layers. The specific method is as follows: For the interface between the semi-transparent coating and the defective layer, based on the conservation of heat flux at the boundary, the sum of all heat fluxes entering the interface is equal to the sum of all heat fluxes leaving the interface, where all heat fluxes entering the interface include the heat conduction heat flux and radiation heat flux inside the semi-transparent coating, and all heat fluxes leaving the interface include the heat conduction heat flux of the air inside the defective layer and the net radiation heat flux at the interface between the defective layer and the semi-transparent coating; For the interfaces of the remaining layers, the interface between the translucent coating and the external environment, and the interface between the substrate layer and the external environment, the sum of all heat flux densities entering the interface at any moment is equal to the sum of all heat flux densities leaving the interface.

5. The method for synchronously estimating the thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 1, characterized in that: The method of using the finite volume method to solve the established one-dimensional, non-steady-state, heat conduction-radiation multilayer coupled heat transfer equations and obtaining the information of the observed quantity represented by the temperature inside and on the surface of the thermal barrier coating system in combination with the determined boundary condition expression is as follows: Considering that the thermal radiation effect in the translucent coating is transmitted layer by layer to the remaining adjacent layers through the radiation heat flux density in the boundary conditions, when the finite volume method is used to discretize the regions of each layer, the local refinement technology is used to encrypt the grids in the areas near the boundaries of each layer in order to better capture the changes in the heat flux density at the boundaries caused by the thermal radiation effect of the translucent coating; on this basis, the control equations in each layer are volume integrated, simplified to obtain the corresponding discrete equations and solved, and finally the information of the observed quantity represented by temperature inside and on the surface of the thermal barrier coating system is obtained.

6. The method for synchronously estimating the thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 1, characterized in that: When determining the observations and inversion intervals required to simultaneously estimate the thermally grown oxide thickness and defect thickness, Combined with the mutual influence mechanism of heat transfer between the layers of the thermal barrier coating system, the influence mechanism of the thermal radiation effect in the semi-transparent coating on the other layers and the parameter sensitivity analysis, the temperature at the contact surface between the semi-transparent coating and the external environment is and the temperature at the interface between the substrate and the external environment The observed quantity required for estimation is selected. After the observed quantity required for estimation is determined, the inversion interval required for estimation of thermally grown oxide thickness and defect thickness is determined according to the sensitivity curve of the observed quantity.

7. A method for synchronously estimating thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 6, characterized in that: When determining the objective function required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect based on the observation quantity required for simultaneously estimating the thickness of the thermally grown oxide and the thickness of the defect, In order to enhance the robustness of the estimation method and reduce the estimation error caused by the measurement error of the observed quantity caused by the environmental thermal interference noise in the thickness synchronization estimation process, the temperature term related to the thermal radiation effect of the semi-transparent coating is set in the objective function to reconstruct the objective function; The objective function is: the observed values ​​of the real system corresponding to the real values ​​of the thermally grown oxide thickness and defect thickness The observed value of the numerical heat transfer model of the thermal barrier coating system corresponding to a certain value of the estimated parameter during the estimation process The difference between them can be expressed as: ， in, is the true value of thermally grown oxide thickness and defect thickness, is the value of thermally grown oxide thickness and defect thickness in the estimation process; and is the temperature of the interface between the semi-transparent coating and the external environment and the temperature at the interface between the substrate and the external environment exist The value of the following; and for and exist The value below.

8. The method for synchronously estimating the thickness of thermally grown oxide and defect thickness of thermal barrier coating according to claim 7, characterized in that: Obtaining the measured values ​​of the real system observation quantities required for simultaneous estimation of the thermally grown oxide thickness and the defect thickness, when the thermally grown oxide thickness and the defect thickness are simultaneously estimated based on the inverse method, The measured value of the observed quantity of the real system , is the observed value in the established numerical heat transfer model of the thermal barrier coating system , This is achieved by adding noise that conforms to the law of random distribution. By changing the intensity of random noise, the different degrees of observation measurement errors caused by environmental thermal interference noise in real situations can be simulated. The estimation based on the inverse method is to find the minimum value of the objective function with the help of particle swarm optimization algorithm. This minimum value is recorded as , is an estimate of the thermally grown oxide thickness and defect thickness.

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