Hot Wall Heat Flow Reverse Estimation Method Based on Model Predictive Control

Abstract

This invention discloses a method for inverse estimation of hot wall heat flux based on model predictive control. It utilizes pseudo-random input square wave heat flux data obtained through calibration experiments, along with dual-point temperature data corresponding to a one-dimensional nonlinear heat transfer body. A forward heat transfer model of the one-dimensional nonlinear heat transfer body is identified through a nonlinear autoregressive artificial neural network. Using the temperature signal of the first measured point on the heat transfer body as the reference input signal for trajectory control, and the temperature signal of the second measured point as an additional input variable, the one-dimensional nonlinear forward heat transfer model from step two is employed, and the heat flux estimate as the control input variable is obtained through a model predictive optimal control algorithm. This invention provides a method for inverse estimation of hot wall heat flux based on model predictive control. It employs a forward nonlinear heat transfer model identification, reducing the impact of thermocouple colored noise on the accuracy of model identification. Combined with experimental calibration identification methods, it effectively overcomes the adverse effects of thermocouple temperature field disturbances and the nonlinear time-varying thermal properties of the heat transfer body.

Description

Technical Field

[0001] This invention belongs to the technical field of ground-based heat protection testing and flight testing of hypersonic vehicles. More specifically, this invention relates to a method for inverse estimation of hot wall heat flux based on model predictive control. Background Technology

[0002] In aerodynamic thermal and thermal protection experiments, the effective acquisition of heat flux data plays a crucial role in improving the prediction of aerodynamic thermal environments and refining the thermal response of thermal protection materials. Cold wall heat flux testing methods, including plug calorimeters, zero-point calorimeters, water calorimeters, and Gordon calorimeters, have been widely used in aerodynamic thermal and thermal protection experiments. However, during prolonged aerodynamic heating, inconsistencies between the cold wall heat flux sensor and the surrounding model in terms of material and surface temperature can lead to significant differences in heat exchange processes such as catalytic thermal effects, convective boundary layer heat transfer characteristics, and convective and radiative heat dissipation. Consequently, cold wall heat flux measurements cannot fully and accurately reflect the surface hot wall heat flux of the thermal protection model in hypersonic vehicle flight environments / ground simulation experiments.

[0003] The existing technology, application number 2019109996909, entitled "A Dynamic Heat Flow Test Method Based on Transfer Function Identification", is also a dynamic heat flow test method based on heat flow sensor calibration test identification. However, its limitation is that it uses single-point temperature measurement and can only be applied to short-term dynamic heat flow tests when the heat transfer parameters of the heat transfer body are constant or do not change with temperature in detail. It is completely unsuitable for long-term inverse estimation of hot wall heat flow in a one-dimensional nonlinear dynamic heat transfer process where the heat transfer parameters of the heat transfer body change with temperature. Summary of the Invention

[0004] One object of the present invention is to solve at least the above-mentioned problems and / or defects, and to provide at least the advantages described below.

[0005] To achieve these objectives and other advantages of the present invention, a method for inverse estimation of hot wall heat flux based on model predictive control is provided, comprising:

[0006] Step 1: Based on a one-dimensional nonlinear heat transfer body with dual temperature measurement points and heat transfer disturbance at the rear boundary, a nonlinear autoregressive artificial neural network forward heat transfer model with short-delay time-series dual input variables is constructed.

[0007] Step 2: Obtain pseudo-random input square wave heat flux data q using calibration test methods. c The temperature data T1(k) and T2(k) of the two measuring points corresponding to the one-dimensional nonlinear heat transfer body are used to identify the forward heat transfer model of the one-dimensional nonlinear heat transfer body through the nonlinear autoregressive artificial neural network forward heat transfer model in step one.

[0008] Step 3: Using the temperature signal of the first measuring point of the heat transfer body measured on-site as the reference input signal for trajectory control, and the temperature signal of the second measuring point as the additional input variable, the one-dimensional nonlinear forward heat transfer model in Step 2 is adopted, and the heat flow estimate as the control input variable is obtained through the model prediction optimal control algorithm.

[0009] Preferably, in step one, the dual input variables are heat flux time-series vectors. Second measurement point temperature response time sequence vector

[0010] Therefore, the relationship between the input variable and the output temperature response T1(k) at the first measuring point can be approximately represented by the following nonlinear autoregressive artificial neural network model:

[0011]

[0012] in, Let K be the parameter vector, and K be the total number of parameters in the nonlinear autoregressive artificial neural network forward heat transfer model.

[0013] Preferably, in step two, the process for obtaining the one-dimensional nonlinear forward heat transfer model is configured to include:

[0014] S20, pseudo-random input square wave heat flux data q obtained using calibration test methods. c The calibrated net input heat flux q(k) is obtained;

[0015] S21 employs the Levenberg-Marquardt optimized identification algorithm, combining q(k), T1(k), and T2(k), based on the optimal objective function:

[0016]

[0017] This allows the first temperature measurement point to predict the temperature. The optimal parameter vector is obtained by minimizing the root mean square error between the actual output temperature T1(K) at the first measuring point and the actual output temperature.

[0018] Among them, Γ K Let N be a K-dimensional vector space; N is the logarithm of the calibration test data.

[0019] S22, based on what was obtained in S21 The following one-dimensional nonlinear forward heat transfer model is obtained:

[0020]

[0021] Preferably, in step three, the process for obtaining the heat flux estimate is configured to include:

[0022] S30, based on a one-dimensional nonlinear forward heat transfer model, uses the time-series temperature of the first temperature measurement point as the trajectory control input reference signal, and the forward heat transfer model predicts the temperature signal. As a feedback signal, a quasi-Newton optimization algorithm is used for offline nonlinear model predictive control to obtain the optimal control variable increment at the current moment. Minimize the following objective function:

[0023]

[0024] In the iterative feedback process of temperature prediction in the forward heat transfer model, it also involves iterative updates of the model input variable values ​​within future time steps p. Therefore, the input variable vectors in the objective function can be expressed as follows:

[0025]

[0026] S31, based on Obtain the optimal inverse estimate of heat flux at the current time step and the previous time step.

[0027]

[0028] S32, update the current time to k+1→k, return to S30 to perform temperature prediction control for the next time step, and thus obtain the optimal control quantity.

[0029] Preferably, the one-dimensional nonlinear heat transfer body is configured as a cylindrical heat transfer body;

[0030] Thermocouple pair I and thermocouple pair II are respectively provided at x1 and x2 distances from the first end face of the heat transfer body, and the first end face is the incoming flow side that cooperates with the heat transfer body;

[0031] A heat-insulating boundary layer is provided on the outer side of the heat transfer body wall.

[0032] The present invention has at least the following beneficial effects: First, the present invention identifies the forward heat transfer model based on heat flow calibration test data and nonlinear autoregressive artificial neural network. Therefore, the accuracy of the obtained identification model is not affected by the density, specific heat and thermal conductivity of the heat transfer body, thermocouple temperature measurement error, time delay characteristics and geometric dimension error, etc.

[0033] Secondly, the method of the present invention is based on nonlinear model predictive control, which can effectively overcome the influence of the time-varying nonlinear heat transfer process of the heat flow sensor caused by significant temperature rise on the inverse estimation of heat flow.

[0034] Third, in the forward heat transfer identification model of this invention, since the noise contained in the test data of the first temperature measurement point of the output variable is not correlated with the input heat flux, it will not affect the identification of the forward heat transfer model. On this basis, adaptive inverse control can be performed, thereby reducing the adverse effects caused by object disturbance (output signal noise).

[0035] Fourth, the heat transfer medium of the present invention can be made of the same material as the model and does not require water cooling. Therefore, the heat flow reversal method of the present invention can provide a possibility for effectively solving the problem of heat flow testing of hot walls in non-ablative models.

[0036] Other advantages, objectives and features of the present invention will become apparent in part from the following description, and in part from those skilled in the art through study and practice of the invention. Attached Figure Description

[0037] Figure 1 A schematic diagram of a one-dimensional nonlinear heat transfer body structure with dual temperature measurement points and rear boundary heat transfer disturbance provided by the present invention.

[0038] Figure 2 This is the topology of the one-dimensional nonlinear autoregressive artificial neural network forward heat transfer model of the present invention;

[0039] Figure 3 This invention provides an optimal inverse heat flow estimation method based on a forward heat transfer identification model.

[0040] Figure 4 The present invention provides the inverse estimation results of heat flux of the heat transfer body under nonlinear dynamic heat transfer conditions. Detailed Implementation

[0041] The present invention will now be described in further detail with reference to the accompanying drawings, so that those skilled in the art can implement it based on the description.

[0042] To meet the need for rapid and effective testing of surface hotwall heat flux in ground / flight test environment models, this invention addresses the adverse effects of factors such as temperature field disturbances caused by embedded thermocouples within the heat transfer body, thermocouple measurement errors and time delays, and the nonlinear time-varying characteristics of thermal properties on the numerical inverse identification of hotwall heat flux. Based on a one-dimensional nonlinear heat transfer model with dual embedded temperature measurement points, this invention proposes a novel forward heat transfer prediction model structure based on a nonlinear autoregressive artificial neural network and employs a model prediction optimal control method. This establishes a nonlinear dynamic hotwall heat flux inverse estimation method that does not rely on known thermal property parameters and measurement accuracy. It is suitable for testing hotwall heat flux in long-term nonlinear dynamic heat transfer processes where thermal property parameters change with temperature. Compared to existing technologies, the forward heat transfer model in this patent is a nonlinear autoregressive artificial neural network model, not a linear dynamic transfer function model.

[0043] This invention discloses a novel method for inverse estimation of hot wall heat flux based on model predictive control, comprising: a one-dimensional nonlinear heat transfer body with dual temperature measurement points containing heat transfer disturbance at the rear boundary; constructing a forward heat transfer model structure of a nonlinear autoregressive artificial neural network with short-delay time-series dual input variables; then, using pseudo-random input square wave heat flux data and corresponding dual measurement point temperature data of the heat transfer body obtained by calibration experiment, identifying the forward nonlinear dynamic heat transfer model; based on this, using the field-measured temperature signal of the first measurement point of the heat transfer body as the trajectory control reference input signal, and the temperature signal of the second measurement point as the additional input variable (i.e., as can be seen from the expression of the nonlinear autoregressive artificial neural network model, the model input variables of this invention not only include the heat flux estimate q(k), but also the additional input variable T2(k)), and using a model predictive optimal control algorithm to obtain the heat flux estimate of the control input variable, specifically including the following steps:

[0044] Step 1: Calibration of the pseudo-random square wave heat flux amplitude on the heat flux sensor calibration test platform: The heat flux sensor calibration test platform provides a pseudo-random square wave input heat flux; then, the absolute heat flux q of the square wave heat flux amplitude is measured using a reference heat flux sensor. c And the measured absolute heat flux q c As Figure 1 The calibration input for the one-dimensional nonlinear heat transfer body is the pseudo-random square wave heat flux amplitude.

[0045] Step 2: Simultaneously acquire the photodiode signal s(k) of the beam splitter for the calibrated square-wave input heat flux at sampling time intervals Δt, as well as the temperature data T1(k) and T2(k) of the temperature measurement points of thermocouple pair I and thermocouple pair II on the heat transfer body based on the one-dimensional nonlinear heat transfer assumption; normalize the s(k) signal that reflects the calibrated heat flux waveform, and combine it with the known amplitude q of the calibrated input square-wave heat flux. c By considering the absorption rate of the high-temperature coating on the induction surface of the heat transfer body, the net input heat flux q(k) of the heat transfer body dynamic calibration based on the assumption of a one-dimensional nonlinear heat transfer body can be obtained. It should be noted that the process of deriving q(k) in steps one and two is existing technology, so it will not be described in detail here.

[0046] Step 3: Employ the Levenberg-Marquardt optimization and identification algorithm, combined with the dynamic calibration input heat flux q(k) and temperature data T1(k) and T2(k) based on the one-dimensional nonlinear heat transfer assumption, and determine the optimal objective function. Adjust the nonlinear autoregressive artificial neural network forward heat transfer model (with 3 neurons in a single hidden layer). Parameter vector in (Weight coefficients and thresholds) enable the prediction of temperature The optimal parameter vector is obtained by minimizing the root mean square error between the actual output temperature T1(k) at the first measuring point and the first measuring point. Where K is the total number of parameters in the nonlinear autoregressive artificial neural network forward heat transfer model; Γ K Let N be a K-dimensional vector space; N be the logarithm of the calibration test data; q(k) be the net input heat flux for calibration; Additionally,

[0047]

[0048] The specific topology of the input variables (a total of (Id+Fd) variables) used in the nonlinear autoregressive artificial neural network is shown in the attached figure. Figure 2 As shown.

[0049] Step 4: Based on the optimal parameter vector obtained in Step 3 The forward heat transfer model of a one-dimensional nonlinear heat transfer body is obtained, namely...

[0050]

[0051] in, Predict the temperature for the first temperature measurement point; This represents the optimal parameter vector for a nonlinear neural network model.

[0052] Step 5, after obtaining Figure 2 Based on the forward heat transfer model of the one-dimensional nonlinear heat transfer body shown, the time-series temperature of the first temperature measurement point is used as the trajectory control input reference signal, and the temperature signal predicted by the forward heat transfer model is used as the feedback signal. A quasi-Newton optimization algorithm is employed for offline nonlinear model predictive control to obtain the optimal control variable increment at the current moment. Right now The objective function can be minimized as follows:

[0053]

[0054] In the iterative feedback process of temperature prediction in the forward heat transfer model, it also involves iterative updates of the model input variable values ​​within future time steps p, such as... Figure 3 The Recurrent Inputs Generator module in the target function; the input variable vectors in the objective function can be represented as follows:

[0055]

[0056] Step 6: Obtain the optimal inverse heat flux estimate for the previous time step at the current time step:

[0057]

[0058] Step 7: Update the current time to k+1→k, return to step 4 to perform temperature prediction control for the next time step, and obtain the optimal control quantity, i.e. the optimal inverse heat flux estimate.

[0059] The hot-wall heat flux inverse estimation method based on model predictive control of the present invention reduces the impact of thermocouple colored noise on the accuracy of model identification by adopting a forward nonlinear heat transfer model identification; combined with the experimental calibration identification method, it can effectively overcome the adverse effects of thermocouple temperature field disturbance and nonlinear time-varying thermal property parameters; on this basis, by adopting the predictive control optimal algorithm, it further reduces the ill-posedness of heat flux inverse estimation and improves the accuracy of hot-wall heat flux inverse estimation.

[0060] According to such Figure 4 The inverse estimation results of the heat flow of the heat transfer body under the nonlinear dynamic heat transfer condition are shown. By comparing the inversely estimated heat flow with the actual input heat flow, it can be concluded that the heat flow test performed by the heat flow inverse estimation method of the heat transfer body based on model predictive control described in this invention has good effect and high accuracy.

[0061] In the above technical solutions, such as Figure 1 The dual-temperature-measuring-point one-dimensional nonlinear heat transfer body with rear boundary heat transfer disturbance provided by the present invention is configured as a cylindrical heat transfer body.

[0062] Thermocouple pair I and thermocouple pair II are respectively provided at x1 and x2 distances from the first end face of the heat transfer body. The first end face is the incoming flow side that cooperates with the heat transfer body. Thermocouple III provided at the second end face b is not involved in the derivation process of this invention and will not be described here.

[0063] The heat transfer body has an insulating boundary layer on its outer side, making its heat transfer process approximately one-dimensional.

[0064] In this scheme, the one-dimensional nonlinear heat transfer body with rear boundary heat transfer disturbance can simplify the explanation of the applicable conditions of the hot wall heat flux inverse estimation method based on model predictive control, and bringing the thermocouple pair I temperature measuring contacts close to the front end face (i.e. the first end face) of the heat flux sensor can improve the response speed.

[0065] The above solution is merely an illustration of a preferred example and is not limited thereto. When implementing this invention, appropriate substitutions and / or modifications can be made according to the user's needs.

[0066] The number of devices and processing scale described herein are for the purpose of simplifying the description of the invention. Applications, modifications, and variations of the invention will be readily apparent to those skilled in the art.

[0067] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. It can be applied to various fields suitable for the present invention. Other modifications can be readily made by those skilled in the art. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and examples shown and described herein.

Claims

1. A method for inverse estimation of hot wall heat flux based on model predictive control, characterized in that, include: Step 1: Based on a one-dimensional nonlinear heat transfer body with dual temperature measurement points and heat transfer disturbance at the rear boundary, a nonlinear autoregressive artificial neural network forward heat transfer model with short-delay time-series dual input variables is constructed. Step 2: Obtain pseudo-random input square wave heat flux data using calibration test methods. and temperature data at two measurement points corresponding to a one-dimensional nonlinear heat transfer body. , The forward heat transfer model of a one-dimensional nonlinear heat transfer body is identified through the nonlinear autoregressive artificial neural network forward heat transfer model in step one. Step 3: Using the temperature signal of the first measuring point of the heat transfer body measured on-site as the reference input signal for trajectory control, and the temperature signal of the second measuring point as the additional input variable, the one-dimensional nonlinear forward heat transfer model in Step 2 is adopted, and the heat flow estimate as the control input variable is obtained through the model prediction optimal control algorithm. In step one, the dual input variables are heat flux time-series vectors. Second measurement point temperature response time sequence vector ; Therefore, the input variable and the output temperature response at the first measuring point are... The relationship between them can be approximated by the following nonlinear autoregressive artificial neural network model: ； in, For parameter vectors; In step two, the process for obtaining the one-dimensional nonlinear forward heat transfer model is configured to include: S20, pseudo-random input square wave heat flux data obtained using calibration test methods. Obtain the calibrated net input heat flux ; S21 employs the Levenberg-Marquardt optimized identification algorithm, combined with , , According to the optimal objective function: To adjust This allows the first temperature measurement point to predict the temperature. Compared with the actual output temperature of the first measuring point To minimize the mean square error, the optimal parameter vector is obtained. , K This represents the total number of parameters in the nonlinear autoregressive artificial neural network forward heat transfer model. in, for K 3D vector space N To calibrate the logarithm of the experimental data; S22, based on what was obtained in S21 The following one-dimensional nonlinear forward heat transfer model is obtained: ； In step three, the process for obtaining the heat flux estimate is configured to include: S30, based on a one-dimensional nonlinear forward heat transfer model, uses the time-series temperature of the first temperature measurement point as the trajectory control input reference signal, and the temperature signal predicted by the forward heat transfer model. As a feedback signal, a quasi-Newton optimization algorithm is used for offline nonlinear model predictive control to obtain the optimal control variable increment at the current moment. Minimize the following objective function: In the iterative feedback process of temperature prediction in the forward heat transfer model, future time steps are also involved. p The model input variable values ​​are iteratively updated, so the input variable vectors in the objective function can be represented as follows: ； S31, based on The optimal inverse heat flow estimate for the previous time step at the current time step is obtained as follows: ； S32, update the current time to Then return to S30 to perform temperature predictive control for the next time step, thereby obtaining the optimal control input.

2. The hot-wall heat flux inverse estimation method based on model predictive control as described in claim 1, characterized in that, one-dimensional... The nonlinear heat transfer element is configured as a cylindrical heat transfer element; Among them, at the distance from the first end face of the heat transfer body , Thermocouple pair I and thermocouple pair II are respectively provided at the location, and the first end face is the incoming flow side that is matched with the heat transfer body; A heat-insulating boundary layer is provided on the outer side of the heat transfer body wall.

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