A method for evaluating temperature stability in an insulated box based on system identification

Abstract

The application discloses a kind of based on system identification's heat insulation box internal temperature stability evaluation method, belong to thermal environment test and thermal characteristic evaluation technical field, this method is by applying external temperature excitation to heat insulation box and collecting its internal and external temperature data, the equivalent heat transfer function model between external temperature disturbance and internal temperature response is constructed, and the experimental data of model construction process are used to carry out fitting verification;On this basis, in combination with temperature fluctuation frequency spectrum and equivalent heat transfer function model, the internal temperature frequency spectrum of heat insulation box is predicted, and the quantitative evaluation of the internal temperature stability of heat insulation box is realized.The application realizes the evaluation of the internal temperature stability of heat insulation box without long-term dependence on high-precision temperature measuring equipment, and is suitable for space gravitational wave telescope ground test, precision thermal environment test and other high-requirement thermal environment stability application scenarios.

Description

Technical Field

[0001] This invention belongs to the field of thermal environment testing and thermal characteristic evaluation technology, specifically relating to a method for evaluating the internal temperature stability of an insulated box based on system identification. Background Technology

[0002] In ground-based testing of space gravitational wave telescopes, thermal environment experiments of precision optical payloads, and other applications sensitive to low-frequency temperature noise, the internal temperature stability of the thermal enclosure is a crucial indicator for evaluating thermal environment performance. For such applications, the evaluation focus is typically not on the time-domain temperature fluctuation amplitude, but rather on the frequency-domain characteristics of temperature disturbances within a specific low-frequency band. Therefore, temperature stability analysis usually needs to be based on power spectral density or amplitude spectral density.

[0003] In existing technologies, a common method for obtaining the internal temperature stability of a thermal insulation box is to directly measure the internal temperature using a high-precision temperature measurement system and then perform frequency domain analysis based on the measured temperature data. While this method can directly obtain information on internal temperature changes, it suffers from problems such as high equipment cost, complex measurement system, and long testing cycle, which to some extent limits its engineering application.

[0004] Furthermore, existing technologies mostly analyze temperature stability based on measured temperature data inside the insulation box, primarily reflecting temperature changes under specific operating conditions, and failing to reveal the dynamic transmission relationship between external temperature disturbances and internal temperature responses. For applications in highly stable thermal environments, relying solely on internal temperature change results is insufficient to comprehensively characterize the temperature stability performance of the insulation box, necessitating further analysis from the perspective of system dynamic characteristics.

[0005] Therefore, the technical problem to be solved by the present invention is that the existing methods for assessing the internal temperature stability of insulation boxes rely on long-term, high-precision temperature measurement systems, which have long testing cycles, high costs, and are difficult to effectively characterize the dynamic thermal stability characteristics of insulation boxes. There is an urgent need for a method for assessing the internal temperature stability of insulation boxes so as to achieve accurate assessment of the internal temperature stability of insulation boxes without relying on long-term, high-precision temperature measurement systems. Summary of the Invention

[0006] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0007] A method for assessing the internal temperature stability of an insulated box based on system identification, comprising:

[0008] An external temperature excitation is applied to the heat insulation box, and the temperature data of the outer surface and the inner surface of the heat insulation box are collected simultaneously.

[0009] Using external and internal surface temperature data, an equivalent heat transfer function model is established through system identification. The equivalent heat transfer function model is used to characterize the dynamic transfer relationship between external temperature disturbances and internal temperature responses of the insulation box.

[0010] The equivalent heat transfer function model was validated using experimental data from the model construction process.

[0011] The external temperature disturbance spectrum of the insulation box under steady-state operating conditions is obtained, and the external temperature disturbance spectrum is mapped to the internal temperature response spectrum using the verified equivalent heat transfer function model, thereby realizing a quantitative assessment of the internal temperature stability of the insulation box.

[0012] The present invention has the following beneficial effects:

[0013] (1) The present invention can evaluate the internal temperature stability of the heat insulation box without relying on a high-precision temperature measurement system for a long time, thereby reducing the testing cost and implementation complexity;

[0014] (2) The present invention uses a system identification method to establish and verify six sets of single-input single-output equivalent heat transfer function models between the temperature disturbance of each outer surface of the heat insulation box and the corresponding temperature response of each inner surface, thereby realizing the parameterized characterization of the heat dynamic transfer characteristics of the heat insulation box and extending the internal temperature stability assessment from direct to predictive analysis based on the thermal dynamic model.

[0015] (3) By combining the temperature spectrum characteristics under steady-state operation conditions of the constant temperature chamber with the verified equivalent heat transfer function model, this invention can predict the temperature response spectrum inside the insulation chamber, realize the quantitative analysis of the transmission characteristics of low-frequency temperature disturbances, and improve the accuracy of thermal environment performance evaluation of the insulation chamber.

[0016] (4) This invention is applicable to high-stability thermal environment testing scenarios that are sensitive to low-frequency temperature noise, including applications such as ground tests related to space precision loads. Attached Figure Description

[0017] Figure 1 A schematic diagram of the experimental platform for obtaining internal and external temperature data of an insulated box, wherein 1-constant temperature box, 2-insulated box, 3-external temperature sensor, 4-internal temperature sensor, 5-data acquisition system;

[0018] Figure 2 This is a schematic diagram of the system identification process based on input-output data;

[0019] Figure 3 This is a flowchart illustrating a method for assessing the internal temperature stability of an insulated box based on system identification. Detailed Implementation

[0020] This invention provides a method for evaluating the internal temperature stability of an insulated box based on system identification. This method addresses the characteristics of the insulated box 2, such as thermal inertia, heat transfer time lag, and varying degrees of attenuation of temperature disturbances at different frequencies, during the transfer of external temperature disturbances to the internal temperature. By obtaining input-output data between the external and internal temperatures of the insulated box 2 through controlled temperature excitation, an equivalent heat transfer function model characterizing the thermal dynamics of the insulated box 2 is established. The equivalent heat transfer function model is then validated using experimental data from its construction process. After successful validation, the internal temperature amplitude spectral density of the insulated box 2 is obtained by combining the external temperature disturbance spectrum obtainable under actual steady-state operating conditions with the validated equivalent heat transfer function model, thereby achieving a quantitative evaluation of the internal temperature stability of the insulated box 2.

[0021] Specifically, it includes:

[0022] An external temperature excitation is applied to the heat insulation box, and the temperature data of the outer surface and the inner surface of the heat insulation box are collected simultaneously.

[0023] Using external surface temperature data and internal surface temperature data, an equivalent heat transfer function model is established through system identification. The equivalent heat transfer function model is used to characterize the dynamic transfer relationship between external temperature disturbance and internal temperature response of the insulation box 2.

[0024] The equivalent heat transfer function model was validated using experimental data from the model construction process.

[0025] The external temperature disturbance spectrum of the insulation box under steady-state operating conditions is obtained, and the external temperature disturbance spectrum is mapped to the internal temperature response spectrum using the verified equivalent heat transfer function model, thereby realizing a quantitative assessment of the internal temperature stability of the insulation box.

[0026] like Figure 1 As shown, the experimental platform used in this embodiment includes a constant temperature chamber 1, a heat-insulated box 2 to be tested set in the test space inside the constant temperature chamber 1, multiple external temperature sensors 3 set on the outer surface of the heat-insulated box 2, multiple internal temperature sensors 4 set on the inner surface of the heat-insulated box 2, and a data acquisition system 5.

[0027] The constant temperature chamber 1 is used to provide a controlled external temperature boundary to the insulated chamber 2, and can form a temperature change excitation and a stable temperature environment by adjusting the set temperature.

[0028] Insulated box 2 is a thermal insulation structure whose internal temperature stability is to be evaluated. It is a multi-layered thermal protection structure consisting of a box shell, an insulation layer, and an internal space. The insulation layer can be made of thermal insulation materials suitable for thermal insulation in this field, such as polyurethane foam, polystyrene foam, aerogel, glass fiber, ceramic fiber, or composite insulation structures formed by the above materials. The specific materials, thickness, and interlayer structure of insulated box 2 are determined according to the actual application.

[0029] External temperature sensor 3 is used to acquire external temperature disturbance data of each outer surface of the insulation box 2; internal temperature sensor 4 is used to acquire internal temperature response data of each inner surface of the insulation box 2; data acquisition system 5 is used to synchronously acquire temperature time series of each temperature measuring point according to a unified sampling clock.

[0030] In this embodiment, the heat insulation box 2 has six outer surfaces and six corresponding inner surfaces, namely the upper surface, lower surface, left side surface, right side surface, front side surface, and rear side surface. Multiple external temperature sensors 3 are respectively disposed at corresponding positions on the six outer surfaces, and multiple temperature measuring points are disposed on each outer surface; multiple internal temperature sensors 4 are disposed at corresponding positions on the six inner surfaces in a manner corresponding to the external temperature sensors 3.

[0031] By setting multiple temperature measurement points on the same surface, the temperature distribution information of the corresponding surface can be obtained, and equivalent temperature data that can characterize the overall temperature state of the surface can be obtained through subsequent equivalent processing, thereby reducing the impact of local temperature fluctuations and individual sensor measurement errors on the system identification results.

[0032] The heat insulation box 2 to be tested is placed inside the constant temperature box 1, so that a stable external thermal environment boundary is formed between the heat insulation box 2 and the constant temperature box 1.

[0033] In this embodiment, the external temperature excitation adopts a step-like temperature excitation, that is: first, the constant temperature chamber 1 is set to the first stable temperature T1 and kept running until the external and internal temperatures of the insulation chamber 2 reach a stable state; then the set temperature of the constant temperature chamber 1 is adjusted to the second stable temperature T2, thereby causing the external temperature of the insulation chamber 2 to change in a controlled manner, and the temperature time series of the outside and inside of the insulation chamber 2 are continuously collected.

[0034] A step-like temperature excitation requires the actual temperature of the constant temperature chamber 1 to transition from a first stable temperature state to a second stable temperature state within a finite time. This temperature change process should enable the insulated chamber 2 to produce a identifiable internal temperature response.

[0035] During the temperature excitation process, the data acquisition system 5 simultaneously collects the temperature data from multiple external temperature measurement points on the six outer surfaces. and the temperature of multiple internal temperature measuring points on the six inner surfaces. .in, This indicates the surface number of insulation box 2. =1, 2, ..., 6; Indicates the temperature sensor number on the same surface; Indicates the sampling time; Indicates the first The first outer surface At time 1, external temperature measuring points Temperature; Indicates the first The first inner surface Each internal temperature measuring point at time The temperature.

[0036] To ensure the correspondence between input and output data, external and internal temperature data are collected synchronously using a unified sampling frequency. The sampling period is determined based on the thermal response time scale of the insulation box to ensure that the main thermal dynamic characteristics during the temperature excitation process can be effectively collected.

[0037] After obtaining the above temperatures, multiple temperature measuring points on the same surface are subjected to equivalent processing.

[0038] For the The outer surface is used to calculate the weighted average of multiple external temperature measurement points to obtain the first... Equivalent external temperature of each outer surface :

[0039] For the first The equivalent internal temperature of the i-th inner surface is obtained by weighted averaging of multiple internal temperature measurement points on the i-th inner surface. :

[0040] ;

[0041] in, Let be the number of external temperature sensors on the i-th outer surface; For the first Number of internal temperature sensors on each inner surface; For the first The outer surface of the first Weighting coefficients for each external temperature measurement point; For the first The inner surface of the first The weighting coefficients for each internal temperature measurement point. Each weighting coefficient satisfies the following relationship:

[0042] ;

[0043] When the installation position and measurement accuracy of each temperature measuring point on the same surface are the same, each measuring point has the same weight. In this case, the above weighted average can be degenerated into an arithmetic average.

[0044] After the above processing, six sets of external temperature and corresponding internal temperature time series data can be obtained:

[0045] ;

[0046] Among them, the Group data As input for system identification As the system identification output.

[0047] like Figure 2 As shown, after completing temperature data acquisition and equivalent processing, the system is identified using six sets of external temperature-internal temperature input and output data, and six sets of single-input single-output equivalent heat transfer function models are established.

[0048] For the For each surface, a second-order equivalent heat transfer function with time delay is used to describe the dynamic heat transfer relationship between its external temperature disturbance and internal temperature response. The expression is as follows:

[0049] ;

[0050] in, For the first The equivalent heat transfer function of each surface; For surface numbering, =1, 2, ..., 6, which correspond to the six surfaces of the insulation box 2, respectively; s is the complex frequency variable in the Laplace transform domain; For the first The static gain of each surface is used to characterize the proportion of steady-state change of internal temperature when the external temperature undergoes a steady-state change; For the first The first thermal time constant of each surface; For the first The second thermal time constant of the surface and Together, they characterize the thermal inertia during the heat transfer process of the insulated box 2; For the first The equivalent heat transfer time delay of each surface is used to characterize the time delay caused by the external temperature disturbance being transmitted to the corresponding internal temperature response; It is a time-delay operator used to describe the pure time-delay characteristics of temperature disturbances in the heat transfer process.

[0051] In this embodiment, the system identification algorithm is used based on and Sure , , and Model parameters, etc.

[0052] For the The input-output relationship of a surface in the frequency domain is expressed as:

[0053] ;

[0054] in, For the first Laplace transform of equivalent external temperature data of an outer surface This involves the Laplace transform of the equivalent internal temperature data for the corresponding inner surface. Model parameters for each of the six surfaces are determined through system identification.

[0055] It should be noted that, Figure 2 The second-order time-delay model shown is used as the optimal implementation in this embodiment. In practical applications, an equivalent heat transfer function of appropriate order can be selected based on the identification results and model accuracy requirements.

[0056] After determining the model parameters, the same set of experimental data used to determine the model parameters was used to fit and verify the established equivalent heat transfer function model.

[0057] Specifically, the model determines the first [number] obtained during the experiment. Equivalent temperature of outer surface As input, the equivalent heat transfer function G with already determined parameters is used. i (s), to obtain the corresponding internal surface temperature response calculated by the model:

[0058] ;

[0059] in, The first value is calculated from the equivalent heat transfer function. The internal surface temperature response.

[0060] Then, the calculated Corresponding internal temperature data actually collected during the experiment Time-by-time comparisons are performed to evaluate the ability of the established equivalent heat transfer function to characterize the actual thermal response process.

[0061] In this embodiment, the goodness of fit (FIT) and mean squared error (MSE) are used as the model fit validation metrics.

[0062] Mean Square Error (MSE) is defined as:

[0063] ;

[0064] in, For the first Mean square error of the equivalent heat transfer function model for each surface; This is the number of valid sampling points in the experimental data used to determine the model; in this example, the value is 5000. The sampling point number; For the first Measured internal temperature values ​​corresponding to each sampling time; The internal temperature prediction is calculated from the equivalent heat transfer function at the same sampling time.

[0065] The goodness-of-fit (FIT) is used to characterize the degree of agreement between the internal temperature response curve calculated by the model and the internal temperature response curve measured experimentally. The goodness-of-fit can be expressed as:

[0066] ;

[0067] in, Indicates the first Goodness of fit of each surface; Represents the L2 norm; Indicates the first The average value of the measured temperature data of the inner surface.

[0068] The FIT and MSE corresponding to the six equivalent heat transfer function models were calculated using the methods described above. When the internal temperature response calculated by the equivalent heat transfer function model has a high degree of consistency with the experimentally measured internal temperature response, that is, when the FIT meets the preset fitting requirements and the MSE is lower than the preset error limit, it is considered that the corresponding equivalent heat transfer function can well characterize the thermal dynamic process of the transfer of external temperature disturbance to internal temperature response of the surface.

[0069] Furthermore, the above fitting verification was performed on each of the six surfaces to obtain the fitting verification results of six sets of equivalent heat transfer function models. Based on the fitting results of the six sets of equivalent heat transfer function models, it was determined whether the established equivalent heat transfer function model met the requirements for subsequent frequency domain analysis.

[0070] It should be noted that the equivalent heat transfer function model fitting verification in this embodiment uses the same experimental data as the model parameter determination. Its purpose is to evaluate the ability of the selected second-order equivalent heat transfer function structure with time delay and the determined model parameters to characterize the actual experimental thermal response process, rather than to evaluate the predictive ability of the equivalent heat transfer function model under independent operating conditions without participation in parameter determination.

[0071] like Figure 3 As shown, after establishing and independently verifying the equivalent heat transfer function model, the internal temperature stability of the insulation box 2 is evaluated in the frequency domain.

[0072] Unlike directly measuring the internal temperature fluctuations of the insulation box 2 over a long period of time, this embodiment first obtains the spectral characteristics of the external temperature disturbance of the insulation box 2 under the steady-state operation conditions of the constant temperature box 1, and then uses the verified equivalent heat transfer function model to map the external temperature disturbance spectrum into the internal temperature response spectrum.

[0073] First, the constant temperature chamber 1 is operated at a preset stable temperature, and the insulated chamber 2 is placed in a stable thermal environment. During the steady-state operation of the constant temperature chamber 1, the temperature time series of each outer surface is continuously collected by the external temperature sensor 3.

[0074] For the For the outer surface of the insulation box 2, frequency domain analysis was performed on the temperature time series of the outer surface under steady-state operating conditions to obtain its temperature amplitude spectral density (TASD). out,i (f). Among them, TASD indicates the frequency of temperature disturbance, in Hz. out,i (f) indicates the first The outer surface at frequency The temperature amplitude spectral density at that location is expressed in K / Hz. 1 / 2 .

[0075] For the verified first Equivalent heat transfer function G i (s), replacing its complex frequency variable s with Obtain the i-th equivalent heat transfer function at frequency Complex frequency response at ... :

[0076] ;

[0077] Where j is a complex factor, .

[0078] The first frequency response can be obtained from the above frequency response. Amplitude-frequency characteristics of each surface ,in, Modulo operation represents the operation on complex numbers, that is, taking the magnitude of a complex number.

[0079] The amplitude-frequency characteristic represents the proportion of amplitude attenuation after an external temperature disturbance is transmitted to the interior at different frequencies. It is an important parameter characterizing the thermal insulation capability of the insulation box 2 as a function of frequency.

[0080] Based on the input-output relationship of a linear system, in the... For each surface, the temperature amplitude spectral density of the internal temperature response can be determined based on the external temperature amplitude spectral density and the amplitude-frequency characteristics of the corresponding equivalent heat transfer function:

[0081] ;

[0082] in, For the first Temperature amplitude spectral density of the outer surface; For the first Temperature amplitude spectral density of each inner surface; Let f be the complex frequency response of the i-th equivalent heat transfer function at frequency f.

[0083] Therefore, the temperature amplitude spectral density of the six inner surfaces can be obtained respectively: , , , , , .

[0084] The internal temperature stability of insulation box 2 was evaluated based on the obtained temperature amplitude spectral densities of the six inner surfaces. For the first... A surface, at frequency At this point, the amplitude transfer ratio of the external temperature disturbance to the internal temperature response is changed from... It has been determined.

[0085] when When, it indicates that the external temperature disturbance at that frequency is attenuated after passing through the heat transfer process of the insulation box; and The smaller the value, the stronger the attenuation capability of temperature disturbances at the corresponding frequency.

[0086] Furthermore, the temperature amplitude spectral density of the inner surface can be determined within the target frequency range [f]. L , f H The size of the interior is used to evaluate internal temperature stability. For the first... Each inner surface can define the root mean square value of the equivalent temperature fluctuation within the target frequency band. for:

[0087] ;

[0088] Among them, f L and f H These are the lower and upper limits of the target frequency range, respectively. For the first The root mean square value of the equivalent temperature fluctuation of an inner surface within the target frequency range. The smaller the value, the smaller the temperature fluctuation of the corresponding inner surface within the target frequency range, and the higher its temperature stability.

[0089] The above description is merely an embodiment of the present invention and does not limit the scope of the invention. Any equivalent structural or procedural transformations made based on the description and drawings of this invention, or direct or indirect applications in other related system fields, are similarly included within the protection scope of this invention. Contents not described in detail in this specification are prior art known to those skilled in the art.

Claims

1. A method for assessing the internal temperature stability of an insulated box based on system identification, characterized in that, include: An external temperature excitation is applied to the heat insulation box, and the temperature data of the outer surface and the inner surface of the heat insulation box are collected simultaneously. Using external and internal surface temperature data, an equivalent heat transfer function model is established through system identification. The equivalent heat transfer function model is used to characterize the dynamic transfer relationship between external temperature disturbances and internal temperature responses of the insulation box. The equivalent heat transfer function model was validated using experimental data from the model construction process. The external temperature disturbance spectrum of the insulation box under steady-state operating conditions is obtained, and the external temperature disturbance spectrum is mapped to the internal temperature response spectrum using the verified equivalent heat transfer function model, thereby realizing a quantitative assessment of the internal temperature stability of the insulation box.

2. The method for assessing the internal temperature stability of an insulated box based on system identification according to claim 1, characterized in that, The external temperature excitation adopts a step-like temperature excitation; firstly, the constant temperature chamber is set to the first stable temperature and kept running until both the external and internal temperatures of the insulation chamber reach a stable state; then the set temperature of the constant temperature chamber is adjusted to the second stable temperature, thereby causing a controlled change in the external temperature of the insulation chamber.

3. The method for evaluating the internal temperature stability of an insulated box based on system identification according to claim 1, characterized in that, Multiple external temperature sensors are installed on the six outer surfaces of the insulation box, and multiple internal temperature sensors are installed on the six inner surfaces of the insulation box. The temperature time series of each temperature measuring point is collected synchronously through a data acquisition system.

4. The method for assessing the internal temperature stability of an insulated box based on system identification according to claim 1, characterized in that, By performing a weighted average of multiple temperature measurement points on the same surface, the equivalent external temperature and equivalent internal temperature of the corresponding surface are obtained.

5. The method for assessing the internal temperature stability of an insulated box based on system identification according to claim 1, characterized in that, The thermal dynamics between the external temperature disturbance and the internal temperature response of the insulated box are described by a second-order equivalent heat transfer function with time delay. The second-order equivalent heat transfer function with time delay includes static gain, first thermal time constant, second thermal time constant and equivalent heat transfer time delay.

6. The method for assessing the internal temperature stability of an insulated box based on system identification according to claim 1, characterized in that, Goodness of fit and mean square error were used as validation metrics for the equivalent heat transfer function model.

7. The method for assessing the internal temperature stability of an insulated box based on system identification according to claim 6, characterized in that, The complex frequency response of the equivalent heat transfer function model is obtained by replacing the complex frequency variables of the equivalent heat transfer function model with... Obtain, among which, For complex factors, The temperature disturbance frequency is the complex frequency response, which is determined by the static gain, the first thermal time constant, the second thermal time constant, and the equivalent heat transfer time delay.

8. The method for assessing the internal temperature stability of an insulated box based on system identification according to claim 1, characterized in that, Frequency domain analysis was performed on the time series of the outer surface temperature of the insulation box under steady-state operating conditions to obtain the temperature amplitude spectral density corresponding to the temperature disturbance of the outer surface.

9. The method for evaluating the internal temperature stability of an insulated box based on system identification according to claim 8, characterized in that, The temperature amplitude spectral density of the internal surface temperature response is determined by multiplying the amplitude-frequency characteristics of the equivalent heat transfer function with the external temperature amplitude spectral density.

10. The method for evaluating the internal temperature stability of an insulated box based on system identification according to claim 9, characterized in that, The internal temperature stability of the insulation box is evaluated based on the root mean square value of the equivalent temperature fluctuation within the target frequency range of the internal surface temperature amplitude spectral density.

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