CN111581720A - Method for evaluating uncertainty of temperature data of all-round program control thermal test of aircraft - Google Patents
Method for evaluating uncertainty of temperature data of all-round program control thermal test of aircraft Download PDFInfo
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Abstract
The invention belongs to the field of aircraft thermal tests, and particularly relates to a method for evaluating uncertainty of temperature data of an all-dimensional program control thermal test of an aircraft. According to the method, mathematical modeling of the full-range program control thermal test indicating value temperature data is established according to the estimated value of the actual temperature data and the expansion uncertainty of the initial actual temperature data with low precision, on the assumption of the probability distribution of the actual temperature data, and according to the principle of a thermocouple temperature measuring system. And finally, based on a Monte Carlo numerical simulation method, calculating uncertainty of the indicating value temperature of the all-dimensional program control thermal test with higher precision.
Description
Technical Field
The invention belongs to the field of aircraft thermal tests, and particularly relates to a method for evaluating uncertainty of temperature data of an all-dimensional program control thermal test of an aircraft.
Background
The existing thermal test control method of the aircraft mainly comprises two modes of temperature control and heat flux density control, aims at the coupling problem of a complex structure pneumatic heating-structure temperature field, is difficult to accurately measure structural thermophysical parameters changing along with temperature because an accurate mathematical model and boundary conditions are difficult to establish, and develops an all-round heat flux density control method (called all-round program control for short) on the basis of the heat flux density control mode. The basic idea of the all-round program control is that parameters such as orbit parameters and aerodynamic data in the actual flying process of a structure are used as original parameters, actually measured structure temperature data are used as real-time feedback signals, the real-time feedback signals are substituted into a pneumatic heating calculation equation to be calculated, the heat flux density required to be added to the surface of the structure is calculated, a heat loss item in a ground heat test is calculated, the heat flux density is compared with the actually measured heat flux density value, and the output of a heater is controlled in real time according to the deviation of the heat flux density and the actually measured heat flux density value. The method uses the structural temperature value measured in real time to participate in heat exchange calculation, and considers the condition that the high-temperature thermophysical parameters of the material change along with the temperature, thereby really realizing the coupling of pneumatic heating and a structural temperature field.
The temperature control thermal test takes a given temperature loading curve as target guidance, and the control system always takes the difference value between the test indication temperature and the given loading temperature as a control parameter, so that the test indication temperature is infinitely close to the target loading temperature. Due to the high precision of the thermal test control system (generally 0.5% F.S), most of the temperature data of the temperature control thermal test are distributed in a very narrow error band of a given loading temperature, so that the uncertainty of the temperature data is small.
The all-round program control thermal test is a non-target-oriented forward test and a repeated iteration dynamic test, the temperature is data generated in the forward direction of the test, and the temperature does not participate in control, namely the control system does not have the right to correct the temperature deviation caused by related influence factors. And the temperature data with certain uncertainty measured in real time is used as an input condition again to control the heat flow density, so that the uncertainty is higher due to N times of iterative transfer of the uncertainty until the test is finished. Based on the characteristics of the all-round program-controlled thermal test, the functional relationship between each influence factor and the highest point temperature is almost impossible to be established; it is too costly to perform a large number of all-round program-controlled thermal tests to obtain enough samples to accurately assess temperature uncertainty, while performing a limited number of all-round program-controlled thermal tests and employing a GUM method to assess temperature uncertainty results in insufficient accuracy. Therefore, it is necessary to establish an effective compromise method for evaluating uncertainty of temperature data of the all-dimensional program-controlled thermal test of the aircraft.
Disclosure of Invention
The purpose of the invention is as follows: the method is effective in compromise evaluation of uncertainty of all-dimensional program control thermal test temperature data of the aircraft. By using the method, the uncertainty of the actual temperature data of the all-round program-controlled thermal test, the mathematical modeling of the indicating value temperature data of the all-round program-controlled thermal test and the MATLAB calculation program based on the Monte Carlo method are obtained, and the uncertainty of the indicating value temperature data with higher precision is obtained.
The technical scheme of the invention is as follows: a method of assessing uncertainty in full program controlled thermal test temperature data for an aircraft is provided, the method comprising:
selecting a test piece with small influence of self factors on the uncertainty of the temperature of the thermal test, and carrying out N times of all-round program control thermal tests to obtain the evaluation value of the indicating value temperature data of the all-round program control thermal test and the uncertainty of the initial indicating value temperature data; according to the uncertainty of the initial indicating value temperature data, the uncertainty of the initial actual temperature data is obtained through an uncertainty synthesis theory; calculating to obtain the expansion uncertainty of the initial actual temperature data;
according to the estimated value of the actual temperature data and the expansion uncertainty of the initial actual temperature data, assuming the probability distribution of the actual temperature data, establishing a mathematical model of the indicating value temperature data of the all-round program control thermal test according to the principle of a thermocouple temperature measuring system,
Aindication value＝A×(1+B)×(1+C)×(1+D) (1)
Wherein A is the highest point of the actual temperature, AIndication valueFor indicating temperature, B is temperature transfer error caused by thermocouple installation process, and C is temperature transfer error caused by thermocouple self systemD is a temperature transfer error caused by the data acquisition system;
and based on the obtained probability distribution and mathematical model of the actual temperature data, obtaining the uncertainty of the indicating value temperature data after the full-formula program control thermal test correction by adopting a Monte Carlo method.
Further, N is not less than 6.
Further, each test piece is subjected to one all-dimensional program control heat test, and the highest-point indicated temperature of each test piece is xi(i 1, 2.. times.n), an estimate of the indicative temperature data is obtained according to equation 2
Further, by means of a Bessel method, uncertainty u of the initial indication temperature data is obtained according to formula 3max2：
Further, uncertainty of the thermocouple temperature measurement system in the all-round program control thermal test is obtained, and according to the uncertainty of the initial indicating value temperature data, the uncertainty of the initial actual temperature data is obtained through an uncertainty synthesis theory.
Further, the calculation formula of the uncertainty of the initial actual temperature data is as follows:
wherein u ismax1Uncertainty of initial actual temperature data, umax2Uncertainty, u, of the initial indicative temperature dataraIs uncertainty u caused by thermocouple installation process in full-range program-controlled thermal testrsFor uncertainty caused by system error of thermocouple in full-range program-controlled thermal test，ucThe method is the uncertainty caused by system errors of a data acquisition system in an all-round program control thermal test.
Further, an extended uncertainty u of the initial actual temperature datamax1.kComprises the following steps:
umax1.k＝2×umax1(5)
further, an estimate of the actual temperature data is taken of an estimate of the indicative temperature data by an engineering approximation method.
The invention has the technical effects that: the evaluation precision is superior to the A-type evaluation method in the simple GUM evaluation, and the invention can improve the precision of the uncertainty of the indicating value temperature data; under the condition of ensuring a certain evaluation accuracy, a large amount of high-cost all-dimensional program control thermal tests are not required; the Monte Carlo simulation method is adopted for evaluation and calculation, and is suitable for various complex models.
Detailed Description
The technical idea of the invention is realized mainly by the following technical scheme: and selecting a test piece with small influence of self factors on the thermal test temperature uncertainty to carry out N times of all-round program control thermal tests to obtain the uncertainty of initial indicating value temperature data with low precision, and further obtaining the uncertainty of the initial actual temperature data with low precision by using an uncertainty synthesis theory. And establishing mathematical modeling of the full-range program control thermal test indicating value temperature data according to the estimated value of the actual temperature data and the expansion uncertainty of the initial low-precision actual temperature data, assuming the probability distribution of the actual temperature data and according to the thermocouple temperature measuring system principle. And finally, obtaining an MATLAB calculation program of the full-program control thermal test indication temperature mathematical model based on a Monte Carlo numerical simulation method, and finally calculating the uncertainty of the full-program control thermal test indication temperature with higher precision. In this embodiment, N is not less than 6. In this embodiment, the estimate of the actual temperature data is the estimate of the indicated temperature data by an engineering approximation method.
In order to fully consider artificial random operation factors and equipment system error factors in the all-round program-controlled thermal test, N standard test pieces with small influence of self factors on the uncertainty of the thermal test temperature are selected, each test piece is respectively subjected to one all-round program-controlled thermal test to obtain the data of the highest point (the most concerned temperature point in the test) of the thermal test temperature, and the uncertainty of the initial indication temperature data is obtained by utilizing a GUM (Bessel method). Because the uncertainty of the thermocouple temperature measurement system is known, the uncertainty of the initial actual temperature data is obtained by inverse extrapolation of an uncertainty synthesis theory, and the probability distribution of the actual temperature data is assumed by an engineering approximation means. Based on an error theory, a mathematical model of the full-range program control thermal test indicating value temperature data, the actual temperature data and the thermocouple temperature measuring system is established. And finally, compiling a mathematical model MATLAB calculation program based on a Monte Carlo method, and calculating to obtain the uncertainty of the temperature of the full-program control thermal test indication value with higher precision.
Example 1
The embodiment provides a method for evaluating uncertainty of temperature data of an all-round program-controlled thermal test of an aircraft, which specifically comprises the following steps:
step 1: selecting a test piece with small influence of self factors on the uncertainty of the temperature of the thermal test, and carrying out N times of all-round program control thermal tests to obtain the evaluation value of the indicating value temperature data of the all-round program control thermal test and the uncertainty of the initial indicating value temperature data; according to the uncertainty of the initial indicating value temperature data, the uncertainty of the initial actual temperature data is obtained through an uncertainty synthesis theory; and calculating to obtain the expansion uncertainty of the initial actual temperature data. Because the samples are few, the uncertainty precision of the initial indicating temperature data is not high when limited tests are carried out. In this embodiment, the following details are described:
(1) selecting N (N is more than or equal to 6) standard test pieces with small influence of self factors on the uncertainty of the thermal test temperature. Welding thermocouples at the same positions of each test piece by manual random operation, namely introducing the influence of a manual welding thermocouple random process; each time of all-round program control thermal test installation (including test piece installation and test equipment installation) is carried out again, namely various random position errors caused by manual operation are introduced; the equipment system error is randomly generated by the system of the equipment. Completing N times of all-round program control thermal tests to obtain N highest point indicating temperature xi(i ═ 1, 2.., n), can be prepared fromEquation (2) yields an estimate of the indicated temperature.
(2) By means of Bessel method, the uncertainty u of the initial indicating temperature data can be obtained according to the formula (3)max2。
(3) In the all-round heat flux density control test of N standard test pieces, all main factors influencing temperature test data are included, and the method mainly comprises the following aspects:
a. systematic error of the control system; b. system error of the data acquisition system; c. systematic errors of the thermocouple itself; d. random effects of thermocouple installation process; e. uncertainty of a calibration value caused by man-made random operation and equipment systems in the heat loss calibration process; f. the uncertainty of the height coefficient caused by artificial random operation and equipment system in the height coefficient calibration process; g. the control principle (real-time temperature measurement and repeated iteration) of the omnidirectional heat flux density control causes repeated iteration of the factors.
In this embodiment, the factors affecting the maximum temperature data are divided into two parts: section 1 is the factor affected before the highest point of the test temperature (i.e., a-g); part 2 is the influencing factor (i.e. b-d) between the maximum of the actual temperature of the test and the indicated temperature.
In this example, the uncertainty u of the initial indication temperature data shown in equation 3max2And removing the standard uncertainty of the influencing factors of the part 2 to obtain the uncertainty of the initial actual temperature data. Specifically, in this embodiment, the uncertainty of the thermocouple temperature measurement system in the all-round program control thermal test is obtained first, and then the uncertainty of the initial actual temperature data is obtained through an uncertainty synthesis theory according to the uncertainty of the initial indication temperature data. The calculation formula of the standard uncertainty of the initial actual temperature is shown in the formula (4),
wherein u ismax1Uncertainty of initial actual temperature data, umax2Uncertainty, u, of the initial indicative temperature dataraIs uncertainty u caused by thermocouple installation process in full-range program-controlled thermal testrsUncertainty u caused by system error of thermocouple in full-range program-controlled thermal testcThe method is the uncertainty caused by system errors of a data acquisition system in an all-round program control thermal test.
(4) In this embodiment, the extended uncertainty is obtained by multiplying the composite standard uncertainty by an inclusion factor k greater than 1, given an interval that is expected to contain most of the measured distribution. If the required interval has an inclusion probability of about 0.95, k is 2, and the expansion uncertainty of the initial actual temperature data is obtained as follows:
umax1.k＝2×umax1(5)
wherein the indication temperature estimate approximates the actual temperature estimate since the actual temperature estimate is not known. In this process, it can be assumed that the maximum actual temperature A follows a normal distribution
The known thermocouple installation technique causes a temperature transfer error estimate of 0, uncertainty uraAssuming that the temperature transfer error caused by the thermocouple installation process follows a normal distribution N (0, u)ra 2)。
The temperature transfer error due to the known thermocouple system error is estimated as 0, uncertainty ursAssuming that the self system error of the thermocouple follows normal distribution N (0, u)rs 2)。
The temperature transfer error estimation value caused by the known data acquisition system error is 0, and the uncertainty ucAssuming that the self system error of the thermocouple follows normal distribution N (0, u)c 2)。
Step 2: and (3) assuming probability distribution of the actual temperature data according to the estimated value of the actual temperature data and the expansion uncertainty of the initial actual temperature data, and establishing a mathematical model of the full-range programmed thermal test indicating value temperature data according to the thermocouple temperature measurement system principle.
In this embodiment, it is assumed that under the influence of the part 1 influencing factor, the test piece reaches the actual maximum temperature point a, and a follows the distribution of a certain characteristic. Under the influence of part 2 influencing factors, the final indicated temperature is AIndication valueThen the following expression can be established:
Aindication value＝A×(l+B)×(1+C)×(1+D) (1)
Wherein, B is the temperature transfer error that the thermocouple mounting process arouses, C is the temperature transfer error that thermocouple self system arouses, and D is the temperature transfer error that data acquisition system arouses.
And step 3: and obtaining uncertainty of the indicating value temperature corrected by the full-formula program control thermal test by adopting a Monte Carlo method based on the probability distribution and the mathematical model of the obtained actual temperature data. Because the Monte Carlo method can carry out a large amount of random sampling, the number of samples can be huge, and the precision is improved.
In this embodiment, based on the obtained probability distribution and mathematical model of the actual temperature data, a mathematical model MATLAB calculation program based on the monte carlo method is written, and the uncertainty of the accurate all-round program control thermal test indication temperature is determined and reported.
Claims (8)
1. A method of assessing uncertainty in full program controlled thermal test temperature data for an aircraft, the method comprising:
selecting a test piece with small influence of self factors on the uncertainty of the temperature of the thermal test, and carrying out N times of all-round program control thermal tests to obtain the evaluation value of the indicating value temperature data of the all-round program control thermal test and the uncertainty of the initial indicating value temperature data; according to the uncertainty of the initial indicating value temperature data, the uncertainty of the initial actual temperature data is obtained through an uncertainty synthesis theory; calculating to obtain the expansion uncertainty of the initial actual temperature data;
according to the estimated value of the actual temperature data and the expansion uncertainty of the initial actual temperature data, assuming the probability distribution of the actual temperature data, establishing a mathematical model of the indicating value temperature data of the all-round program control thermal test according to the principle of a thermocouple temperature measuring system,
Aindication value＝A×(1+B)×(1+C)×(1+D) (1)
Wherein A is the highest point of the actual temperature, AIndication valueThe temperature is indicated, B is a temperature transfer error caused by a thermocouple installation process, C is a temperature transfer error caused by a thermocouple self system, and D is a temperature transfer error caused by a data acquisition system;
and based on the obtained probability distribution and mathematical model of the actual temperature data, obtaining the uncertainty of the indicating value temperature data after the full-formula program control thermal test correction by adopting a Monte Carlo method.
2. The method for assessing aircraft omnirange programmed thermal test temperature data uncertainty as recited in claim 1, wherein N is not less than 6.
3. The method for assessing uncertainty in omnidirectional program-controlled thermal test temperature data for an aircraft of claim 2, wherein each test piece undergoes an omnidirectional program-controlled thermal test, and the peak reading temperature of each test piece is xi(i 1, 2.. times.n), an estimate of the indicative temperature data is obtained according to equation 2
4. A method for assessing uncertainty in an aircraft omnirange programmed thermal test temperature data according to claim 3, characterized in that the uncertainty u of the initial indicative temperature data is obtained according to equation 3 using the bezier methodmax2：
5. The method of claim 4, wherein the uncertainty of the thermocouple temperature measurement system in the all-round programmed thermal test is obtained, and the uncertainty of the initial actual temperature data is obtained by an uncertainty synthesis theory according to the uncertainty of the initial indication temperature data.
6. The method for assessing uncertainty in an all-program-controlled thermal test temperature data for an aircraft of claim 5, wherein the uncertainty in the initial actual temperature data is calculated as follows:
wherein u ismax1Uncertainty of initial actual temperature data, umax2Uncertainty, u, of the initial indicative temperature dataraIs uncertainty u caused by thermocouple installation process in full-range program-controlled thermal testrsUncertainty u caused by system error of thermocouple in full-range program-controlled thermal testcThe method is the uncertainty caused by system errors of a data acquisition system in an all-round program control thermal test.
7. The method for assessing the uncertainty in an all-round programmed thermal test temperature data for an aircraft of claim 6, wherein the extended uncertainty u of the initial actual temperature datamax1.kComprises the following steps:
umax1.k＝2×umax1(5)。
8. a method of assessing uncertainty in an aircraft omnidirectionally controlled thermal test temperature data according to claim 1, wherein the estimate of actual temperature data is an estimate of said indicative temperature data by engineering approximation.
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