A method for evaluating accuracy and recurrence rate based on uncertainty theory

Abstract

This invention discloses a method for evaluating accuracy and reproducibility based on uncertainty theory, comprising: S1, determining the physical quantity of interest in the experiment and related physical quantities involved in the experiment; S2, repeatedly measuring the related physical quantities that can be directly measured to obtain their mean and combined uncertainty; for related physical quantities that cannot be directly measured, deriving formulas based on their relationship with other physical quantities, and calculating their mean and combined uncertainty using error propagation methods; S3, obtaining the theoretical mean and theoretical combined uncertainty of the physical quantity of interest in the experiment; S4, obtaining the measured mean and measured combined uncertainty of the physical quantity of interest in the experiment through measurement methods using experimental instruments. This invention can evaluate the accuracy and reproducibility of calculation methods where there is no obvious error propagation between the various sub-steps of the experiment.

Description

Technical Field

[0001] This invention relates to the field of testing technologies such as structures and marine engineering. More specifically, this invention relates to a method for evaluating accuracy and reproducibility based on uncertainty theory. Background Technology

[0002] In a wide range of experiments, the impact of a single step on the next step or the final result is difficult to express with formulas. Therefore, if there were a method that could evaluate the accuracy and reproducibility of an experiment without relying on the error of a single step, it would be more in line with the actual situation of most structural and marine engineering experiments. Summary of the Invention

[0003] The purpose of this invention is to provide a method for evaluating accuracy and reproducibility based on uncertainty theory, which can evaluate the accuracy and reproducibility of calculation methods where there is no obvious error propagation between sub-steps of an experiment.

[0004] The technical solution adopted by this invention to solve this technical problem is: a method for evaluating accuracy and reproducibility based on uncertainty theory, comprising:

[0005] S1. Determine the physical quantities of interest in the experiment and the related physical quantities involved in the experiment;

[0006] S2. For directly measurable related physical quantities, repeatedly measure them to obtain their mean and combined uncertainty; for related physical quantities that cannot be directly measured, derive formulas through their relationship with other physical quantities, and use error propagation methods to calculate their mean and combined uncertainty.

[0007] S3. Obtain the theoretical mean and theoretical combined uncertainty of the physical quantities of interest in the experiment;

[0008] S4. Obtain the measurement mean and combined measurement uncertainty of the physical quantities of interest in the experiment by means of experimental instruments;

[0009] S5. Solve the probability by finding the intersection of the intervals between the measured mean and combined measurement uncertainty of the physical quantity of interest in the experiment and the theoretical mean and combined uncertainty, and you can obtain the accuracy and reproducibility of interest in the experiment.

[0010] A further aspect of the present invention is as follows: S1 specifically includes: the relevant physical quantities of interest in the experimental results are D, E, F, G, H, J, K, and L; the physical quantities of interest in the experiment are obtained through theoretical analysis, namely A, B, and C, assuming A = D + E - mF, B = mGH / J, and C = K. v +cL y , where a, b, c, m, v, y are constants.

[0011] As a further aspect of the present invention, S2 specifically includes:

[0012] S21. Assuming that physical quantity D cannot be directly measured, derive the correlation between D and other relevant physical quantities required for other experimental results. Assume D = EF. t ;

[0013] S22. For physical quantities that can be directly measured, find the testing instrument and determine its Type B uncertainty through the manufacturer's instructions or calibration certificate. Assuming that the instruments required for measurement are O, P, Q, R, and S, the corresponding Type B uncertainties are δo, δp, δq, δr, and δs.

[0014] S23. The directly measurable physical quantities E, F, G, H, J, K, L are each associated with the Type B uncertainty of their corresponding measuring instruments, and are assumed to be δo, δp, δq, δr, and δs.

[0015] S24. Repeatedly measure physical quantities that can be directly measured, and after eliminating obviously erroneous data, calculate their mean and standard deviation, which can be expressed as (e,δe), (f,δf), (g,δg), (h,δh), (j,δj), (k,δk), (l,δl), respectively.

[0016] S25. Combined Uncertainty Right now Similarly, the mean and combined uncertainty of directly measured physical quantities can be expressed as (e, u) e ), (f,u f ), (g,u g ), (h,u h ), (j,u j ), (k,u k ), (l,u l );

[0017] S26. For a physical quantity D that cannot be directly measured, according to its relationship with other physical quantities, D = EF t It can be seen that, Where d = ef t Therefore

[0018] As a further aspect of the present invention, S3 specifically includes: Similarly, the synthesis uncertainty u a =u d +u e +mu f , The physical quantity of interest in the experiment can be expressed as (a, u) a ), (b,u b ), (c,u c At this point, we obtain the theoretical value range of the physical quantity of interest in the experiment under the experimental conditions.

[0019] As a further aspect of the present invention, step S4 specifically includes: for the physical quantity of interest in the experiment, finding its corresponding testing instruments W, X, and Z, and repeating steps S22 to S25 to obtain the measured value range obtained in the experiment, denoted as (ac, u ac (bc,u) bc ), (cc,u cc ).

[0020] As a further aspect of the present invention, S5 specifically includes:

[0021] S51. According to the Central Limit Theorem, the results of repeated tests follow a normal distribution, that is, the distribution of the theoretical and measured values ​​of the physical quantities of interest in the experiment follows N ~ (a, u). a ), N~(b,u b ), N~(c,u c ) and N~(ac,u ac ), N~(bc,u bc ), N~(cc,u cc );

[0022] S52. Taking physical quantity A as an example, its accuracy can be evaluated as pe=|a-ac| / a*100. The calculation of the reproducibility rate can be regarded as solving N~(ac,u) ac In the interval (a-2u) a ,a+2u a ) and (ac-2u ac ,ac+2u ac The probability of the intersection of the two quantities is denoted as qe; the evaluation of the accuracy and reproducibility of physical quantities B and C is the same.

[0023] The present invention has at least the following beneficial effects:

[0024] (1) This method is applicable to structural and marine engineering tests and can evaluate the accuracy and reproducibility of test measurements.

[0025] (2) This method can simultaneously ignore the impact of a single step in the experimental process on the final result.

[0026] (3) This method can provide an evaluation method with the same repeatability test accuracy and reproducibility.

[0027] (4) This method can meet the requirements of underwater experiments and structural performance tests.

[0028] (4) The principle of this method is simple and convenient, and it is easy to apply and promote.

[0029] (5) This method has a wide range of applications and can play a good role in most structural and marine engineering tests.

[0030] (6) This method is simple to calculate, efficient and saves time.

[0031] (7) This method can be used to perform corresponding calculations based on the theoretical value calculation method and measurement means of specific experiments. It is not limited to a certain structure, static and dynamic, and can even be extended to the range of physical experiments in which the theoretical values ​​of the test results can be obtained.

[0032] (8) This method is stable and reliable. After implementation, the accuracy and reproducibility of the test measurement values ​​are evaluated.

[0033] (9) This method can be applied flexibly. For different experiments, it is only necessary to know the theoretical value of the physical quantity of interest and the corresponding measurement method.

[0034] (10) This method requires little computation, has simple computational logic, and is easy to understand and operate.

[0035] (11) This method is low in cost and economical.

[0036] (12) This method is green and environmentally friendly and does not produce harmful waste.

[0037] (13) This method is simple and practical, and provides valuable reference for researchers to assess accuracy and reproducibility.

[0038] 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

[0039] Figure 1 This is the experimental design diagram of the present invention.

[0040] Attached diagram labeling: 1 Water tank, 2 Pad block. Detailed Implementation

[0041] The present invention will now be described in detail and completely with reference to the accompanying drawings. Those skilled in the art will be able to implement the present invention based on these descriptions. Before describing the present invention with reference to the accompanying drawings, it should be particularly noted that the technical solutions and features provided in various parts of the present invention, including the following description, can be combined with each other without conflict.

[0042] Furthermore, the embodiments of the present invention described below are generally only some, not all, of the embodiments of the present invention. Therefore, all other embodiments obtained by those skilled in the art based on the embodiments of the present invention without inventive effort should fall within the scope of protection of the present invention.

[0043] This invention provides a method for assessing accuracy and reproducibility based on uncertainty theory. First, the physical quantity of interest in the experiment and its related physical quantities are determined. Then, the directly measurable physical quantities are repeatedly measured to calculate their mean and combined uncertainty. For physical quantities that cannot be directly measured, formulas are derived based on their relationship with related physical quantities. The mean and combined uncertainty are then calculated using the error propagation method. This method can also obtain the theoretical mean and theoretical combined uncertainty of the physical quantity of interest in the experiment. Finally, the measurement mean and measurement combined uncertainty of the physical quantity of interest in the experiment are obtained through experimental instrument measurement. The probability of the intersection of these values ​​with the intervals of the theoretical mean and theoretical combined uncertainty is solved, thus obtaining the accuracy and reproducibility of interest in the experiment. The following examples illustrate this in detail:

[0044] Example 1

[0045] In a marine engineering test focusing on a suspended tunnel, the influence of airborne suspension on the dynamic response of the tunnel was investigated. For example... Figure 1 The diagram shows the experimental design. The experimental setup includes a water tank 1 and several pads 2 placed below the water tank. The structure is fixed in the water tank. The method for evaluating the accuracy and reproducibility based on uncertainty theory specifically includes the following steps.

[0046] Step 1: When the structure is in an elastic working state, the relevant physical quantities in the experiment include: foam diameter D, foam density ρ, steel rod diameter d, steel rod length L, steel rod mass m, elastic modulus E, moment of inertia I, etc. The physical quantity required to determine the experimental results is the frequency ω, and the theoretical value of the fundamental frequency is... (The same applies to fixed supports, taking a simple support as an example);

[0047] Step Two: Confirm that the physical quantities foam diameter D, steel rod diameter d, steel rod length L, and steel rod mass m can be directly measured (foam density ρ is provided by the manufacturer). Elastic modulus E and moment of inertia I cannot be directly measured. The measurement of E is derived from the formula for the deflection of a cantilever beam under the action of a concentrated force at the beam end in mechanics of materials.

[0048] Step 3: For physical quantities that can be directly measured, find a suitable testing instrument and determine its Type B uncertainty using the manufacturer's instructions or calibration certificate. See Table 1 below for an example:

[0049] Table 1. Results of Type B Uncertainty Tests

[0050]

[0051]

[0052] Steps four through six: After repeated measurements, the mean and uncertainty of the directly measurable physical quantities are shown in Table 2 below:

[0053] Table 2 Uncertainty Test Results

[0054]

[0055] Step 7: For physical quantities that cannot be directly measured, such as the elastic modulus E and moment of inertia I, determine their relationship with other physical quantities. as well as The corresponding uncertainty can be obtained, and the results are shown in Table 2.

[0056] Step 8: Similarly, it can be concluded that... The corresponding uncertainty was obtained, and the results are shown in Table 3.

[0057] Steps 9-11: For the physical quantity ω of interest in the experiment, locate its corresponding accelerometer sensor. Repeat steps 3-6 to obtain the measured value range. Evaluate the accuracy and reproducibility based on the central limit theorem and the uncertainty range of the theoretical and measured values. The results are shown in Table 3. The working conditions 50-S-12-A-156-pa-3 and 50-S-12-A-156-fa-3 represent the test conditions of a 12-meter-long steel rod with a diameter of 50 mm, wrapped with 156 mm diameter foam, undergoing free vibration under simply supported and fixed conditions, respectively. The test site is as follows: Figure 1 As shown.

[0058] Table 3

[0059]

[0060] Although embodiments of the present invention have been disclosed above, they are not limited to the applications listed in the specification and embodiments. They can be applied to various fields suitable for the present invention. For those skilled in the art, other modifications can be easily made. 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 embodiments shown and described herein.

Claims

1. A method for evaluating accuracy and reproducibility based on uncertainty theory, characterized in that, Applicable to test scenarios in structural and marine engineering testing where there is no significant error propagation between sub-steps, including: S1. Determine the physical quantities of interest in the experiment and the related physical quantities involved in the experiment; S2. For directly measurable related physical quantities, repeatedly measure them to obtain their mean and combined uncertainty; for related physical quantities that cannot be directly measured, derive formulas through their relationship with other physical quantities, and use error propagation methods to calculate their mean and combined uncertainty. S3. Obtain the theoretical mean and theoretical combined uncertainty of the physical quantities of interest in the experiment; S4. Obtain the measurement mean and combined measurement uncertainty of the physical quantities of interest in the experiment by means of experimental instruments; S5. Solve the probability by finding the intersection of the intervals of the measurement mean and combined measurement uncertainty of the physical quantity of interest in the experiment with the theoretical mean and combined uncertainty. This will give you the accuracy and reproducibility of the experiment. S5 specifically includes: S51. According to the Central Limit Theorem, the results of repeated tests follow a normal distribution, that is, the distributions of the theoretical and measured values ​​of the physical quantity of interest in the experiment follow a normal distribution. S52. Taking physical quantity A as an example, its accuracy can be assessed as follows: The calculation of the recurrence rate can be regarded as solving a problem. In the interval The probability of the intersection is denoted as qe; the evaluation of the accuracy and reproducibility of physical quantities B and C is the same.

2. The method for evaluating accuracy and reproducibility based on uncertainty theory as described in claim 1, characterized in that, S1 specifically includes: the relevant physical quantities of interest in the experimental results are D, E, F, G, H, J, K, and L; the physical quantities of interest in the experiment are obtained through theoretical analysis, A, B, and C; and assumptions are made. , where a, b, c, m, v, y are constants.

3. The method for evaluating accuracy and reproducibility based on uncertainty theory as described in claim 2, characterized in that, S2 specifically includes: S21. Assuming that physical quantity D cannot be directly measured, deduce the correlation between D and other relevant physical quantities required for other experimental results. ; S22. For directly measurable physical quantities, locate the testing instrument and determine its Type B uncertainty using the manufacturer's instructions or calibration certificate. Assuming the required instruments for measurement are O, P, Q, R, and S, the corresponding Type B uncertainty is: ; S23. Assume that each directly measurable physical quantity E, F, G, H, J, K, L is associated with a Type B uncertainty of its corresponding measuring instrument. ; S24. For directly measurable physical quantities, after repeated measurements and elimination of obviously erroneous data, calculate their mean and standard deviation, which can be expressed as follows: ; S25. Combined Uncertainty Similarly, the mean and combined uncertainty of directly measured physical quantities can be expressed as: ; S26. For a physical quantity D that cannot be directly measured, its relationship with other physical quantities can be used as a reference. It can be seen that, ,in Therefore .

4. The method for evaluating accuracy and reproducibility based on uncertainty theory as described in claim 3, characterized in that, S3 specifically includes: combined uncertainty. , The physical quantity of interest in the experiment can be expressed as At this point, we obtain the theoretical value range of the physical quantity of interest in the experiment under the experimental conditions.

5. The method for evaluating accuracy and reproducibility based on uncertainty theory as described in claim 4, characterized in that, S4 specifically includes: for the physical quantity of interest in the experiment, finding its corresponding testing instruments W, X, and Z, and repeating steps S22 to S25 to obtain the range of measured values ​​obtained in the experiment, denoted as... .

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