Step rise time identification method based on quasi-second-order response

Abstract

The present invention provides a step rise time identification method based on quasi-second-order response, comprising the following steps: (1) reading step test data to obtain a set of disturbed data containing a time series; (2) constructing a quasi-second-order response function; (3) solving the undetermined coefficients in the quasi-second-order response function using a genetic function so that the variance between the fitted function and the original data is minimized; (4) based on the obtained undetermined coefficients, taking the moment when the data on the quasi-second-order response function reaches a final value of 0.9 as the rise time. The present invention identifies the rise time by calculating the quasi-second-order response function, thereby avoiding errors caused by manual interpretation based on experience. The present invention is suitable for performance testing and parameter setting of various control systems.

Description

Technical Field

[0001] The present invention relates to a method for identifying test data containing disturbance, in particular to a method for identifying step rise time based on quasi-second-order response. Background Art

[0002] When performing step tests on automated control systems, the rise time is defined as the time it takes for the output response to reach 90% of the step value. This reflects system performance and is a crucial test metric. However, actual field tests are inevitably affected by various environmental interference factors, and the test data contains a certain amount of disturbance. Without data processing, directly reading the step rise time from raw data can result in significant errors. Summary of the Invention

[0003] In response to the above-mentioned deficiencies in the prior art, the present invention proposes a step rise time identification method based on quasi-second-order response. By fitting a quasi-second-order response function to the step curve, the influence of the disturbance data can be eliminated while retaining all the information of the original data, and the rise time can be accurately identified.

[0004] A step rise time identification method based on quasi-second-order response includes the following steps:

[0005] Read the step response test data to obtain a set of time series noise data with a step amount a and an initial value f:

[0006] X={t i ,x i},i=1,2,…,n (1)

[0007] where t i is an equally spaced time series with a time series interval of Δt, x i is a data sequence, n is a positive integer greater than or equal to 3;

[0008] Construct the following quasi-second-order response function:

[0009] f(t)=a*(1-be -ct sin(dt+e))+f (2)

[0010] Where a is the step amount, f is the initial value of the step, b, c, d, e are the coefficients to be determined;

[0011] The genetic algorithm based on population migration is used to solve the unknown coefficients b, c, d, and e in the quasi-second-order response function so that the variance of the fitted function and the original data is

[0012]

[0013] Reach a minimum value;

[0014] Based on the obtained undetermined coefficients b, c, d, and e, the time t at which the data reaches the final value of 0.9 is taken from the pseudo-second-order response function. up is the rise time:

[0015] t up =t j |f(t j )=0.9a+f (4).

[0016] Furthermore, the method of using a genetic algorithm based on population migration to solve the unknown coefficients b, c, d, and e in the quasi-second-order response function specifically includes:

[0017] 1) Generate the first generation of individuals;

[0018] 2) Calculate the objective function according to formula (2) and formula (3):

[0019]

[0020] 3) Compare the objective function values ​​of each individual, select the largest 50% individuals for crossover, and generate a new 50% of individuals;

[0021] 4) Randomly generate 50% individuals;

[0022] 5) Merge the individuals from step 3) and step 4) into a new generation group;

[0023] 6) Calculate the objective function of the new generation group according to formula (5);

[0024] 7) If the objective function does not decrease after 200 iterations, end the calculation; otherwise, jump to step 3);

[0025] 8) After the calculation is completed, the b, c, d, and e of the individual with the smallest objective function are the solved values.

[0026] The present invention has the following beneficial effects:

[0027] 1. The quasi-second-order response function is used for approximation, which is consistent with the actual system characteristics and makes the identification results more credible;

[0028] 2. It has strong anti-interference performance and can accurately calculate the rise time in the presence of data disturbance;

[0029] 3. Using a genetic algorithm based on population migration to solve the problem can avoid local convergence and minimize the variance of the approximated function. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 This is a test data diagram of one embodiment of the rise time identification method based on the pseudo-second-order response function of the present invention;

[0031] Figure 2 It is a comparison diagram of the pseudo-second-order response function curve calculated by the present invention and the original data;

[0032] Figure 3 It is the convergence curve of the iterative objective function of the genetic algorithm using population migration;

[0033] Figure 4 It is a flow chart of the genetic algorithm based on population migration in the present invention. DETAILED DESCRIPTION

[0034] The technical solutions of the present invention will be described clearly and completely below with reference to the accompanying drawings of the present invention.

[0035] An embodiment of the present invention provides a step rise time identification method based on a pseudo-second-order response, the method comprising the following steps:

[0036] Read the step test data and get a set of time series noise data with step amount a and initial value f (such as Figure 1 shown):

[0037] X={t i ,x i},i=1,2,…,n (1)

[0038] where t i is an equally spaced time series with a time series interval of Δt; x i is a data sequence.

[0039] (2) Construct the following quasi-second-order response function:

[0040] f(t)=a*(1-be -ct sin(dt+e))+f (2)

[0041] Where a is the step amount, f is the initial step value, and b, c, d, and e are unknown coefficients.

[0042] (3) Solve b, c, d, and e using a genetic algorithm based on population migration, so that the variance of the fitted function and the original data is:

[0043]

[0044] Reached minimum value.

[0045] The genetic algorithm based on population migration is used to solve the unknown coefficients b, c, d, and e in the quasi-second-order response function, which specifically includes the following steps (such as Figure 4 shown):

[0046] 1) Generate the first generation of individuals;

[0047] 2) Calculate the objective function according to formula (2) and formula (3):

[0048]

[0049] 3) Compare the objective function values ​​of each individual, select the smallest first 50% individuals for crossover, and generate a new 50% of individuals;

[0050] 4) Randomly generate 50% individuals;

[0051] 5) Merge the individuals in steps 3) and 4) into a new generation group;

[0052] 6) Calculate the objective function of the new generation group according to formula (4);

[0053] 7) If the objective function does not decrease after 200 iterations, end the calculation; otherwise, jump to step 3);

[0054] 8) After the calculation is completed, the b, c, d, and e of the individual with the smallest objective function are the solved values.

[0055] Finally, from the fitting function, the moment when the data reaches 0.9% of the step amount is taken as the rise time:

[0056] t up =t j |f(t j )=0.9a+f.

[0057] The method is further described below with reference to the accompanying drawings and a specific example:

[0058] A synchronous generator excitation system performs a step-down response test on the terminal voltage. After giving the excitation reference voltage a step-down signal, the terminal voltage step data is measured as follows: Figure 1 Read the step test data and get a set of disturbed data containing time series as shown in Table 1. The initial value f of the test experiment is 20020, and the step amount a is 1003:

[0059] Table 1

[0060]

[0061]

[0062]

[0063]

[0064]

[0065]

[0066] Construct the following quasi-second-order response function:

[0067] f(t)=1003*(1-be -ct sin(dt+e))+20020, where b, c, d, and e are unknown coefficients.

[0068] According to the genetic algorithm, 20,000 first-generation individuals are randomly generated, and then the genetic algorithm based on population migration is used to calculate the minimum objective function value of each generation of individuals as follows:

[0069] Table 2

[0070] Algebra Objective function value 1-5 280308.9135 6-18 250456.9126 19-52 165248.4957 53-156 143907.1285 157-171 133614.8629 172-257 113804.9286 258-393 117013.5759

[0071] The convergence diagram of the objective function is as follows Figure 3 After the calculation converges, the individual with the smallest objective function is selected, and the values ​​of each item are as follows:

[0072] Table 3

[0073] project Numerical b 14.79 c 1.82 d 0.1 e 3.068 SSE 1.17e5

[0074] From Table 3, we can get the quasi-second-order response function:

[0075] f(t)=1003*(1-14.78e -1.82t sin(0.1t+3.068))+20020

[0076] Figure 2 Comparison diagram of the pseudo-second-order response function and the original data.

[0077] When f(t) = 0.9*a + f = 0.9*1003 + 20020 = 20972.85, t = 0.3485s can be obtained from the curve, which is the rise time.

[0078] The above description is merely a specific embodiment of the present invention. However, the scope of protection of the present invention is not limited to generator excitation system step response testing. Any step response test for an automated control system falls within the technical scope of the present invention. Any modifications or substitutions readily conceivable by those skilled in the art within the technical scope disclosed herein are also encompassed within the scope of protection of the present invention. Therefore, the scope of protection of the present invention should be determined by the scope of protection of the claims.

Claims

1. A step rise time identification method based on quasi-second-order response, characterized in that The steps include: The machine-end voltage step data obtained by performing a step response test on the machine-end voltage is read to obtain a set of disturbed data containing a time series with a step amount a and an initial value f: X={t i ,x i },i=1,2,…,n (1) where t i is an equally spaced time series with a time series interval of Δt, x i is a data sequence, n is a positive integer greater than or equal to 3; Construct the following quasi-second-order response function: f(t)=a*(1-be -ct sin(dt+e))+f (2) Among them, a is the step amount, f is the initial value of the step, and b, c, d, and e are unknown coefficients; The genetic algorithm based on population migration is used to solve the unknown coefficients b, c, d, and e in the quasi-second-order response function so that the variance of the fitted function and the original data is Reach a minimum value; Based on the obtained unknown coefficients b, c, d, and e, take the time t when the data reaches the final value of 0.9 from the pseudo-second-order response function up For the rise time: t up =t j |f(t j )=0.9a+f (4)。 2. The step rise time identification method based on quasi-second-order response according to claim 1, characterized in that: The method of solving the unknown coefficients b, c, d, and e in the quasi-second-order response function using a genetic algorithm based on population migration specifically includes: 1) Generate the first generation of individuals; 2) Calculate the objective function according to formula (2) and formula (3): 3) Compare the objective function values ​​of each individual, select the largest 50% individuals for crossover, and generate a new 50% of individuals; 4) Randomly generate 50% individuals; 5) Merge the individuals in step 3) and step 4) into a new generation group; 6) Calculate the objective function of the new generation group according to formula (5); 7) If the objective function does not decrease after 200 iterations, end the calculation, otherwise jump to step 3); 8) After the calculation is completed, the b, c, d, and e of the individual with the smallest objective function are the solved values.

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