Step time identification method based on broken line function fitting

Abstract

The present invention provides a step time identification method based on broken line function fitting, comprising the following steps: (1) reading step response test data to obtain a set of disturbed data containing a time series; (2) constructing a broken line function; (3) solving the parameters of the broken line function using a genetic algorithm based on population fusion so as to minimize the data variance, and taking the moment at the turning point of the broken line function as the step time. The present invention identifies the step time by fitting a broken line function, thereby avoiding the error caused by manual interpretation based on experience, and can identify the step time in the presence of disturbed data, thereby achieving accurate interpretation of the test data and improving the accuracy of the test data interpretation.

Description

Technical Field

[0001] The invention relates to a method for identifying test data containing disturbance, in particular to a step time identification method based on broken line function fitting. Background Art

[0002] When performing step tests on automatic control systems such as PSS, the performance indicators of the system, such as the rise time and adjustment time, are based on the step time. However, in actual field tests, it is inevitable to be affected by various interference factors in the environment. The test data contains a certain amount of disturbance, making the step time difficult to identify. If data processing is not performed, directly reading the step time with the original data will cause a large error. Summary of the invention

[0003] The present invention provides a step time identification method based on broken line function fitting, which is aimed at a step curve obtained in a step test, can identify the step time in the presence of interference data, achieve accurate interpretation of the test data, and improve the accuracy of the test data interpretation.

[0004] A step time identification method based on broken line function fitting includes the following steps:

[0005] Step 1: Read the step response test data to obtain a set of disturbed data containing time series:

[0006] X={t i ,x i},i=1,2,…,n, n≥3 (1)

[0007] where t i is an equally spaced time series with a time series interval of Δt, x i is the data sequence, n is the data length;

[0008] Step 2: Construct the following broken line function:

[0009]

[0010] Among them, y0, x1, y1, y2 are the coefficients to be determined, x0, x2 are the starting time of the specified identification area, t is the test time, and the obtained x1 is the time corresponding to the turning point;

[0011] Step 3: Use a genetic algorithm based on population fusion to solve y0, x1, y1, y2 so that the variance of the fitted function and the original step test data is:

[0012]

[0013] To reach the minimum value, the value of x1 at the turning point of the broken line function is taken as the step time.

[0014] Furthermore, the specific steps of step three include:

[0015] 1) Generate the first generation of individuals;

[0016] 2) Randomly generate the same number of new individuals;

[0017] 3) merging the individuals generated in step 2) and the original population into a new generation population;

[0018] 4) Calculate the objective function according to formula (2) and formula (3):

[0019]

[0020] 5) If the minimum value of the objective function of all individuals does not decrease after 100 iterations, end the calculation and jump to step 8), otherwise jump to step 6);

[0021] 6) Compare the objective function values ​​of each individual, select the 50% individuals with the smallest objective function values ​​for crossover, generate a new 50% of individuals, and eliminate the remaining individuals;

[0022] 7) Skip to step 2);

[0023] 8) After the calculation is completed, the optimal individual, that is, the x1 value with the smallest objective function, is taken as the step moment.

[0024] The present invention has the following beneficial effects:

[0025] 1. The broken line function is used for approximation, which conforms to the actual characteristics of the step function at the step point, making the identification result more credible;

[0026] 2. Use a genetic algorithm based on population fusion to solve the problem. This method first introduces a new population fusion and then performs elimination and crossover operations, which can better avoid local convergence. BRIEF DESCRIPTION OF THE DRAWINGS

[0027] Figure 1 This is a test data diagram of one embodiment of the step time identification method based on broken line function fitting of the present invention;

[0028] Figure 2 It is a broken line function curve graph calculated by the present invention;

[0029] Figure 3 It is the convergence curve of the objective function iteratively using the population fusion genetic algorithm;

[0030] Figure 4 It is a flow chart of the population fusion genetic algorithm of the present invention. DETAILED DESCRIPTION

[0031] The technical solution of the present invention will be clearly and completely described below in conjunction with the accompanying drawings of the present invention.

[0032] An embodiment of the present invention provides a step time identification method based on broken line function fitting, the method comprising the following steps:

[0033] Step 1: Read the step test data to obtain a set of disturbed data containing time series with a step amount of a and an initial value of f:

[0034] X={t i ,x i},i=1,2,…,n,n≥3; (1)

[0035] where t i is an equally spaced time series with a time series interval of Δt; x i is the data sequence, and n is the data length.

[0036] Step 2: Construct the following broken line function:

[0037]

[0038] Among them, y0, x1, y1, y2 are the coefficients to be determined, x0, x2 are the starting time of the specified identification area, t is the test time, and the obtained x1 is the time corresponding to the turning point;

[0039] Step 3: Use a genetic algorithm based on population fusion to solve y0, x1, y1, y2 so that the fitted function and the original data and variance are

[0040]

[0041] To reach the minimum value, the value of x1 at the turning point of the broken line function is taken as the step time.

[0042] Among them, see Figure 4 , the specific steps of step three are:

[0043] 1) Generate the first generation of individuals;

[0044] 2) Randomly generate the same number of new individuals;

[0045] 3) merging the individuals generated in step 2) and the original population into a new generation population;

[0046] 4) Calculate the objective function according to formula (2) and formula (3):

[0047]

[0048] 5) If the minimum value of the objective function of all individuals does not decrease after 100 iterations, end the calculation and jump to step 8), otherwise jump to step 6).

[0049] 6) Compare the objective function values ​​of each individual, select the 50% individuals with the smallest objective function values ​​for crossover, generate a new 50% of individuals, and eliminate the remaining individuals;

[0050] 7) Skip to step 2);

[0051] 8) After the calculation is completed, the x1 value of the optimal individual (with the smallest objective function) is taken as the step moment.

[0052] The method is further described below with reference to the accompanying drawings and a specific example:

[0053] A synchronous generator excitation system conducts a voltage step response test on the PSS. After giving the excitation reference voltage a step signal, the voltage step data at the machine end is measured. Figure 1 As shown. Read the step test data and get a set of disturbed data containing time series as follows:

[0054] Table 1

[0055]

[0056]

[0057]

[0058]

[0059]

[0060]

[0061] From the curve, we can see that the step time is around 12800, and the starting time of the identification area is selected from 10000 to 13000. The following broken line function can be constructed (such as Figure 2 shown):

[0062]

[0063] Among them, y0, x1, y1, and y2 are unknown coefficients.

[0064] According to the genetic algorithm, 20,000 first-generation individuals are randomly generated, and then step three is used to calculate the minimum objective function value of each generation of individuals as follows:

[0065] Table 2

[0066] Algebra Objective function value 1 65628.83 6 47498.03 7 36823.63 8 23022.86 17 14602.17 31 11694.55 81 9351.558 97 8308.014 188 8057.265 221 8033.647 230 7927.816 291 7759.282 314 7696.086 333 7684.761 339 7668.266 386 7455.947 440 7238.037 444 7207.833 545 7192.159

[0067] The objective function convergence diagram is as follows Figure 3After the calculation converges, the individual with the smallest objective function is selected, and the values ​​of each item are as follows:

[0068] Table 3

[0069] project Numeric <![CDATA[y0]]> 20028.46 <![CDATA[x1]]> 12777.63 <![CDATA[y1]]> 20025.84 <![CDATA[x2]]> 19511.59 SSE 7192.16

[0070] The x1 of this individual is 12777.63 (ms), so 12.77s is taken as the step time.

[0071] The present invention proposes a step time identification method based on a broken angle function. By fitting a broken line function to a step curve, the influence of disturbance data can be eliminated while retaining all the information of the original data, and the step time can be accurately identified.

[0072] The above is only a specific implementation of the present invention, but the protection scope of the present invention is not limited to the step response test of the PSS system. The step response test of any automated control system is included in the technical field of the present invention. Changes or substitutions that can be easily thought of by technicians in this technical field within the technical scope disclosed by the present invention should be covered within the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A step time identification method based on broken line function fitting, characterized in that The steps include: Step 1: Read the step response test data to obtain a set of disturbed data containing time series: X={t i ,x i },i=1,2,…,n, n≥3 (1) where t i is an equally spaced time series with a time series interval of Δt, x i is the data sequence, n is the data length; Step 2: Construct the following broken line function: Among them, y0, x1, y1, y2 are the coefficients to be determined, x0, x2 are the starting time of the specified identification area, t is the test time, and the obtained x1 is the time corresponding to the turning point; Step 3: Use a genetic algorithm based on population fusion to solve y0, x1, y1, y2 so that the variance of the fitted function and the original step test data is: To reach the minimum value, the value of x1 at the turning point of the broken line function is taken as the step time.

2. The step time identification method based on broken line function fitting according to claim 1, characterized in that: The specific steps of step three include: 1) Generate the first generation of individuals; 2) Randomly generate the same number of new individuals; 3) merging the individuals generated in step 2) and the original population into a new generation population; 4) Calculate the objective function according to formula (2) and formula (3): 5) If the minimum value of the objective function of all individuals does not decrease after 100 iterations, end the calculation and jump to step 8), otherwise jump to step 6); 6) Compare the objective function values ​​of each individual, select the 50% individuals with the smallest objective function values ​​for crossover, generate a new 50% of individuals, and eliminate the remaining individuals; 7) Skip to step 2); 8) After the calculation is completed, the optimal individual, that is, the x1 value with the smallest objective function, is taken as the step moment.

Images