Constant-temperature water bath kettle fractional order system parameter identification method with noise measurement function

Abstract

The invention discloses a constant-temperature water bath kettle fractional order system parameter identification method with measurement noise, which comprises the following steps: acquiring input data and output data of a constant-temperature water bath kettle, judging whether pulse noise exists in the output data or not, and constructing a wavelet operation matrix based on a pulse noise judgment result; obtaining a non-periodic time-delay integral operation matrix according to the wavelet operation matrix, and converting the input data and the output data into an input data operation matrix and an output data operation matrix based on the wavelet operation matrix and the non-periodic time-delay integral operation matrix; judging whether Gaussian noise and local noise exist in the output data or not, adjusting a matrix coefficient in an operation matrix corresponding to the output data based on a judgment result, constructing a system model of the constant-temperature water bath kettle, and solving the adjusted system model to obtain an identification result of system model parameters of the constant-temperature water bath kettle. And reflecting the correlation between the input data and the output data of the constant-temperature water bath kettle through the system model of the constant-temperature water bath kettle with the identification result.

Description

Technical Field

[0001] The invention belongs to the technical field of fractional-order system identification and parameter estimation, and in particular relates to a parameter identification method for a constant-temperature water bath fractional-order system with measurement noise. Background Art

[0002] As a pollution-free and intelligent electric thermal energy conversion device, the constant temperature water bath is widely used in the fields of machinery manufacturing, petrochemical industry, food processing industry, etc. With the increasing application demand of constant temperature water bath, its safety performance and temperature control accuracy have become the focus of increasing attention. The control of the temperature of the water bath depends on its mathematical model. However, the water bath has large lag and time-varying characteristics, and the traditional integer-order model cannot accurately characterize the dynamic temperature change characteristics. Fractional calculus has history dependence and memory. Domestic and foreign scholars have proved that the fractional-order model established by fractional calculus can more accurately describe the temperature change process of boilers, heaters and other devices.

[0003] At present, the modeling of fractional-order systems is mainly divided into mechanism modeling and system identification. The system identification method estimates the unknown parameters of the model through the input and output data of the actual physical system. The constructed model is more accurate, so it has received widespread attention from scholars. The existing methods for parameter identification of fractional-order systems mainly include frequency domain subspace method, three-point method, filter approximation method, modulation function method, least squares method, integral operation matrix method, particle swarm, bee colony, ant colony, fish swarm and other swarm intelligence optimization algorithms. Among the above methods, all of them are for parameter identification of fractional-order time-delay systems without measurement noise, and most of the methods remain in the theoretical stage and have not been actually applied in physical systems.

[0004] The fractional-order system parameter identification method based on the integral operation matrix has fast calculation speed and high accuracy, and can simultaneously identify the time-delay coefficient and model parameters. However, the existing integral operation matrices all have fixed sampling periods, and do not specifically discuss and analyze the noise reduction characteristics of the integral operation matrix and how to use the integral operation matrix to identify the parameters of the fractional-order time-delay system with noise. More importantly, in actual engineering, mechanical vibration or sensor failure can cause pulse noise, Gaussian noise or local noise in the collected data, and even data anomalies or data loss. In the presence of the above-mentioned multiple measurement noises and uncertain data, the accuracy of parameter identification will be greatly affected, which will lead to the problem that the system or control model cannot accurately characterize the dynamic temperature change process of the water bath. Summary of the invention

[0005] In order to solve the above technical problems, the present invention proposes a method for identifying the parameters of a fractional-order system of a constant temperature water bath with measurement noise, constructs a non-periodic integral operation matrix, and uses the distribution characteristics of the matrix coefficients to separate the noise and temperature signal of the water bath, so as to solve the problems that the existing fixed-periodic integral operation matrix method cannot accurately estimate the fractional-order system parameters of a constant temperature water bath with measurement noise, and the dynamic change process of the water bath temperature is inaccurately characterized.

[0006] To achieve the above object, the present invention provides a method for identifying parameters of a fractional-order system of a constant temperature water bath with measurement noise, comprising:

[0007] Obtaining input data and output data of a constant temperature water bath, determining whether the output data has impulse noise, and constructing a Legendre wavelet non-periodic operation matrix based on the impulse noise determination result;

[0008] According to the non-periodic Legendre wavelet operation matrix, a non-periodic time-delay integral operation matrix is ​​obtained, and based on the Legendre wavelet non-periodic operation matrix and the non-periodic time-delay integral operation matrix, the input data and the output data are converted into an input data operation matrix and an output data operation matrix;

[0009] Determine whether the output data has Gaussian noise and local noise, and adjust the matrix coefficients in the operation matrix corresponding to the output data based on the determination result, wherein the Gaussian noise and the local noise are set to zero at positions corresponding to the non-periodic operation matrix coefficients;

[0010] A system model of a constant temperature water bath is constructed, the system model is adjusted according to the input data operation matrix and the output data operation matrix of the replacement matrix coefficients, the adjusted system model is solved by the multi-innovation least squares method, and the identification results of the system model parameters of the constant temperature water bath are obtained. The system model of the constant temperature water bath with the identification results reflects the relationship between the input data and the output data of the constant temperature water bath.

[0011] Optionally, the process of determining whether the output data contains impulse noise includes:

[0012]

[0013] Among them, y(t) represents the output data at time t, and σ They represent the mean and standard deviation of the interval in which y(t) lies.

[0014] Optional, Legendre wavelet aperiodic operation matrix for:

[0015]

[0016] in, i=1,2,3…N s , t i represents the non-periodic sampling point time, j i t s is the data moving point, -L / 2N s <j i <L / 2N s ∈Z is the data movement step, N s is the number of wavelet spatial distributions, L is the total length of collected data, t s is the data collection interval, i represents the sampling point number, is the Legendre wavelet function vector, where the data moving step length j i Adjustments are made based on the location of impulse noise in the output data.

[0017] Optional, non-periodic delay integration matrix for:

[0018]

[0019] in represents the non-periodic integral operation matrix;

[0020] Optional, where the non-periodic integration matrix for:

[0021]

[0022] where f 1 =1,f p =p α+1 -2(p-1) α+1 +(p-2) α+1 ,p=2,3…N s , T f represents the data acquisition time, Γ(·) is the gamma function, and α is the fractional-order integral operator.

[0023] Optionally, the process of converting the input data and the output data includes:

[0024] The input data operation matrix is:

[0025]

[0026] The output data operation matrix is:

[0027]

[0028] Among them, u(t i-τ) is the input data for removing the lag time, t is the working time of the water bath, y(t) is the output data, represents the Legendre wavelet non-periodic operation matrix, To calculate the matrix coefficients for the output data, Ψ represents the input data operation matrix coefficient, N s is the number of wavelet space distribution.

[0029] Optionally, the process of adjusting the system model is:

[0030] The system model is:

[0031]

[0032] The system model is adjusted, and the adjusted system model is:

[0033]

[0034] Among them, u(t) is the input data, y(t) is the output data; τ is the lag time, a 1 ,a 2 ,b 0 is the system parameter, β 2 ,β 1 is the fractional order of the system. t is the working time of the water bath, They are the two fractional derivatives of the water bath temperature output.

[0035] Optionally, the input data and output data of the constant temperature water bath are the driving voltage of the water bath heating rod and the boiler temperature data of the water bath, respectively.

[0036] Optionally, the identification results of the system model parameters of the constant temperature water bath are brought into the system model, and a negative feedback control method is used to calculate the adjustment drive voltage corresponding to the adjustment temperature by bringing into the system model after the identification results are brought in. The temperature of the constant temperature water bath is adjusted by adjusting the drive voltage.

[0037] Compared with the prior art, the present invention has the following advantages and technical effects:

[0038] 1. The present invention can accurately identify the parameters of the fractional-order model of a constant temperature water bath, and the constructed model can accurately describe the dynamic change process of temperature.

[0039] 2. The non-periodic sampling principle adopted in the present invention can construct a non-periodic integral operation matrix, which can effectively avoid the influence of impulse noise on parameter identification.

[0040] 3. The present invention can reduce the influence of global Gaussian white noise and local Gaussian white noise on parameter identification and improve the parameter estimation accuracy of the constant temperature water bath model by decomposing and reconstructing the non-periodic integral operation matrix.

[0041] 4. The parameter estimation of the present invention is of high accuracy, and the constructed constant temperature water bath fractional order model can be widely used in the design of intelligent control systems, laying a foundation for the simulation and application of advanced control technologies. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] The drawings constituting a part of the present application are used to provide a further understanding of the present application. The illustrative embodiments and descriptions of the present application are used to explain the present application and do not constitute an improper limitation on the present application. In the drawings:

[0043] Figure 1 is a flow chart of a method for identifying parameters of a fractional-order system of a constant temperature water bath with measurement noise according to an embodiment of the present invention;

[0044] Figure 2 It is a fitting effect diagram of the constant temperature water bath identification model of the embodiment of the present invention and the actual system;

[0045] Figure 3 It is a normalized absolute error diagram of the constant temperature water bath identification model and the actual system under the influence of impulse noise and global Gaussian noise in the embodiment of the present invention;

[0046] Figure 4 It is a normalized absolute error diagram between the constant temperature water bath identification model and the actual system under the influence of impulse noise and local Gaussian noise in the embodiment of the present invention. DETAILED DESCRIPTION

[0047] It should be noted that, in the absence of conflict, the embodiments and features in the embodiments of the present application can be combined with each other. The present application will be described in detail below with reference to the accompanying drawings and in combination with the embodiments.

[0048] It should be noted that the steps shown in the flowcharts of the accompanying drawings can be executed in a computer system such as a set of computer executable instructions, and that, although a logical order is shown in the flowcharts, in some cases, the steps shown or described can be executed in an order different from that shown here.

[0049] The present invention designs a method for identifying the parameters of a fractional-order system of a constant-temperature water bath with measurement noise, comprising the following steps: first, constructing a Legendre wavelet non-periodic integral operation matrix and a non-periodic time-delay integral operation matrix. Then, according to the non-periodic sampling principle, the impulse noise of the output data of the constant-temperature water bath system is removed, and the decomposition and reconstruction method of the wavelet is used to reduce the influence of the global Gaussian white noise and the local Gaussian white noise on the identification of the system parameters. Finally, the fractional-order model of the constant-temperature water bath is converted into an algebraic equation using the non-periodic time-delay integral operation matrix, and the algebraic equation is solved by the multi-innovation least squares iteration method to identify the unknown parameters and fractional orders of the model. The present invention solves the problem that the existing traditional integral operation matrix method cannot accurately estimate the parameters of the fractional-order system of the constant-temperature water bath with measurement noise, and the temperature change process of the water bath is inaccurately characterized.

[0050] The present invention proposes a parameter identification method for a constant temperature water bath fractional-order system with measurement noise, identifies the model parameters of the water bath using a non-periodic integral operation matrix, constructs a precise model of the constant temperature water bath, and realizes an accurate description of the dynamic temperature change process.

[0051] In order to achieve the above object, the technical solution of the present invention is:

[0052] Step 1: Design the non-periodic sampling points of Legendre wavelet and construct the non-periodic integral operation matrix of Legendre wavelet.

[0053]

[0054] where j i t s is the data moving point, -L / 2N s <j i <L / 2N s ∈Z is the data movement step, Z is the integer space, N s is the number of wavelet spatial distributions, L is the total length of collected data, t s is the data collection interval, i represents the sampling point number, t i Indicates non-periodic sampling points.

[0055] The Legendre wavelet non-periodic operation matrix is:

[0056]

[0057] in is the Legendre wavelet function vector, where N s ×N s Represents the corresponding dimensional space.

[0058] Legendre wavelet non-periodic integral operation matrix for:

[0059]

[0060] where f 1 =1,f p =p α+1 -2(p-1) α+1 +(p-2) α+1 ,p=2,3…N s , p represents the fractional order sequence, T f represents the data acquisition time, Γ(·) is the gamma function, and α is the fractional-order integral operator.

[0061] Step 2: Combine the different non-periodic sampling points of the Legendre wavelet non-periodic operation matrix to construct the Legendre wavelet non-periodic time-delay integral operation matrix.

[0062] Legendre wavelet non-periodic delay integral operation matrix It can be expressed as:

[0063]

[0064] Step 3: Divide the output data of the constant temperature water bath temperature into N s intervals, and take the average value of the data in each interval and standard deviation y σ , if the data in the interval is in the output data The output data is abnormal data caused by impulse noise, and the abnormal data is removed by changing the non-periodic sampling point.

[0065]

[0066] Step 4: Utilizing the distribution characteristics of the non-periodic operation matrix coefficients, the temperature output data of the constant temperature water bath with measurement noise is separated from the noise by global decomposition and reconstruction of the matrix coefficients.

[0067] Step 5: To address the problem of local noise in the constant temperature water bath data caused by sensor anomalies, the impact of local noise on parameter identification accuracy is reduced by decomposing and reconstructing the local coefficients of the non-periodic integral operation matrix.

[0068] Step 6: Use the non-periodic integral operation matrix to convert the constant temperature water bath fractional order system into an algebraic equation, and solve the algebraic equation through the multi-innovation least squares method to estimate the model parameters and the fractional order, that is, the identification results of the system model parameters.

[0069] The identification results of the system model parameters of the constant temperature water bath are brought into the system model. The negative feedback control method is used to calculate the adjustment driving voltage corresponding to the adjustment temperature by substituting the system model after the identification results. The temperature of the constant temperature water bath is adjusted by adjusting the driving voltage.

[0070] The above technical solution is elaborated in detail:

[0071] The constant temperature water bath consists of two nested boilers, a heating rod, and a temperature transmitter. The boiler capacity is 3L, the operating voltage is 220V, the operating frequency is 50Hz, and the power control range is 0-2.5KW. The constant temperature water bath system collects input voltage and output temperature data through the Quarc data acquisition card. Since the temperature change has hysteresis and nonlinearity, the fractional order modeling method can more accurately characterize the temperature change process of the constant temperature water bath. In addition, during the data collection process, affected by the sensor, the collected data will contain pulse noise and Gaussian noise. Therefore, the fractional order model is used to describe the constant temperature water bath system with measurement noise.

[0072]

[0073] Where u(t) is the input data, i.e., the driving voltage; y(t) is the output data, i.e., the temperature with noise; τ is the lag time, a 1 ,a 2 ,b 0 is the system parameter, β 2 ,β 1 is the fractional order of the system. t is the working time of the water bath, They are the two fractional derivatives of the water bath temperature output.

[0074] The implementation process of the present invention is as follows Figure 1 As shown. First, the Legendre wavelet non-periodic integral operation matrix and the non-periodic time-delay integral operation matrix are constructed. Then, according to the non-periodic sampling principle, the impulse noise of the collected data is removed, and the decomposition and reconstruction method of the wavelet is used to reduce the influence of the global Gaussian white noise and the local Gaussian white noise on the parameter identification. Finally, the constant temperature water bath fractional order model is converted into an algebraic equation using the non-periodic time-delay integral operation matrix, and the algebraic equation is solved by the multi-innovation least squares iteration method to identify the unknown parameters of the model.

[0075] Step 1: Design the non-periodic sampling points of Legendre wavelet and construct the non-periodic integral operation matrix of Legendre wavelet.

[0076] Explain the basic principle: Any function f(t) can be expanded into the form of Legendre wavelet

[0077]

[0078] in is the scale; c 0,0 is the scaling function coefficient; N s =2 k =512 is the number of wavelet spatial distributions, that is, the number of intervals into which f(t) is decomposed within time t. k,n is the Legendre wavelet coefficient; is the coefficient vector; is the Legendre wavelet function vector, ψ k,n (t) represents Legendre wavelet.

[0079] Designing the non-periodic sampling points of Legendre wavelet function vector

[0080]

[0081] where j i t s is the data moving point, -L / 2N s <j i <L / 2N s ∈Z is the data moving step length, L=5000 is the total length of the collected data, t s =0.01 is the collection interval of identification data.

[0082] Let the Legendre wavelet function vector In t i By taking values ​​at , we can get the Legendre wavelet non-periodic operation matrix:

[0083]

[0084] When N s =8,j i = 0, the sampling points are t i =1 / 16,3 / 16,5 / 16,7 / 16,9 / 16,11 / 16,13 / 16,15 / 16. If the data related to the sampling point is missing or abnormal, such as at t i = If the sampling point data at 3 / 16, 5 / 16, 9 / 16, 13 / 16, and 15 / 16 are abnormal or missing, the data is shifted. First, the sampling point data value point is shifted back by one sampling interval. If the data of the sampling point is abnormal, the sampling point data value point is shifted forward by one sampling interval. If the data of the sampling point is abnormal, the sampling point data value point is shifted back by two sampling intervals. If the data of the sampling point is abnormal, the sampling point data value point is shifted forward by two sampling intervals. This is repeated until there is no abnormal data. 2 ,j 7 ,=1;j3 ,j 5 ,j 8 =-1, indicating t 2 =3 / 16,t 7 =13 / 16 value point is shifted backward by t s ;t 3 =5 / 16,t 5 =9 / 16,t 8 =15 / 16 value point is shifted forward by t s , then the Legendre wavelet non-periodic operation matrix can be expressed as:

[0085]

[0086] If t 3 =5 / 16-t s ,t 5 =9 / 16-t s ,t 7 =13 / 16+t s The data at j is still abnormal, and we can continue to translate until we get reliable data. 3 =-2; j 7 =2; t 3 ,t 7 Move forward and backward 2t respectively s ;j 5 =-3, t 5 Move forward 3t s ,but

[0087]

[0088] The Legendre wavelet non-periodic integral operation matrix can be expressed as

[0089]

[0090] where f 1 =1,f p =p α+1 -2(p-1) α+1 +(p-2) α+1 ,p=2,3…N s , T f =50 represents the data acquisition time, Γ(·) is the gamma function, and α is the fractional-order integral operator.

[0091] Step 2: Combine different non-periodic sampling points of the Legendre wavelet operation matrix to construct the Legendre wavelet non-periodic time-delay integral operation matrix.

[0092] The non-periodic time-delay integral operation matrix is ​​obtained by using the matrix translation method to convert Horizontally shift back j units, combined with the Legendre wavelet non-periodic operation matrix The time lag coefficient τ of the system is calculated from different sampling points in , where j represents the number of translation units.

[0093]

[0094] The Legendre wavelet non-periodic delay integral operation matrix can be expressed as

[0095]

[0096] In formula (4), the first row and the j+1th column of the matrix are 1, the second row and the j+2th column are 1, and so on, and the rest are 0.

[0097] Step 3: Impulse noise is usually much larger or smaller than the actual system output data. If the collected data contains impulse noise, the current data is abnormal data. In order to identify impulse noise and abnormal data, the present invention divides the system output data y(t) into N s interval, t NS-1 represents the last data of the first interval, then y(t) can be expressed as

[0098]

[0099] Take the average of the data in each interval

[0100]

[0101] Where n = L / N s For the number of data in each interval, find the standard deviation of the data in each area

[0102]

[0103] If the data in the interval Then the data is abnormal data caused by impulse noise, that is

[0104]

[0105] Let j in formula (1) i The initial state is 0, using t i Sample the data and determine whether the sampling point is impulse noise according to formula (5). If the sampling point is impulse noise, change j i The value of changes the Legendre wavelet sampling period, and the Legendre wavelet non-periodic operation matrix expression of the output signal is obtained.

[0106]

[0107] in is the output Legendre wavelet non-periodic operation matrix coefficient. The non-periodic sampling characteristics can remove the impulse noise in the identification data.

[0108] The Legendre wavelet non-periodic operation matrix is ​​used to remove abnormal data, and the input data u(t-τ) is expanded through the non-periodic time-delay integral operation matrix.

[0109]

[0110] in The input Legendre wavelet non-periodic operation matrix coefficients.

[0111] Step 4: Utilizing the distribution characteristics of the non-periodic operation matrix coefficients, the temperature output data of the constant temperature water bath with measurement noise is separated from the noise by global decomposition and reconstruction of the matrix coefficients.

[0112] In the constant temperature water bath system, impulse noise can be identified and removed, but Gaussian white noise is inevitable. At this time, the Legendre wavelet variable period integral operation matrix also contains Gaussian noise. Gaussian noise and local noise can be obtained by judging the standard deviation presented by a single formula (13). When the standard deviation of some signals is greater than a certain threshold, such as 0.5, it is considered that noise occurs. If the standard deviation is less than a certain threshold, it is judged as normal signal data. When the noise conforms to the Gaussian distribution, it is considered that Gaussian noise occurs, otherwise it is local noise. According to formula (7), it can be seen that the coefficient of the wavelet determines the degree of data fitting. The larger the Legendre wavelet spatial distribution coefficient k is, the higher the distribution frequency is. Gaussian white noise also has a higher frequency. Therefore, the high-frequency wavelet coefficient can characterize Gaussian noise. The present invention uses a method for decomposing the global coefficient of the non-periodic operation matrix to discard the high-frequency Legendre wavelet coefficient in the matrix, so that the real data can be separated from the Gaussian noise.

[0113] When N s =512, using formula (7) to expand the system output data y(t) into

[0114]

[0115] According to formula (5), the abnormal data in y(t) are marked and the abnormal data in y(t) are marked by changing j i The value of removes abnormal data. Combined with formula (14), formula (16) can be rewritten as

[0116]

[0117] It can be seen from formula (17) that the Legendre wavelet non-periodic operation matrix is ​​unchanged, and any function can be constructed by changing the matrix coefficients.

[0118] The Gaussian noise and local noise are obtained by using the above noise judgment method through the collected data to obtain the relevant noise position. Assuming that all Gaussian white noise is projected into the high-frequency Legendre wavelet with k=9, then y 9,1 ,y 9,2 ,…,y 9,256 Represents the Gaussian white noise coefficient. The present invention sets these coefficients to 0, and the Legendre wavelet non-periodic operation matrix coefficient becomes

[0119]

[0120] If the output data is greatly affected by Gaussian noise, the matrix coefficients can be further decomposed. becomes

[0121]

[0122] Using the matrix coefficients of formula (19) to reconstruct the output data, the real data can be separated from the Gaussian noise, reducing the impact of Gaussian noise on system identification. The output data reconstruction equation is

[0123]

[0124] Step 5: To address the problem of local noise in the constant temperature water bath data caused by sensor anomalies, the influence of local noise on parameter identification accuracy is reduced by decomposing and reconstructing the local coefficients of the non-periodic integral operation matrix.

[0125] During the system identification data collection process, external vibration will cause noise in the local data. The local noise is M = [t a ,t b ], t a and t b By calculating the distribution of local noise M in the data acquisition time t and combining the Legendre wavelet spatial distribution coefficient k, the present invention can obtain the distribution M of M in the wavelet coefficients. k_c , and the number of wavelet coefficients of local noise M k

[0126]

[0127] Among them, M k_c The wavelet coefficients and M k All are integers.

[0128] Assume that the input data y(t) has noise in the interval [0.5t,t], and also at t i Sampling at , we get the Legendre wavelet non-periodic operation matrix, discarding the wavelet coefficients of local noise, that is

[0129]

[0130] If the input data y(t) has noise in [0.3t,0.8t], then

[0131]

[0132] Reconstruct the output signal using the matrix coefficients of formula (23)

[0133]

[0134] Step 6: Use the non-periodic integral operation matrix to convert the constant temperature water bath fractional order system into an algebraic equation, and solve the algebraic equation through the multi-innovation least squares method to estimate the model parameters and fractional order.

[0135] Rewrite the constant temperature water bath fractional order system (Formula (6)) using the non-periodic integral operation matrix

[0136]

[0137] make

[0138] A(N s ) and B(N s ) is the known parameter matrix, X(N s ) is the unknown parameter matrix.

[0139] Using the multi-innovation theory, the first known parameter matrix A(N s ) and the second known parameter matrix B(N s ) is expanded into a multi-innovation matrix.

[0140]

[0141] Where p=5 is the multi-innovation length.

[0142] The process of solving the fractional-order algebraic equation of the constant temperature water bath with multiple innovations can be expressed as

[0143]

[0144] Where E(p,N s ) and P(N s) are the multi-innovation error matrix and gain matrix of the constant temperature water bath, respectively. By iterating formula (27), the model parameters and fractional orders can be accurately identified. The identification results are as follows

[0145] 120.6069D 2.3 y(t)+16.3437D 1.05 y(t)+y(t)=16.7012u(t-0.3516) (28)

[0146] The main function of a constant temperature water bath is to enable the boiler to reach the set temperature quickly, accurately and stably. Therefore, the premise for effective boiler temperature control is to build an accurate constant temperature water bath model. This patent uses the driving voltage u(t) of the water bath heating rod as input data, and inputs it into the constant temperature water bath system with measurement noise shown in formula (28). The boiler temperature data of the constant temperature water bath is output in real time. By comparing it with the set temperature, the real-time temperature error is obtained, and then the feedback control method is used to change the driving voltage of the heating rod in real time to achieve dynamic adjustment of the boiler temperature.

[0147] Figure 2 It shows that when the actual temperature data is affected by Gaussian noise and impulse noise, the non-periodic integral operation matrix (VPIOM) method proposed in this patent can still accurately identify the model parameters and fractional orders of the constant temperature water bath system, and the constructed fractional-order model can accurately characterize the temperature change process.

[0148] Figure 3 It shows that when global Gaussian white noise and impulse noise with SNR=30dB coexist, the global matrix coefficient decomposition and reconstruction method proposed in this patent can effectively improve the system parameter identification accuracy, and can effectively judge and remove abnormal data through non-periodic sampling, reducing its impact on the parameter identification process. Figure 4 It can be seen that even when local Gaussian white noise with SNR=30dB and impulse noise coexist, by continuously decomposing the VPIOM coefficient, the noise at the value point is continuously reduced and the recognition accuracy is continuously improved.

[0149] The above are only preferred specific implementations of the present application, but the protection scope of the present application is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed in the present application should be included in the protection scope of the present application. Therefore, the protection scope of the present application should be based on the protection scope of the claims.

Claims

1. A method for identifying parameters of a fractional-order system of a constant temperature water bath with measurement noise, characterized in that: include: Obtaining input data and output data of a constant temperature water bath, determining whether the output data has impulse noise, and constructing a Legendre wavelet non-periodic operation matrix based on the impulse noise determination result; According to the Legendre wavelet non-periodic operation matrix, a non-periodic time-delay integral operation matrix is ​​obtained, and based on the Legendre wavelet non-periodic operation matrix and the non-periodic time-delay integral operation matrix, the input data and the output data are converted into an input data operation matrix and an output data operation matrix; Determine whether the output data has Gaussian noise and local noise, and adjust the matrix coefficients in the operation matrix corresponding to the output data based on the determination result, wherein the Gaussian noise and the local noise are set to zero at positions corresponding to the non-periodic operation matrix coefficients; A system model of a constant temperature water bath is constructed, the system model is adjusted according to the input data operation matrix and the output data operation matrix of the replacement matrix coefficients, the adjusted system model is solved by the multi-innovation least squares method, and the identification results of the system model parameters of the constant temperature water bath are obtained. The system model of the constant temperature water bath with the identification results reflects the relationship between the input data and the output data of the constant temperature water bath.

2. The method according to claim 1, characterized in that: The process of determining whether the output data has impulse noise includes: Among them, y(t) represents the output data at time t, and σ They represent the mean and standard deviation of the interval where y(t) lies.

3. The method according to claim 1, characterized in that Legendre wavelet non-periodic operation matrix for: in, i=1,2,3…N s , t i represents the non-periodic sampling point time, j i t s is the data moving point, -L / 2N s <j i <L / 2N s ∈Z is the data movement step, N s is the number of wavelet spatial distributions, L is the total length of collected data, t s is the data collection interval, i represents the sampling point number, is the Legendre wavelet function vector, where the data moving step length j i Adjustments are made based on the location of impulse noise in the output data.

4. The method according to claim 3, characterized in that Non-periodic time-delay integral operation matrix for: in Represents a non-periodic integral operation matrix.

5. The method according to claim 4, characterized in that in, Non-periodic integral operation matrix for: Where f1=1,f p =p α+1 -2(p-1) α+1 +(p-2) α+1 ,p=2,3…N s , T f represents the data acquisition time, Γ(·) is the gamma function, and α is the fractional-order integral operator.

6. The method according to claim 1, characterized in that The process of converting the input data and the output data into: The input data operation matrix is: The output data operation matrix is: Among them, u(t i -τ) is the input data for removing the lag time, t is the working time of the water bath, y(t) is the output data, represents the Legendre wavelet non-periodic operation matrix, To calculate the matrix coefficients for the output data, Ψ represents the input data operation matrix coefficient, N s is the number of wavelet space distribution.

7. The method according to claim 1, characterized in that The process of adjusting the system model is: The system model is: The system model is adjusted, and the adjusted system model is: Where u(t) is the input voltage, y(t) is the temperature output with noise, τ is the lag time, a1, a2, b0 are system parameters, β2, β1 are the system fractional orders. t is the working time of the water bath, They are the two fractional derivatives of the water bath temperature output.

8. The method according to claim 1, characterized in that: The input data and output data of the constant temperature water bath are the driving voltage of the water bath heating rod and the boiler temperature data of the water bath respectively.

9. The method according to claim 1, characterized in that: The identification results of the system model parameters of the constant temperature water bath are brought into the system model, and the negative feedback control method is used to calculate the adjustment driving voltage corresponding to the adjustment temperature by bringing into the system model after the identification results are brought in. The temperature of the constant temperature water bath is adjusted by adjusting the driving voltage to achieve temperature regulation of the constant temperature water bath.

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