Measurement-based dynamic system stability essential feature estimation method and device

Abstract

The invention provides a measurement-based dynamic system stability essential characteristic estimation method and device. The method comprises the following steps: acquiring a measurement result of any state variable or output variable of a dynamic system in a stable state containing noise in system input; based on the measurement result of the state variable or the output variable, obtaining an estimation result of the dynamic system noise response statistical characteristic; wherein the dynamic noise response statistical characteristics comprise variance, an auto-covariance function, a mean value, skewness, kurtosis and range; based on the estimation result of the noise response statistical characteristics of the dynamic system, obtaining the estimation result of the stable essential characteristics of the dynamic system; wherein the dynamic system stable essential feature comprises a system feature root. According to the method, on the basis of a measurement result of any state variable or output variable of a dynamic system in a stable state containing noise in system input, noise response statistical characteristics and stable essential characteristics of the dynamic system are estimated; the method solves the problem that the random response statistical characteristics and the stable essential characteristics of the dynamic system under the noise effect are difficult to estimate, can efficiently calculate the statistical characteristics and the stable essential characteristics of the dynamic system, and facilitates the stability analysis of the subsequent dynamic system and the dynamic analysis and stability judgment based on the random response statistical characteristics.

Description

Technical Field

[0001] The present invention relates to the technical field of statistical physics, and in particular to a method and device for estimating the stable essential characteristics of a dynamic system based on measurement. Background Art

[0002] In the field of statistical physics and critical transition research, the statistical characteristics of the random response of dynamic systems under noise have always been one of the key topics. When a system is disturbed by external noise, its response contains rich information, which can reflect the characteristics and state of the system, including but not limited to the stability of the system, the parameters of the system, etc., which helps to understand and predict the behavior of complex systems.

[0003] However, current related research is often computationally complex and inaccurate when it comes to obtaining the statistical characteristics of random responses of dynamic systems under noise based on actual measurement data, and most of them are unable to obtain the stable essential characteristics of the system, and their applicability is limited when dealing with actual systems.

[0004] Therefore, how to solve the problem that existing technologies cannot accurately and efficiently estimate the statistical characteristics of random responses and the essential characteristics of stability of dynamic systems under noise based on actual measurement data is an important issue that needs to be urgently addressed in the field of statistical physics. Summary of the invention

[0005] The present invention provides a method and device for estimating the stable essential characteristics of a dynamic system based on measurement, which is used to solve the problem that the prior art cannot accurately and efficiently estimate the random response statistical characteristics and stable essential characteristics of a dynamic system under noise based on actual measurement data. The method and device can efficiently calculate its statistical characteristics and stable essential characteristics, which is helpful for subsequent stability analysis of the dynamic system and dynamic analysis and stability judgment based on random response statistical characteristics.

[0006] On the one hand, the present invention provides a method for estimating the stable essential characteristics of a dynamic system based on measurement, comprising: obtaining the measurement results of any state variable or output variable of the dynamic system in a stable state in which the system input contains noise; based on the measurement results of the state variable or output variable, obtaining the estimation results of the statistical characteristics of the noise response of the dynamic system; wherein the statistical characteristics of the dynamic noise response include variance, autocovariance function, mean, skewness, kurtosis and range; based on the estimation results of the statistical characteristics of the noise response of the dynamic system, obtaining the estimation results of the stable essential characteristics of the dynamic system; wherein the stable essential characteristics of the dynamic system include the system characteristic roots.

[0007] Furthermore, the acquisition of the measurement result of any state variable or output variable of the dynamic system in a steady state with noise in the system input includes: according to a given time constant, a relative error limit and its correspondingm - The multiple of the standard deviation in the -sigma criterion is used to determine the observation window length of the system measurement; according to the observation window length of the system measurement and the sampling interval, the number of sampling points is determined; and equidistant sampling is performed according to the observation window length, the sampling interval, and the number of sampling points to obtain the measurement result of the state variable or the output variable.

[0008] Further, based on the measurement result of the state variable or the output variable, an estimation result of the statistical characteristics of the dynamic system noise response is obtained, including: calculating the estimation result of the variance and the estimation result of the autocovariance function through the first formula group; in the case where the calculation speed of the first formula group is lower than the set speed or the calculation time is higher than the set duration, calculating the estimation result of the variance and the estimation result of the autocovariance function through the second formula group; and calculating the estimation results of the mean, skewness, kurtosis, and range through the third formula group.

[0009] Further, based on the estimation result of the statistical characteristics of the dynamic system noise response, an estimation result of the stable essential characteristics of the dynamic system is obtained, including: solving the discrete poles based on the estimation result of the autocovariance function; obtaining the estimation result of the system characteristic root parameters according to the discrete poles; and taking the opposite of the estimation result of the system characteristic root parameters to obtain the estimation result of the system characteristic roots.

[0010] Further, the solving of the discrete poles based on the estimation result of the autocovariance function includes: determining the model order of the autocovariance function waveform fitting according to the estimation result of the autocovariance function and selecting the fitting length; wherein, the fitting length covers the key features of the autocovariance function waveform and the fitting length is greater than or equal to the sum of the model order and the numerator order plus one; extracting the first fitting length data points in the estimation result of the autocovariance function to obtain a discrete sequence; based on the discrete sequence, constructing and solving a linear equation set according to the fitting length, the numerator order, and the model order to obtain the denominator coefficients; performing matrix multiplication on the denominator coefficients and the discrete sequence to obtain the numerator coefficients; constructing a polynomial fraction according to the denominator coefficients and the numerator coefficients and performing root extraction on the polynomial fraction to obtain the discrete poles.

[0011] Further, it further includes: solving the estimation result of the algebraic coefficients based on the estimation result of the autocovariance function; and obtaining the fitting curve of the autocovariance function according to the estimation result of the algebraic coefficients and the estimation result of the system characteristic roots; wherein, the estimation result of the algebraic coefficients and the fitting curve of the autocovariance function are both included in the statistical characteristics of the dynamic system noise response.

[0012] Further, the first formula group specifically includes: The estimation formula for variance: ; Estimation formula for autocovariance function: ; The second set of formulas specifically includes: Estimation formula for autocovariance function: ; ; ; ; Estimation formula for variance: ; The third set of formulas specifically includes: Estimation formula for mean: ; Estimation formula for skewness: ; Estimation formula for kurtosis: ; Estimation formula for range: ; Among them, is the variance, is the number of sampling points, is the current sampling point, is the measurement result of the state variable or output variable, is the autocovariance function, is the time interval, is the sampling interval, is the sequence length of the estimated result of the autocovariance function to be observed, is the inverse fast Fourier transform, is the fast Fourier transform, is the length of the discrete sequence obtained by padding zeros to the measurement result of the state variable or output variable, is the mean, is the skewness, is the kurtosis, is the range.

[0013] Furthermore, when the order of the numerator is equal to the order of the model, the fitting curve of the autocovariance function is defined as follows: ; When the order of the numerator is less than the order of the model, the fitting curve of the autocovariance function is defined as follows: ; Among them, is the fitting curve of the autocovariance function, is the estimation result of the algebraic coefficients, is the estimation result of the system characteristic roots, is the model order.

[0014] In a second aspect, the present invention further provides a device for estimating the stable essential characteristics of a dynamic system based on measurement, including: a system state variable or output variable measurement module, configured to obtain the measurement result of any state variable or output variable of the dynamic system in a stationary state where the system input contains noise; a dynamic system noise response statistical characteristic estimation module, configured to obtain an estimation result of the dynamic system noise response statistical characteristics based on the measurement result of the state variable or output variable; wherein, the dynamic noise response statistical characteristics include variance, autocovariance function, mean, skewness, kurtosis, and range; a dynamic system stable essential characteristic estimation module, configured to obtain an estimation result of the dynamic system stable essential characteristics based on the estimation result of the dynamic system noise response statistical characteristics; wherein, the dynamic system stable essential characteristics include system characteristic roots.

[0015] In a third aspect, the present invention further provides an electronic device, including a memory, a processor, and a computer program stored on the memory and executable on the processor, wherein when the processor executes the computer program, it implements the method for estimating the stable essential characteristics of a dynamic system based on measurement as described in any one of the above.

[0016] The method for estimating the stable essential characteristics of a dynamic system based on measurement provided by the present invention obtains the measurement result of any state variable or output variable of the dynamic system in a stationary state where the system input contains noise, and based on the measurement result of the state variable or output variable, obtains an estimation result of the dynamic system noise response statistical characteristics; wherein, the dynamic noise response statistical characteristics include variance, autocovariance function, mean, skewness, kurtosis, and range; based on the estimation result of the dynamic system noise response statistical characteristics, obtains an estimation result of the dynamic system stable essential characteristics; wherein, the dynamic system stable essential characteristics include system characteristic roots. This method estimates the dynamic system noise response statistical characteristics and stable essential characteristics based on the measurement result of any state variable or output variable of the dynamic system in a stationary state where the system input contains noise, solves the problem of difficult estimation of the random response statistical characteristics and stable essential characteristics of the dynamic system under the action of noise, can efficiently calculate its statistical characteristics and stable essential characteristics, and is helpful for the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the random response statistical characteristics. Description of the Drawings

[0017] To more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the accompanying drawings required in the description of the embodiments or the prior art. Obviously, the accompanying drawings in the following description are some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other accompanying drawings can also be obtained based on these drawings.

[0018] Figure 1 It is a schematic flowchart of a method for estimating the stable essential characteristics of a dynamic system based on measurement provided by an embodiment of the present invention.

[0019] Figure 2 It is a schematic structural diagram of a device for estimating the stable essential characteristics of a dynamic system based on measurement provided by an embodiment of the present invention.

[0020] Figure 3 It is a schematic physical structure diagram of an electronic device provided by an embodiment of the present invention. Detailed implementation manners

[0021] To make the objectives, technical solutions, and advantages of the present invention clearer, the following will clearly and completely describe the technical solutions in the present invention with reference to the accompanying drawings in the present invention. Obviously, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art without creative efforts based on the embodiments in the present invention belong to the scope of protection of the present invention.

[0022] It should be noted that how to solve the problem of estimating the stochastic response statistical characteristics and stable essential characteristics of a dynamic system under the action of noise is an important issue that has always needed to be solved in the research fields related to statistical physics and critical transitions. In the prior art, an accurate and efficient method for estimating the statistical characteristics of the noise response and stable essential characteristics of a dynamic system has not been proposed.

[0023] Considering this, the present invention proposes a method for estimating the stable essential characteristics of a dynamic system based on measurement. Specifically, Figure 1 It shows a schematic flowchart of a method for estimating the stable essential characteristics of a dynamic system based on measurement provided by an embodiment of the present invention.

[0024] As Figure 1As shown, the method includes: S110, obtaining the measurement result of any state variable or output variable of the kinetic system in a stationary state where the system input contains noise; S120, obtaining an estimation result of the statistical characteristics of the kinetic system noise response based on the measurement result of the state variable or output variable; wherein, the statistical characteristics of the kinetic system noise response include variance, autocovariance function, mean, skewness, kurtosis, and range; S130, obtaining an estimation result of the stable essential characteristics of the kinetic system based on the estimation result of the statistical characteristics of the kinetic system noise response; wherein, the stable essential characteristics of the kinetic system include system characteristic roots.

[0025] The following will elaborate on steps S110–S130 and related steps in detail.

[0026] S110, obtaining the measurement result of any state variable or output variable of the kinetic system in a stationary state where the system input contains noise.

[0027] It is easy to understand that, first, a stochastic differential equation can be used to describe the dynamic behavior of the kinetic system under the action of random noise and analyze the characteristics of the random noise, such as the type of random noise (Gaussian white noise, colored noise, etc.), intensity, frequency distribution, etc.

[0028] During the operation of the system, data of the state variable or output variable are collected. Filtering algorithms can be considered to reduce the influence caused by fluctuations and drifts, etc. The filtering algorithms can include Kalman filtering, Wiener filtering, low-pass filtering, etc.

[0029] When it is determined that the system has reached a stationary state, the value of the state variable or output variable is measured and recorded. The premise is that the system has reached a stationary state because only when the system reaches a stationary state, the statistical characteristics of its noise response do not change with time.

[0030] In a specific embodiment, step S110 includes: determining the observation window length of the system measurement according to the given time constant, relative error bound, and the multiple of the standard deviation in the corresponding m -sigma criterion; determining the number of sampling points according to the observation window length of the system measurement and the sampling interval; performing equally spaced sampling according to the observation window length, sampling interval, and the number of sampling points to obtain the measurement result of the state variable or output variable.

[0031] Specifically, based on a preliminary understanding of the kinetic system, a rough estimate of the system's time constant is given, and the relative error bound of the estimation result of the statistical characteristics of the system noise response is specified m and its corresponding multiple in the " -sigma criterion", then the observation window length of the system measurement It can be defined as the following formula (1).

[0032] (1) Subsequently, based on the approximate time constant of the system , a sampling interval is selected such that the sampling interval is one to two orders of magnitude smaller than the time constant of the system , and the observation window length is an integer multiple of the sampling interval . Then, under the condition of equidistant sampling, the number of sampling points within the observation window of the system measurement can be defined as the following formula (2).

[0033] (2) For the measurement of any state variable or output variable of the dynamic system in a stationary state with noise in the system input, equidistant sampling is performed with an observation window length of , a sampling interval of , and a number of sampling points of . The obtained series of measurement / observation results are denoted as for subsequent estimation of the statistical characteristics of the dynamic system noise response.

[0034] Furthermore, step S120 is started to be executed.

[0035] S120. Based on the measurement results of the state variable or output variable, an estimation result of the statistical characteristics of the dynamic system noise response is obtained; wherein, the statistical characteristics of the dynamic noise response include variance, autocovariance function, mean, skewness, kurtosis, and range.

[0036] Specifically, the estimation result of the variance and the estimation result of the autocovariance function are calculated through the first formula group; in the case where the calculation speed of the first formula group is lower than the set speed or the calculation time is higher than the set duration, the estimation result of the variance and the estimation result of the autocovariance function are calculated through the second formula group; the estimation results of the mean, skewness, kurtosis, and range are calculated through the third formula group. Among them, the set speed and the set duration can be set according to actual needs and are not specifically limited here.

[0037] Among them, the first formula group specifically includes the variance estimation formula (3) and the autocovariance function estimation formula (4).

[0038] (3) (4) The estimation result of the autocovariance function is a sequence, and its length It can be specified according to the actual observation requirements.

[0039] If the calculation speed of the estimated results of the variance and the autocovariance function is higher than the set speed and the calculation time is lower than the set duration when calculating according to Equations (3)–(4), then continue to calculate the estimated results of the variance and the autocovariance function according to Equations (3)–(4).

[0040] If the calculation speed of the estimated results of the variance and the autocovariance function is lower than the set speed and / or the calculation time is higher than the set duration when calculating according to Equations (3)–(4), then calculate the estimated result of the variance and the estimated result of the autocovariance function through the second formula group.

[0041] Specifically, for a series of observed results obtained by sampling , the number of sampling points is , and zero-padding it to a sequence length of , to obtain the discrete sequence as shown in Equation (5) below.

[0042] (5) The sequence length after zero-padding needs to satisfy Equation (6) below.

[0043] (6) In Equation (6), is the sequence length of the estimated result of the autocovariance function to be observed. In actual calculation, the sequence length is zero-padded to the smallest power of 2 that satisfies the requirements of Equation (6).

[0044] Immediately afterwards, perform a fast Fourier transform on the discrete sequence , to obtain Equation (7) below.

[0045] (7) Perform an inverse fast Fourier transform on the square of the complex modulus of the discrete sequence , to obtain Equation (8) below.

[0046] (8) Then, the estimated result of the autocovariance function can be calculated from the first data points of the discrete sequence , and specifically, refer to Equation (9) below.

[0047] (9) The estimated result of the variance can be directly obtained from the first data point in the estimated result of the autocovariance function, and specifically, refer to Equation (10) below.

[0048] (10) Among them, the second set of formulas includes the estimation formulas (5), (7)-(9) of the autocovariance function and the estimation formula (10) of the variance.

[0049] The statistical characteristics of the dynamic noise response not only include the variance and the autocovariance function, but also include the mean, skewness, kurtosis, and range. Therefore, subsequently, the estimation results of the mean, skewness, kurtosis, and range are calculated through the third set of formulas.

[0050] Among them, the third set of formulas specifically includes the estimation formula (11) of the mean, the estimation formula (12) of the skewness, the estimation formula (13) of the kurtosis, and the estimation formula (14) of the range.

[0051] (11) (12) (13) (14) Based on the above, the estimation results of the statistical characteristics of the dynamic system noise response can be obtained, that is, the estimation results of the variance, autocovariance function, mean, skewness, kurtosis, and range.

[0052] Further, step S130 is started to be executed.

[0053] S130, based on the estimation results of the statistical characteristics of the dynamic system noise response, obtain the estimation results of the stable essential characteristics of the dynamic system; among them, the stable essential characteristics of the dynamic system include system eigenvalues.

[0054] In this embodiment, by obtaining the measurement result of any state variable or output variable in the stationary state where the system input of the dynamic system contains noise, and based on the measurement result of the state variable or output variable, obtain the estimation result of the statistical characteristics of the dynamic system noise response; among them, the statistical characteristics of the dynamic noise response include variance, autocovariance function, mean, skewness, kurtosis, and range. This method estimates the statistical characteristics of the dynamic system noise response based on the measurement result of any state variable or output variable in the stationary state where the system input of the dynamic system contains noise, solves the problem of difficult estimation of the random response statistical characteristics of the dynamic system under the action of noise, can efficiently calculate its statistical characteristics, and helps the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the random response statistical characteristics.

[0055] It is easy to understand that after obtaining the estimation results of the statistical characteristics of the noise response of the dynamic system, based on the estimation results of the autocovariance function, discrete poles are solved; according to the discrete poles, the estimation results of the system characteristic root parameters are obtained; the opposite of the estimation results of the system characteristic root parameters is taken to obtain the estimation results of the system characteristic roots.

[0056] Based on the estimation results of the autocovariance function, solving discrete poles specifically includes: according to the estimation results of the autocovariance function, determining the model order of the autocovariance function waveform fitting and selecting the fitting length; wherein, the fitting length covers the key features of the autocovariance function waveform, and the fitting length is greater than or equal to the sum of the model order and the numerator order plus one; extracting the first fitting length data points from the estimation results of the autocovariance function to obtain a discrete sequence; based on the discrete sequence, according to the fitting length, the numerator order and the model order, constructing a linear equation system and solving it to obtain the denominator coefficients; performing matrix multiplication on the denominator coefficients and the discrete sequence to obtain the numerator coefficients; constructing a polynomial fraction according to the denominator coefficients and the numerator coefficients, and performing root extraction on the polynomial fraction to obtain discrete poles.

[0057] It can be understood that based on the estimation results of the autocovariance function, the model order of the autocovariance function waveform fitting is specified , and the fitting length is selected such that the first data points of the estimation results of the autocovariance function can cover the key features of its waveform.

[0058] Specifically, if the waveform of the autocovariance function has decaying oscillations, then its first data points generally need to cover more than half of the oscillation period of the decaying oscillation component, that is, include the complete process of the curve decreasing from the starting point to the minimum value and the subsequent rising section; if the waveform of the autocovariance function only has a decaying form, then its first data points need to cover the part with obvious decaying form.

[0059] For the estimation results of the autocovariance function, taking its first data points, the following discrete sequence of formula (15) can be obtained.

[0060] (15) The fitting length In addition to satisfying the aforementioned requirement that the first data points of the estimation results of the autocovariance function can cover the key features of its waveform, it also needs to satisfy the following formula (16).

[0061] (16) In formula (16), is the molecular order. If there is noise such as measurement noise in the measurement data of the state variable or output variable, which is directly superimposed on the measurement without passing through the differential dynamic system, there is a drop corresponding to the directly superimposed Gaussian white noise at the starting point of the waveform of its autocovariance function, then select the molecular order ; otherwise, select the molecular order .

[0062] In the case of the molecular order , construct a system of linear equations, specifically, see the following formula (17).

[0063] (17) Solve the system of linear equations (17) to obtain the denominator coefficients . If the system of linear equations is an overdetermined system of equations, then find the least squares solution of the system of linear equations.

[0064] Then, perform matrix multiplication on the denominator coefficients and the discrete sequence to obtain the numerator coefficients , specifically, see the following formula (18).

[0065] (18) Subsequently, construct a polynomial fraction according to the denominator coefficients and the numerator coefficients , specifically, see the following formula (19).

[0066] (19) Restore the polynomial fraction (19) to the form of a fraction sum plus a constant term. Specifically, find the roots of the polynomial of the denominator to obtain the discrete poles , thereby factorize the denominator, and then through methods such as the partial fraction method or the residue method, the algebraic coefficients can be obtained, and finally the form of a fraction sum plus a constant term is obtained, as shown in the following formula (20).

[0067] (20) In the case of the molecular order , construct a system of linear equations, specifically, see the following formula (21).

[0068] (21) Solve the system of linear equations (21) to obtain the denominator coefficients . If the system of linear equations is an overdetermined system of equations, then find the least squares solution of the system of linear equations.

[0069] Then, for the denominator coefficients and the discrete sequence perform matrix multiplication operation to obtain the numerator coefficients , as shown in Equation (22) below.

[0070] (22) Subsequently, according to the denominator coefficients and the numerator coefficients construct a polynomial fraction, as shown in Equation (23) below.

[0071] (23) Restore the polynomial fraction (23) to the form of the sum of fractions. Specifically, find the roots of the polynomial in the denominator to obtain the discrete poles , and then factorize the denominator. Then, through methods such as the partial fraction method or the residue method, the algebraic coefficients can be obtained, and finally the form of the sum of fractions is obtained, as shown in Equation (24) below.

[0072] (24) It should be noted that the estimated results of the algebraic coefficients obtained in this embodiment or are included in the statistical characteristics of the noise response of the dynamic system.

[0073] Based on the above, the discrete poles in different value cases of the numerator order can be obtained.

[0074] After obtaining the discrete poles, according to the discrete poles, the estimated results of the system characteristic root parameters can be obtained. Specifically, refer to Equation (25) below.

[0075] (25) Furthermore, take the opposite of the estimated results of the obtained system characteristic root parameters to obtain the estimated results of the system characteristic roots .

[0076] The estimated results of the system characteristic roots are the estimated results of the stable essential characteristics of the dynamic system based on the measurement of state variables or output variables.

[0077] In this embodiment, by obtaining the measurement result of any state variable or output variable of the dynamic system in the stationary state where the system input contains noise, and based on the measurement result of the state variable or output variable, an estimation result of the statistical characteristics of the dynamic system noise response is obtained; wherein, the statistical characteristics of the dynamic noise response include variance, autocovariance function, mean, skewness, kurtosis, and range; based on the estimation result of the statistical characteristics of the dynamic system noise response, an estimation result of the stable essential characteristics of the dynamic system is obtained; wherein, the stable essential characteristics of the dynamic system include system characteristic roots. This method estimates the statistical characteristics of the dynamic system noise response and the stable essential characteristics based on the measurement result of any state variable or output variable of the dynamic system in the stationary state where the system input contains noise, solves the problem of difficult estimation of the statistical characteristics of the stochastic response and the stable essential characteristics of the dynamic system under the action of noise, can efficiently calculate its statistical characteristics and stable essential characteristics, and helps the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the statistical characteristics of the stochastic response.

[0078] In some other embodiments, the statistical characteristics of the dynamic system noise response further include the fitting curve of the autocovariance function.

[0079] According to the estimation result of the algebraic coefficients or and the estimation result of the system characteristic roots , the fitting curve of the autocovariance function is obtained; wherein, the estimation result of the algebraic coefficients and the fitting curve of the autocovariance function are both included in the statistical characteristics of the dynamic system noise response.

[0080] In the case of the molecular order , the discrete sequence of the fitting curve of the autocovariance function is as follows in formula (26).

[0081] (26) In formula (26), is the unit impulse function.

[0082] The fitting curve of the autocovariance function is as follows in formula (27).

[0083] (27) In the case of the molecular order , the discrete sequence of the fitting curve of the autocovariance function is as follows in formula (28).

[0084] (28) The fitting curve of the autocovariance function is as follows in formula (29).

[0085] (29) Based on the above, the fitting curve of the autocovariance function can be solved to obtain the statistical characteristics of the noise response of the dynamic system.

[0086] In this embodiment, based on the estimation result of the autocovariance function, the estimation result of the algebraic coefficients is solved, and according to the estimation result of the algebraic coefficients and the estimation result of the system characteristic roots, the fitting curve of the autocovariance function is obtained; wherein, the estimation result of the algebraic coefficients and the fitting curve of the autocovariance function are both included in the statistical characteristics of the noise response of the dynamic system. This method estimates the statistical characteristics and stable essential characteristics of the noise response of the dynamic system by measuring any state variable or output variable of the dynamic system in a stationary state where the system input contains noise, solves the problem of difficult estimation of the statistical characteristics and stable essential characteristics of the random response of the dynamic system under the action of noise, can efficiently calculate its statistical characteristics and stable essential characteristics, and helps the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the statistical characteristics of the random response.

[0087] It should be noted that after the first round of estimation, any moment can be used as the starting moment of observation, and the statistical characteristics of the noise response of the dynamic system and the stable essential characteristics are estimated again to obtain a new estimation result. Further, a series of moments can be used as the starting moments of observation at equal intervals, and the statistical characteristics of the noise response of the dynamic system and the stable essential characteristics are estimated again to obtain new estimation results, so as to achieve continuous estimation. This time interval can be denoted as the estimation interval , by reasonably selecting the estimation interval , the computational amount in the continuous estimation process can be reduced. At the same time, the statistical characteristics of the noise response of the dynamic system and the stable essential characteristics can also be estimated for the measurement of any other state variable or output variable of the dynamic system to obtain the estimation results based on the measurement of other state variables or output variables.

[0088] In addition, after the above steps are completed, the observation window length , sampling interval , model order , fitting length and other parameters can be adjusted, and the statistical characteristics of the noise response of the dynamic system and the stable essential characteristics are estimated again to try to obtain a better estimation effect.

[0089] Corresponding to the method for estimating the stable essential characteristics of the dynamic system based on measurement described in the above embodiment, the present invention also proposes an apparatus for estimating the stable essential characteristics of the dynamic system based on measurement.

[0090] Specifically, Figure 2The structural schematic diagram of the measurement-based kinetic system stability essential feature estimation device provided by the embodiment of the present invention is shown.

[0091] As Figure 2 shown, the device includes: a system state variable or output variable measurement module 210, configured to obtain the measurement result of any state variable or output variable of the kinetic system in a stationary state where the system input contains noise; a kinetic system noise response statistical characteristic estimation module 220, configured to obtain an estimation result of the kinetic system noise response statistical characteristic based on the measurement result of the state variable or output variable; wherein, the kinetic noise response statistical characteristic includes variance, autocovariance function, mean, skewness, kurtosis, and range; a kinetic system stability essential feature estimation module 230, configured to obtain an estimation result of the kinetic system stability essential feature based on the estimation result of the kinetic system noise response statistical characteristic; wherein, the kinetic system stability essential feature includes system characteristic roots.

[0092] In this embodiment, the system state variable or output variable measurement module 210 obtains the measurement result of any state variable or output variable of the kinetic system in a stationary state where the system input contains noise, and the kinetic system noise response statistical characteristic estimation module 220 obtains an estimation result of the kinetic system noise response statistical characteristic based on the measurement result of the state variable or output variable; wherein, the kinetic noise response statistical characteristic includes variance, autocovariance function, mean, skewness, kurtosis, and range; the kinetic system stability essential feature estimation module 230 obtains an estimation result of the kinetic system stability essential feature based on the estimation result of the kinetic system noise response statistical characteristic; wherein, the kinetic system stability essential feature includes system characteristic roots. The device estimates the kinetic system noise response statistical characteristic and the stability essential feature based on the measurement result of any state variable or output variable of the kinetic system in a stationary state where the system input contains noise, solves the problem of difficult estimation of the random response statistical characteristic and the stability essential feature of the kinetic system under the action of noise, can efficiently calculate its statistical characteristic and stability essential feature, and helps the subsequent stability analysis of the kinetic system and the dynamic analysis and stability judgment based on the random response statistical characteristic.

[0093] It should be noted that the measurement-based kinetic system stability essential feature estimation provided by the embodiment of the present invention can be correspondingly referred to the measurement-based kinetic system stability essential feature estimation method described in the above embodiment, and will not be elaborated here.

[0094] Figure 3 The entity structure schematic diagram of an electronic device is exemplified. As Figure 3As shown, the electronic device may include: a processor 310, a communications interface 320, a memory 330, and a communication bus 340; wherein, the processor 310, the communications interface 320, and the memory 330 communicate with each other via the communication bus 340. The processor 310 may invoke the logical instructions in the memory 330 to execute a method for estimating the essential characteristics of the stability of a dynamic system based on measurements, and the method includes: obtaining a measurement result of any state variable or output variable of the dynamic system in a stationary state where the system input contains noise; based on the measurement result of the state variable or output variable, obtaining an estimation result of the statistical characteristics of the noise response of the dynamic system; wherein, the statistical characteristics of the dynamic noise response include variance, autocovariance function, mean, skewness, kurtosis, and range; based on the estimation result of the statistical characteristics of the noise response of the dynamic system, obtaining an estimation result of the essential characteristics of the stability of the dynamic system; wherein, the essential characteristics of the stability of the dynamic system include system characteristic roots.

[0095] In addition, the logical instructions in the above-mentioned memory 330 may be implemented in the form of software functional units and sold or used as independent products, and may be stored in a computer-readable storage medium. Based on such an understanding, the technical solution of the present invention, in essence, or the part that contributes to the prior art, or a part of this technical solution, may be embodied in the form of a software product. This computer software product is stored in a storage medium and includes several instructions for causing a computer device (which may be a personal computer, a server, or a network device, etc.) to execute all or part of the steps of the methods described in the various embodiments of the present invention. The foregoing storage medium includes: various media such as USB flash drives, mobile hard disks, read-only memories (ROM, Read-Only Memory), random access memories (RAM, Random Access Memory), magnetic disks, or optical discs that can store program codes.

[0096] The device embodiments described above are merely illustrative. The units described as separate components may or may not be physically separated, and the components shown as units may or may not be physical units, that is, they may be located in one place, or may be distributed to multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment. A person of ordinary skill in the art can understand and implement it without creative labor.

[0097] Through the description of the above embodiments, those skilled in the art can clearly understand that each embodiment can be implemented by means of software plus a necessary general hardware platform, and of course, it can also be implemented by hardware. Based on such an understanding, the above technical solution, in essence, or the part that contributes to the prior art can be embodied in the form of a software product. This computer software product can be stored in a computer-readable storage medium, such as ROM / RAM, magnetic disk, optical disk, etc., and includes several instructions to enable a computer device (which can be a personal computer, server, or network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0098] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them; although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions described in the foregoing embodiments, or perform equivalent replacements for some of the technical features; and these modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. A method for estimating the essential characteristics of stability of a dynamic system based on measurement, characterized in that: include: Obtain the measurement results of any state variable or output variable of the dynamic system in a steady state with noise in the system input; Based on the measurement results of the state variables or output variables, obtaining estimation results of the statistical characteristics of the noise response of the dynamic system; wherein the statistical characteristics of the dynamic noise response include variance, autocovariance function, mean, skewness, kurtosis and range; Based on the estimation result of the statistical characteristic of the noise response of the dynamic system, the estimation result of the stable essential characteristics of the dynamic system is obtained; wherein the stable essential characteristics of the dynamic system include the system characteristic root.

2. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 1, characterized in that: The step of obtaining the measurement result of any state variable or output variable of the dynamic system in a steady state where the system input contains noise includes: According to the given time constant, relative error limit and its corresponding m -The multiple of the standard deviation in the sigma criterion determines the observation window length of the system measurement; Determine the number of sampling points based on the observation window length and sampling interval measured by the system; The sampling is performed at equal intervals according to the observation window length, the sampling interval and the number of sampling points to obtain the measurement result of the state variable or the output variable.

3. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 1, characterized in that: Based on the measurement results of the state variables or output variables, an estimation result of the statistical characteristics of the noise response of the dynamic system is obtained, including: Calculate the estimated result of the variance and the estimated result of the autocovariance function through the first formula group; When the calculation speed of the first formula group is lower than the set speed, or the calculation time is longer than the set time, the estimation result of the variance and the estimation result of the autocovariance function are calculated by the second formula group; The estimated results of mean, skewness, kurtosis and range are calculated by the third formula group.

4. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 1, characterized in that: Based on the estimation result of the statistical characteristic of the noise response of the dynamic system, the estimation result of the stable essential characteristic of the dynamic system is obtained, including: Based on the estimation results of the autocovariance function, the discrete poles are solved; Obtaining estimation results of system characteristic root parameters according to the discrete poles; The estimation result of the system characteristic root parameters is negated to obtain the estimation result of the system characteristic root.

5. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 4, characterized in that: The method of solving the discrete poles based on the estimation result of the autocovariance function includes: According to the estimation result of the autocovariance function, the model order of the autocovariance function waveform fitting is determined, and the fitting length is selected; wherein the fitting length covers the key features of the autocovariance function waveform, and the fitting length is greater than or equal to the sum of the model order and the numerator order plus one; Extracting the first fitting length data points from the estimation result of the autocovariance function to obtain a discrete sequence; Based on the discrete sequence, according to the fitting length, the numerator order and the model order, a linear equation system is constructed and solved to obtain the denominator coefficient; Performing matrix multiplication on the denominator coefficient and the discrete sequence to obtain a numerator coefficient; A polynomial fraction is constructed according to the denominator coefficient and the numerator coefficient, and the polynomial fraction is rooted to obtain the discrete poles.

6. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 5, characterized in that: Also includes: Based on the estimation results of the autocovariance function, the estimation results of the algebraic coefficients are solved; Obtaining a fitting curve of the autocovariance function according to the estimation results of the algebraic coefficients and the estimation results of the system characteristic roots; Among them, the estimation results of algebraic coefficients and the fitting curve of the autocovariance function are both included in the statistical characteristics of the noise response of the dynamic system.

7. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 3, characterized in that: The first formula group specifically includes: The estimation formula of variance is: ； The estimation formula of the autocovariance function is: ； The second formula group specifically includes: The estimation formula of the autocovariance function is: ； ； ； ； The estimation formula of variance is: ； The third formula group specifically includes: The estimation formula for the mean is: ； The estimation formula for skewness is: ； The estimation formula of kurtosis is: ； The estimation formula of the range is: ； in, is the variance, is the number of sampling points, is the current sampling point, is the measurement result of the state variable or output variable, is the autocovariance function, is the time interval, is the sampling interval, is the length of the sequence of estimated results of the autocovariance function to be observed, is the inverse fast Fourier transform, is the fast Fourier transform, is the length of the discrete sequence obtained by padding the measurement results of the state variable or output variable with zeros, is the mean, is the skewness, is the kurtosis, Very poor.

8. The method for estimating the stability essential characteristics of a dynamic system based on measurement according to claim 6, characterized in that: When the molecular order is equal to the model order, the fitting curve of the autocovariance function is defined as follows: ； In the case where the molecular order is less than the model order, the fitting curve of the autocovariance function is defined as follows: ； in, is the fitting curve of the autocovariance function, is the estimated result of the algebraic coefficient, is the estimated result of the system characteristic root, is the model order.

9. A device for estimating the essential characteristics of stability of a dynamic system based on measurement, characterized in that: include: A system state variable or output variable measurement module is used to obtain the measurement result of any state variable or output variable of the dynamic system in a stable state where the system input contains noise; A dynamic system noise response statistical characteristic estimation module, used for obtaining an estimation result of the dynamic system noise response statistical characteristic based on the measurement result of the state variable or the output variable; wherein the dynamic noise response statistical characteristic includes variance, autocovariance function, mean, skewness, kurtosis and range; The dynamic system stable essential characteristics estimation module is used to obtain the estimation results of the dynamic system stable essential characteristics based on the estimation results of the dynamic system noise response statistical characteristics; wherein the dynamic system stable essential characteristics include system characteristic roots.

10. An electronic device comprising a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein: When the processor executes the computer program, the method for estimating the essential characteristics of stability of a dynamic system based on measurement as claimed in any one of claims 1 to 8 is implemented.

Images