Method and device for calculating noise response statistical characteristics of dynamic system and electronic equipment

Abstract

The invention provides a dynamic system noise response statistical property calculation method and device and electronic equipment, and the method comprises the steps: determining a stochastic differential equation of a dynamic system according to a current noise type; calculating noise response statistical characteristics of the dynamic system based on a system matrix, an input matrix, an output matrix and a direct transfer matrix in a stochastic differential equation; wherein the noise response statistical characteristics comprise a mean value, a variance, a steady-state response variance, an auto-covariance function and a steady-state response auto-covariance function. According to the method, the form of the stochastic differential equation corresponding to the dynamic system is unified according to the current noise type, and the noise response statistical characteristics of the dynamic system are further calculated based on the form, so that the problem that the stochastic response statistical characteristics of the dynamic system under the noise effect are difficult to calculate is solved; the stochastic differential equation of the dynamic system influenced by noise can be comprehensively and accurately described, the statistical property of the stochastic differential equation is further efficiently calculated, and stability analysis of the subsequent dynamic system and dynamic analysis and stability judgment based on the stochastic response statistical property are facilitated.

Description

Technical Field

[0001] The present invention relates to the technical field of statistical physics, and in particular to a method, a device and an electronic device for calculating the statistical characteristics of noise response of a dynamic system. 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, most current related studies use measurement-based methods to obtain the statistical characteristics of the random response of dynamic systems under noise, but they are often unable to perform theoretical calculations, have low accuracy, and have limited applicability when dealing with actual systems.

[0004] Therefore, how to solve the problem that existing technologies are unable to accurately and efficiently calculate the statistical characteristics of the random response of dynamic systems under the influence of noise 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, device and electronic device for calculating the statistical characteristics of the noise response of a dynamic system, which are used to solve the problem that the prior art cannot accurately and efficiently calculate the statistical characteristics of the random response of a dynamic system under the action of noise. The method can comprehensively and accurately describe the stochastic differential equations of the dynamic system affected by noise, and further efficiently calculate its statistical characteristics, which is helpful for the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the statistical characteristics of the random response.

[0006] On the one hand, the present invention provides a method for calculating the statistical characteristics of the noise response of a dynamic system, comprising: determining the stochastic differential equation of the dynamic system according to the current noise type; calculating the statistical characteristics of the noise response of the dynamic system based on the system matrix, input matrix, output matrix and direct transfer matrix in the stochastic differential equation; wherein the statistical characteristics of the noise response include mean, variance, steady-state response variance, autocovariance function and steady-state response autocovariance function.

[0007] Further, determining the stochastic differential equation of the dynamic system according to the current noise type includes: when the current noise type is standard Gaussian white noise and there is no measurement noise in the system, determining the stochastic differential equation of the dynamic system as the first stochastic differential equation; when the current noise type is colored noise obtained by passing Gaussian white noise through a dynamic system in advance and there is no measurement noise in the system, determining the stochastic differential equation of the dynamic system as the second stochastic differential equation; when the current noise type is standard Gaussian white noise and there is measurement noise in the system, determining the stochastic differential equation of the dynamic system as the third stochastic differential equation; when the current noise type is colored noise obtained by passing Gaussian white noise through a dynamic system in advance and there is measurement noise in the system, determining the stochastic differential equation of the dynamic system as the fourth stochastic differential equation.

[0008] Further, based on the system matrix, input matrix, output matrix, and direct transfer matrix in the stochastic differential equation, calculating the statistical characteristics of the noise response of the dynamic system includes: calculating the mean according to a preset formula; when the system matrix can be diagonalized, calculating the variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function through a first set of formulas; when the system matrix cannot be diagonalized, calculating the variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function through a second set of formulas.

[0009] Further, the first stochastic differential equation is defined as follows: ; The second stochastic differential equation is defined as follows: ; ; ; The third stochastic differential equation is defined as follows: ; ; The fourth stochastic differential equation is defined as follows: ; ; ; where is the -dimensional state variable, is the time derivative of the state variable , is the system matrix of is the input matrix, is the number of inputs, is the external input vector containing standard Gaussian white noise, and its components are independent of each other, is the output vector, is the output matrix, is the number of outputs, is the direct transfer matrix, is the system state variable except for noise, is the time derivative of, is the noise state variable, is the time derivative of, is the system matrix except for noise, is the input matrix of noise to the system state variable, is the noise system matrix, is the input matrix of standard Gaussian white noise to noise, is the output matrix of the system state variable to the output vector, is the direct transfer matrix of noise to the output vector, is the input matrix except for measurement noise, is the external input vector containing standard Gaussian white noise except for measurement noise, is the direct transfer matrix except for measurement noise, is the measurement noise, which is also standard Gaussian white noise, and its components are independent of each other, is the direct transfer matrix of measurement noise.

[0010] Furthermore, the preset formula is defined as follows: ; wherein, is the mean of the state variable, is the mean of the output vector.

[0011] Furthermore, the first formula group specifically includes: The calculation formula of the variance: ; The calculation formula of the steady-state response variance: ; The calculation formula of the autocovariance function: ; The calculation formula of the steady-state response autocovariance function: ; Wherein, is the state variable, is the output vector, is the time, , is the loop variable for summation, is the number of characteristic roots of the system, , are the characteristic roots of the system , are the corresponding left eigenvectors, is the input matrix, , are the characteristic roots of the system, , are the characteristic roots of the system , are the corresponding right eigenvectors, is the output matrix, is the direct transfer matrix.

[0012] Furthermore, the second formula group specifically includes: The calculation formula of the variance: ; The calculation formula of the steady-state response variance: ; The calculation formula of the autocovariance function: ; The calculation formula of the steady-state response autocovariance function: ; Wherein, is the state variable, is the output vector, is the time, is the system matrix, is the integral variable, is the input matrix, is the output matrix, is the direct transfer matrix.

[0013] In a second aspect, the present invention further provides a computing device for the statistical characteristics of the noise response of a dynamic system, including: a stochastic differential equation determination module for determining the stochastic differential equation of the dynamic system according to the current noise type; a noise response statistical characteristic calculation module for calculating the statistical characteristics of the noise response of the dynamic system based on the system matrix, input matrix, output matrix, and direct transmission matrix in the stochastic differential equation; wherein the noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function.

[0014] 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 calculation method for the statistical characteristics of the noise response of a dynamic system as described in any one of the above.

[0015] In a fourth aspect, the present invention further provides a non-transitory computer-readable storage medium, on which a computer program is stored, and when the computer program is executed by a processor, it implements the calculation method for the statistical characteristics of the noise response of a dynamic system as described in any one of the above.

[0016] The calculation method for the statistical characteristics of the noise response of a dynamic system provided by the present invention determines the stochastic differential equation of the dynamic system according to the current noise type, and calculates the statistical characteristics of the noise response of the dynamic system based on the system matrix, input matrix, output matrix, and direct transmission matrix in the stochastic differential equation; wherein the noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function. This method unifies the form of the stochastic differential equation corresponding to the dynamic system according to the current noise type, and further calculates the statistical characteristics of the noise response of the dynamic system based on this, solving the problem of difficult calculation of the stochastic response statistical characteristics of the dynamic system under the action of noise, being able to comprehensively and accurately describe the stochastic differential equation of the dynamic system affected by noise, and further efficiently calculate its statistical characteristics, which is helpful for the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the stochastic response statistical characteristics. Description of the Drawings

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

[0018] Figure 1 It is a schematic flowchart of the calculation method for the statistical characteristics of the noise response of a dynamic system provided by an embodiment of the present invention.

[0019] Figure 2 It is a schematic structural diagram of a computing device for the statistical characteristics of the noise response of a dynamic system 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 technical solutions in the present invention will be clearly and completely described below 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 based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention.

[0022] It should be noted that how to solve the problem of calculating the statistical characteristics of the stochastic response 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. No accurate and efficient method for calculating the statistical characteristics of the noise response of a dynamic system has been proposed in the prior art.

[0023] Considering this, the present invention proposes a method for calculating the statistical characteristics of the noise response of a dynamic system. Specifically, Figure 1 shows a schematic flowchart of the method for calculating the statistical characteristics of the noise response of a dynamic system provided by an embodiment of the present invention.

[0024] As Figure 1 shown, the method includes: S110, determining the stochastic differential equation of the dynamic system according to the current noise type; S120, calculating the statistical characteristics of the noise response of the dynamic system based on the system matrix, input matrix, output matrix, and direct transfer matrix in the stochastic differential equation; where the noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function.

[0025] The following will elaborate on steps S110–S120 and related steps in detail.

[0026] S110, determining the stochastic differential equation of the dynamic system according to the current noise type.

[0027] It is easy to understand that the stochastic differential equation is an important tool for describing the dynamic behavior of a dynamic system under the action of random noise. It can not only describe the stochastic evolution process of the dynamic system but also help understand the influence of noise on the system stability, response characteristics, control, and optimization. Under the action of different types of noise, the corresponding stochastic differential equations of the dynamic system are also different.

[0028] In this step, it is first necessary to identify the possible sources of random noise in the dynamic system. These noise sources may be external noise or internal noise, so as to determine the current type of noise acting on the dynamic system. Among them, the current type of noise includes but is not limited to Gaussian white noise, colored noise, etc.

[0029] For different current types of noise, the stochastic differential equations of the dynamic system will also be different. In this regard, in this embodiment, the stochastic differential equation of the dynamic system under the action of standard Gaussian white noise is set to a general form / target form. In the case where the current noise includes other noises other than standard Gaussian white noise, the form of the stochastic differential equation satisfied by the dynamic system is converted into the target form, so as to participate in the calculation of the statistical characteristics of the subsequent noise response with the stochastic differential equation in the target form.

[0030] For example, in a specific embodiment, the current type of noise is standard Gaussian white noise and there is no measurement noise in the system. At this time, the stochastic differential equation of the dynamic system is determined as the first stochastic differential equation, and the form of the first stochastic differential equation is the target form. Specifically, it can be seen in the following formula (1).

[0031] (1) Among them, the first stochastic differential equation (1) has zero initial conditions, as can be seen in the following formula (2).

[0032] (2) In formulas (1)–(2), is a state variable of dimension is the time derivative of the state variable is the system matrix of is the input matrix of is the number of inputs, is an external input vector containing standard Gaussian white noise, and its components are all independent of each other, is the output vector, is the output matrix of is the number of outputs, is the direct transfer matrix of

[0033] When the stochastic differential equation of the dynamic system satisfies the above formulas (1)–(2), step S120 can be directly executed.

[0034] ​In another specific embodiment, the current noise type is colored noise obtained by passing Gaussian white noise through a dynamic system in advance, and there is no measurement noise in the system. At this time, the stochastic differential equation of the dynamic system is determined as the second stochastic differential equation. The second stochastic differential equation is obtained after transformation, and its form is the same as the target form, but the matrix definitions involved are different.

[0035] It is easy to understand that when the stochastic differential equation of the dynamic system does not satisfy the above equations (1)–(2) and there is no measurement noise in the system, it is necessary to transform the original stochastic differential equation of the dynamic system at this time to obtain the second stochastic differential equation.

[0036] Among them, the original stochastic differential equation is as follows in equation (3).

[0037] (3) In equation (3), .

[0038] Let , then the following equation (4) can be obtained. The form of equation (4) is the same as the target form and is the second stochastic differential equation obtained by transformation.

[0039] , that is (4) According to equation (4), in the second stochastic differential equation, .

[0040] In equations (3)–(4), is the system state variable except for the noise, is the time derivative of, is the noise state variable, is the time derivative of, is the system matrix except for the noise, is the input matrix of the noise to the system state variable, is the noise system matrix, is the input matrix of the standard Gaussian white noise to the noise, is the output matrix of the system state variable to the output vector, is the direct transfer matrix of the noise to the output vector.

[0041] The second stochastic differential equation (4) obtained by transformation satisfies the form of the above equation (1) and can directly start to execute step S120.

[0042] In another specific embodiment, the current noise type is standard Gaussian white noise, and there is measurement noise in the system. At this time, the stochastic differential equation of the dynamic system is determined as the third stochastic differential equation. Similarly, the third stochastic differential equation is also obtained after transformation, and its form is the same as the target form, but the matrix definitions involved are different.

[0043] It is easy to understand that if there is measurement noise in the system, the measurement noise is directly superimposed on the output variable of the system without passing through the differential dynamic system. At this time, the original stochastic differential equation of the dynamic system is as follows in Equation (5).

[0044] (5) At this time, it is necessary to transform the original stochastic differential equation (5) of the dynamic system into the form of Equation (1) to obtain the third stochastic differential equation, as shown in the following Equation (6).

[0045] ,that is (6) According to Equation (6), in the third stochastic differential equation, .

[0046] In Equations (5)–(6), is the input matrix except for the measurement noise, is the external input vector containing standard Gaussian white noise except for the measurement noise, is the direct transfer matrix except for the measurement noise, is the measurement noise, which is also standard Gaussian white noise, and its components are all independent of each other, is the direct transfer matrix of the measurement noise.

[0047] The third stochastic differential equation (6) obtained after transformation satisfies the form of the above Equation (1), and step S120 can be directly executed.

[0048] In still another specific embodiment, the current noise type is colored noise obtained by passing Gaussian white noise through a dynamic system in advance, and there is measurement noise in the system. At this time, the stochastic differential equation of the dynamic system is determined as the fourth stochastic differential equation. Similarly, the fourth stochastic differential equation is also obtained after transformation, and its form is the same as the target form, but the matrix definitions involved are different.

[0049] It is easy to understand that the current noise type is colored noise obtained by passing Gaussian white noise through a dynamic system in advance, and there is measurement noise in the system. The measurement noise is directly superimposed on the output variable of the system without passing through the differential dynamic system. At this time, the original stochastic differential equation of the dynamic system is as follows in Equation (7).

[0050] (7) In Equation (7), .

[0051] At this time, let , then the original stochastic differential equation (7) of the dynamical system can be transformed into the form of Equation (1) to obtain the fourth stochastic differential equation, as shown in the following Equation (8).

[0052] , that is (8) According to Equation (8), in the fourth stochastic differential equation, .

[0053] The fourth stochastic differential equation (8) obtained through transformation satisfies the form of the above Equation (1), and step S120 can be directly executed.

[0054] According to the above description, determining the stochastic differential equation of the dynamical system according to the current noise type mainly lies in determining the system matrix , input matrix , output matrix and direct transfer matrix in Equation (1). After that, step S120 is started to be executed.

[0055] S120. Calculate the noise response statistical characteristics of the dynamical system based on the system matrix, input matrix, output matrix, and direct transfer matrix in the stochastic differential equation; wherein, the noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function.

[0056] It is easy to understand that for the first stochastic differential equation, the second stochastic differential equation, the third stochastic differential equation, or the fourth stochastic differential equation, and the dynamical system represented by the initial conditions of Equation (2), one of the noise response statistical characteristics of the dynamical system, namely the mean, can be calculated through the following preset formula (9).

[0057] (9) In Equation (9), is the mean of the state variables, is the mean of the output vector.

[0058] Furthermore, according to whether the system matrix can be diagonalized, a formula group for calculating other noise response statistical characteristics of the dynamical system can be further determined.

[0059] Specifically, first solve the system matrix The eigenvalues, and for each eigenvalue, find the corresponding eigenvector. The system matrix The necessary and sufficient condition for being diagonalizable is that the system matrix has a preset number of linearly independent eigenvectors, where the preset number is the order of the system matrix .

[0060] In a specific embodiment, the system matrix is diagonalizable. In this case, the variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function are calculated through the first set of formulas.

[0061] Specifically, when the system matrix is diagonalizable, the following equation (10) holds.

[0062] (10) In equation (10), is the system matrix, is the number of characteristic roots of the system, is the matrix composed of left eigenvectors, is the matrix composed of right eigenvectors, is the diagonal matrix composed of the system characteristic roots, is the identity matrix, to are the characteristic roots of the system, to are the characteristic roots of the system to corresponding left eigenvectors, to are the characteristic roots of the system to corresponding right eigenvectors.

[0063] For this dynamic system, the variance of its solution process can be calculated through the following equation (11).

[0064] (11) The steady-state response variance of the solution process of the dynamic system can be calculated through the following equation (12).

[0065] (12) The autocovariance function of the solution process of the dynamic system can be calculated through the following equation (13).

[0066] (13) The steady-state response autocovariance function of the solution process of the dynamic system can be calculated through the following equation (14).

[0067] (14) In equations (11)–(14), is the state variable, is the output vector, is the time, , is the loop variable for summation, is the number of characteristic roots of the system, , are the characteristic roots of the system , are the corresponding left eigenvectors, is the input matrix, , are the characteristic roots of the system, , are the characteristic roots of the system , are the corresponding right eigenvectors, is the output matrix, is the direct transfer matrix.

[0068] The calculation results of the above equation (9) and the first set of equations (11)–(14) are the statistical characteristics of the noise response of the dynamic system.

[0069] In another specific embodiment, the system matrix cannot be diagonalized. In this case, the variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function are calculated through the second set of equations.

[0070] Specifically, when the system matrix cannot be diagonalized, for the dynamic system, the variance of its solution process can be calculated through the following equation (15).

[0071] (15) The steady-state response variance of the solution process of the dynamic system can be calculated through the following equation (16).

[0072] (16) The autocovariance function of the solution process of the dynamic system can be calculated through the following equation (17).

[0073] (17) The steady-state response autocovariance function of the solution process of the dynamic system can be calculated through the following equation (18).

[0074] (18) In equations (15)–(18), is the state variable, is the output vector, is the time, is the system matrix, is the integral variable, is the input matrix, is the output matrix, is the direct transfer matrix.

[0075] The calculation results of the above formula (9) and the second set of formulas (15)–(18) are the statistical characteristics of the noise response of the dynamic system.

[0076] It should be noted that the calculation method for the statistical characteristics of the noise response of the dynamic system provided in the embodiments of the present invention can be applied to multiple different scenarios, such as the fields of mechanical engineering, economy and finance, physics and chemistry, etc., which are not specifically limited herein.

[0077] For example, in the field of economy and finance, price changes in the financial market are often affected by various unpredictable factors. By analyzing this "noise" data, models can be established to predict future market trends.

[0078] Another example is in the field of mechanical engineering. Understanding the vibration response of mechanical structures or components under random excitation is crucial for predicting fatigue life, reducing noise, and improving ride comfort. By analyzing the system's response to noise, early fault signs such as bearing wear and gear damage can be detected.

[0079] In this embodiment, by determining the stochastic differential equation of the dynamic system according to the current noise type, and based on the system matrix, input matrix, output matrix, and direct transfer matrix in the stochastic differential equation, the statistical characteristics of the noise response of the dynamic system are calculated; among them, the statistical characteristics of the noise response include the mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function. This method unifies the form of the stochastic differential equation corresponding to the dynamic system according to the current noise type, and further calculates the statistical characteristics of the noise response of the dynamic system based on this, solving the problem of difficult calculation of the stochastic response statistical characteristics of the dynamic system under the action of noise, being able to comprehensively and accurately describe the stochastic differential equation of the dynamic system affected by noise, and further efficiently calculating its statistical characteristics, which is helpful for the subsequent stability analysis of the dynamic system and the dynamic analysis and stability judgment based on the stochastic response statistical characteristics.

[0080] Corresponding to the calculation method for the statistical characteristics of the noise response of the dynamic system described in the above embodiments, the present invention also proposes a calculation device for the statistical characteristics of the noise response of the dynamic system.

[0081] Specifically, Figure 2 shows a schematic structural diagram of the calculation device for the statistical characteristics of the noise response of the dynamic system provided in the embodiments of the present invention.

[0082] As shown Figure 2 in the figure, the device includes: a stochastic differential equation determination module 210, configured to determine the stochastic differential equation of the dynamical system according to the current noise type; a noise response statistical property calculation module 220, configured to calculate the noise response statistical properties of the dynamical system based on the system matrix, input matrix, output matrix, and direct transfer matrix in the stochastic differential equation; wherein, the noise response statistical properties include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function.

[0083] In this embodiment, the stochastic differential equation determination module 210 determines the stochastic differential equation of the dynamical system according to the current noise type, and the noise response statistical property calculation module 220 calculates the noise response statistical properties of the dynamical system based on the system matrix, input matrix, output matrix, and direct transfer matrix in the stochastic differential equation; wherein, the noise response statistical properties include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function. The device solves the problem of difficult calculation of the stochastic response statistical properties of the dynamical system under the action of noise by unifying the form of the stochastic differential equation corresponding to the dynamical system according to the current noise type, and further calculating the noise response statistical properties of the dynamical system based on this. It can comprehensively and accurately describe the stochastic differential equation of the dynamical system affected by noise, and further efficiently calculate its statistical properties, which is helpful for the subsequent stability analysis of the dynamical system and the dynamic analysis and stability judgment based on the stochastic response statistical properties.

[0084] It should be noted that the calculation of the noise response statistical properties of the dynamical system provided in the embodiments of the present invention can be correspondingly referred to the calculation method of the noise response statistical properties of the dynamical system described in the above embodiments, and will not be elaborated here.

[0085] Figure 3 illustrates a schematic physical structure diagram of an electronic device. As shown Figure 3As shown in the figure, the electronic device may include: a processor 310, a communications interface 320, a memory 330, and a communication bus 340; among them, the processor 310, the communications interface 320, and the memory 330 complete communication with each other through the communication bus 340. The processor 310 may call the logic instructions in the memory 330 to execute a calculation method for the statistical characteristics of the noise response of a dynamic system. The method includes: determining a stochastic differential equation of the dynamic system according to the current noise type; calculating the statistical characteristics of the noise response of the dynamic system based on the system matrix, input matrix, output matrix, and direct transmission matrix in the stochastic differential equation; where the noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function.

[0086] In addition, the logic 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. The 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 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.

[0087] On the other hand, the present invention also provides a non-transitory computer-readable storage medium, on which a computer program is stored. When the computer program is executed by a processor, it implements the calculation method for the statistical characteristics of the noise response of a dynamic system provided by the above-mentioned various methods. The method includes: determining a stochastic differential equation of the dynamic system according to the current noise type; calculating the statistical characteristics of the noise response of the dynamic system based on the system matrix, input matrix, output matrix, and direct transmission matrix in the stochastic differential equation; where the noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function, and steady-state response autocovariance function.

[0088] 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 distributed to multiple network units. Some or all of the modules can be selected according to actual needs to achieve the purpose of the solution of this embodiment. Those of ordinary skill in the art can understand and implement it without creative efforts.

[0089] 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 this understanding, the essence of the above technical solution, or the part that contributes to the prior art, can be embodied in the form of a software product. The 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 for causing a computer device (which can be a personal computer, a server, or a network device, etc.) to execute the methods described in each embodiment or some parts of the embodiments.

[0090] 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 recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. 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 calculating the statistical characteristics of noise response of a dynamic system, characterized in that: include: According to the current noise type, the stochastic differential equation of the dynamic system is determined; Calculating the noise response statistical characteristics of the dynamic system based on the system matrix, input matrix, output matrix and direct transfer matrix in the stochastic differential equation; The noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function and steady-state response autocovariance function.

2. The method for calculating the statistical characteristics of noise response of a dynamic system according to claim 1, characterized in that: The step of determining the stochastic differential equation of the dynamic system according to the current noise type includes: When the current noise type is standard Gaussian white noise and there is no measurement noise in the system, determining the stochastic differential equation of the dynamic system as a first stochastic differential equation; When the current noise type is a color noise obtained by passing Gaussian white noise through a dynamic system in advance, and there is no measurement noise in the system, determining the stochastic differential equation of the dynamic system as a second stochastic differential equation; When the current noise type is standard Gaussian white noise and there is measurement noise in the system, determining the stochastic differential equation of the dynamic system as a third stochastic differential equation; When the current noise type is colored noise obtained by passing Gaussian white noise through a dynamic system in advance, and measurement noise exists in the system, the stochastic differential equation of the dynamic system is determined as a fourth stochastic differential equation.

3. The method for calculating the statistical characteristics of noise response of a dynamic system according to claim 1, characterized in that: Based on the system matrix, input matrix, output matrix and direct transfer matrix in the stochastic differential equation, the noise response statistical characteristics of the dynamic system are calculated, including: Calculate the mean value according to the preset formula; When the system matrix can be diagonalized, the variance, the steady-state response variance, the autocovariance function, and the steady-state response autocovariance function are calculated by the first formula group; In the case that the system matrix cannot be diagonalized, the variance, the steady-state response variance, the autocovariance function, and the steady-state response autocovariance function are calculated by the second formula group.

4. The method for calculating the statistical characteristics of noise response of a dynamic system according to claim 2, characterized in that: The first stochastic differential equation is defined as follows: ； The second stochastic differential equation is defined as follows: ； ； ； The third stochastic differential equation is defined as follows: ； ； The fourth stochastic differential equation is defined as follows: ； ； ； in, for dimensional state variables, is a state variable The time derivative of for The system matrix, for The input matrix is is the number of inputs, is an external input vector containing standard Gaussian white noise, and its components are independent of each other. is the output vector, for The output matrix of is the number of outputs, for The direct transfer matrix of is the system state variable excluding noise, for The time derivative of is the noise state variable, for The time derivative of is the system matrix excluding noise, is the input matrix of noise to the system state variables, is the noise system matrix, is the input matrix of the standard Gaussian white noise pair, is the output matrix of the system state variables to the output vector, is the direct transfer matrix of noise to the output vector, is the input matrix excluding the measurement noise, is an external input vector containing standard Gaussian white noise in addition to the measurement noise, is the direct transfer matrix excluding the measurement noise, is the measurement noise, which is also standard Gaussian white noise, and its components are independent of each other. is the direct transfer matrix of the measurement noise.

5. The method for calculating the statistical characteristics of noise response of a dynamic system according to claim 3, characterized in that: The preset formula is defined as follows: ； in, is the mean of the state variable, is the mean of the output vector.

6. The method for calculating the statistical characteristics of noise response of a dynamic system according to claim 3, characterized in that: The first formula group specifically includes: The calculation formula of the variance is: ； The calculation formula of the steady-state response variance is: ； The calculation formula of the autocovariance function is: ； The calculation formula of the steady-state response autocovariance function is: ； in, is the state variable, is the output vector, For time, , is the loop variable for summation, is the number of characteristic roots of the system, , is the characteristic root of the system , The corresponding left eigenvector is is the input matrix, , is the characteristic root of the system, , is the characteristic root of the system , The corresponding right eigenvector is is the output matrix, is a direct transfer matrix.

7. The method for calculating the statistical characteristics of noise response of a dynamic system according to claim 3, characterized in that: The second formula group specifically includes: The calculation formula of the variance is: ； The calculation formula of the steady-state response variance is: ； The calculation formula of the autocovariance function is: ； The calculation formula of the steady-state response autocovariance function is: ； in, is the state variable, is the output vector, For time, is the system matrix, is the integration variable, is the input matrix, is the output matrix, is a direct transfer matrix.

8. A device for calculating the statistical characteristics of noise response of a dynamic system, characterized in that: include: A stochastic differential equation determination module is used to determine the stochastic differential equation of the dynamic system according to the current noise type; A noise response statistical characteristic calculation module, used for calculating the noise response statistical characteristics of the dynamic system based on the system matrix, input matrix, output matrix and direct transfer matrix in the stochastic differential equation; The noise response statistical characteristics include mean, variance, steady-state response variance, autocovariance function and steady-state response autocovariance function.

9. 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 calculating the statistical characteristics of noise response of a dynamic system according to any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that: When the computer program is executed by a processor, the method for calculating the statistical characteristics of noise response of a dynamic system according to any one of claims 1 to 7 is implemented.

Images