Random stability analysis method for electromechanical composite transmission system

Abstract

The invention discloses a random stability analysis method for an electromechanical composite transmission system, and belongs to the technical field of electromechanical transmission. The method comprises the following steps: acquiring operation data of the electromechanical composite transmission system, and estimating drift term parameters and diffusion term parameters of an Irat stochastic differential equation representing a random road load by adopting a maximum likelihood method; establishing a random state space model according to the current balance relationship, and judging the random stability of the model by adopting a moment stability analysis method to obtain a system stability analysis result; and performing numerical simulation according to the random state space model, verifying the accuracy of the system stability analysis result, and outputting a random stability verification conclusion. According to the method, random excitation can be processed by estimating the Italian process parameters based on the maximum likelihood method and adopting the moment stability analysis method, and the method has the advantages of being good in adaptability, high in calculation efficiency and high in stability.

Description

Technical Field

[0001] This invention relates to the field of electromechanical transmission technology, and more specifically to a method for stochastic stability analysis of electromechanical composite transmission systems. Background Technology

[0002] Electromechanical hybrid drive systems, as a core component of hybrid vehicles, play a crucial role in modern transportation, especially in off-road vehicles. Their electric drive systems, through efficient energy conversion and regulation mechanisms, enhance vehicle power performance and fuel economy. However, off-road conditions are harsh, and road loads (such as random slope excitations) exhibit significant randomness and uncertainty, easily causing fluctuations in system operating states and affecting vehicle reliability and safety. Traditional analysis methods are mostly based on deterministic system models, assuming fixed loads or known disturbances, which cannot accurately describe the impact of random factors (such as road surface unevenness) on the system's dynamic processes, thus making it difficult to effectively model random excitations in simulations.

[0003] In the field of stochastic stability analysis, existing research mainly focuses on fixed scenarios such as power systems. For example, for wind power grid-connected systems, scholars have introduced Iton's stochastic integral theory and stochastic differential equation methods to establish small-disturbance stability analysis models and proposed concepts such as moment stability to describe system behavior under random disturbances. Specifically, stability is proven by constructing mathematical models of multi-machine systems containing stochastic disturbance terms, using Iton's equation theory, or by combining Lyapunov's second method and energy function method for nonlinear analysis. These methods have achieved certain results in power systems, but they do not fully consider the special characteristics of electromechanical composite transmission systems, such as the strong coupling between current balance models and road loads, and the need for real-time control. In addition, stochastic analysis methods based on scenario sets require a large number of samples to cover random factors, resulting in high computational costs, poor real-time performance, and difficulty in fully reflecting the diversity and transient characteristics of off-road conditions.

[0004] Therefore, existing technologies have the following main problems: deterministic methods cannot handle stochastic excitations, resulting in insufficient model accuracy; high computational complexity makes it difficult to meet the real-time requirements of engineering; and existing stochastic methods have poor applicability in electromechanical systems and lack targeted modeling. This restricts the stable operation of electromechanical composite transmission systems in stochastic environments, and there is an urgent need for an efficient and adaptable stochastic stability analysis method. Summary of the Invention

[0005] The purpose of this invention is to provide a method for analyzing the stochastic stability of an electromechanical composite transmission system, so as to solve the above-mentioned problems in the prior art. This method can handle stochastic excitations and has the advantages of good adaptability, high computational efficiency and strong stability.

[0006] To achieve the above objectives, the technical solution adopted by the present invention is as follows: A method for stochastic stability analysis of an electromechanical composite transmission system includes the following steps: S1. Stochastic process parameter estimation: Obtain the operating data of the electromechanical composite transmission system, including vehicle pitch angle data and random road load, and use the maximum likelihood method to estimate the drift term parameters and diffusion term parameters of Iton's stochastic differential equation characterizing the random road load. S2. System stability modeling and analysis: Based on the drift term parameters and diffusion term parameters, and according to the current balance relationship of the electromechanical composite transmission system, a stochastic state-space model of the electromechanical composite transmission system is established, and the moment stability analysis method is used to judge the stochastic stability of the stochastic state-space model to obtain the system stability analysis results. S3. Stochastic stability simulation verification: Based on the drift term parameters and diffusion term parameters, and according to the stochastic state space model, numerical simulation and modeling are performed to verify the accuracy of the system stability analysis results, and the final stochastic stability verification conclusion is output.

[0007] Furthermore, the Iton stochastic differential equation described in S1 is discretized using the Euler-Maruyama method.

[0008] Furthermore, the maximum likelihood method includes constructing the negative log-conditional probability as the objective function and solving for the parameter estimates through numerical optimization methods.

[0009] Furthermore, the operational data mentioned in S1 is used to establish a vehicle dynamics model including the vehicle body, power system, and transmission system through multibody dynamics simulation, and a standard road surface excitation is applied for simulation. The random road load is derived based on the vehicle pitch angle data.

[0010] Furthermore, the stochastic state-space model described in S2 includes the dynamic equation of DC bus voltage derived based on the current balance relationship and the stochastic road load excitation term.

[0011] Furthermore, the moment stability analysis method described in S2 includes solving the analytical solution of the Iton stochastic differential equation and analyzing whether the mean of the state variables converges and whether the variance is bounded, in order to determine the moment stability of the system.

[0012] Furthermore, S3 also includes: Before the numerical simulation, the accuracy of solving the Iton stochastic differential equation is verified. The verification process uses the Monte Carlo method to obtain numerical solutions to the equations, and the accuracy of the numerical simulation method is confirmed by comparing the error between the numerical solutions and the analytical solutions of the Iton stochastic differential equations.

[0013] Furthermore, the verification of the system stability analysis results includes: In the simulation environment, the random road load excitation is applied to the random state-space model; Observe and analyze the changes in system state variables over time; When the mean of the state variable fluctuates within a preset range and its variance remains bounded, the system is determined to have random stability.

[0014] Another object of the present invention is to provide a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for stochastic stability analysis of an electromechanical composite transmission system.

[0015] Another object of the present invention is to provide an electronic device, including a memory and a processor, wherein the memory is used to store a computer program, and the processor runs the computer program to enable the electronic device to perform the aforementioned method for analyzing the stochastic stability of an electromechanical composite transmission system.

[0016] The present invention provides a method for stochastic stability analysis of electromechanical composite transmission systems, which has the following significant advantages compared with the prior art: First, by estimating the parameters of the Iton process based on the maximum likelihood method, we can directly use historical data to perform efficient and accurate parameter identification when the probability distribution of unknown random factors is unknown. This significantly reduces the dependence on a large number of scenario samples, fundamentally reduces computational complexity, and improves the engineering applicability and real-time performance of the method.

[0017] Secondly, the moment stability analysis method adopted starts from the analytical solution of the stochastic differential equation and evaluates the stability by determining the boundedness of the mean and variance of the system state variables. This method avoids the difficulty of constructing complex Lyapunov functions, provides a direct and rigorous theoretical guarantee for the stability judgment of stochastic systems, and significantly enhances the stability robustness of the system when facing stochastic excitations.

[0018] Finally, this invention systematically applies the Ito process to the random road load modeling and stability analysis of electromechanical hybrid transmission systems, making the system highly adaptable to the variable random excitation under off-road conditions. It can effectively maintain the stability of the DC bus voltage while ensuring efficient calculation, preventing voltage drops or sudden increases, thereby greatly improving the operational reliability and control performance of hybrid off-road vehicles in complex and harsh environments. Attached Figure Description

[0019] Figure 1 This is a flowchart of the method of the present invention; Figure 2 This is a schematic diagram illustrating the division of the training set and dataset for the random road load of this invention; Figure 3 This is a schematic diagram of the maximum likelihood method of the present invention; Figure 4 This is a schematic diagram illustrating the influence of different parameter values ​​on the objective function value in this invention, where (a) represents the drift term parameter. A schematic diagram illustrating the effect on the objective function value, where (b) represents the parameters of the diffusion term. A schematic diagram illustrating the impact on the objective function value; Figure 5 The frequency distribution diagram of random road load of the present invention is shown in (a) for the training set and (b) for the test set. Figure 6 This is a schematic diagram of the current balance model of the present invention; Figure 7 This is a schematic diagram of the solution to the Ito stochastic differential equation of the present invention; Figure 8 This is a schematic diagram illustrating the error between the numerical solution and the analytical solution of this invention; Figure 9 This is a schematic diagram of the simulation results of random road load 1 of the present invention, wherein (a) is a schematic diagram of random road load and (b) is a schematic diagram of bus voltage; Figure 10 This is a schematic diagram of the simulation results of random road load 2 of the present invention, wherein (a) is a schematic diagram of random road load and (b) is a schematic diagram of bus voltage; Figure 11 This is a schematic diagram of the simulation results of random road load 3 of the present invention, wherein (a) is a schematic diagram of random road load and (b) is a schematic diagram of bus voltage; Figure 12 This is a schematic diagram showing the comparison results of bus voltage under random load and without random load according to the present invention. Detailed Implementation

[0020] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0021] This invention provides a method for stochastic stability analysis of electromechanical composite transmission systems. Its core lies in forming a complete closed-loop analysis process through steps such as stochastic process parameter estimation, system stability analysis, and stochastic stability simulation verification. For example... Figure 1As shown, the method includes: stochastic process parameter estimation, acquiring operating data of the electromechanical hybrid transmission system, including vehicle pitch angle data and stochastic road loads, and using the maximum likelihood method to estimate the drift term parameters and diffusion term parameters of the Iton stochastic differential equation characterizing the stochastic road loads; system stability modeling and analysis, based on the drift term parameters and diffusion term parameters, and according to the current balance relationship of the electromechanical hybrid transmission system, establishing a stochastic state-space model of the electromechanical hybrid transmission system, and using the moment stability analysis method to judge the stochastic stability of the stochastic state-space model to obtain the system stability analysis results; stochastic stability simulation verification, based on the drift term parameters and diffusion term parameters, and according to the stochastic state-space model, performing numerical simulation to verify the accuracy of the system stability analysis results, and outputting the final stochastic stability verification conclusion. The details are explained below.

[0022] I. Stochastic Process Parameter Estimation: Obtain the operating data of the electromechanical composite transmission system, including vehicle pitch angle data and random road loads, and use the maximum likelihood method to estimate the drift term parameters and diffusion term parameters of Iton's stochastic differential equation characterizing the random road loads.

[0023] The purpose of this step is to estimate the parameters of Iton's stochastic differential equation, which characterizes stochastic road loads, based on the running data, so as to provide an accurate stochastic input model for subsequent stability analysis.

[0024] First, operational data of the electromechanical hybrid transmission system is acquired. This data forms the basis for parameter estimation. Operational data can be obtained through multibody dynamics simulation (dynamics simulation software). A vehicle dynamics model including the vehicle body, powertrain, and transmission system is established, and a standard road surface excitation (such as a Class E road surface) is applied for simulation. The random road load is derived based on the vehicle pitch angle data.

[0025] In the simulation results, the change in the pitch angle during vehicle movement is approximated as a random slope excitation from the road surface. Since this random excitation is unpredictable in actual driving, the vehicle pitch angle needs to be extracted from the dynamic simulation results for data processing and analysis. By approximating the pitch angle as the slope angle and calculating the corresponding slope resistance component, the road load is calculated using a formula, including both the deterministic and random components. The deterministic component can be calculated; that is, assuming a zero driving slope, the deterministic part of the road load is: (1) m represents the vehicle mass, a known quantity, and is set according to the target vehicle model; in this embodiment, it is taken as a reference value for a 20-ton off-road vehicle. g represents the gravitational acceleration, taken as 9.8. f represents the rolling resistance coefficient, a known quantity, and is set according to the road surface type; in this embodiment, it is taken as 0.03 (corresponding to a typical off-road surface). Even if the random portion cannot be measured, it can be calculated based on the total road load and the determined portion, i.e.: (2) in, For random road loads, Total road load, To determine the partial load.

[0026] After obtaining the above data, it is necessary to extract the sequence representing the random road load. For example... Figure 2 As shown, the total road load is decomposed into a deterministic part and a random part, and the processed data is divided into a training set and a test set to prepare for subsequent parameter estimation. In this embodiment, the first 70% of the data is used as the training set, and the last 30% of the data is used as the test set.

[0027] Next, the maximum likelihood method is used for parameter estimation, such as... Figure 3 As shown, its core principle is to construct a likelihood function and solve for its maximum value. In statistics, a likelihood function is a function of the parameters in a statistical model, representing the likelihood of the model parameters. In simpler terms, likelihood is used to estimate parameters of sample properties given known observations. The maximum likelihood method involves constructing a negative log-conditional probability as the objective function and solving for the parameter estimates using numerical optimization methods.

[0028] At this point, the problem of determining the maximum likelihood estimator transforms into the problem of finding the maximum value of the equation. To avoid the calculation results exceeding the lower limit of computer floating-point numbers and for ease of computation, the likelihood function is usually... Take the logarithm and then solve for it. Differentiate to obtain the parameters. The estimated value, namely: (3) By parameterizing the drift and diffusion terms of the Iton stochastic differential equation model of random road load, the following Iton stochastic differential equation with undetermined parameters is obtained: (4) in and These represent the parameterized drift and diffusion terms, respectively. These are parameters to be determined. Depending on the different random data and the desired model fit, different function forms and parameters to be determined can be selected. The more parameters to be determined, the stronger the model fit, but at the same time, the higher the requirements for the sample data.

[0029] Since the running data are all in discrete form, the above formula needs to be discretized. According to the Euler-Maruyama method, the discretization formula for the Itō process is as follows: (5) In the formula Since the sampling step size is a known quantity, it is set according to the data acquisition frequency, and in this embodiment, it is taken to be between 0.01s and 0.1s. Based on the properties of the Wiener process, Satisfies Gaussian distribution Therefore, equation (5) can be written as: (6) In the formula, (7) The maximum likelihood estimation method is used to solve for the undetermined parameters, with the goal of minimizing the negative log-conditional probability. (8) Since the Itō process has the property of incremental independence, the expression for the objective function can be obtained as follows: (9) Based on the values ​​of the running data, it can be calculated that... As shown below: (10) In the formula, (11) Based on equations (9) and (10), the specific form of the likelihood function can be obtained as follows: (12) The above equation is the objective function for parameter estimation using the maximum likelihood method. The minimum objective function value is obtained by finding the optimal parameter values, and it can be solved using numerical methods.

[0030] This invention uses a linear Iton process to model stochastic road loads, taking the training set data as known discrete data of stochastic road loads, and employing the maximum likelihood method for parameter estimation. The parameters to be estimated are the drift term parameters. and diffusion term parameters When using the Iton process model for stochastic road loads as shown in the following formula, the parameter vector θ is specifically defined as the drift term parameters. and diffusion term parameters .

[0031] (13) To verify the accuracy of the parameter estimation, the objective function values ​​of different parameter values ​​were compared on the training and test sets. The Euler-Maruyama method was used to perform numerical simulations on the estimated model, and the simulation results were compared with the probability distribution of the actual data.

[0032] The objective function value is calculated according to equation (12), and the objective function values ​​with different parameter values ​​are compared in the training and test sets. For ease of comparison, the function values ​​are normalized to the interval [0,1], as follows: Figure 4 As shown, the parameter combination that yields the lowest objective function value in the training set still achieves good results in the test set.

[0033] The Euler-Maruyama method was used to numerically simulate the Iton process model of stochastic road load after parameter estimation. Statistical analysis was performed on the obtained stochastic process to obtain its probability distribution histogram, which was then compared with the probability distribution of actual stochastic road load. Figure 5 As shown in the table, the probability distribution of the training set can be well described by the Itoh model, while the probability distribution of the test set deviates slightly from that of the Itoh model, but the overall trend is roughly the same. The distributions of the actual data and the Itoh model data within the 95% confidence intervals are calculated, as shown in Tables 1 and 2. The data in the tables show that the mean and the upper and lower limits of the 95% confidence intervals for the actual data and the Itoh model are very close, while the standard deviation and the upper and lower limits of the 95% confidence interval for the standard deviation differ slightly. However, overall, the Itoh model still has high quantitative accuracy.

[0034] Table 1. Data distribution within the 95% confidence interval of the training set.

[0035] Table 2 shows the data distribution within the 95% confidence interval of the test set.

[0036] The above analyses all demonstrate that, in the case of unknown data probability distribution, the Iton process obtained through parameter estimation based on operational data is relatively accurate and can be applied to the formulation of subsequent control strategies.

[0037] II. System Stability Modeling and Analysis: Based on the drift term parameters and diffusion term parameters, and according to the current balance relationship of the electromechanical composite transmission system, a stochastic state-space model of the electromechanical composite transmission system is established. The moment stability analysis method is used to judge the stochastic stability of the stochastic state-space model and obtain the system stability analysis results.

[0038] After obtaining accurate stochastic process model parameters, this step aims to establish a stochastic state-space model of the system and perform theoretical analysis using the moment stability method.

[0039] First, a stochastic state-space model of the electric drive system is established. The current balance model of the series hybrid off-road vehicle is as follows: Figure 6 As shown. Considering the stochastic nature of vehicle driving demand caused by road conditions, the subsequent design of the control model only considers the power consumption of the engine, motor, and energy storage equipment. The power consumption of other equipment is considered as a known quantity and is not specifically shown in the formula for ease of calculation.

[0040] Based on the DC bus voltage, the current balance relationship between the engine-generator set, battery, supercapacitor, and load is as follows: (14) in, For engine-generator set current, For battery current, For supercapacitor current, This is the load current.

[0041] Based on the aforementioned Iton process model of stochastic road load, the longitudinal drive demand power of the vehicle, which includes stochasticity, can be calculated as follows: (15) in, To drive the required power vertically, For road load, For air resistance, To increase resistance, The longitudinal speed of the vehicle. For the deterministic components of road load, This represents the random component of the road load. For deterministic power, It represents random power.

[0042] This paper analyzes and controls the electric drive system of a hybrid off-road vehicle from the perspective of a DC microgrid. Considering the DC bus voltage stability problem, the power model described above is transformed into a current-voltage model based on the current balance equation, as shown below: (16) Right now: (17) in, The load current is equal to, For deterministic current, It is a nondeterministic current.

[0043] Based on the dynamic model of the supercapacitor, the dynamic balance equation of the DC bus voltage can be obtained as follows: (18) Where C represents the capacitance.

[0044] Combining equations (13) and (18), a first-order inertial element is used to describe the generator response delay, ultimately establishing a stochastic state-space equation to describe the dynamic behavior of the system under stochastic excitation. The stochastic state-space model includes the DC bus voltage dynamic equation derived from the current balance relationship and the stochastic road load excitation term, expressed as follows: (19) In the formula, For a standard Gaussian process, the variables of the stochastic system are defined as follows: (20) Subsequently, the stability of the above stochastic system was determined using moment stability analysis, and the system stability analysis results were obtained.

[0045] (1) Solve the analytical solution of Iton's stochastic differential equation. For linear Itō stochastic differential equations We can use the Itô formula to find its analytical solution.

[0046] First, the fundamental solution matrix of the equation is: .

[0047] According to the method of variation of constants and the theory of stochastic calculus, this stochastic differential equation is in the initial state Analytical solution below The format is: The first term of the above equation The second term is the response of the deterministic part (drift term). This is the response (diffusion term) to the random disturbance term.

[0048] (2) Determine the mean stability (first moment stability) of the system. For analytical solutions Taking the expected value from both sides Due to Ito's integral The expected value of is 0, therefore: Judgment criterion: If all eigenvalues ​​of system matrix A have negative real parts (i.e., the original deterministic system is stable), then when time... At that time, the state transition matrix .

[0049] Conclusion: If the following conditions are met If the mean is satisfied, the electromechanical composite transmission system is determined to be mean-stable. In this embodiment, the mean is ensured by using pole placement or feedback control to make matrix A satisfy the Hurwitz condition.

[0050] (3) Determine the mean square stability (second moment stability) of the system. Modulus of system state Take the expected value to determine whether the energy is diverging. Based on the analytical solution and Itô's isometry property: in This represents the Frobenius norm.

[0051] The expression for the system's mean square error is: Judgment basis: Since matrix A is stable, there exist constants K>0 and λ>0 such that Therefore, the integral term is: along with The integral converges to a finite upper bound. .

[0052] Conclusion: If (C is a constant), meaning the variance of the system state is bounded, then the system is determined to be mean-square stable.

[0053] (4) Output analysis results Based on the calculations in steps (2) and (3), if the system simultaneously satisfies the condition that the mean tends to zero and the variance is bounded, then the analysis result "the system has random stability" is output; otherwise, the system is indicated to be at risk of instability.

[0054] The moment stability analysis method involves solving the analytical solution of the Iton stochastic differential equation and analyzing whether the mean and variance of the state variables converge to determine the moment stability of the system. Specifically, based on the theory of Iton stochastic differential equations, by solving the analytical solution of the system's state equations, the mean and variance of the state variables (such as DC bus voltage) are analyzed to determine whether the system is mean-square stable mathematically. This avoids the difficulty of constructing complex Lyapunov functions and provides a clear mathematical basis for stability judgment.

[0055] III. Stochastic Stability Simulation Verification: Based on the drift term parameters and diffusion term parameters, and according to the stochastic state-space model, numerical simulation and modeling are performed to verify the accuracy of the system stability analysis results, and the final stochastic stability verification conclusion is output.

[0056] After obtaining the drift term parameters With diffusion term parameters Based on the established stochastic state-space model, this step verifies the accuracy of the aforementioned system stability analysis results through numerical simulation and modeling. The analysis mainly focuses on two aspects: simulation of the solutions to the stochastic differential equations and verification of the stability of the stochastic system. Since subsequent computer simulations primarily employ numerical simulation, the accuracy of solving the Iton stochastic differential equations is first verified before the numerical simulation and modeling. This verification uses the Monte Carlo method to obtain the numerical solutions to the equations, and the accuracy of the numerical simulation method is confirmed by comparing the errors between the numerical solutions and the analytical solutions to the Iton stochastic differential equations.

[0057] In the preceding content, the discretization formula (5) of Itō's stochastic differential equation was given based on the Euler-Maruyama method. The numerical solution of Itō's stochastic differential equation can be simulated using Monte Carlo simulation. The preceding content also derived the form of the analytical solution of the linear Itō stochastic differential equation, which can also be simulated using MATLAB. The numerical and analytical solutions obtained from the simulation are shown below. Figure 7 As shown.

[0058] from Figure 7 As can be seen, the numerical solution obtained by Monte Carlo simulation is almost identical to the analytical solution. Specific error details are as follows: Figure 8 As shown, the error value fluctuates in the range of -0.05 to 0.04, with most of it concentrated between -0.02 and 0.02. The overall error is small, so the accuracy of the numerical solution is good and can be used in subsequent system simulation calculations.

[0059] Finally, a system model was built in the MATLAB / Simulink environment to verify closed-loop stochastic stability. In the simulation environment, the stochastic road load excitation was applied to the stochastic state-space model; the changes in the system state variables over time were observed and analyzed; when the mean of the state variables fluctuated within a preset range and their variance remained bounded, the system was determined to have stochastic stability. The determination of the road load was similar, based on the estimated parameters. and Three different intensities of random road load excitation (26%, 52%, and 78% of the defined portion) were applied (loads 1 to 3). A system model was built using the MATLAB / Simulink simulation environment, and simulations were performed. The random portion of the road load was zero before 100 seconds; random excitation was added starting from the 100th second. The results are as follows. Figures 9 to 11 As shown. The overall range of fluctuations in random load 1 is relatively small, in to Between, and mainly concentrated to The overall range of random load 2 fluctuations is in to Between, and mainly concentrated to The overall range of random load fluctuation is relatively large. to Between, and mainly concentrated to Because the determining part of the road load is Therefore, the three sets of random excitations account for 26%, 52%, and 78% of the deterministic portion, respectively, indicating that the intensity of random road load excitation in the system is relatively large. The results of the three bus voltage sets show that as the intensity of random road load excitation increases, the fluctuation of the DC bus voltage after 100 seconds also gradually increases. However, it fluctuates within a limited range around a stable value of 900V, with maximum fluctuation amplitudes of 8V, 10V, and 12V, respectively. No uncontrolled voltage drop or sudden increase that is difficult to recover from was observed.

[0060] The bus voltage results without considering random road load excitation are compared with the results under the three different excitation intensities mentioned above. The intensity of random road load is quantified, and its quantified mean and diffusion degree are obtained using the Iton process parameter estimation method proposed earlier. Figure 12 As shown in Table 3, it can be seen that as the diffusion intensity of random loads increases, the variance of the bus voltage also increases, that is, the fluctuation of the bus voltage also increases, but its fluctuation is still bounded.

[0061] Table 3 Simulation results under different random loads

[0062] Therefore, under high-intensity random excitation, the system remains mean-stable and mean-square-stable. This step, through the aforementioned simulation platform, outputs the stability analysis results (i.e., the conclusion that the system remains mean-stable and mean-square-stable under different random loads) as the final stochastic stability verification conclusion. This conclusion can be in the form of a simulation report, a data file, or directly displayed on the simulation interface, thus completing the entire stochastic stability verification process.

[0063] In summary, this invention reduces computational complexity and improves engineering applicability through maximum likelihood parameter estimation; it provides a direct stability criterion for stochastic systems through moment stability analysis; and finally, through system simulation verification, it is proved that the method can effectively maintain the stability of the system under strong stochastic excitation while ensuring computational efficiency, thus significantly improving the operational reliability of the vehicle.

[0064] This embodiment provides a computer-readable storage medium storing a computer program that, when executed by a processor, implements the aforementioned method for analyzing the stochastic stability of an electromechanical composite transmission system.

[0065] This embodiment provides an electronic device, including a memory and a processor. The memory stores a computer program, and the processor runs the computer program to enable the electronic device to perform the aforementioned method for analyzing the stochastic stability of an electromechanical composite transmission system.

[0066] Embodiments of the present invention may be provided as methods, systems, or computer program products. Therefore, the present invention may take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention may take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0067] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0068] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0069] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0070] Contents not described in detail in this specification are prior art known to those skilled in the art. It is hereby indicated that the above description is intended to help those skilled in the art understand this invention, but does not limit the scope of protection of this invention. Any equivalent substitutions, modifications, improvements, or simplifications of the above descriptions that do not depart from the essential content of this invention fall within the scope of protection of this invention.

Claims

1. A method for stochastic stability analysis of an electromechanical composite transmission system, characterized in that, Includes the following steps: S1. Stochastic process parameter estimation: Obtain the operating data of the electromechanical composite transmission system, including vehicle pitch angle data and random road load, and use the maximum likelihood method to estimate the drift term parameters and diffusion term parameters of Iton's stochastic differential equation characterizing the random road load. S2. System stability modeling and analysis: Based on the drift term parameters and diffusion term parameters, and according to the current balance relationship of the electromechanical composite transmission system, a stochastic state-space model of the electromechanical composite transmission system is established, and the moment stability analysis method is used to judge the stochastic stability of the stochastic state-space model to obtain the system stability analysis results. S3. Stochastic stability simulation verification: Based on the drift term parameters and diffusion term parameters, and according to the stochastic state space model, numerical simulation and modeling are performed to verify the accuracy of the system stability analysis results, and the final stochastic stability verification conclusion is output.

2. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1, characterized in that: The Iton stochastic differential equation described in S1 is discretized using the Euler-Maruyama method.

3. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1 or 2, characterized in that: The maximum likelihood method involves constructing the negative log-conditional probability as the objective function and solving for the parameter estimates using numerical optimization methods.

4. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1, characterized in that: The operational data described in S1 is used to establish a vehicle dynamics model including the vehicle body, power system, and transmission system through multibody dynamics simulation, and a standard road surface excitation is applied for simulation. The random road load is derived based on the vehicle pitch angle data.

5. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1, characterized in that: The stochastic state-space model described in S2 includes the dynamic equation of DC bus voltage derived based on the current balance relationship and the stochastic road load excitation term.

6. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1, characterized in that: The moment stability analysis method described in S2 includes solving the analytical solution of the Iton stochastic differential equation and analyzing whether the mean of the state variables converges and whether the variance is bounded, in order to determine the moment stability of the system.

7. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1, characterized in that, S3 also includes: Before the numerical simulation, the accuracy of solving the Iton stochastic differential equation is verified. The verification process uses the Monte Carlo method to obtain numerical solutions to the equations, and the accuracy of the numerical simulation method is confirmed by comparing the error between the numerical solutions and the analytical solutions of the Iton stochastic differential equations.

8. The method for stochastic stability analysis of an electromechanical composite transmission system according to claim 1, characterized in that, The verification of the system stability analysis results includes: In the simulation environment, the random road load excitation is applied to the random state-space model; Observe and analyze the changes in system state variables over time; When the mean of the state variable fluctuates within a preset range and its variance remains bounded, the system is determined to have random stability.

9. A computer-readable storage medium, characterized in that: It stores a computer program that, when executed by a processor, implements a method for stochastic stability analysis of an electromechanical composite transmission system as described in any one of claims 1-8.

10. An electronic device, characterized in that: It includes a memory and a processor, wherein the memory is used to store computer programs and the processor runs the computer programs to enable the electronic device to perform the stochastic stability analysis method for an electromechanical composite transmission system according to any one of claims 1-8.

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