Double-rate diesel engine vibration isolation nonlinear system parameter estimation method based on simulated annealing

Abstract

The invention discloses a simulated annealing-based dual-rate diesel engine vibration isolation nonlinear system parameter estimation method, which comprises the following steps of: obtaining a first identification model of a dual-rate Hammerstein diesel engine vibration isolation nonlinear system based on a dual-rate Hammerstein diesel engine vibration isolation nonlinear system model; based on auxiliary model identification, converting the first identification model to obtain a second identification model; and based on an improved simulated annealing algorithm, combining the improved simulated annealing algorithm with multi-innovation identification to obtain parameters of the second identification model. According to the method, the problem of incomplete data caused by double-rate sampling is solved by adopting the idea of an auxiliary model; and then, optimizing the fitness function based on an improved multi-information simulated annealing algorithm (MI-SA) of an auxiliary model, and realizing parallel search for unknown parameter estimation. In addition, a Doppler cooling effect type cooling function is introduced, the convergence rate of the algorithm is improved, and the identification precision and the optimization speed are improved.

Description

Technical Field

[0001] The present application belongs to the field of mechanical design and modeling technology, and specifically relates to a parameter estimation method for a dual-rate diesel engine vibration isolation nonlinear system based on simulated annealing. Background Art

[0002] The nonlinear vibration isolation system of a diesel engine primarily involves the technical challenges of reducing vibration and controlling the impact of mechanical vibration on equipment and the environment. As an internal combustion engine, the diesel engine generates strong periodic and impact vibrations during operation. This vibration not only reduces the service life of the mechanical equipment but may also affect the surrounding structure and environment. Therefore, diesel engine vibration isolation technology is very important. In recent years, active vibration control has made great progress in theory, technology, and methods. It has been widely used in aerospace, shipbuilding, vehicle engineering and other fields, such as the research on active vibration isolation technology for diesel engine devices, and has made breakthroughs in the transformation of nonlinear vibration to active and passive vibration control technology. By establishing a nonlinear dynamic model of the diesel engine and the vibration isolation device, the vibration response characteristics of the vibration isolation system under different operating conditions can be analyzed. Therefore, studying the modeling problem of the nonlinear vibration isolation system of the diesel engine is of great research significance.

[0003] Nonlinear system parameter estimation stems primarily from the widespread presence of nonlinear systems in fields such as engineering, physics, and economics. As the complexity of nonlinear systems increases in practical problems, accurately estimating their internal parameters has become a critical step in system modeling, control, and optimization. Compared to linear systems, nonlinear systems exhibit more complex dynamic characteristics, such as multistability, periodicity, and chaotic behavior. Therefore, effectively estimating their parameters is a significant challenge. For example, the paper "Parameter estimation of nonlinear system based on genetic algorithms" addresses the diversity of nonlinear system modes and proposes a universal parameter estimation method based on genetic algorithms, which can be applied to most nonlinear system modes. The paper "Frequency domain identification of continuous-time Hammerstein systems with adaptive continuous-time rational orthonormal basis functions" proposes a continuous-time nonlinear system identification method based on adaptive generalized rational orthonormal basis functions. Therefore, nonlinear system parameter estimation has significant application in engineering problems. However, research on nonlinear dual-rate systems remains to be further explored. This paper proposes an identification method combining auxiliary models and multi-innovation optimization for systems with dual-rate sampling and verifies its effectiveness.

[0004] The simulated annealing algorithm (SA) is a global optimization algorithm based on the annealing process in thermodynamics. First proposed by Kirkpatrick et al. in 1983, it is widely used to solve combinatorial optimization problems. The paper "A simulated annealing algorithm for constrained multi-objective optimization" introduces a simulated annealing algorithm for constrained multi-objective optimization. When searching in the feasible region, the algorithm behaves similarly to the recently proposed archived multi-objective simulated annealing algorithm, while when searching in the infeasible region, it attempts to minimize constraint violations by moving in an approximate descent direction. In the paper "A hybrid harmony search and simulated annealing algorithm for continuous optimization," the authors propose a hybrid algorithm based on harmony search and simulated annealing, combining the strengths of both in a complementary manner. Therefore, the simulated annealing algorithm has superior optimization speed and can be applied in system identification. Summary of the Invention

[0005] This application provides a dual-rate diesel engine vibration isolation nonlinear system parameter estimation method based on simulated annealing to solve the above technical problems.

[0006] To solve the above technical problems, a technical solution adopted in this application is: a dual-rate diesel engine vibration isolation nonlinear system parameter estimation method based on simulated annealing, comprising:

[0007] Based on the dual-rate Hammerstein diesel engine vibration isolation nonlinear system model, a first identification model of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system is obtained;

[0008] Based on auxiliary model identification, converting the first identification model to obtain a second identification model;

[0009] Based on the improved simulated annealing algorithm, the improved simulated annealing algorithm is combined with multi-innovation identification to obtain parameters of the second identification model.

[0010] Furthermore, the method for obtaining a first identification model of a dual-rate Hammerstein diesel engine vibration isolation nonlinear system based on the dual-rate Hammerstein diesel engine vibration isolation nonlinear system model includes:

[0011] Based on formulas (1)-(2), the Hammerstein diesel engine vibration isolation nonlinear system model is obtained; wherein, the formulas (1)-(2) are:

[0012] μ(t)=h[x(t)] (1);

[0013]

[0014] Among them, the nonlinearity h is derived from the basis function h i The linear combination of x(t) is the system input, y(t) is the system output, μ(t) is the unmeasurable intermediate variable, and A(z -1 ), B(z -1 ), C(z -1 ), D(z -1 ) is the unit shift operator z -1 polynomial, e(t) is a Gaussian white noise signal;

[0015] Based on formula (3), the nonlinear part of the Hammerstein diesel engine vibration isolation nonlinear system is constructed; wherein, the formula (3) is:

[0016]

[0017] Among them, α i is the nonlinear coefficient, n α is the number of basis functions;

[0018] Based on formula (4), the first identification model of the Hammerstein diesel engine vibration isolation nonlinear system is constructed; wherein, the formula (4) is:

[0019]

[0020] Among them, H(t), is the information vector of the system; α, a, c and d are the parameter vectors of the system, and the superscript T represents the transpose.

[0021] Furthermore, the method for obtaining the second identification model includes:

[0022] Initializing parameters of the first identification model;

[0023] constructing an output vector in the auxiliary model based on active control error input data and position output data of the actuator;

[0024] Based on the input information vector and parameter vector, obtaining estimated values ​​of the information vector and parameter vector in the auxiliary model, and constructing a stacked information matrix;

[0025] Based on the stacked information matrix, an estimated value of a parameter vector, an estimated value of an unsampled output, and an estimated value of noise are obtained.

[0026] Furthermore, the method for obtaining the parameters of the second identification model based on the improved simulated annealing algorithm by combining the improved simulated annealing algorithm with multi-innovation identification includes:

[0027] Initialize the parameters of the second identification model; wherein, initialize the initial temperature, generate the initial solution using a random generation function, set the Markov chain length, decay parameter, step factor, termination temperature, tolerance, upper limit of the solution, and lower limit of the solution;

[0028] Calculate the information vector and output vector based on the solution vector and construct the fitness function;

[0029] Performing a perturbation operation on the initial solution based on a random function to generate a new solution, and calculating an increment between the new solution and the initial solution;

[0030] Based on the increment, parameters of the second identification model are obtained.

[0031] Furthermore, the method for obtaining the parameters of the second identification model based on the increment includes:

[0032] Determine whether the increment is less than zero; if so, accept the new solution; if not, accept it based on probability using the Metropolis probability criterion;

[0033] Determine whether the new solution is the optimal solution; if so, update the solution vector; if not, retain the initial solution;

[0034] Enable the "Doppler" type attenuation function to attenuate the temperature value, continue the optimization iteration process, and determine whether the current temperature iteration number has been reached; if so, reduce the temperature; if not, continue to execute the previous step;

[0035] Determine whether the temperature value reaches the termination temperature; if so, terminate the calculation; if not, continue to execute the loop steps;

[0036] Repeat the above steps until the termination condition is met, and use the optimal solution obtained in the final iteration as the parameters of the second identification model.

[0037] The beneficial effects of this application are as follows: First, the application adopts the concept of an auxiliary model to solve the data incompleteness problem caused by dual-rate sampling. Then, based on the auxiliary model, an improved multi-innovation simulated annealing algorithm (MI-SA) is used to optimize the fitness function, enabling parallel search for unknown parameter estimates. Furthermore, a Doppler cooling effect-based cooling function is introduced to improve the algorithm's convergence rate, enhancing identification accuracy and optimization speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0038] Figure 1 This is a simplified structural diagram of the diesel engine active vibration isolation nonlinear system of the present application;

[0039] Figure 2 This is a flow chart of an embodiment of a dual-rate diesel engine vibration isolation nonlinear system parameter estimation method based on simulated annealing of the present application;

[0040] Figure 3 yes Figure 1 A Hammerstein system structure diagram of an embodiment of step S1 in FIG.

[0041] Figure 4 for Figure 1 A structural diagram of an auxiliary model of an embodiment of step S2 in FIG.

[0042] Figure 5 Figure 1 A schematic flow chart of an embodiment of step S2 in FIG.

[0043] Figure 6 Figure 1 A schematic flow chart of an embodiment of step S3 in FIG.

[0044] Figure 7 Figure 6 A schematic flow chart of an embodiment of step S34 in FIG.

[0045] Figure 8 1 is a schematic diagram showing the variation of parameter estimation error of the MI-SA algorithm for the dual-rate Hammerstein diesel engine vibration isolation nonlinear system with the number of iterations in Example 1;

[0046] Figure 9 1 is a schematic diagram showing how the adaptation curve of the MI-SA algorithm for the dual-rate Hammerstein diesel engine vibration isolation nonlinear system changes with the number of iterations in Example 1;

[0047] Figure 10 1 is a schematic diagram showing the change of parameter estimation values ​​of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system with the number of iterations in Example 1;

[0048] Figure 11 is a fitting curve of the estimated output and actual output of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system based on the MI-SA algorithm in Example 1;

[0049] Figure 12 2 is a schematic diagram showing the variation of parameter estimation error of the MI-SA algorithm for the dual-rate Hammerstein diesel engine vibration isolation nonlinear system with the number of iterations in Example 2;

[0050] Figure 13 Schematic diagram of the change of the adaptation curve of the MI-SA algorithm of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system with the number of iterations in Example 2;

[0051] Figure 14 Schematic diagram showing the change of parameter estimation values ​​of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system with the number of iterations in Example 2;

[0052] Figure 15 It is a fitting curve of the estimated output and actual output of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system based on the MI-SA algorithm in Example 2. DETAILED DESCRIPTION

[0053] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with specific embodiments.

[0054] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways than those described herein. Therefore, the present invention is not limited to the specific embodiments disclosed below.

[0055] See Figure 1 The diesel engine active vibration isolation nonlinear system is mainly composed of the diesel engine upper mass subsystem composed of the diesel engine, dynamometer and coupling, as well as the subsystems such as the common bracket, vibration isolator-hydraulic actuator, intermediate mass, lower mass and foundation beam. Its active control error channel has a coupling effect, and the hardware decoupling is carried out by adopting four intermediate mass blocks, four actuators and independent control channels to form four decoupling channels of the error channel. Using the actual diesel engine as the primary vibration source, a diesel engine vibration isolation double-layer vibration isolation system is established to conduct active vibration control research. Due to the coupled nonlinear vibration of the vibration isolation system and the fact that the actuator is a hydraulic servo system, the vibration active control error channel has serious pure input type nonlinearity, which constitutes Hammerstei n Therefore, this application studies the modeling process of a dual-rate Hammerstein diesel engine vibration isolation nonlinear system based on active control error input and actuator position output.

[0056] See Figure 2 , Figure 2 This is a flow chart of an embodiment of a dual-rate diesel engine vibration isolation nonlinear system parameter estimation method based on simulated annealing in this application. The method includes:

[0057] Step S1. Based on the dual-rate Hammerstein diesel engine vibration isolation nonlinear system model, a first identification model of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system is obtained.

[0058] For details, see Figure 3 , Figure 3 yes Figure 2The Hammerstein system structure of an embodiment of step S1 in the embodiment of the invention is as follows: Based on formulas (1)-(2), a dual-rate Hammerstein diesel engine vibration isolation nonlinear system model is obtained; wherein formulas (1)-(2) are:

[0059] μ(t)=h[x(t)] (1);

[0060]

[0061] Among them, the nonlinearity h is derived from the basis function h i The linear combination of x(t) is the system input, y(t) is the system output, μ(t) is the unmeasurable intermediate variable, e(t) is the Gaussian white noise signal, A(z -1 ), B(z -1 ), C(z -1 ), D(z -1 ) is the unit shift operator z -1 The polynomials are:

[0062]

[0063] Based on formula (3), the nonlinear part of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system is obtained; where formula (3) is:

[0064]

[0065] Among them, α i is the nonlinear coefficient, n α is the number of basis functions;

[0066] Based on formula (5), obtain the intermediate variable Wherein, formula (5) is:

[0067]

[0068] Based on formula (2), we can get formula (6)

[0069]

[0070] Substituting formula (3) into formula (6) yields formula (7):

[0071]

[0072] Based on formula (5), we can get:

[0073]

[0074] Substituting formula (8) into formula (7) yields:

[0075]

[0076] Define some parameter vectors as:

[0077]

[0078] Then define some information vectors H(t), Expressed as:

[0079]

[0080] Then, the first identification model of the Hammerstein diesel engine vibration isolation nonlinear system is obtained based on formula (4); wherein, formula (4) is:

[0081]

[0082] Step S2: Based on auxiliary model identification, convert the first identification model to obtain a second identification model.

[0083] For details, see Figure 4 ,Based on the auxiliary model identification, the system model is transformed to obtain a second identification model that can be directly identified using dual-rate data.

[0084] See Figure 5 , Figure 5 yes Figure 2 Flowchart of an embodiment of step S2 in FIG. Step S2 includes:

[0085] Step S21: Initialize the parameters of the first identification model.

[0086] Step S22: Constructing an output vector in the auxiliary model based on the active control error input data and the position output data of the actuator.

[0087] Specifically, the output variables under the auxiliary model are obtained based on formulas (10)-(12); wherein formulas (10)-(12) are:

[0088]

[0089] in, Know is the estimated value of the intermediate variable, is the estimated output; is the estimated value of the polynomial.

[0090] Step S23. Based on the input information vector and parameter vector, obtain estimated values ​​of the information vector and parameter vector in the auxiliary model, and construct a stacked information matrix.

[0091] Specifically, the output variables under the auxiliary model are obtained based on formulas (10)-(12); wherein formulas (10)-(12) are:

[0092]

[0093] in, and is the estimated value of the intermediate variable, is the estimated output; is the estimated value of the polynomial.

[0094] Step S24: Based on the stacked information matrix, obtain an estimated value of the parameter vector, an estimated value of the unsampled output, and an estimated value of the noise.

[0095] Specifically, based on formulas (13)-(16), the transformed polynomial A(z -1 ), B(z -1 ), C(z -1 ), D(z -1 ) estimated value, and then calculate the estimated output according to formulas (17) and (18) respectively and estimated intermediate variables Wherein, formulas (13)-(17) are:

[0096]

[0097] For parameters The estimated value of For parameters The estimated value of For parameters The estimated value of For parameters The estimated value of , based on formula (18), can be obtained as:

[0098]

[0099] Among them, the information vector in formula (19) and parameter vector for:

[0100]

[0101] Substituting formula (3) and formula (19) into formula (17), we can obtain formula (20):

[0102]

[0103] At this time, the parameter vector θ, It can be expressed as:

[0104]

[0105] Information Vector and Φ(t) is

[0106]

[0107] In the dual-rate system, pt is used instead of t, and the entire model can be expressed as formula (21):

[0108]

[0109] Under this dual-rate system model, is the dual-rate estimation output, is the dual-rate estimation intermediate variable, e(pt) is the dual-rate noise; the dual-rate information vector Φ(pt) can be expressed as:

[0110]

[0111] Step S3: Based on the improved simulated annealing algorithm, the improved simulated annealing algorithm is combined with multi-innovation identification to obtain parameters of the second identification model.

[0112] For details, see Figure 5 , Figure 5 for Figure 2 Flowchart of an embodiment of step S3 in FIG. Step S3 includes:

[0113] Step S31. Initialize the parameters of the second identification model; among which, initialize the initial temperature, generate the initial solution using a random generation function, set the Markov chain length, attenuation parameter, step factor, termination temperature, tolerance, upper limit of solution and lower limit of solution.

[0114] Specifically, the parameters of the second identification system model are initialized, that is, the appropriate Markov chain length ML, attenuation parameter J, step size factor S, initial temperature T0, and termination temperature T are selected. f , tolerance YZ, solution upper limit Solve the lower limit

[0115] Step S32: Calculate the information vector and the output vector according to the solution vector, and construct a fitness function.

[0116] Initialize the solution vector according to formula (22); formula (22) is:

[0117]

[0118] in, is the initial solution vector, and rand represents a random number between 0 and 1.

[0119] Step S33: Perform a perturbation operation on the initial solution based on a random function to generate a new solution, and calculate the increment between the new solution and the initial solution.

[0120] Specifically, based on formulas (23)-(28), an estimate of the k-th iteration parameter vector is created: Formulas (23)-(28) are:

[0121]

[0122] in, is the estimated value of the k-th iteration polynomial; For parameters The estimated value of For parameters The estimated value of For parameters The estimated value of For parameters The estimated value of For parameters estimated value of;

[0123] Then, the k-th iteration noise estimate is calculated based on formula (29) and formula (30): and the kth information vector estimate Based on formula (31), the estimated value of the information matrix for the kth iteration is obtained Formula (29), formula (30) and formula (31) are:

[0124]

[0125]

[0126] Among them, r represents the length of the new information, is the k-1th output estimate, The estimated value of the k-th intermediate variable μ(pt-i), is the estimated value of the k-1th intermediate variable q(pt-i).

[0127] Finally, based on formula (32) and formula (33), the information vector V can be obtained k (r, pt) and the output vector Y(r, pt), formulas (32) and (33) are:

[0128]

[0129] Calculate the fitness value based on formula (34) Formula (34) is:

[0130]

[0131] Step S34: Based on the increment, obtain the parameters of the second identification model.

[0132] Specifically, step S341. If ΔE < 0, then accept the new solution; if ΔE > 0, then use the Metropolis probability criterion to accept the new current solution with probability pM. T represents the current temperature, and the Metropolis probability formula (37) is:

[0133]

[0134] Step S342: Determine whether the new solution is the optimal solution. If the fitness value of the new solution is greater than the fitness value of the initial solution, then the new solution is the optimal solution. will replace the initial solution in the next iteration; otherwise, the initial solution Will be saved; formula (38) is:

[0135]

[0136] Step S343. Execute the temperature attenuation function, k is the number of iterations, K is the total number of cooling times, J is the attenuation parameter, and the "Doppler" type attenuation function is enabled to attenuate the T value according to formula (39). Return to step S33 to continue the optimization iteration process until the termination temperature T is reached. f The iteration is terminated when T0 is the initial temperature, T f is the termination temperature, formula (39) is:

[0137] T=T0J k (cos(π / 2(1-k / K)))+cos(π / (2T0(1-k / K))) (39);

[0138] The "Doppler" curve effectively combines the advantages of both methods while eliminating their drawbacks. It not only approaches low temperatures at a moderate pace, but also undergoes a continuous "tempering" process during the latter half of the annealing process. This allows the algorithm multiple opportunities to escape local optima during the optimization process, making it easier to find the global optimal solution. Because of the multiple cooling processes, the algorithm incorporates a memory function to prevent the optimal solution from being lost during these cooling steps.

[0139] Step S344: After the temperature decay is completed, the optimal objective function value is returned, and the optimal solution of the final iteration is used as the parameter of the second identification model of the dual-rate Hammerstein diesel engine vibration isolation nonlinear system, and the program ends.

[0140] Example 1

[0141] See Figure 8-11 , the Hammerstein diesel engine vibration isolation nonlinear system of this example 1 is:

[0142]

[0143] A(z -1 )=1+a1z -1 +a2z -2 =1+0.71z -1 -0.16z -2

[0144] B(z -1 )=1+b1z -1 +b2z -2 =1+0.558z -1 +0.68z -2

[0145] μ(t)=h(x(t))=α1h1(x(t))+α2h2(x(t))

[0146] =0.31sin(x(t))-0.11cos(x(t))

[0147] C(z -1 )=1+c1z -1 =1-0.10z -1

[0148] D(z -1 )=1+d1z -1 +d2z -2 =1-0.167z -1 -0.55z -2

[0149] The parameter vector is defined as follows:

[0150] a=[a1,a2] T =[0.71, -0.16] T

[0151] b = [b1, b2] T =[-0.558,0.68] T

[0152] c=[c1] T =[-0.10] T

[0153] d = [d1, d2] T =[-0.167, -0.55] T

[0154] α=[α1,α2] T =[0.31, -0.11] T

[0155] At this time, the actual system parameter vector is:

[0156] β=[a T , b T , α T , c T , d T ] T

[0157] =[0.71, -0.16, -0.558, 0.68, 0.31, -0.11, -0.10, -0.167, -0.55] T

[0158] It can be seen that the parameter vector dimension D is 9. In the simulation, the interval p of the double rate sampling is 2 and the noise variance is 0.10 2 The multi-innovation improved simulated annealing (MI-SA) method is used to identify the above two-rate Hammerstein nonlinear model. The basic parameters of the MI-SA algorithm initialization phase are set as follows: Markov chain length ML = 100, decay parameter J = 0.1, step size factor S = 0.01, initial temperature T0 = 100, and termination temperature T f =0.01, tolerance YZ=0.1, solution upper limit Solve the lower limit The calculation formula for identification error is:

[0159]

[0160] The identification results are shown in Figures 8-11 .

[0161] Example 2

[0162] The Hammerstein model of Example 2 is applied to approximate the diesel engine vibration isolation nonlinear system, and the following model relationship is obtained:

[0163] μ(t)=-0.162x 2 (t)-0.094e x(t)

[0164]

[0165] A(z -1 )=1-0.28z -1 +0.37z -2

[0166] B(z-1 )=1+0.67z -1 +0.33z -2

[0167] C(z -1 )=1+0.167z -1 -0.356z -2

[0168] D(z -1 )=1-0.85z -1 +0.19z -2

[0169] At this time, the actual system parameter vector is:

[0170] β=[a1, a2, b1, b2, γ1, γ2, c1, c2, d1, d2] T

[0171] =[-0.28, 0.37, 0.67, 0.33, -0.162, -0.094, 0.167, -0.356, -0.85, 0.19] T

[0172] In this embodiment, the double rate sampling p is set to 3, and the noise variance is 0.50 2 The proposed MI-SA algorithm is used to identify the dual-rate Hammerstein diesel engine vibration isolation nonlinear system model, and the innovation length r is set to 4. The identification results are shown in Figure 12-15 .

[0173] Furthermore, the figure shows that the MI-SA identification error gradually converges over multiple iterations, ultimately remaining below 1%. The parameter estimates eventually converge to near the true values ​​after multiple iterations. These results demonstrate the effectiveness and feasibility of the MI-SA algorithm for the dual-rate Hammerstein diesel engine vibration isolation nonlinear system. Simulations demonstrate the high accuracy and fast convergence of the MI-SA algorithm. The fitting curves show that the MI-SA fitting output is very close to the true output value, demonstrating superior algorithm performance.

[0174] The present application proposes a parameter estimation method for a dual-rate diesel engine vibration isolation nonlinear system based on simulated annealing. First, an auxiliary model is introduced to solve the problem of incomplete data caused by dual-rate sampling. In order to prevent the algorithm from converging to a suboptimal solution too early, a Doppler cooling effect type cooling function is specially added. This improvement not only improves the accuracy of identification and the efficiency of optimization, but also further confirms the effectiveness of the MI-SA algorithm through application on the simulation model. The simulation experimental results show that MI-SA has accurate identification accuracy, and the estimation error eventually stabilizes near zero. The present application cleverly derives a multi-information simulated annealing method based on simulated annealing optimization to improve the convergence speed and estimation accuracy. Thereby, high-precision parameter estimation of a dual-rate diesel engine vibration isolation nonlinear system is achieved.

[0175] The above description is merely an embodiment of the present application and does not limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A dual-rate diesel engine vibration isolation nonlinear system parameter estimation method based on simulated annealing, characterized in that: The following steps are involved: Based on the double-rate Hammerstein diesel engine vibration isolation nonlinear system model, a first identification model of the double-rate Hammerstein diesel engine vibration isolation nonlinear system is obtained; Based on auxiliary model identification, converting the first identification model to obtain a second identification model; Based on the improved simulated annealing algorithm, the improved simulated annealing algorithm is combined with multi-innovation identification to obtain the parameters of the second identification model.

2. The method according to claim 1, characterized in that: The method for obtaining a first identification model of a dual-rate Hammerstein diesel engine vibration isolation nonlinear system based on a dual-rate Hammerstein diesel engine vibration isolation nonlinear system model comprises: Based on formulas (1)-(2), the Hammerstein diesel engine vibration isolation nonlinear system model is obtained; wherein the formulas (1)-(2) are: μ(t)=h[x(t)] (1); The nonlinearity h is given by the basis function h i is a linear combination of x(t) and y(t), where x(t) is the system input, y(t) is the system output, μ(t) is an unmeasurable intermediate variable, and A(z -1 ),B(z -1 ),C(z -1 ),D(z -1 ) is the unit shift operator z -1 The polynomial of , e(t) is a Gaussian white noise signal; Based on formula (3), the nonlinear part of the Hammerstein diesel engine vibration isolation nonlinear system is constructed; wherein the formula (3) is: Among them, α i is the nonlinear coefficient, n α is the number of basis functions; Based on formula (4), the first identification model of the Hammerstein diesel engine vibration isolation nonlinear system is constructed; wherein, the formula (4) is: Among them, H(t), is the information vector of the system; α, a, c and d are the parameter vectors of the system, and the superscript T represents the transpose.

3. The method according to claim 2, characterized in that The method for obtaining the second identification model comprises: Initializing parameters of the first identification model; constructing an output vector in the auxiliary model based on active control error input data and position output data of the actuator; Based on the input information vector and parameter vector, obtaining estimated values ​​of the information vector and parameter vector in the auxiliary model, and constructing a stacked information matrix; Based on the stacked information matrix, an estimated value of a parameter vector, an estimated value of an unsampled output, and an estimated value of noise are obtained.

4. The method according to claim 3, characterized in that: The method for obtaining the parameters of the second identification model based on the improved simulated annealing algorithm by combining the improved simulated annealing algorithm with multi-innovation identification includes: Initializing the parameters of the second identification model; wherein, initializing the initial temperature, generating an initial solution using a random generation function, setting the Markov chain length, attenuation parameter, step factor, termination temperature, tolerance, upper limit of the solution, and lower limit of the solution; Calculate the information vector and output vector according to the solution vector and construct the fitness function; Performing a perturbation operation on the initial solution based on a random function to generate a new solution, and calculating an increment between the new solution and the initial solution; Based on the increment, parameters of the second identification model are obtained.

5. The method according to claim 4, characterized in that The method for obtaining the parameters of the second identification model based on the increment includes: Determine whether the increment is less than zero; if so, accept the new solution; if not, accept it according to probability using the Metropolis probability criterion; Determine whether the new solution is the optimal solution; if so, update the solution vector; if not, retain the initial solution; Enable the "Doppler" type attenuation function to attenuate the temperature value, continue the optimization iteration process, and determine whether the current temperature iteration number has been reached; if so, reduce the temperature; if not, continue to execute the previous step; Determine whether the temperature value reaches the termination temperature; if so, the calculation is terminated; if not, continue to execute the loop steps; Repeat the above steps until the termination condition is met, and use the optimal solution obtained by the final iteration as the parameters of the second identification model.

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