Hydraulic excavator system identification method based on two-stage estimation

Abstract

The invention provides a hydraulic excavator system identification method based on two-stage estimation, belongs to the technical field of mechanical equipment system identification, and solves the technical problems that a self-adaptive moment estimation algorithm is low in convergence speed and low in identification precision. According to the technical scheme, the hydraulic excavator system identification method based on two-stage estimation comprises the following steps that (1) a Hammerstein model of a fractional order hydraulic excavator system is established; and step 2) constructing an identification process of a two-stage least square adaptive moment estimation algorithm. The method has the beneficial effects that the two-stage least square adaptive moment estimation algorithm provided by the invention has relatively high convergence speed and relatively high convergence precision, and can be well suitable for modeling and parameter identification of the fractional order hydraulic excavator system.

Description

Technical Field

[0001] The present invention relates to the technical field of excavator system identification, and in particular to a hydraulic excavator system identification method based on two-stage estimation. Background Art

[0002] With the gradual development of society, high-rise buildings have become the main living and working space for urban residents. The manual workload on construction sites can no longer meet the work requirements of construction sites. Hydraulic excavator work has become the most common site operation method at present. The hydraulic execution control system of the hydraulic excavator consists of a hydraulic system, a working device, and a slewing device. The hydraulic working device is articulated by a boom, a dipper, and a bucket. The slewing device is the body of the hydraulic excavator, and a power unit and a transmission system are provided on the upper part of the turntable. The transmission system transmits the power of the servo motor to the hydraulic motor, hydraulic cylinder and other actuators through the hydraulic system, that is, the hydraulic pump, and controls the action of the working device through the extension and contraction of the boom, dipper, and bucket cylinders, thereby completing various operations. In order to better analyze and predict the excavation process, it is necessary to establish a corresponding system model for the hydraulic excavator and identify the parameters of the established model. To this end, researchers have also proposed different identification methods, such as Newton iteration algorithm, least squares algorithm and particle swarm algorithm.

[0003] The Newton iteration algorithm is an iterative algorithm. Each step requires solving the inverse matrix of the Hessian matrix of the objective function, and the calculation is relatively complicated. The least squares algorithm has the problem of data saturation due to the increase in data volume in the process of tracking time-varying parameters. Although the particle swarm algorithm as a swarm intelligence algorithm can be well applied in different working conditions, the generation of new individuals depends on the organic combination within and between groups, which has certain limitations.

[0004] Literature based on the application of Hammerstein model modeling in hydraulic excavator systems points out that for hydraulic excavator systems, people generally use the sampling mechanism modeling method, usually using the first-order or second-order plus pure lag method, or the state space method to model. The order of the model and the selection of model parameters cannot match the actual model well. The Hammerstein model is a complete model that describes the characteristics of the system. It can not only describe the input and output relationship of the system, but also describe the color of the noise. While estimating some coefficients, it also estimates the noise characteristic coefficients. Our invention uses a two-stage least squares adaptive moment estimation algorithm to identify the fractional-order hydraulic excavator model in order to solve the problem that the general sampling mechanism modeling of the hydraulic excavator cannot match the actual object well.

[0005] How to solve the above technical problems is the subject faced by the present invention. Summary of the invention

[0006] The purpose of the present invention is to provide a hydraulic excavator system identification method based on two-stage estimation, which solves the technical problems of slow convergence speed and low identification accuracy of the adaptive moment estimation algorithm; the identification method of the present invention has a faster convergence speed and higher convergence accuracy, and can be well applied to the modeling and parameter identification of fractional-order hydraulic excavator systems.

[0007] The present invention is achieved by the following measures: a hydraulic excavator system identification method based on two-stage estimation, specifically comprising the following steps:

[0008] Step 1) Establish the input and output mathematical model of the fractional-order hydraulic excavator system. Establishing a mathematical model can help us improve the efficiency and accuracy of problem solving. By abstracting the actual problem into a mathematical model, we can accurately describe and analyze it, so as to solve the problem more effectively. It can also help us deeply understand the essence of the problem and discover the laws and connections therein.

[0009] Step 2) Construct the identification process of the two-stage least squares adaptive moment estimation algorithm. Constructing the identification process of the algorithm allows us to accurately classify new data and quickly process large amounts of data, helping us better understand the model.

[0010] As a further optimization scheme of the hydraulic excavator system identification method based on two-stage estimation provided by the present invention, the specific modeling steps of step 1) are as follows:

[0011] (1-1) Construct the structure of a fractional-order Hammerstein model of a hydraulic excavator system.

[0012] (1-2) Based on this model, the Hammerstein model expression of the fractional-order hydraulic excavator system is constructed as follows:

[0013]

[0014] ξ(ι)=ρ(ι)+σ(ι), (3)

[0015] Among them, κ(ι) is the model input signal, ρ(ι) and σ(ι) are intermediate variables, ξ(ι) is the model output signal, is the parameter to be estimated. υ(ι) is a parameter with a mean of 0 and a variance of σ 2 And it is white noise that satisfies Gaussian distribution. -1 is the unit delay symbol: z -1 y(t)=y(t-1), A(z), B(z) and D(z) are constant polynomials with the following definitions:

[0016]

[0017] Among them, the polynomial factor a i , b j and d m is the parameter to be estimated, n a ,n b and n d is a known order.

[0018] The present invention adopts the Grünwald Letnikov (GL) definition to solve the fractional derivative. The GL definition can be expressed as:

[0019]

[0020] where Δ is the discrete fractional difference operator, is a function of The fractional derivative is in is the sampling interval and ι is the number of samples over which the derivative approximation is computed.

[0021] (1-3) The identification model of the Hammerstein model of the fractional-order hydraulic excavator system is obtained:

[0022]

[0023] The basic idea of ​​the two-stage least squares adaptive moment estimation algorithm is to decompose the Hammerstein model of the fractional-order hydraulic excavator system into two directly usable subsystems, and then identify the parameter vector of each subsystem separately, which reduces the complexity of the model.

[0024] From (5), the identification model of the decomposed fractional-order hydraulic excavator system’s OEMA model can be obtained:

[0025] ξ(ι)=ξ1(ι)+ξ2(ι),(6)

[0026] In the above formula, ξ1(ι) and ξ2(ι) represent the outputs of subsystem 1 and subsystem 2 respectively, which can be expressed as:

[0027]

[0028] and is the parameter vector of the system, expressed as:

[0029]

[0030] ψ1(ι) and ψ2(ι) are the information vectors of the system, expressed as:

[0031]

[0032] Define the criterion function and for:

[0033]

[0034]

[0035] make and Respectively, the parameter vector and The partial derivative of is zero, and we get:

[0036]

[0037] The further design of the OEMA model parameter identification method for the excavator system based on two-stage estimation is that the step 2) is specifically as follows:

[0038] Step 2-1) Initialization, given the number of cycles L;

[0039] Step 2-2) using the standardized operating lever position as the input data κ(ι) of the hydraulic excavator system model and the cylinder displacement as the output data ξ(ι);

[0040] Step 2-3) Replace ψ1(ι) and ψ2(ι) with their estimated values and According to formula (12) and (13), and

[0041]

[0042] Will and Replace with its estimated value and According to formula (14) and (15), and

[0043]

[0044] Step 2-4) Calculate the information vector according to formula (16)

[0045]

[0046] Where L1(ι) is the gain vector and P1(ι) is the covariance matrix.

[0047] Step 2-5) Calculate the information vector according to formula (19)

[0048]

[0049] Among them, V(ι) is called the first-order moment estimate, is the first-order moment estimate after bias correction. S(ι) is called the second-order moment estimate, is the second-order moment estimate after bias correction. In formula (19), r(ι) is called the initial step size. In the gradient descent process, r(ι) controls the step size of each step when searching for the optimal value, while in the parameter identification process, It is possible that the value is 0, so ε takes a smaller number to prevent the denominator from being 0, for example, ε = 0.0001. β1 and β2 are hyperparameters that control the exponential decay rate, and their value ranges are both [0,1].

[0050] Step 2-6) Calculate the fractional derivative of the intermediate variable according to the GL definition of formula (4) and

[0051]

[0052] Step 2-7) determines whether the maximum number of cycles has been reached. If not, the program jumps to step 2-3). If reached, it proceeds to step 2-8);

[0053] Step 2-8) Output the result and complete the identification.

[0054] Compared with the prior art, the present invention has the following beneficial effects:

[0055] (1) The present invention establishes a model for parameter identification of the fractional-order hydraulic excavator Hammerstein system, takes the standardized operating lever position as the input data κ(ι) of the hydraulic excavator system model, and the cylinder displacement as the output data ξ(ι), and uses a two-stage least squares adaptive moment estimation algorithm to identify the model parameters; Figure 4 It can be seen that the algorithm can identify the internal parameters of the model very well.

[0056] (2) Compared with the two-stage least squares algorithm, the two-stage least squares adaptive moment estimation algorithm updates the variables and noise in each cycle to obtain the estimated information vector, which improves the convergence speed. The two-stage least squares adaptive moment estimation algorithm can better identify the Hammerstein system, and the identification accuracy is also high, and the estimation error is small; at the same time, it also shows that this identification method has good applicability to the fractional-order hydraulic excavator Hammerstein model. BRIEF DESCRIPTION OF THE DRAWINGS

[0057] The accompanying drawings are used to provide further understanding of the present invention and constitute a part of the specification. They are used to explain the present invention together with the embodiments of the present invention and do not constitute a limitation of the present invention.

[0058] Figure 1 The present invention provides an overall flow chart of the hydraulic excavator Hammerstein system identification method based on two-stage estimation.

[0059] Figure 2 A schematic diagram of a simplified model of a fractional-order hydraulic excavator according to the hydraulic excavator system parameter identification method based on two-stage estimation provided by the present invention.

[0060] Figure 3 A schematic diagram of a general model of the two-stage estimation method for identifying system parameters of a hydraulic excavator provided by the present invention.

[0061] Figure 4 Schematic diagram of the error between the identification parameters and the true values ​​of the two-stage least squares adaptive moment estimation algorithm of the present invention.

[0062] Figure 5 Schematic diagram of the error between the identification parameters and the true values ​​of the two-stage least squares algorithm of the present invention. DETAILED DESCRIPTION

[0063] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. Of course, the specific embodiments described here are only used to explain the present invention and are not used to limit the present invention.

[0064] Example 1

[0065] See also Figures 1 to 4 The technical solution provided by this embodiment is a hydraulic excavator system identification method based on two-stage estimation, and the specific steps are as follows:

[0066] Step 1) Establish the input-output mathematical model of the fractional-order hydraulic excavator system.

[0067] Step 2) Construct the identification process of the two-stage least squares adaptive moment estimation algorithm.

[0068] As a further optimization scheme of the hydraulic excavator system identification method based on two-stage estimation provided by the present invention, the specific modeling steps of step 1) are as follows:

[0069] (1-1) Construct the structure of a fractional-order Hammerstein model of a hydraulic excavator system.

[0070] (1-2) Based on this model, the Hammerstein model expression of the fractional-order hydraulic excavator system is constructed as follows:

[0071]

[0072] ξ(ι)=ρ(ι)+σ(ι), (3)

[0073] Among them, κ(ι) is the model input signal, ρ(ι) and σ(ι) are intermediate variables, ξ(ι) is the model output signal, is the parameter to be estimated. υ(ι) is a parameter with a mean of 0 and a variance of σ 2 And it is white noise that satisfies Gaussian distribution. -1 is the unit delay symbol: z -1 y(t)=y(t-1), A(z), B(z) and D(z) are constant polynomials with the following definitions:

[0074]

[0075] Among them, the polynomial factor a i , b j and d m is the parameter to be estimated, n a ,n b and n d is a known order.

[0076] The Grünwald Letnikov (GL) definition is used to solve the fractional derivatives. The GL definition is expressed as:

[0077]

[0078] where Δ is the discrete fractional difference operator, is a function of The fractional derivative is in is the sampling interval and ι is the number of samples over which the derivative approximation is computed.

[0079] (1-3) The identification model of the Hammerstein model of the fractional-order hydraulic excavator system is obtained:

[0080]

[0081] The basic idea of ​​the two-stage least squares adaptive moment estimation algorithm is to decompose the Hammerstein model of the fractional-order hydraulic excavator system into two directly usable subsystems, and then identify the parameter vector of each subsystem separately, which reduces the complexity of the model.

[0082] From (5), the identification model of the decomposed Hammerstein model of the fractional-order hydraulic excavator system can be obtained:

[0083] ξ(ι)=ξ1(ι)+ξ2(ι),(6)

[0084] In the above formula, ξ1(ι) and ξ2(ι) represent the outputs of subsystem 1 and subsystem 2 respectively, which can be expressed as:

[0085]

[0086] and is the parameter vector of the system, expressed as:

[0087]

[0088] ψ1(ι) and ψ2(ι) are the information vectors of the system, expressed as:

[0089]

[0090] Define the criterion function and for:

[0091]

[0092] make and Respectively, the parameter vector and The partial derivative of is zero, and we get:

[0093]

[0094] Preferably, the model in step 1) is a fractional-order Hammerstein model.

[0095] Preferably, the specific steps of step 2) constructing the identification process of the two-stage least squares adaptive moment estimation algorithm are as follows:

[0096] Step 2-1) Initialization, given the number of cycles L;

[0097] Step 2-2) using the standardized operating lever position as the input data κ(ι) of the hydraulic excavator system model and the cylinder displacement as the output data ξ(ι);

[0098] Step 2-3) Replace ψ1(ι) and ψ2(ι) with their estimated values and According to formula (12) and (13), and

[0099]

[0100] Will and Replace with its estimated value and According to formula (14) and (15), and

[0101]

[0102] Step 2-4) Calculate the information vector according to formula (16)

[0103]

[0104] Where L1(ι) is the gain vector and P1(ι) is the covariance matrix.

[0105] Step 2-5) Calculate the information vector according to formula (19)

[0106]

[0107] Among them, V(ι) is called the first-order moment estimate, is the first-order moment estimate after bias correction. S(ι) is called the second-order moment estimate, is the second-order moment estimate after bias correction. In formula (19), r(ι) is called the initial step size. In the gradient descent process, r(ι) controls the step size of each step when searching for the optimal value, while in the parameter identification process, It is possible that the value is 0, so ε takes a smaller number to prevent the denominator from being 0, for example, ε = 0.0001. β1 and β2 are hyperparameters that control the exponential decay rate, and their value ranges are both [0,1].

[0108] Step 2-6) Calculate the fractional derivative of the intermediate variable according to the GL definition of formula (4) and

[0109]

[0110] Step 2-7) determines whether the maximum number of cycles has been reached. If not, the program jumps to step 2-3). If reached, it proceeds to step 2-8);

[0111] Step 2-8) Output the result and complete the identification.

[0112] The schematic diagram of the fractional-order hydraulic excavator system used in this embodiment is as follows: Figure 2As shown in the figure, the standardized operating lever position is used as the input data κ(ι) of the hydraulic excavator system model, and the cylinder displacement is used as the output data ξ(ι);

[0113] Through the above-mentioned fractional-order Hammerstein model, the following model can be established in this embodiment:

[0114]

[0115] Fractional order ι = 0.90

[0116] Comparing the above model with step 1), we can get

[0117] a1=3.726, a2=3.868, b1=4.427, b2=-2.499,

[0118] c1=0.168, d1=0.195, d2=0.206

[0119] In order to facilitate the substitution of the parameters to be identified into the two-stage least squares adaptive moment estimation algorithm, the parameters to be identified are composed into a parameter vector and The parameters to be identified are as follows:

[0120]

[0121] Initialize according to step 2-1) and give a given number of loops L;

[0122] According to step 2-2), the input and output data of the fractional-order hydraulic excavator system model are obtained;

[0123] According to step 2-3) calculate the estimated value of the information vector and

[0124] Calculate the first-order moment estimate according to steps 2-4) Second moment estimate Gain vector L1(ι) and covariance matrix P1(ι);

[0125] Update the estimated value of the parameter vector according to steps 2-5) and

[0126] Calculate the fractional derivative according to step 2-6) and

[0127] Complete the loop according to step 2-7) and step 2-8) and output the result.

[0128] Among them, several issues need to be considered when setting the number of loops L: if the number of loops is too small, the identification result will be unsatisfactory, thus resulting in low identification accuracy. If the number of loops is too large, it will cause a large amount of calculation.

[0129] The parameter identification results using the two-stage least squares adaptive moment estimation algorithm of the present invention are as follows: Figure 4 As shown in the figure, it can be seen that the identification accuracy of this method is high, and the estimated value of the parameter to be identified is very close to the true value. At the same time, it also shows that this identification method has good applicability for parameter identification of fractional-order hydraulic excavator model.

[0130] Example 2

[0131] See also Figure 5 The technical solution provided by this embodiment is a two-stage estimation method for hydraulic excavator system identification, and the specific steps are as follows:

[0132] Step 1) Establish the input-output mathematical model of the fractional-order hydraulic excavator system.

[0133] Step 2) Construct the identification process of the two-stage least squares algorithm.

[0134] Preferably, the specific steps of step 2) constructing the identification process of the two-stage least squares algorithm are as follows:

[0135] Step 2-1) Initialization, given the number of cycles L;

[0136] Step 2-2) using the standardized operating lever position as the input data κ(ι) of the hydraulic excavator system model and the cylinder displacement as the output data ξ(ι);

[0137] Step 2-3) Replace ψ1(ι) and ψ2(ι) with their estimated values and According to formula (13) and (14), and

[0138]

[0139] Will and Replace with its estimated value and According to equations (26) and (27), and

[0140]

[0141] Step 2-4) Calculate the information vector according to formula (28)

[0142]

[0143] Where L1(ι) is the gain vector and P1(ι) is the covariance matrix.

[0144] Step 2-5) Calculate the information vector according to formula (20)

[0145]

[0146] Where L2(ι) is the gain vector and P2(ι) is the covariance matrix.

[0147] Step 2-6) Calculate the fractional derivative of the intermediate variable according to the GL definition of formula (4) and

[0148]

[0149] Step 2-7) determines whether the maximum number of cycles has been reached. If not, the program jumps to step 2-3). If reached, it proceeds to step 2-8);

[0150] Step 2-8) Output the result and complete the identification.

[0151] The schematic diagram of the fractional-order hydraulic excavator system used in this embodiment is as follows: Figure 2 As shown in the figure, the standardized operating lever position is used as the input data κ(ι) of the hydraulic excavator system model, and the cylinder displacement is used as the output data ξ(ι).

[0152] Through the above-mentioned fractional-order Hammerstein model, the following model can be established in this embodiment:

[0153]

[0154] Fractional order ι = 0.90

[0155] Comparing the above model with step 1), we can get

[0156] a1=3.726, a2=3.868, b1=4.427, b2=-2.499,

[0157] c1=0.168, d1=0.195, d2=0.206

[0158] In order to facilitate the substitution of the parameters to be identified into the two-stage least squares algorithm, the parameters to be identified are composed into a parameter vector and The parameters to be identified are as follows:

[0159]

[0160] Initialize according to step 2-1) and give a given number of loops L;

[0161] According to step 2-2), the standardized operating lever position is used as the input data κ(ι) of the hydraulic excavator system model, and the cylinder displacement is used as the output data ξ(ι);

[0162] According to step 2-3) calculate the estimated value of the information vector and

[0163] According to step 2-4), the gain vectors L1(ι) and L2(ι) are calculated, and the covariance matrices P1(ι) and P2(ι) are calculated;

[0164] Update the estimated value of the parameter vector according to steps 2-5) and

[0165] Calculate the fractional derivative according to step 2-6) and

[0166] Complete the loop according to step 2-7) and step 2-8) and output the result.

[0167] Among them, several issues need to be considered when setting the number of loops L: if the number of loops is too small, the identification result will be unsatisfactory, thus resulting in low identification accuracy. If the number of loops is too large, it will cause a large amount of calculation.

[0168] The parameter identification results of the hydraulic excavator system identification method using the two-stage least squares algorithm of the present invention are as follows: Figure 5 As shown in Figure 2, it can be seen that the identification accuracy of this method is greater than the identification error of the two-stage least squares adaptive moment estimation algorithm.

[0169] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims

1. A hydraulic excavator system identification method based on two-stage estimation, It is characterized in that The following steps are involved: Step 1) establishing an input-output mathematical model of a fractional-order hydraulic excavator system; Step 2) Construct the identification process of the two-stage least squares adaptive moment estimation algorithm.

2. The hydraulic excavator system identification method based on two-stage estimation according to claim 1, It is characterized in that The modeling steps of step 1) are as follows: (1-1) Construct the structure of a fractional-order Hammerstein model of a hydraulic excavator system; (1-2) Based on this model, the Hammerstein model expression of the fractional-order hydraulic excavator system is constructed as follows: ξ(ι)=ρ(ι)+σ(ι), (3) Among them, κ(ι) is the model input signal, ρ(ι) and σ(ι) are intermediate variables, ξ(ι) is the model output signal, is the parameter to be estimated, υ(ι) is a parameter with a mean of 0 and a variance of σ 2 And the white noise satisfies Gaussian distribution, z -1 is the unit delay symbol: z -1 y(t)=y(t-1), A(z), B(z) and D(z) are constant polynomials with the following definitions: Among them, the polynomial factor a i , b j and d m is the parameter to be estimated, n a ,n b and n d is a known order; The GL definition is used to solve the fractional derivatives. The GL definition is expressed as: where Δ is the discrete fractional difference operator, is a function of The fractional derivative is in is the sampling interval, ι is the number of samples for computing the derivative approximation; (1-3) The identification model of the Hammerstein model of the fractional-order hydraulic excavator control system is obtained: The basic idea of ​​the two-stage least squares adaptive moment estimation algorithm is to decompose the Hammerstein model of the fractional-order hydraulic excavator system into two directly usable subsystems, and then identify the parameter vector of each subsystem separately; The identification model of the decomposed Hammerstein model of the fractional-order hydraulic excavator system is obtained from (5): ξ(i)=ξ 1 (i)+ξ 2 (j), (6) In the above formula, ξ 1 (ι) and ξ 2 (ι) are the outputs of subsystem 1 and subsystem 2, respectively, and are expressed as: θ 1 and θ 2 is the parameter vector of the system, expressed as: ψ 1 (ι) and ψ 2 (ι) is the information vector of the system, expressed as: Define the criterion function J 1 (θ 1 ) and J 2 (θ 2 )for: Let J 1 (θ 1 ) and J 2 (θ 2 ) respectively about the parameter vector θ 1 and θ 2 The partial derivative of is zero, and we get:

3. The hydraulic excavator system identification method based on two-stage estimation according to claim 2, It is characterized in that The model in step 1-1 is a fractional-order Hammerstein model.

4. The hydraulic excavator system identification method based on two-stage estimation according to claim 1, It is characterized in that The steps of constructing the identification process of the two-stage least squares adaptive moment estimation algorithm in step 2) are as follows: Step 2-1) Initialization, given the number of cycles L; Step 2-2) using the standardized operating lever position as the input data κ(ι) of the hydraulic excavator system model and the cylinder displacement as the output data ξ(ι); Step 2-3) Set ψ 1 (ι) and ψ 2 (ι) is replaced by its estimated value and According to formula (13) and (14), and θ 1 (ι) and θ 2 (ι) is replaced by its estimated value and According to formula (14) and (15), and Step 2-4) Calculate the information vector according to formula (16) Where L 1 (ι) is the gain vector, P 1 (ι) is the covariance matrix; Step 2-5) Calculate the information vector according to formula (19) Among them, V(ι) is called the first-order moment estimate, is the first-order moment estimate after bias correction, S(ι) is called the second-order moment estimate, is the second-order moment estimate after bias correction. In formula (19), r(ι) is called the initial step size. In the gradient descent process, r(ι) controls the step size of each step when searching for the optimal value. Step 2-6) Calculate the fractional derivative of the intermediate variable according to the GL definition of formula (4) and Step 2-7) determines whether the maximum number of cycles has been reached. If not, the program jumps to step 2-3). If reached, it proceeds to step 2-8); Step 2-8) Output the result and complete the identification.

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