A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least squares method

Abstract

The present invention discloses a lithium battery parameter identification method based on an improved initial value with forgetting factor recursive least squares method. The method includes establishing a second-order Thevenin equivalent circuit model of a lithium battery; determining the functional relationship between each parameter and the SOC through the HPPC working condition, and determining the functional relationship between the open circuit voltage and the SOC through the intermittent constant current discharge working condition; measuring the initial open circuit voltage to obtain the initial SOC; substituting the initial SOC into the parameter fitting expression to obtain the parameter value corresponding to the SOC; substituting each parameter into the recursive formula to obtain the initial value of the improved initial value with forgetting factor recursive least squares method; and finally using the improved initial value with forgetting factor recursive least squares method to perform parameter identification. The present invention solves the problem of the difficulty in selecting the initial value of the recursive least squares method with forgetting factor, improves the accuracy of parameter identification, and has practical significance.

Description

Technical Field

[0001] The present invention relates to the field of lithium batteries, and in particular to a method for identifying parameters of lithium batteries. Background Art

[0002] At present, the development of renewable energy and electric vehicles has become a highlight in the energy field. Among them, battery energy storage technology has broad development prospects in the field of electric vehicles. Lithium batteries are the core devices of electric vehicles. They are widely used because of their high energy density, long cycle life, safety and reliability, strong adaptability, and no memory effect. The estimation of the internal state of lithium batteries requires an accurate model, and an equivalent circuit model is usually used to describe the electrochemical process of the battery.

[0003] The lithium battery parameter identification algorithm determines the identification accuracy. Commonly used parameter identification methods include circuit analysis (CA), particle swarm algorithm (PSO), genetic algorithm (GA) and recursive least squares algorithm (RLS). Circuit analysis is an offline identification method with simple calculation, but it cannot identify parameters in real time and has low parameter identification accuracy. Particle swarm algorithm has high identification accuracy, but it needs to identify parameters repeatedly, the calculation speed is slow, and the calculation result is related to the selection of initial particles. Genetic algorithm has a good effect on battery parameter identification, but it has too many iterations, the algorithm is complex, the calculation amount is large, and the result is highly dependent on the initial population. RLS algorithm has high identification accuracy and can be used for online identification, but as the covariance matrix increases, the old data accounts for a large proportion in the recursive process, so there is a "data saturation" problem. Therefore, the forgetting factor λ is introduced in the RLS algorithm to reduce the weight of old data and increase the weight of new data. At the same time, the selection of initial parameter values ​​has a great influence on the accuracy and convergence speed of the forgetting factor recursive least squares identification algorithm (FFRLS). If the parameter settings are unreasonable, the accuracy is often poor, the algorithm converges very slowly, and even iterative non-convergence may occur. Summary of the invention

[0004] The present invention proposes a lithium battery parameter identification method based on an improved initial value recursive least squares algorithm with forgetting factor (IIV-FFRLS), which is used to solve the problem of difficulty in selecting initial values ​​of the recursive least squares identification algorithm with forgetting factor. The algorithm has a relatively accurate iterative initial value, which can accelerate the algorithm convergence speed and improve the identification accuracy.

[0005] The technical solution of the present invention is as follows:

[0006] Step 1: Establish a second-order Thevenin equivalent circuit model of a lithium battery;

[0007] Step 2: Determine the functional relationship between each parameter and SOC through the HPPC working condition, and determine the functional relationship between the open circuit voltage and SOC through the intermittent constant current discharge working condition;

[0008] Step 3: Measure the initial open circuit voltage to obtain the initial SOC;

[0009] Step 4: Substitute the initial SOC into the parameter fitting expression to obtain the parameter value corresponding to this SOC;

[0010] Step 5: Substitute each parameter back into the recursive formula to obtain the initial value of the improved initial value with the forgetting factor recursive least squares method;

[0011] Step 6: Use the improved initial value with forgetting factor recursive least squares method to identify parameters.

[0012] Preferably, an equivalent circuit model is established. The equivalent circuit model adopts a second-order Thevenin model, which consists of a voltage source, an ohmic internal resistance, and two RC parallel networks. OC It represents the open circuit voltage of the battery, which is a nonlinear function related to the state of charge (SOC); the ohmic internal resistance R0 represents the resistance of the electrode, electrolyte, and diaphragm to Li + The R1C1 network represents the concentration difference polarization effect of lithium batteries, and the R2C2 network represents the electrochemical polarization effect of lithium-ion batteries. t It represents the terminal voltage of lithium battery, I represents the lithium battery current (discharge is positive), and U1 and U2 represent the polarization voltage.

[0013] The circuit equation is expressed as:

[0014]

[0015] Assuming that the initial value of SOC is SOC0, according to the ampere-hour current method, the expression of SOC can be obtained:

[0016]

[0017] Where η is the coulombic efficiency of the lithium battery, which is generally 1 at room temperature. c is the rated capacity of the lithium battery. Combining the lithium battery equivalent circuit model with the ampere-hour current method, take the state variable x k =[SOC k ,U 1,k ,U 2,k ] T , the input variable is I(k) and the output variable is y k =[U t,k ], the state space expression of lithium battery is obtained as:

[0018]

[0019] Where T is the sampling period, w k is the system noise, v k To measure noise.

[0020] Furthermore, the functional relationship between each parameter and SOC is determined through the HPPC working condition, and the functional relationship between the open circuit voltage and SOC is determined through the intermittent constant current discharge working condition.

[0021] Step 2.1: HPPC working condition: (1) Charge the battery to full capacity with constant current and constant voltage and let it stand for a long time; (2) Discharge with 1C current pulse for 10 seconds; let it stand for 40 seconds after discharge. (3) Charge with 1C current pulse for 10 seconds, let it stand for 3 minutes after charging; (4) Discharge with 0.5C current constant current for 12 minutes to reduce the SOC by 10%, let it stand for 20 minutes after discharge. (5) Repeat steps (1) to (4) until the SOC drops below 10%.

[0022] Step 2.2: Analyzing the voltage curve of HPPC working condition, the following conclusions can be drawn:

[0023] 1) When the discharge starts from t1 to t2, the voltage at the lithium battery terminal drops sharply from U1 to U2, which is the voltage change caused by the ohmic internal resistance R0;

[0024] 2) The period from t2 to t3 is the change in the terminal voltage of the lithium battery caused by the discharge current charging the polarized capacitor;

[0025] 3) When the discharge ends in the time period t3-t4, the voltage at the lithium battery terminal rises suddenly from U3 to U4, which is the voltage change caused by the ohmic internal resistance R0;

[0026] 4) The time period from t4 to t5 is the static stage after the discharge is completed, which is the change of the lithium battery terminal voltage caused by the discharge of polarized capacitors;

[0027] The value of the ohmic internal resistance can be calculated from conclusions 1) and 3), where I is the lithium battery current.

[0028]

[0029] From conclusions 2) and 4), we can get the terminal voltage U t The relationship between t and time.

[0030]

[0031] The parameters corresponding to every 10% change in SOC are obtained through HPPC conditions.

[0032] Step 2.3: Fit the parameters obtained from the HPPC operating condition identification through cubic Hermite interpolation to obtain the relationship between each parameter and SOC.

[0033] Step 2.4: Intermittent constant current discharge condition: (1) Charge the battery to full capacity with constant current and constant voltage and let it stand for a long time; (2) Discharge at a constant current of 1 / 3C for 30 minutes to reduce the SOC by 10%, and let it stand for 40 minutes after the discharge; (3) Repeat step (2) until the SOC drops below 10%.

[0034] Step 2.5: Obtain the open circuit voltage corresponding to every 10% change in SOC through intermittent constant current discharge conditions.

[0035] Step 2.6: Fit the open circuit voltage by cubic Hermite interpolation to obtain the SOC-OCV fitting curve.

[0036] Furthermore, the initial open circuit voltage of the lithium battery is measured, and the initial SOC of the lithium battery is obtained through the SOC-OCV fitting curve.

[0037] Furthermore, the initial SOC is substituted into the parameter fitting expression to obtain R0, R1, R2, C1, and C2 corresponding to the SOC.

[0038] Furthermore, the recursive formula of the recursive least squares algorithm with forgetting factor is:

[0039]

[0040] In the formula, and is the estimated value of the k-1th and kth times; K(k) is the gain matrix of the kth time, and the error The product with the gain matrix is ​​the correction value at time k, P(k-1) and P(k) are the error covariance matrices of the k-1th and kth times; λ is the forgetting factor, which is generally between 0.95 and 1.

[0041] From the port voltage equation (1), the frequency domain transfer function of the system can be obtained as:

[0042]

[0043] U(s)=U OC (s)-U t (s)(8)

[0044] Where s is the Laplace operator, and the transfer function of the second-order model of lithium battery is obtained as follows:

[0045]

[0046] Bilinear transformation method Discretize the transfer function, z -1 is the discretization operator, and T represents the sampling period.

[0047]

[0048] In the formula, a1, a2, a3, a4, a5 are the parameters to be identified.

[0049]

[0050] Take τ1 as the concentration difference polarization time constant, take τ2 as the electrochemical polarization time constant, θ1, θ2, θ3, θ4, θ5 as intermediate parameters, and write the parameters to be identified as formula (12).

[0051]

[0052] The standard difference form is written as:

[0053] U(k)=a1U(k-1)+a2U(k-2)+a3I(k)+a4I(k-1)+a5I(k-2)(13)

[0054] The regression form is written as:

[0055]

[0056] Where: y(k) = U(k), θ T (k) = [a1, a2, a3, a4, a5].

[0057] The intermediate parameters θ1, θ2, θ3, θ4, and θ5 are obtained by inverse deduction from formula (12).

[0058]

[0059] Solve the equivalent circuit model parameters by equations (16) and (17):

[0060]

[0061]

[0062] Furthermore, the parameters R0, R1, R2, C1, and C2 are substituted into the recursive formulas (11) and (12) to obtain the iterative initial parameters a1, a2, a3, a4, and a5.

[0063] Furthermore, the initial parameters a1, a2, a3, a4, and a5 are used as initial values ​​of the improved initial value with forgetting factor recursive least squares algorithm for parameter identification.

[0064] Compared with the prior art, the present invention has the following beneficial effects:

[0065] 1. When using the improved initial value with forgetting factor recursive least squares algorithm for lithium battery parameter identification, compared with the recursive least squares algorithm with forgetting factor, it has more accurate iterative initial values. The average absolute error is small and the accuracy is high during the whole algorithm identification process.

[0066] 2. When the improved initial value with forgetting factor recursive least squares algorithm is used for lithium battery parameter identification, the error begins to converge in the early stage of algorithm identification, and the convergence speed is fast.

[0067] 3. When using the improved initial value with forgetting factor recursive least squares algorithm for lithium battery parameter identification, the root mean square error is small and the algorithm has good robustness. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 To improve the initial value with forgetting factor recursive least squares algorithm process

[0069] Figure 2 The second-order Thevenin equivalent circuit diagram

[0070] Figure 3 This is the current diagram for HPPC operation

[0071] Figure 4 This is the voltage diagram for HPPC working conditions

[0072] Figure 5 This is the absolute error comparison chart for working condition 1

[0073] Figure 6 This is the absolute error comparison chart for working condition 2

[0074] Figure 7 This is the absolute error comparison chart for working condition 3

[0075] Figure 8 This is the absolute error comparison chart for working condition 4 DETAILED DESCRIPTION

[0076] The present invention is further described in detail below with reference to the accompanying drawings.

[0077] like Figure 1 As shown, a lithium battery parameter identification method based on an improved initial value with forgetting factor recursive least squares algorithm mainly includes the following steps:

[0078] Step 1: Establish a second-order Thevenin equivalent circuit model of a lithium battery;

[0079] Step 2: Determine the functional relationship between each parameter and SOC through the HPPC working condition, and determine the functional relationship between the open circuit voltage and SOC through the intermittent constant current discharge working condition;

[0080] Step 3: Measure the initial open circuit voltage to obtain the initial SOC;

[0081] Step 4: Substitute the initial SOC into the parameter fitting expression to obtain the parameter value corresponding to this SOC;

[0082] Step 5: Substitute each parameter back into the recursive formula to obtain the initial value of the improved initial value with the forgetting factor recursive least squares method;

[0083] Step 6: Use the improved initial value with forgetting factor recursive least squares method to identify parameters.

[0084] The step 1 is to establish an equivalent circuit model. The equivalent circuit model adopts a second-order Thevenin model, such as Figure 2 As shown: The model consists of a voltage source, an ohmic internal resistor and two RC parallel networks. OC It represents the open circuit voltage of the battery, which is a nonlinear function related to the state of charge (SOC); the ohmic internal resistance R0 represents the resistance of the electrode, electrolyte, and diaphragm to Li + The R1C1 network represents the concentration difference polarization effect of lithium batteries, and the R2C2 network represents the electrochemical polarization effect of lithium-ion batteries. t It represents the terminal voltage of lithium battery, I represents the lithium battery current (discharge is positive), and U1 and U2 represent the polarization voltage.

[0085] The circuit equation is expressed as:

[0086]

[0087] Assuming that the initial value of SOC is SOC0, according to the ampere-hour current method, the expression of SOC can be obtained:

[0088]

[0089] Where η is the coulombic efficiency of the lithium battery, which is generally 1 at room temperature. c is the rated capacity of the lithium battery. Combining the lithium battery equivalent circuit model with the ampere-hour current method, take the state variable x k =[SOC k ,U 1,k ,U 2,k ] T , the input variable is I(k) and the output variable is y k =[U t,k ], the state space expression of lithium battery is obtained as:

[0090]

[0091] Where T is the sampling period, w k is the system noise, v k To measure noise.

[0092] In the step 2, the functional relationship between each parameter and the SOC is determined through the HPPC working condition, and the functional relationship between the open circuit voltage and the SOC is determined through the intermittent constant current discharge working condition.

[0093] Step 2.1: HPPC working condition: (1) Charge the battery to full capacity with constant current and constant voltage and let it stand for a long time; (2) Discharge with 1C current pulse for 10 seconds; let it stand for 40 seconds after discharge. (3) Charge with 1C current pulse for 10 seconds, let it stand for 3 minutes after charging; (4) Discharge with 0.5C current constant current for 12 minutes to reduce the SOC by 10%, let it stand for 20 minutes after discharge. (5) Repeat steps (1) to (4) until the SOC drops below 10%. The current and voltage curves of the HPPC working condition are shown in the figure below. Figure 3 , Figure 4 shown.

[0094] Step 2.2: Analyzing the voltage curve of HPPC working condition, the following conclusions can be drawn:

[0095] 1) When the discharge starts from t1 to t2, the voltage at the lithium battery terminal drops sharply from U1 to U2, which is the voltage change caused by the ohmic internal resistance R0;

[0096] 2) The period from t2 to t3 is the change in the terminal voltage of the lithium battery caused by the discharge current charging the polarized capacitor;

[0097] 3) When the discharge ends in the time period t3-t4, the voltage at the lithium battery terminal rises suddenly from U3 to U4, which is the voltage change caused by the ohmic internal resistance R0;

[0098] 4) The time period from t4 to t5 is the static stage after the discharge is completed, which is the change of the lithium battery terminal voltage caused by the discharge of polarized capacitors;

[0099] The value of the ohmic internal resistance can be calculated from conclusions 1) and 3), where I is the lithium battery current.

[0100]

[0101] From conclusions 2) and 4), we can get the terminal voltage U t The relationship between t and time.

[0102]

[0103] The parameters corresponding to each 10% change in SOC obtained through HPPC working conditions are shown in Table 1.

[0104] Table 1 Offline identification results of the second-order Thevenin equivalent circuit model parameters

[0105]

[0106] Step 2.3: Fit the parameters obtained from the HPPC operating condition identification through cubic Hermite interpolation to obtain the relationship between each parameter and SOC.

[0107] Step 2.4: Intermittent constant current discharge condition: (1) Charge the battery to full capacity with constant current and constant voltage and let it stand for a long time; (2) Discharge at a constant current of 1 / 3C for 30 minutes to reduce the SOC by 10%, and let it stand for 40 minutes after the discharge; (3) Repeat step (2) until the SOC drops below 10%.

[0108] Step 2.5: Obtain the open circuit voltage corresponding to every 10% change in SOC through intermittent constant current discharge conditions.

[0109] Step 2.6: Fit the open circuit voltage by cubic Hermite interpolation to obtain the SOC-OCV fitting curve.

[0110] The step 3 is to measure the initial open circuit voltage of the lithium battery and obtain the initial SOC of the lithium battery through the SOC-OCV fitting curve.

[0111] In step 4, the initial SOC is substituted into the parameter fitting expression to obtain R0, R1, R2, C1, and C2 corresponding to the SOC.

[0112] Furthermore, the recursive formula of the recursive least squares algorithm with forgetting factor is:

[0113]

[0114] In the formula, and is the estimated value of the k-1th and kth times; K(k) is the gain matrix of the kth time, and the error The product with the gain matrix is ​​the correction value at time k, P(k-1) and P(k) are the error covariance matrices of the k-1th and kth times; λ is the forgetting factor, which is generally between 0.95 and 1.

[0115] From the port voltage equation (1), the frequency domain transfer function of the system can be obtained as:

[0116]

[0117] U(s)=U OC (s)-U t (s) (8)

[0118] Where s is the Laplace operator, and the transfer function of the second-order model of lithium battery is obtained as follows:

[0119]

[0120] Bilinear transformation method Discretize the transfer function, z -1 is the discretization operator, and T represents the sampling period.

[0121]

[0122] In the formula, a1, a2, a3, a4, a5 are the parameters to be identified.

[0123]

[0124] Take τ1 as the concentration difference polarization time constant, take τ2 as the electrochemical polarization time constant, θ1, θ2, θ3, θ4, θ5 as intermediate parameters, and write the parameters to be identified as formula (12).

[0125]

[0126] The standard difference form is written as:

[0127] U(k)=a1U(k-1)+a2U(k-2)+a3I(k)+a4I(k-1)+a5I(k-2)(13)

[0128] The regression form is written as:

[0129]

[0130] Where: y(k) = U(k), θ T (k) = [a1, a2, a3, a4, a5].

[0131] The intermediate parameters θ1, θ2, θ3, θ4, and θ5 are obtained by inverse deduction from formula (12).

[0132]

[0133] Solve the equivalent circuit model parameters by equations (16) and (17):

[0134]

[0135]

[0136] In step 5, the parameters R0, R1, R2, C1, and C2 are substituted back into the recursive formula (11) (12) to obtain the iterative initial parameters a1, a2, a3, a4, and a5.

[0137] In step 6, the initial parameters a1, a2, a3, a4, and a5 are used as initial values ​​of the improved initial value with forgetting factor recursive least squares algorithm for parameter identification.

[0138] The algorithm is verified through experimental test conditions.

[0139] Working condition 1: (1) Charge the battery to full capacity at constant current and constant voltage and let it rest for a long time; (2) Discharge it with a 1C current pulse until the terminal voltage of the lithium battery drops to the discharge cut-off voltage.

[0140] Condition 2: (1) Charge the battery to full capacity at constant current and constant voltage and let it rest for a long time; (2) Discharge it at 1C current pulse for 12 minutes and let it rest for 20 minutes; (3) Discharge it at 1C current pulse until the terminal voltage of the lithium battery drops to the discharge cut-off voltage.

[0141] Working condition 3: (1) Charge the battery to full capacity at constant current and constant voltage and let it stand for a long time; (2) Perform a cyclic dynamic stress test (DST) on the lithium battery until the terminal voltage of the lithium battery drops to the discharge cut-off voltage.

[0142] Working condition 4: (1) Charge the battery to full capacity at constant current and constant voltage and let it stand for a long time; (2) Discharge with 1C current pulse for 12 minutes and let it stand for 20 minutes; (3) Perform DST test on the lithium battery until the terminal voltage of the lithium battery drops to the discharge cut-off voltage.

[0143] Experimental conditions 1 and 2 are constant current discharge conditions, and the initial SOCs are 100% and 80% respectively; experimental conditions 3 and 4 are DST conditions, and the initial SOCs are 100% and 80% respectively. For different conditions, the iterative initial values ​​are shown in Table 2.

[0144] Table 2 Initial values ​​of iterations for each working condition

[0145]

[0146] Parameter identification is performed for working conditions 1 to 4 respectively. For each working condition, the recursive least squares algorithm with forgetting factor (FFRLS) and the improved initial value recursive least squares algorithm with forgetting factor (IIV-FFRLS) are used for parameter identification. The forgetting factor of the two algorithms is set to 0.995. Figure 5 , Figure 6 , Figure 7 and Figure 8 This is a comparison chart of the absolute errors of each working condition.

[0147] The mean absolute error and root mean square error are used to analyze the identification results of the four algorithms to verify the accuracy of the parameter identification algorithm. The mean absolute error and root mean square error are shown in formula (18). The mean absolute error and root mean square error obtained by the two algorithms for the four experimental conditions are shown in Table 3.

[0148]

[0149] Table 3 E of each working condition MAE and E RMSE Comparison

[0150]

[0151] From the results, it can be seen that for simple constant current discharge conditions and complex DST conditions, the improved initial value with forgetting factor recursive least squares algorithm converges faster than the recursive least squares algorithm with forgetting factor. MAE and E RMSE It can be seen that the improved initial value with forgetting factor recursive least squares algorithm is effective in the identification process of each working condition. MAE Smallest, highest recognition accuracy, E RMSE The smallest, the most robust algorithm.

[0152] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. For those skilled in the art, the present invention may have various modifications and variations. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention shall be included in the protection scope of the present invention.

Claims

1. A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least squares method mainly includes the following steps: Step 1: Establish a second-order Thevenin equivalent circuit model of a lithium battery; Step 2: Determine the functional relationship between each parameter and SOC through the HPPC working condition, and determine the functional relationship between the open circuit voltage and SOC through the intermittent constant current discharge working condition; Step 2.1: HPPC working condition: (1) Charge the battery to full capacity with constant current and constant voltage and let it stand for a long time; (2) Discharge with 1C current pulse for 10 seconds; let it stand for 40 seconds after discharge; (3) Charge with 1C current pulse for 10 seconds, let it stand for 3 minutes after charging; (4) Discharge with 0.5C current constant current for 12 minutes to reduce the SOC by 10%, let it stand for 20 minutes after discharge; (5) Repeat steps (1) to (4) until the SOC drops below 10%; Step 2.2: Obtain the parameters corresponding to each 10% change in SOC through the HPPC operating condition; Step 2.3: Fit the parameters obtained by HPPC working condition identification through cubic Hermite interpolation to obtain the relationship between each parameter and SOC; Step 2.4: Intermittent constant current discharge condition: (1) Charge the battery to full capacity with constant current and constant voltage and let it stand for a long time; (2) Discharge at a constant current of 1 / 3C for 30 minutes to reduce the SOC by 10%, and let it stand for 40 minutes after the discharge; (3) Repeat step (2) until the SOC drops below 10%; Step 2.5: Obtain the open circuit voltage corresponding to each 10% change in SOC through intermittent constant current discharge conditions; Step 2.6: Fit the open circuit voltage by cubic Hermite interpolation to obtain the SOC-OCV fitting curve; Step 3: Measure the initial open circuit voltage to obtain the initial SOC; Step 4: Substitute the initial SOC into the parameter fitting expression to obtain the parameter value corresponding to this SOC; Step 5: Substitute each parameter back into the recursive formula to obtain the initial value of the improved initial value with the forgetting factor recursive least squares method; Step 6: Use the improved initial value with forgetting factor recursive least squares method to identify parameters.

2. A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least squares method according to claim 1, characterized in that: The parameters of the lithium battery second-order Thevenin equivalent circuit model established in step 1 include R0, R1, R2, C1, C2 and open circuit voltage U oc .

3. A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least square method according to claim 1, characterized in that: The initial open circuit voltage of the lithium battery was measured, and the initial SOC of the lithium battery was obtained through the SOC-OCV fitting curve.

4. A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least square method according to claim 1, characterized in that: Substitute the initial SOC into the parameter fitting expression to obtain R0, R1, R2, C1, and C2 corresponding to this SOC.

5. A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least square method according to claim 1, characterized in that: Substitute the parameters R0, R1, R2, C1, and C2 back into the recursive formula to obtain the iterative initial parameters a1, a2, a3, a4, and a5.

6. A lithium battery parameter identification method based on improved initial value with forgetting factor recursive least square method according to claim 1, characterized in that: The initial parameters a1, a2, a3, a4, and a5 are used as the initial values ​​of the improved initial value with forgetting factor recursive least squares algorithm and parameter identification is performed.

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