A method for measuring static flux of a coil of a direct-current electromagnetic mechanism

Abstract

The present application relates to the technical field of static magnetic chain measurement of electromagnetic mechanism, and particularly discloses a DC electromagnetic mechanism coil static magnetic chain measurement method, which comprises the following steps: step one, building a DC electromagnetic mechanism coil current test platform; step two, establishing a measured current decomposition and filtering model to filter out irrelevant high-frequency noise signal interference; step three, establishing a DC electromagnetic mechanism coil inductance equivalent improved first-order RC mathematical model; step four, establishing an improved first-order RC weighted fitting model of the coil current-time relationship; step five, establishing an optimal improved first-order RC weighted fitting model of the DC electromagnetic mechanism coil current-time relationship; and step six, solving the total magnetic chain of the coil based on the magnetic chain model.The present application has the beneficial effect that the fast and accurate measurement and calculation of the electromagnetic mechanism coil magnetic chain can effectively determine the saturation degree of the DC electromagnetic mechanism, and better assist the electromagnetic mechanism design.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of static magnetic chain measurement of electromagnetic mechanisms, and particularly relates to a method for measuring the static magnetic chain of a coil of a direct-current electromagnetic mechanism. BACKGROUND

[0002] In real life, the use amount of low-voltage electrical appliances is very large, and the application range is also very wide. As an important component of low-voltage electrical appliances, an electromagnetic mechanism plays a decisive role in the normal work of low-voltage electrical appliances. In the product development process such as low-voltage electrical appliance virtual prototype simulation, the design of the magnetic circuit of the electromagnetic mechanism is related to the magnetic state of components such as an iron core, an armature and a yoke. If the magnetic circuit of the electromagnetic mechanism passes through too much magnetic chain, the components such as the iron core will enter a supersaturated state, so that the magnetic permeability thereof rapidly decreases, thereby reducing the magnetic conduction capability of the electromagnetic mechanism, and in a serious case, reaching a state of almost no magnetic conduction, which greatly reduces the working performance of the electromagnetic mechanism and affects the normal work of the low-voltage electrical appliance. Therefore, the rapid and accurate measurement and calculation of the static magnetic chain of the coil of the electromagnetic mechanism play an important role in the development of low-voltage electrical appliances. A general method for measuring the static magnetic chain of the coil of the direct-current electromagnetic mechanism is needed to assist the design of the electromagnetic mechanism. SUMMARY

[0003] The application aims to solve the above problems, and provides a method for measuring the static magnetic chain of the coil of a direct-current electromagnetic mechanism.

[0004] To achieve the above object, the application provides a method for measuring the static magnetic chain of the coil of a direct-current electromagnetic mechanism, which comprises the following steps:

[0005] Step 1: a direct-current electromagnetic mechanism coil current test platform is built, and the coil current-time relationship under different currents and different positions of the electromagnetic mechanism is obtained;

[0006] Step 2: a measured current decomposition and filtering model is established based on a variational mode decomposition algorithm and a Pearson correlation coefficient, the measured current-time relationship is filtered, and irrelevant high-frequency noise signal interference is filtered out;

[0007] Step 3: the coil of the direct-current electromagnetic mechanism is equivalent to an improved first-order RC circuit, and an improved mathematical model of the coil inductance of the direct-current electromagnetic mechanism is established;

[0008] Step 4: an improved first-order RC weighted fitting model of the coil current-time relationship is established based on a double square weight algorithm and a trust region algorithm;

[0009] Step 5: an optimal improved first-order RC weighted fitting model of the coil current-time relationship of the direct-current electromagnetic mechanism is established based on a sparrow search algorithm, and the advantages and disadvantages of the fitting model are judged based on the goodness of fit.

[0010] Step six, based on the establishment of the coil magnetic chain model of the direct current electromagnetic mechanism, based on the coil current-time relationship optimal improvement of the first order RC weighted fitting model to solve the coil total magnetic chain.

[0011] The step one of building a coil current test platform of the direct current electromagnetic mechanism includes the following processes:

[0012] First, the non-magnetic plug gauge is placed between the armature and the iron core to fix the position of the armature, and the position of the armature is adjusted by adjusting the thickness of the plug gauge;

[0013] Secondly, the specific position of the armature required in the test process is determined by the angle ruler;

[0014] Thirdly, then build a coil current test platform of the direct current electromagnetic mechanism, adjust the direct current constant voltage and constant current linear power supply to the constant direct current voltage required in the test process, adjust the oscilloscope, current probe and voltage probe to the measurement conditions required in the test process;

[0015] Finally, press the switch to turn on the circuit, capture the current flowing through the coil of the electromagnetic mechanism and the voltage across the coil through the current probe and the voltage probe, and display the corresponding coil current and coil voltage data on the oscilloscope, complete the measurement of the coil current-time relationship and the coil voltage-time relationship of the coil under different positions of the armature and different currents of the coil.

[0016] The process of establishing the measured current decomposition and filtering model based on the variational mode decomposition algorithm and the Pearson correlation coefficient in step two is as follows: first, based on the variational mode decomposition algorithm, the coil current-time relationship original signal is decomposed into several sub-signal components, which are divided into construction of variational problem and solution of variational problem. Among them, the constrained variational problem model is represented as:

[0017] (1)

[0018] In the formula: 、 is the coil current modal component and its corresponding center frequency; is the number of coil current modal components with center frequency limited bandwidth; is the partial derivative of time ; is the unit impulse function; is the coil current original signal.

[0019] By introducing Lagrange multiplier and quadratic penalty factor into formula (1), it is transformed into an unconstrained variational problem, which is represented as:

[0020] (2)

[0021] The optimal solution of the function is obtained based on the saddle point of formula (2) solved by an alternating direction multiplier method.

[0022] The correlation between the coil current original signal and the sub-signal component is calculated based on a Pearson correlation coefficient, and is expressed as:

[0023] (3)

[0024] In the formula: is the correlation coefficient between the coil current original signal and the sub-signal component; is the number of coil current signal data; , is the coil current original signal and the sub-signal of the first data point;

[0025] According to the Pearson correlation coefficient, the sub-signal component with the largest correlation coefficient is selected, and other sub-signal components are filtered out to obtain the coil current-time relationship after filtering.

[0026] In the step three, the coil inductance equivalent mathematical model of the direct current electromagnetic mechanism is established according to the working characteristics of the coil of the direct current electromagnetic mechanism, the coil of the direct current electromagnetic mechanism is equivalent to a first-order RC circuit, and the coil inductance equivalent mathematical model is established, that is, the voltage balance equation of the coil of the direct current electromagnetic mechanism can be expressed as:

[0027] (4)

[0028] In the formula: is the coil voltage; is the coil current; is the coil resistance; is the coil inductance.

[0029] The first-order RC fitting model formula (4) of the coil current-time relationship is transformed to obtain formula (5) expressed as:

[0030] (5)

[0031] The distance parameter d is introduced to represent the small distance translation phenomenon of the coil current, and the first-order RC fitting model is corrected. The improved first-order RC fitting model of the coil current-time relationship of the direct current electromagnetic mechanism can be expressed as:

[0032] (9)

[0033] In the formula: : small distance translation distance of the coil current of the direct current electromagnetic mechanism;

[0034] The process of establishing the improved first-order RC weighted fitting model of the coil current-time relationship in the step four is:​

[0035] Different double square weights are given to different current-time relationship data points based on the double square weight algorithm, that is, the data points farther away from the fitting line have lower weights, which can minimize the influence of abnormal values in the current-time relationship data measured by the oscilloscope due to external electromagnetic interference and other factors. The double square weight is represented as:

[0036] (6)

[0037] In the formula: is the ordinary least squares residual, is the least squares fitting leverage value;

[0038] (7)

[0039] In the formula: is the tuning constant 4.685; is the robust standard deviation MAD / 0.6745, where MAD is the median absolute deviation of the residual;

[0040] (8)

[0041] In the formula: is the double square weight of different current data points, and the weighted residual in the first-order RC fitting model of the coil current-time relationship is iteratively optimized based on the confidence domain algorithm to obtain the optimal fitting inductance value corresponding to the minimum weighted residual.

[0042] The process of establishing the optimal improved first-order RC weighted fitting model of the coil current-time relationship of the direct current electromagnetic mechanism in step five is:

[0043] The maximum value of the fitting goodness of the improved first-order RC fitting model is taken as the optimization target of the sparrow search algorithm, and the translation distance is taken as the optimization variable, which can be represented as:

[0044] (10)

[0045] The sparrow search algorithm optimizes the fitting goodness of the improved first-order RC fitting model The specific steps are:

[0046] Step 1: According to the coil current-time relationship of the direct current electromagnetic mechanism, determine the sparrow population size, the maximum number of iterations, the translation distance upper and lower limits, the ratio of discoverers and joiners in the sparrow population, and the safety threshold, etc.

[0047] Step 2: The fitting goodness of the improved first-order RC fitting model As sparrow individual fitness, initial sparrow population is randomly generated and the best and optimal translation distance ;

[0048] Step 3: update the finder position and fitness in sparrow population, i.e. translation distance and goodness of fit ; the finder position update is expressed as:

[0049] (11)

[0050] In the formula: is the current iteration number; is the position of the th sparrow; is a random number, ; is the maximum iteration number; is the early warning value, ; is the safety value, ; is a random number subject to normal distribution; is a constant 1;

[0051] Step 4: update the joiner position and fitness in sparrow population, i.e. translation distance and goodness of fit ; the joiner position update is expressed as:

[0052] (12)

[0053] In the formula: is the optimal position currently occupied by the finder, i.e. optimal distance ; is the global worst position, i.e. worst distance ; is randomly assigned as 1 or -1, ; is the population size;

[0054] Step 5: update the early warning position and fitness in sparrow population, i.e. translation distance and goodness of fit , expressed as:

[0055] (13)

[0056] In the formula: is the current global optimal position; is a step control parameter, and is a random number, ; is a random number, ; , is the current global optimum and the worst fitness; is a very small constant to avoid zero in denominator;

[0057] Step 6: update the next generation of sparrow population position and fitness, i.e. translation distance and goodness of fit , and keep the historical optimal sparrow individual;

[0058] Step 7: judge whether the iteration stopping criterion is met; if met, output the global optimal sparrow position and optimal fitness; otherwise, go to step 3 to continue iteration and optimization until the optimal translation distance and the corresponding optimal are found.

[0059] The process of solving the total magnetic chain of the coil based on the optimal improved first-order RC weighted fitting model of the coil current-time relationship in the step six is: based on the magnetic chain model , formula (4) can be transformed into:

[0060] (14)

[0061] In the formula: : coil magnetic chain initial value; : coil magnetic chain final value; : time initial value; : time final value;

[0062] The improved improved first-order RC optimal fitting model and the magnetic chain initial value are substituted into formula (14), and the coil static magnetic chain of the direct current electromagnetic mechanism at different currents and different positions can be obtained.

[0063] Compared with the prior art, the present application has the following beneficial effects:

[0064] The present application can quickly and accurately test the coil static magnetic chain, solve the problem that it is difficult to accurately judge the magnetic field state of the electromagnetic mechanism according to the coil magnetic chain in the magnetic circuit design process of the direct current electromagnetic mechanism, effectively avoid the problem that the electromagnetic mechanism is over-saturated in the magnetic circuit design process, leading to unreasonable electromagnetic mechanism design, and has important significance for the production and design of the direct current electromagnetic mechanism. BRIEF DESCRIPTION OF DRAWINGS

[0065] Figure 1 is a structural schematic diagram of the coil static magnetic chain measurement method of the direct current electromagnetic mechanism according to the present application;

[0066] Figure 2 is a physical diagram of the coil current and voltage test platform of the direct current electromagnetic mechanism according to the present application;

[0067] Figure 3This is the equivalent first-order RC circuit diagram of the DC electromagnetic mechanism coil described in this invention;

[0068] Figure 4 This is a comparison chart of the results of three methods for determining the coil current-time relationship of the DC electromagnetic mechanism described in this invention. Detailed Implementation

[0069] The present invention will now be described in detail with reference to the accompanying drawings, such as... Figures 1-4 As shown;

[0070] 1. Flowchart of the method for measuring static flux linkage of a DC electromagnetic mechanism coil is shown below. Figure 1 As shown.

[0071] First, place a non-magnetic feeler gauge between the armature and the core to fix the armature position, and adjust the armature position by adjusting the thickness of the feeler gauge; second, use an angle gauge to determine the specific position of the armature required during the test; then build... Figure 2 The DC electromagnetic mechanism coil current test platform shown involves adjusting the DC constant voltage and constant current linear power supply to the constant DC voltage value required during the test, and adjusting the oscilloscope, current probe, and voltage probe to the required measurement conditions. Finally, the switch is pressed to turn on the circuit, and the current flowing through the electromagnetic mechanism coil and the voltage across its terminals are captured by the current probe and voltage probe, and the corresponding coil current and coil voltage data are displayed on the oscilloscope. This completes the measurement of the coil current-time relationship and coil voltage-time relationship when the armature of the DC electromagnetic mechanism is in different positions and the coil is at different currents.

[0072] Second, the process of establishing the measured current decomposition and filtering model based on the variational mode decomposition algorithm and Pearson correlation coefficient is as follows: First, the original signal of the coil current-time relationship is decomposed into several sub-signal components based on the variational mode decomposition algorithm, specifically divided into the construction of the variational problem and the solution of the variational problem. The constrained variational problem model is expressed as:

[0073] (1)

[0074] In the formula: , For each coil current mode component and its corresponding center frequency; The number of coil current mode components with a finite bandwidth and a center frequency; For time The partial derivatives; Unit impact function; This is the original signal of the coil current.

[0075] By introducing the Lagrange multiplier into equation (1) and secondary penalty factor This transforms into an unconstrained variational problem, expressed as:

[0076] (2)

[0077] The optimal solution of the function is obtained by solving the saddle point of equation (2) using the alternating direction multiplier method.

[0078] The correlation between the original coil current signal and its sub-signal components, calculated based on the Pearson correlation coefficient, is expressed as follows:

[0079] (3)

[0080] In the formula: This is the correlation coefficient between the original coil current signal and the sub-signal components; The number of coil current signal data; , The original signal and sub-signal of the coil current One data point;

[0081] Based on the Pearson correlation coefficient, the sub-signal component with the largest correlation coefficient is selected, and other sub-signal components are filtered out to obtain the filtered coil current-time relationship.

[0082] Third, based on the operating characteristics of the DC electromagnetic mechanism coil, the DC electromagnetic mechanism coil is equivalent to a first-order RC circuit, and an equivalent mathematical model of the coil inductance is established. That is, the voltage balance equation of the DC electromagnetic mechanism coil can be expressed as:

[0083] (4)

[0084] In the formula: The coil voltage; The coil current; The coil resistance; It represents the coil inductance.

[0085] Equation (4) of the first-order RC fitting model of the coil current-time relationship is transformed to obtain equation (5), which is expressed as:

[0086] (5)

[0087] During the testing of the coil current of a DC electromagnetic mechanism, a small-distance translation phenomenon of the coil current caused by uncontrollable human factors and external interference occurs. This phenomenon affects the accuracy of the first-order RC fitting of the coil current, therefore, a distance parameter is introduced. Characterize the small-distance translation phenomenon and correct the first-order RC fitting model.

[0088] (9)

[0089] In the formula: : DC electromagnetic mechanism coil current small distance translation distance;

[0090] Fourth, based on the different current-time relationship data points of different double square weight algorithm, that is, the farther away from the data points of the fitting line weight is lower, can maximize the influence of the measured oscilloscope current-time relationship data due to external electromagnetic interference and other factors, double square weight is expressed as:

[0091] (6)

[0092] In the formula: The ordinary least squares residual, The least squares fitting lever value;

[0093] (7)

[0094] In the formula: The tuning constant 4.685; The robust standard deviation MAD / 0.6745, where MAD is the median absolute deviation of the residual;

[0095] (8)

[0096] In the formula: The double square weight of different current data points, based on the confidence domain algorithm iterative optimization coil current-time relationship improved first-order RC fitting model in the weighted residual, get the minimum weighted residual corresponding to the optimal fitting inductance value.

[0097] Fifth, based on the sparrow search algorithm to optimize the compensation coil current small distance translation phenomenon, the optimal improved first-order RC fitting model of DC electromagnetic mechanism coil current-time relationship can be expressed as:

[0098] The maximum value of the improved first-order RC fitting model fitting goodness The sparrow search algorithm optimization target, the translation distance As the optimization variable, can be expressed as:

[0099] (10)

[0100] The sparrow search algorithm optimization improved first-order RC fitting model fitting goodness The specific steps are:

[0101] Step 1: According to the DC electromagnetic mechanism coil current-time relationship to determine the sparrow population size, the maximum number of iterations, the translation distance Upper and lower limits, the ratio of discoverer and joiner in sparrow population and safety threshold, etc.

[0102] Step 2: Update the fitness of the improved first-order RC fitting model As the sparrow individual fitness, the initial sparrow population is randomly generated, and the optimal and optimal translation distance ;

[0103] Step 3: Update the finder position and fitness in the sparrow population, i.e. translation distance and fitness ; the finder position update is represented as:

[0104] (11)

[0105] In the formula: is the current iteration number; is the position of the th sparrow; is a random number, ; is the maximum iteration number; is the early warning value, ; is the safety value, ; is a random number following a normal distribution; is a constant 1;

[0106] Step 4: Update the joiner position and fitness in the sparrow population, i.e. translation distance and fitness ; the joiner position update is represented as:

[0107] (12)

[0108] In the formula: is the optimal position currently occupied by the finder, i.e. optimal distance ; is the global worst position, i.e. worst distance ; is randomly assigned as 1 or -1, ; is the population size;

[0109] Step 5: Update the early warning position and fitness in the sparrow population, i.e. translation distance and fitness , represented as:

[0110] (13)

[0111] In the formula: is the current global optimal position; is a step control parameter, ; is a random number, ; , is the current global optimum and the worst fitness; is a very small constant to avoid zero in denominator;

[0112] Step 6: update the next generation of sparrow population position and fitness, i.e. translation distance and goodness of fit , and keep the historical optimal sparrow individual;

[0113] Step 7: judge whether the iteration stopping criterion is met; if met, output the global optimal sparrow position and optimal fitness; otherwise, go to step 3 to continue iteration and optimization until the optimal translation distance and the corresponding optimal are found.

[0114] Sixth, based on the magnetic chain model , formula (4) can be transformed into:

[0115] (14)

[0116] In the formula: : coil initial magnetic chain value; : coil final magnetic chain value; : time initial value; : time final value;

[0117] The improved first-order RC model optimal fitting and the initial magnetic chain value are substituted into formula (14) to obtain the coil static magnetic chain of the direct current electromagnetic mechanism under different currents and different positions.

[0118] Embodiment

[0119] Taking a certain type of direct current electromagnetic mechanism as an example, the measurement value of the coil static magnetic chain measured by the present application and the simulation value of the coil static magnetic chain of the direct current electromagnetic mechanism simulated by the finite element electromagnetic simulation software ANSYS Maxwell are compared and analyzed to verify the effectiveness of the coil static magnetic chain measurement method of the direct current electromagnetic mechanism proposed by the present application. The comparison of the coil static magnetic chain measurement value and the simulation value of the electromagnetic mechanism armature under different steady-state currents at a certain position is shown in Table 1.

[0120] Table 1 Comparison of coil static magnetic chain measurement value and simulation value of a certain type of direct current electromagnetic mechanism

[0121] Current / A Flux linkage measured / Wb Flux linkage simulated / Wb Percentage difference / % 0 0.2026 0.2026 —— 0.01 0.2464 0.2588 5.03 0.02 0.2997 0.3138 4.70 0.03 0.3474 0.3693 6.30 0.04 0.4009 0.4241 5.79 0.05 0.4468 0.483 8.10 0.06 0.5122 0.5435 6.11 0.07 0.5721 0.6033 5.45 0.08 0.6293 0.6624 5.26 0.09 0.6833 0.7198 5.34 0.1 0.7294 0.7746 6.20 0.11 0.7681 0.8293 7.97 0.12 0.8291 0.8845 6.68 0.13 0.8773 0.9331 6.36 0.14 0.9317 0.9777 4.94 0.15 0.9853 1.0154 3.05

[0122] Table 1 shows that the maximum difference between the coil static magnetic chain measurement value and the simulation value of the direct current electromagnetic mechanism is about 8%.

[0123] The coil current of a certain type of DC electromagnetic mechanism is compared as shown in the figure Figure 4 A represents the measured coil current-time relationship, B represents the coil current-time relationship based on the measured coil static flux, and C represents the coil current-time relationship based on the ANSYS static flux simulation value.

[0124] Figure 4 It is shown that the overall trends of the A, B and C curves are consistent, and the consistency is high. The maximum error between the B curve and the C curve is about 6% when approaching the steady state.

[0125] Table 1 and Figure 4 The effectiveness and correctness of the DC electromagnetic mechanism coil static flux measurement method proposed in the application are verified.

[0126] The application proposes a DC electromagnetic mechanism coil static flux testing method, which can quickly and accurately test the coil static flux, solves the problem that it is difficult to accurately determine the electromagnetic mechanism magnetic field state according to the coil flux in the process of magnetic circuit design of the DC electromagnetic mechanism, effectively avoids the problem that the electromagnetic mechanism design is unreasonable due to over-saturation of the electromagnetic mechanism in the process of magnetic circuit design, and has important significance for the production design of the DC electromagnetic mechanism.

[0127] It should be noted that in this paper, relationship terms such as first and second are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between the entities or operations. Moreover, the term "includes", "contains" or any other variant thereof is intended to cover non-exclusive inclusion, so that the process, method, article or equipment including a series of elements not only includes those elements, but also includes other elements not explicitly listed or inherent to such process, method, article or equipment. Without more limitations. The statement "includes a limited element" does not exclude the presence of additional identical elements in the process, method, article or equipment including the element.

[0128] The above technical solutions only reflect the preferred technical solutions of the application, and some changes made by the skilled in the art to some parts thereof also reflect the principles of the application and are within the protection scope of the application.

Claims

1. A method for measuring the static flux linkage of a DC electromagnetic mechanism coil, characterized in that, The method includes the following steps: Step 1: Build a DC electromagnetic mechanism coil current testing platform to obtain the coil current-time relationship under different currents and positions of the electromagnetic mechanism; Step 2: Based on the variational mode decomposition algorithm and Pearson correlation coefficient, establish the measured current decomposition and filtering model, and filter the measured current-time relationship to remove irrelevant high-frequency noise signal interference. Step 3: Equivalently transform the DC electromagnetic mechanism coil into an improved first-order RC circuit and establish an equivalent mathematical model of the DC electromagnetic mechanism coil inductance. In step three, establishing the equivalent mathematical model of the DC electromagnetic mechanism coil inductance is based on the working characteristics of the DC electromagnetic mechanism coil. The coil is equivalent to a first-order RC circuit, and the equivalent mathematical model of the coil inductance is established. That is, the voltage balance equation of the DC electromagnetic mechanism coil can be expressed as: （4） In the formula: The coil voltage; The coil current; The coil resistance; For coil inductance; Equation (4) of the first-order RC fitting model of the coil current-time relationship is transformed to obtain equation (5), which is expressed as: （5） Introducing distance parameters To characterize the small-distance translation phenomenon, the improved first-order RC fitting model of the DC electromagnetic mechanism coil current-time relationship can be expressed as follows: （6） In the formula: : DC electromagnetic mechanism coil current small distance translation distance; Step 4: Establish an improved first-order RC weighted fitting model for the coil current-time relationship based on the bisquared weighting algorithm and the trust region algorithm; Step 5: Based on the sparrow search algorithm, establish the optimal improved first-order RC weighted fitting model of the current-time relationship of the DC electromagnetic mechanism coil, and judge the quality of the fitting model based on the goodness of fit. Step 6: Establish a coil flux linkage model based on the DC electromagnetic mechanism, and solve the total coil flux linkage based on the optimal improved first-order RC weighted fitting model of the coil current-time relationship.

2. The method for measuring the static flux linkage of a DC electromagnetic mechanism coil according to claim 1, characterized in that, The process of setting up the DC electromagnetic mechanism coil current testing platform in step one includes the following steps: First, place a non-magnetic feeler gauge between the armature and the core component to fix the position of the armature, and adjust the position of the armature by adjusting the thickness of the feeler gauge; Secondly, the specific position of the armature required during the test is determined by using an angle ruler; Next, a DC electromagnetic mechanism coil current test platform is set up, and the DC constant voltage and constant current linear power supply is adjusted to the constant DC voltage value required during the test. The oscilloscope, current probe and voltage probe are adjusted to the measurement conditions required during the test. Finally, press the switch to turn on the circuit. The current flowing through the electromagnetic mechanism coil and the voltage across its two ends are captured by the current probe and voltage probe, and the corresponding coil current and voltage data are displayed on the oscilloscope. This completes the measurement of the coil current-time relationship and coil voltage-time relationship when the armature of the DC electromagnetic mechanism is in different positions and the coil is at different currents.

3. The method for measuring the static flux linkage of a DC electromagnetic mechanism coil according to claim 1, characterized in that, The process of establishing the measured current decomposition and filtering model based on the variational mode decomposition algorithm and Pearson correlation coefficient in step two is as follows: First, the original signal of the coil current-time relationship is decomposed into several sub-signal components based on the variational mode decomposition algorithm, specifically divided into the construction of the variational problem and the solution of the variational problem; among which, the constrained variational problem model is expressed as: （1） In the formula: , For each coil current mode component and its corresponding center frequency; The number of coil current mode components with a finite bandwidth and a center frequency; For time The partial derivatives; Unit impact function; This is the original signal of the coil current; By introducing the Lagrange multiplier into equation (1) and secondary penalty factor This transforms into an unconstrained variational problem, expressed as: （2） The optimal solution of the function is obtained by solving the saddle point of equation (2) using the alternating direction multiplier method; The correlation between the original coil current signal and its sub-signal components, calculated based on the Pearson correlation coefficient, is expressed as follows: （3） In the formula: This is the correlation coefficient between the original coil current signal and the sub-signal components; The number of coil current signal data; , The original signal and sub-signal of the coil current One data point; Based on the Pearson correlation coefficient, the sub-signal component with the largest correlation coefficient is selected, and other sub-signal components are filtered out to obtain the filtered coil current-time relationship.

4. The method for measuring the static flux linkage of a DC electromagnetic mechanism coil according to claim 1, characterized in that, The process of establishing the equivalent improved first-order RC weighted fitting model of the coil current-time relationship in step four is as follows: The double-square weighting algorithm assigns different double-square weights to different current-time relationship data points, meaning that data points farther from the fitted line have lower weights. This minimizes the impact of outliers in the current-time relationship data measured by the oscilloscope due to external electromagnetic interference. The double-square weighting is expressed as follows: （7） In the formula: For ordinary least squares residuals, The least squares fitted lever value; （8） In the formula: The tuning constant is 4.685; s is the robust standard deviation MAD / 0.6745, where MAD is the median absolute deviation of the residuals; （9） In the formula: By using a double-squared weighting for different current data points, the weighted residual in the first-order RC fitting model is improved by iteratively optimizing the coil current-time relationship based on the trust region algorithm, and the optimal fitting inductance value corresponding to the minimum weighted residual is obtained.

5. The method for measuring the static flux linkage of a DC electromagnetic mechanism coil according to claim 1, characterized in that, The process of establishing the optimal improved first-order RC weighted fitting model for the current-time relationship of the DC electromagnetic mechanism coil in step five is as follows: Improve the goodness of fit of the first-order RC fitting model The maximum value is used as the optimization objective of the sparrow search algorithm, and the translation distance is... As an optimization variable, it can be represented as: （10） Sparrow Search Algorithm Optimization and Improvement: First-Order RC Fitting Model Goodness of Fit The specific steps are as follows: Step 1: Determine the sparrow population size, maximum number of iterations, and translation distance based on the current-time relationship of the DC electromagnetic mechanism coil. Upper and lower limits, the ratio of discoverers to joiners in a sparrow population, and safety thresholds; Step 2: Calculate the goodness of fit of the improved first-order RC fitting model. As a measure of individual sparrow fitness, an initial sparrow population is randomly generated, and the best sparrows are retained. and optimal translation distance ; Step 3: Update the location and fitness (i.e., translation distance) of the finders in the sparrow population. and goodness of fit The discoverer's location update is represented as: （11） In the formula: This represents the current iteration number; For the first The position of a sparrow; For a random number, ; This represents the maximum number of iterations. This is a warning value. ; For safety values, ; These are random numbers that follow a normal distribution. It is a constant of 1; Step 4: Update the location and fitness (i.e., translation distance) of newcomers in the sparrow population. and goodness of fit The update of joiner positions is represented as follows: （12） In the formula: The optimal position, i.e., the optimal distance, occupied by the current discoverer. ; The worst position is the global worst distance. ; It is randomly assigned the value 1 or -1. ; Population size; Step 5: Update the location and fitness (i.e., translation distance) of the early warning sparrows in the sparrow population. and goodness of fit , is represented as: （13） In the formula: This is the current globally optimal position; The step size control parameter is a random number. ; For a random number, ; , The current global best and worst fitness; It is a very small constant to avoid zero in the denominator; Step 6: Update the location and fitness of the next generation of sparrow populations, i.e., the translation distance. and goodness of fit And retain the best historical sparrow individual; Step 7: Determine if the iteration stopping criterion is met; if so, output the globally optimal sparrow position and optimal fitness; otherwise, return to Step 3 to continue iterative optimization until the optimal translation distance is found. and corresponding optimal .

6. The method for measuring the static flux linkage of a DC electromagnetic mechanism coil according to claim 1, characterized in that, The process of solving the total flux linkage of the coil in step six, based on the optimal improved first-order RC weighted fitting model of the coil current-time relationship, is as follows: Based on the flux linkage model... Equation (4) can be transformed into: （14） In the formula: Initial value of coil flux; Final value of coil flux; Initial time value; Final value of time; Substituting the optimal fit of the improved first-order RC model and the initial value of the flux linkage into equation (14) yields the static flux linkage of the coil in the DC electromagnetic mechanism under different currents and positions.

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