A Method for Modeling an Ultrasonic Transducer with Load

Abstract

The present invention relates to a method for on-load modeling of an ultrasonic transducer. First of all, based on the MSD equivalent model established by dynamic simulation and Mason circuit, given the transducer parameters, through Matlab simulation and load experiment, the simulation data on impedance change and the experimental data on load force change are obtained. Then, by changing one parameter in the transducer, the next set of data is obtained, and the relationship matrix is obtained by data matching using the least squares method. Finally, the data is trained through an adaptive attribute weight neural network model. By inputting a set of material parameters and load force, the corresponding impedance can be obtained. The present invention can well reflect the corresponding relationship between the load force and the impedance, and even in the case of dynamic load, its impedance can be accurately and quickly corresponded.

Description

Technical Field

[0001] The present invention relates to a modeling method, specifically a method for modeling an ultrasonic transducer with a load. Background Art

[0002] Ultrasonic waves are widely used in medicine, military, and manufacturing industries due to their low cost, high safety, and high precision. Studying the reasons for changing the internal acoustic wave transmission law of the ultrasonic vibration system, mastering the influence law of dynamic load and thermal effect on the performance change of the ultrasonic vibration system, improving the working stability of the system, and increasing the energy transmission efficiency have always been the goals pursued by researchers in the ultrasonic field.

[0003] Currently, most of the research in this area is still in the preliminary stage and no breakthrough has been achieved. Therefore, it is of great significance to establish a load-bearing model of the transducer. Currently, a similar implementation scheme is to establish a Thevenin equivalent circuit according to the Thevenin theorem, and then further complete the establishment of the model.

[0004] The prior art also involves a mathematical equivalent transducer M-C-K model, as shown in Figure 1 , and then analyze its impedance through matlab simulation. Establish an M-C-K model according to the ultrasonic transducer structure, and its formula can be expressed as follows:

[0005]

[0006] Wherein, m0 is the mass of the piezoelectric ceramic, m1 is the mass of the pre-tightening bolt and the front cover plate, m2 is the mass of the horn rod and the tool, c1 is the damping coefficient of the pre-tightening bolt and the front cover plate, c2 is the damping coefficient of the horn rod and the tool, k1 is the spring coefficient of the pre-tightening bolt and the front cover plate, k2 is the spring coefficient of the horn rod and the tool, x0 is the displacement of the piezoelectric ceramic, x1 is the displacement of the pre-tightening bolt and the front cover plate, x2 is the displacement of the horn rod and the tool, and F0 is the force on the horn rod at the piezoelectric ceramic.

[0007] However, the impedance of the transducer is affected by factors such as materials, geometric structures, and loads. The prior art solutions are based on the no-load condition, and they cannot meet the characteristics of uncertain loads. Because once a load is added, the resonance frequency of the transducer will change, and the corresponding impedance will become extremely complex and difficult to determine. Ordinary models established based on no-load conditions cannot be well applied. Summary of the Invention

[0008] In view of the problems of mutation, randomness, and uncertainty in the case of the transducer with a load, the present invention proposes a method for modeling an ultrasonic transducer with a load.

[0009] The method of the present invention includes the following steps:

[0010] First step: Establish an equivalent model based on dynamic simulation and Mason's circuit:

[0011]

[0012] Among them, L p is the thickness of the piezoelectric ceramic stack, Z0 s =ρgS is the product of the density, sound velocity, and cross-sectional area of the piezoelectric ceramic crystal stack, τ s is the sound propagation constant of the piezoelectric ceramic stack material, Z R s and Z L s are the right equivalent impedance and left equivalent impedance of the T-shaped equivalent circuit respectively, and Z M S is the equivalent impedance in the middle of the T-shaped equivalent circuit.

[0013] Second step: Change a certain parameter of the materials in the piezoelectric transducer. The materials include the front cover plate, rear cover plate, and piezoelectric ceramic stack of the piezoelectric transducer; the parameters include the cross-sectional area S of the piezoelectric ceramic stack, the density ρ of the piezoelectric ceramic stack, the Young's modulus E of the front and rear cover plate materials, and the length l of the front and rear cover plates.

[0014] Third step: Based on the established model, simulate the impedance, and record the matrix [EZ i m1 corresponding to m groups of impedance and electrical parameters.

[0015] Fourth step: Based on the established model, conduct a load experiment, and record the matrix [EF k n1 corresponding to n groups of load force changes and electrical parameters.

[0016] Fifth step: Change another parameter of the materials in the piezoelectric transducer, keep other parameters unchanged, and repeat the impedance simulation and load experiment to obtain [EZ i m2 and [EF k n2 ;

[0017] Repeat this step multiple times to obtain a total of R groups of matrix relationships between simulation and load force experiments, that is, [EZ i mt and [EF k nt .

[0018] Sixth step: These R groups of [EZ i mt and [EF k nt ​​​​​​​​Match the matrices, match the data by the least squares method, and find the set of data that is the closest. In this way, the relationship formula can be obtained. Among them, T t is the material parameter corresponding to this set of matrices, and Fk y，t is the load force of the y-th row in [EF k nt . Zi x(y，t) is the impedance that best matches the load force of the y-th row in [EF k nt corresponding to [EZ i mt . y = 1, 2,..., n. x(y, t) is the impedance that best matches the load force Fk t when the fixed material type is T y,t , and the index number (or row number) of the impedance in [EZ i mt .

[0019] Step 7: Input as a set of training data into the adaptive attribute weight neural network. Among them, Fk y，t and T t are the inputs of the neural network, and the output of the neural network is Zi x(y，t) corresponding to the true value θ0; then optimize θ0 with the θ0' predicted by the neural network to obtain the corresponding network parameters, and thus a set of relationships between the load force, material, and impedance can be obtained;

[0020] Input all the R group pairing relationship matrices in the sixth step into the neural network for training to obtain the trained neural network; when any set of material parameters and load force are input subsequently, the impedance can be obtained.

[0021] Advantages of the present invention: Based on the electromechanical equivalent model, the impedance data under different materials and load force changes are obtained through a large number of experiments and simulations. Then, the data is fitted by the least squares method and trained through the adaptive attribute weight neural network to obtain the relationship between the parameters of the load force and material with respect to the impedance. Later, when the transducer is known, only a set of load forces need to be input to quickly obtain the impedance.

[0022] The present invention is a hybrid model that combines theory with practice. It can well reflect the corresponding relationship between the load force and the impedance, and even in the case of dynamic loads, the impedance can be accurately and quickly corresponding. Description of the Drawings

[0023] Figure 1 is the equivalent transducer M-C-K model;

[0024] Figure 2 ​​​​This is the flow chart of the method of the present invention;

[0025] Figure 3 This is the matching flow chart of the matrix relationship;

[0026] Figure 4 This is the adaptive attribute weight neural network. Detailed implementation manner

[0027] The present invention will be further described below with reference to the accompanying drawings.

[0028] First of all, based on the MSD equivalent model established by kinetic simulation and Mason circuit, and given the transducer parameters, through Matlab simulation and load experiment, the simulation data on impedance change and the experimental data on load force change are obtained. Then, by changing one parameter in the transducer, the next set of data is obtained, and the relationship matrix is obtained by data matching using the least square method. Finally, the data is trained through the adaptive attribute weight neural network model. By inputting a set of material parameters and load force, the corresponding impedance can be obtained.

[0029] As Figure 2 shown, the specific steps of the present invention are as follows:

[0030] In the first step, an equivalent model is established based on kinetic simulation and Mason circuit, and the formula is as follows:

[0031]

[0032] Based on this formula, a T-type equivalent circuit is formed. Among them, L p is the thickness of the piezoelectric ceramic stack, Z0 s is a calculation parameter, ρ, g, and s are respectively the product of the density, sound velocity, and cross-sectional area of the piezoelectric ceramic crystal stack, τ s is the sound propagation constant of the piezoelectric ceramic stack material, Z R s 、Z L s are respectively the right equivalent impedance and the left equivalent impedance of the T-type equivalent circuit, and Z M S is the equivalent impedance in the middle of the T-type equivalent circuit.

[0033] In the second step, since the piezoelectric transducer is composed of a front cover plate, a rear cover plate, and a piezoelectric ceramic stack, the present invention changes a certain parameter T i of the material in the piezoelectric transducer, such as the cross-sectional area S of the piezoelectric ceramic stack, the density ρ of the piezoelectric ceramic stack, the Young's modulus E of the front and rear cover plate materials, the length l of the front and rear cover plates, etc.

[0034] Step 3: Based on the MSD equivalent model established above, perform Matlab simulation on the impedance. Record the matrix of m impedances corresponding to electrical parameters, the matrix [EZ i m1 is as follows:

[0035]

[0036] where, f s1 , f s2 ,......, f sm are the forward resonance frequencies obtained from the simulation, f p1 , f p2 ,......, f pm are the reverse resonance frequencies obtained from the simulation, and are the half-power points obtained from the simulation, C1, C2,......, C m are the dynamic capacitances obtained from the simulation, L1, L2,......, L m are the dynamic inductances obtained from the simulation, Q1, Q2,......, Q m are the mechanical quality factors obtained from the simulation, R1, R2,......, R m are the dynamic resistances obtained from the simulation, and each row of parameters in the matrix corresponds to an impedance value.

[0037] Step 4: Based on the above MSD equivalent model, conduct a load experiment and record the matrix of n load force changes corresponding to electrical parameters, the matrix [EF k n1 is as follows:

[0038]

[0039] where, f s1 ’, f s1 ’...... f sn ’ are the forward resonance frequencies obtained from the experiment, f p1 ’, f p2 ’......, f pn ’ are the reverse resonance frequencies obtained from the experiment, and are the half-power points obtained from the experiment, C1’, C2’,......, C n ’ are the dynamic capacitances obtained from the experiment, L1', L2',......, L n ' are the dynamic inductances obtained from the experiment, Q1', Q2',......, Q n ' are the mechanical quality factors obtained from the experiment, R1’, R2’,......, R n ​​’ is the dynamic resistance obtained from experiments, and each row of parameters corresponds to an impedance value.

[0040] The [EZ i m1 obtained in the above third and fourth steps k n1 and the [EF

[0041] Step 5: Change one parameter in T i while keeping other parameters unchanged, perform Matlab simulation on the transducer under this parameter, and obtain the new [EZ i m2 matrix. Then conduct a load experiment to obtain the new [EF k n2 matrix, which is the second set of matrix relationships.

[0042] Repeat the simulation and load experiment steps in Step 5 to obtain a total of R sets of matrix relationships between simulation and load force experiments, that is, [EZ i mt and [EF k nt (t = 1, 2,......, R).

[0043] Step 6: Pair these R sets of [EZ i mt and [EF k nt matrices. Match the data by the least squares method to find the closest set of data. Take the matching of the first set of matrix relationships as an example to illustrate the matching method, as Figure 3 shown:

[0044] Perform the sum of squared differences operation on the load force parameters corresponding to the first row in [EF k n1 and the parameters corresponding to the m rows of impedance in [EZ i m1 respectively.

[0045]

[0046] Among them, P1 is the sum of squared differences between the impedance corresponding to the first row in the matrix data obtained from simulation and the load force parameters corresponding to the first row in the matrix data obtained from experiments; P2 is the sum of squared differences between the impedance corresponding to the second row in the matrix data obtained from simulation and the load force parameters corresponding to the first row in the matrix data obtained from experiments; P m is the sum of squared differences between the impedance corresponding to the mth row in the simulation data and the load force parameters corresponding to the first row in the experimental data.

[0047] P1 → P​​​​​​​​​​m The impedance corresponding to the minimum value among them is the impedance that best matches this load force.

[0048] Perform the above matching operation on the n rows of parameters in the load force experiment matrix with the m rows of data in the simulation matrix, and the impedance corresponding to each row of the load force can be obtained.

[0049] Take the R groups [EZ i mt and [EF k nt and pair up all the matrices to obtain the final pairing relationship.

[0050] The relational expression of, where T t is the material corresponding to this set of relational expressions, Fk y，t is the load force of the y-th row in [EF k nt and Zi x(y，t) is the impedance that best matches the load force of the y-th row in [EF k nt in [EZ i mt

[0051] Step 7, take as a set of training data and input it into the adaptive attribute weight neural network, as shown in Figure 4 , and the adaptive attribute weight neural network calculates the attribute weights, and the weights are fully connected to the input.

[0052] The present invention adopts a double-input single-output neural network structure, the input parameters are T t , Fk y，t , and the output parameter is Zi x(y，t) , and take a set of as the training input.

[0053] 1. Attribute weight V i . T t , Fk y，t are the inputs, W i is the weight vector, and V i is calculated as follows:

[0054] When the input is Fk y，t ,

[0055] When the input is T t ,

[0056] 2. Weight α i . f w is the weight calculation function, f​​​​​​wa is the weight activation function, f w and f wa are the hypothesis values, and their calculation methods are as follows:

[0057] α i = f wa (f w (V i , V c ), i = T t , Fk y，t

[0058] V c is an auxiliary vector that assists in the calculation of the weights of each attribute. It will be continuously optimized during the learning process of the neural network to capture changes in material parameters or loads and then applied to the calculation of attribute weights. V c and W i will be optimized during subsequent network training.

[0059] 3. Fully connected input V in . After obtaining the weights of each attribute in the weight calculation, the attribute vectors are weighted and summed to obtain the input of the subsequent fully connected module.

[0060]

[0061] After passing through the calculation of the fully connected layer, the predicted value θ i ' of the final key variable can be obtained. Next, the network is trained, and the output is derived according to the following formula:

[0062]

[0063] where k is the input dimension. In the present invention, there are two inputs, so k = 2. V ik is the attribute weight of dimension k, x i (i = T t , Fk y，t i.e., ) is the neural network input, W ik is the weight vector of dimension k, V ck is the auxiliary vector of dimension k, V ink is the fully connected input of dimension k, W hk and b h are the hidden layer weights and bias units, W 0h and b0 are the output layer weights and bias units, f1, f2 are the activation functions, y h is the hidden layer output, and θ0' is the network predicted value.

[0064] In the present invention, Zi x(y，t)is the true value θ0 in the network, and after obtaining the predicted value θ0', it is optimized with the true value θ0 to obtain the loss function E:

[0065]

[0066] Let r be the current iteration round, η be the learning rate, and optimize the network parameters based on the following formula:

[0067]

[0068] Then, the auxiliary vector V ck , weight vector W ik The adjustment strategy obtained by partial derivative optimization is as follows:

[0069]

[0070] Among them, f1', f2', f wa ' is f1, f2, f wa Derivative. After optimization, the final W can be obtained hk 、b h , W oh , b0 and other network parameters. So far, the training of the neural network has been completed.

[0071] Thus, a set of relationships between load force, material and impedance can be obtained. Then all R groups of pairing relationship matrices in step 6 are trained and input into the neural network. In the future, only any set of material parameters T i With load force F k , we can get the impedance Z i .

Claims

1. An on-load modeling method for an ultrasonic transducer, characterized in that The method comprises the following steps: First, an equivalent model is established based on kinetic simulation and Mason's circuit: Among them, L p is the thickness of the piezoelectric ceramic stack, and Z0 s = ρgS is the product of the density, sound velocity, and cross-sectional area of the piezoelectric ceramic stack. τ s is the sound propagation constant of the piezoelectric ceramic stack material, and Z R s , Z L s are the right equivalent impedance and left equivalent impedance of the T-type equivalent circuit respectively, and Z M S is the equivalent impedance in the middle of the T-type equivalent circuit; Second, a certain parameter of the material in the piezoelectric transducer is changed. The materials include the front cover plate, the rear cover plate and the piezoelectric ceramic stack of the piezoelectric transducer; the parameters include the cross-sectional area S of the piezoelectric ceramic stack, the density ρ of the piezoelectric ceramic stack, the Young's modulus E of the front and rear cover plate materials, and the lengths l of the front and rear cover plates; In the third step, impedance is simulated based on the established model, and a matrix [EZ corresponding to m groups of impedance and electrical parameters is recorded i m1 ;​ Step 4: Conduct a load experiment based on the established model, and record an n×matrix [EF k corresponding to the changes in load force and electrical parameters n1 ; Step 5: Change another parameter of the material in the piezoelectric transducer, keep other parameters unchanged, repeat impedance simulation and load experiment, and obtain [EZ i m2 and [EF k n2 ;​​ Repeat this step multiple times to obtain a matrix relationship of a total of R groups of simulation and load force experiments, namely [EZ i mt and [EF k nt ;​​ Step 6: Pair these R groups of [EZ i mt with the [EF k nt matrix, match the data by the least squares method, find the group of data that is the closest, and obtain the relationship, where Fk y，t is the load force of the y-th row in [EF k nt , Zi x(y，t) is an impedance that best matches the load force of the y-th row in [EF k nt , T t is the corresponding material under this group of matrices, and x(y,t) is the row number of the impedance that best matches the load force Fk t when the fixed material type is T y，t in [EZ i mt ;​​​​​ Step 7: Input as a set of training data into the adaptive attribute weight neural network, where Fk y，t and T t are the inputs of the neural network, and the output of the neural network is Zi x(y，t) corresponding to the true value θ0; then optimize θ0 with θ0' predicted by the neural network to obtain the corresponding network parameters, and thus a set of relationships between load capacity, material, and impedance can be obtained; All the R group pairing relationship matrices in the sixth step are input into the neural network for training to obtain the trained neural network; when any group of material parameters and load forces are input subsequently, the impedance can be obtained; The adaptive attribute weight neural network adopts a double-input and single-output neural network structure, and the input parameters are T t , Fk y，t , and the output parameter is Zi x(y，t) , and a group of is used as the training input; For the attribute weight V i : T t , Fk y，t is the input, W i is the weight vector, and V i is calculated as follows: When the input is Fk y，t , When the input is T t , For weight α i : f w is the weight calculation function, f wa is the weight activation function, f w and f wa are the hypothesis values, and their calculation methods are as follows: α i = f wa (f w (V i ,V c )), i = T t ,Fk y，t V c is an auxiliary vector that assists in the calculation of the weights of each attribute. It will be continuously optimized during the learning process of the neural network to capture changes in material parameters or loads and then applied to the calculation of attribute weights. V c and W i will be optimized during network training; For the fully-connected input V in : After obtaining the weights of each attribute in the weight calculation, the attribute vectors are weighted and summed to obtain the input of the subsequent fully-connected module: After the calculation of the fully connected layer, the predicted value θ of the final key variable can be obtained i ’; Next, the network is trained, and the output is deduced according to the following formula: where k is the input dimension, k = 2, V ik is the attribute weight of dimension k, x i is the neural network input, i = T t , Fk y，t W ik is the weight vector of dimension k, V ck is the auxiliary vector of dimension k, V ink is the fully connected input of dimension k, W hk and b h are the hidden layer weight and bias unit, W 0h and b0 are the output layer weight and bias unit, f1, f2 are activation functions, y h is the hidden layer output, θ0’ is the network prediction value; Zi x(y，t) For the true value θ0 in the network, after obtaining the predicted value θ0' and optimizing it with the true value θ0, the loss function E can be obtained: Let r be the current iteration round and η be the learning rate. The network parameters are optimized based on the following formula: Then, the auxiliary vector V ck , the weight vector W ik are respectively optimized by taking partial derivatives, and the adjustment strategy is as follows: where f1’, f2’, f wa ’ are the derivatives of f1, f2, f wa respectively; After optimization, the final W is obtained hk , b h , W oh , and the network parameters of b0. Thus, the training of the neural network is completed.

2. The on-load modeling method of an ultrasonic transducer according to claim 1, characterized in that: The simulation in the third step is carried out using Matlab software.

3. A method for on-load modeling of an ultrasonic transducer according to claim 1, characterized in that: The electrical parameters in the third step and the fourth step include the forward resonance frequency, the reverse resonance frequency, the half-power point, the dynamic capacitance, the dynamic resistance, the dynamic inductance and the mechanical quality factor.

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