Piezoelectric sensor dynamic test calibration method based on short memory grey model

Abstract

The invention discloses a piezoelectric sensor dynamic test calibration method based on a short memory grey model. The method comprises the following steps: constructing a piezoelectric sensor dynamic test short memory grey model; converting the short memory grey model into an algebraic model; establishing a model parameter identification algorithm based on the calibration of the piezoelectric sensor; based on the output of the sensor, the input of the piezoelectric sensor is calibrated through a short memory gray model. Modeling is carried out according to the dynamic response characteristic of the piezoelectric sensor, the response characteristic of the pressure input signal in a future period of time is utilized, and in turn, the pressure input signal is calibrated by utilizing the output in the future period of time. The model better conforms to the dynamic response characteristics of the pressure signals, and calibration is more accurate. According to the method, the short memory model is obtained by truncating the response according to the response rapidity of the sensor, so that the calibration precision is ensured, the calculation complexity is reduced, the calculation time is shortened, and the measurement rapidity is not obviously reduced.

Description

Technical Field

[0001] The present application belongs to the technical field of dynamic error calibration, and specifically relates to a dynamic test calibration method for a piezoelectric sensor based on a short memory grey model. Background Art

[0002] Piezoelectric sensors convert pressure signals into electrical signals for measurement and are widely used in pressure and vibration signal acquisition.

[0003] From a system perspective, the piezoelectric sensor can be regarded as a system, the input signal of which is a pressure signal, and the output signal is an electrical signal. Therefore, the pressure signal can be regarded as the system input, and the electrical signal can be regarded as the system output. The system output is the convolution of the system output and the system impulse response. The measured electrical signal is not only related to the current input pressure signal, but also to the historical input pressure signal. Correspondingly, the system input has a response process, but the response speed of different systems is different, and the response speed varies.

[0004] The test process is to calibrate the input according to the output, and accurately reproduce the input according to the output. According to the system response characteristics, the input at any time has a response process. Correspondingly, the input at any time requires the output within a certain period of time to invert. If the input changes very slowly relative to the system response, that is, the input changes very slowly during the response process, and the input signal does not change much during the response process, the instantaneous measurement results can be used for calibration. However, when the input signal has a large dynamic, such processing will inevitably have a large error. Summary of the invention

[0005] The present application provides a piezoelectric sensor dynamic test calibration method based on a short memory grey model to solve the technical problem of the piezoelectric sensor dynamic test calibration dilemma.

[0006] In order to solve the above technical problems, a technical solution adopted in this application is: a piezoelectric sensor dynamic test calibration method based on a short memory grey model, comprising:

[0007] Construct a short memory grey model for dynamic testing of piezoelectric sensors;

[0008] Transform the short memory grey model into an algebraic model;

[0009] Based on the calibration of piezoelectric sensors, a model parameter identification algorithm is established;

[0010] Based on the output of the sensor, the piezoelectric sensor input is calibrated using a short memory grey model.

[0011] Further, a method for constructing a short memory grey model for dynamic testing of a piezoelectric sensor includes:

[0012] Based on the high-precision sensor sampling output as the nominal pressure value, a calibration grey model for the piezoelectric sensor input and output is established;

[0013] Convert the calibrated grey model into an additive model;

[0014] Based on the cumulative model and memory length, a short memory grey model for dynamic test calibration of piezoelectric sensors is obtained.

[0015] Further, based on the cumulative model and the memory length, a method for obtaining a short memory grey model for dynamic test calibration of a piezoelectric sensor includes:

[0016] Based on formula (1), the calibration grey model of the piezoelectric sensor input and output is obtained; wherein formula (1) is:

[0017] y(n)=(x1(nT) α +c2)*x(n) (1);

[0018] Among them, (nT) α Indicates t α At the sampling time nT, c1, c2 and α are the parameters to be identified, and the symbol * represents the convolution operation. The calibrated gray model represents the impulse response of the piezoelectric sensor as: c1(t) α +c2; where c1(nT) α +c2 is the discretization of the impulse response.

[0019] Further, a method for obtaining a short memory grey model for dynamic test calibration of a piezoelectric sensor includes:

[0020] Based on formula (2), the short memory grey model is obtained; wherein formula (2) is:

[0021]

[0022] Among them, Sm represents the starting point of memory. When nL≥0, Sm=nL; when nL<0, Sm=0.

[0023] Furthermore, based on the calibration of the piezoelectric sensor, a method for establishing a model parameter identification algorithm includes:

[0024] Construct cost function based on algebraic model;

[0025] Based on the cuckoo optimization search algorithm and cost function, the model parameters are obtained.

[0026] Furthermore, based on the cuckoo optimization search algorithm and the cost function, a method for obtaining model parameters includes:

[0027] Initialize the nest position and calculate the corresponding cost function, and save it as the optimal cost function;

[0028] Global search to obtain the new nest location, update the nest location and calculate the corresponding cost function; compare the cost function corresponding to the updated nest location with the optimal cost function, select the smallest cost function to update and save it as the optimal cost function, and globally update the optimal nest location and the corresponding cost function;

[0029] Local search obtains the new nest position, updates the nest position for the second time and calculates the corresponding cost function; compares the cost function corresponding to the second updated nest position with the optimal cost function, selects the smallest cost function for update and saves it as the optimal cost function, and locally updates the optimal nest position and the corresponding cost function;

[0030] Repeat the above steps until the optimal cost function is less than the preset threshold, save the final nest position as the optimal nest position, and use the optimal nest position parameters as model parameters.

[0031] The beneficial effects of the present application are as follows: the present application models the dynamic response characteristics of the piezoelectric sensor, utilizes the response characteristics of the pressure input signal in a future period of time, and conversely, utilizes the output in the future period of time to calibrate the pressure input signal. The model is more consistent with the dynamic response characteristics of the pressure signal, and the calibration is more accurate. The present application utilizes the response truncation based on the rapidity of the sensor response to obtain a short memory model, which not only ensures the calibration accuracy, but also reduces the computational complexity, reduces the computational time, and does not significantly reduce the measurement rapidity. The present application utilizes secondary learning identification parameters based on the bionic principle, which is conducive to improving the identification convergence and avoiding local optimality. BRIEF DESCRIPTION OF THE DRAWINGS

[0032] Figure 1 It is a flow chart of an embodiment of a piezoelectric sensor dynamic test calibration method based on a short memory grey model of the present application;

[0033] Figure 2 for Figure 1 A schematic flow chart of an embodiment of step S1;

[0034] Figure 3 It is a simulation diagram in an embodiment of a piezoelectric sensor dynamic test calibration method based on a short memory grey model of the present application;

[0035] Figure 4 for Figure 1 A schematic flow chart of an embodiment of step S3;

[0036] Figure 5 for Figure 4 A schematic diagram of a flow chart of an embodiment of step S32;

[0037] Figure 6This is a piezoelectric sensor dynamic short memory model calibration flow chart of an embodiment of a piezoelectric sensor dynamic test calibration method based on a short memory grey model of the present application. DETAILED DESCRIPTION

[0038] In order to make the objectives, technical solutions and advantages of the present invention more clear, the present invention is further described in detail below in conjunction with specific embodiments.

[0039] In the following description, many specific details are set forth to facilitate a full understanding of the present invention. However, the present invention may also be implemented in other ways than those described herein. Therefore, the present invention is not limited to the specific embodiments of the following disclosure.

[0040] See also Figure 1 , Figure 1 1 is a flow chart of an embodiment of a piezoelectric sensor dynamic test calibration method based on a short memory grey model of the present application, the method comprising the following steps:

[0041] S1. Construct a short memory grey model for dynamic testing of piezoelectric sensors.

[0042] For details, see Figure 2 , Figure 2 for Figure 1 Schematic diagram of a flow chart of an embodiment of step S1 in FIG. Step S1 includes:

[0043] S11. Based on the high-precision sensor sampling output as the nominal pressure value, a calibration gray model for the piezoelectric sensor input and output is established.

[0044] Specifically, the sampling interval is T, and the calibration is performed based on the output of a higher-precision sensor. The sampling output of the high-precision sensor is set as the nominal pressure value. x(0), x(1), ..., x(n) represent the input pressure at the initial time 1T, 2T, ..., nT respectively. The piezoelectric sensor output signals at the corresponding time are measured as y(0), y(1), ..., y(n). The gray model of piezoelectric sensor input and output calibration is established as shown in formula (1):

[0045] y(n)=(c1(nT) α +c2)*x(n) (1);

[0046] Among them, (nT) α Indicates t α At the sampling time nT, c1, c2 and α are the parameters to be identified, and the symbol * represents the convolution operation. The calibrated gray model represents the impulse response of the piezoelectric sensor as: c1(t) α +c2; where c1(nT) α +c2 is the discretization of the impulse response.

[0047] S12. Convert the calibrated grey model into an accumulation model.

[0048] Specifically, the formula of the cumulative model is:

[0049]

[0050] The above-mentioned cumulative model reflects that the output of the piezoelectric sensor is the combined effect of all pressure signal inputs before the current moment, rather than just the current pressure signal. Conversely, the current input pressure signal will affect the output of the piezoelectric sensor for a period of time after the current moment.

[0051] S13. Based on the cumulative model and memory length, a short memory grey model for dynamic test calibration of piezoelectric sensors is obtained.

[0052] Specifically, according to the memory decay characteristics, the memory length L is set. For any sensor system, when the input changes in a bounded manner, its output must converge quickly, and the faster the convergence speed, the better. Therefore, to achieve this goal, α must be less than 0, and the impulse response of the piezoelectric sensor converges quickly. Although all pressure input signals will affect the output of the piezoelectric sensor, this effect decays rapidly over time, and the impact of historical information exceeding a certain time length on the output can be ignored. Based on this, according to the attenuation characteristics of the piezoelectric sensor, the historical information with a fixed length of L is intercepted for research, and the short memory gray model of the piezoelectric sensor is obtained. Based on formula (2), the short memory gray model is obtained; wherein, formula (2) is:

[0053]

[0054] Among them, Sm represents the starting point of memory. When nL≥0, Sm=nL; when nL<0, Sm=0.

[0055] S2. Convert the short memory grey model into an algebraic model.

[0056] Specifically,

[0057] The model in formula (2) is represented by a matrix:

[0058]

[0059] The matrix satisfy:

[0060]

[0061]

[0062] in, Represents the element in the i-th row and j-th column.

[0063] Combined with the short memory model definition, the short memory model is expressed as:

[0064]

[0065] The short memory matrix satisfy:

[0066]

[0067]

[0068] in, Represents the element in the i-th row and j-th column.

[0069] Thus, the short memory grey model for dynamic test and calibration of piezoelectric sensors is obtained.

[0070] See also Figure 3 , for example: let h(t) = t -0.5 , get:

[0071] y2(t)=[h(t)(u(t)-u(t-2))]*[t -0.5 (u(t)-u(t)-2))];

[0072] y3(t)=[h(t)(u(t))]*[t -0.5 (u(t))];

[0073] e1(t)=y3(t)-y2(t);

[0074] Where u(t) represents the unit step function simulation diagram t -0.5 (u(t)-u(t-2)) represents the interception of t -0.3 From the current moment to the previous period of 2, the simulation results (such as Figure 3 ) shows that due to the memory decay characteristics, intercepting a period of historical information and obtaining a short memory model will not significantly affect the error accuracy.

[0075] S3. Based on the calibration of piezoelectric sensors, a model parameter identification algorithm is established.

[0076] For details, see Figure 4 , Figure 4 for Figure 1 Schematic diagram of a flow chart of an embodiment of step S3 in FIG. Step S3 includes:

[0077] S31. Construct cost function based on algebraic model.

[0078]

[0079] in, It is calculated according to formula (4), that is:

[0080]

[0081] The core of the above formula is to identify The unknown parameters in the cost function are optimal, that is, the calibration error is minimized.

[0082] S32. Obtain model parameters based on the cuckoo optimization search algorithm and the cost function.

[0083] Specifically, in order to improve the convergence of the optimization search and avoid falling into the local optimum, the improved quadratic learning cuckoo optimization search algorithm is used to identify the unknown model parameters c1, c2 and α.

[0084] See also Figure 5 , Figure 5 for Figure 4 Schematic diagram of a flow chart of an embodiment of step S32 in FIG. Step S32 includes:

[0085] S321. Initialize the nest position and calculate the corresponding cost function, saving it as the optimal cost function.

[0086] Specifically, the parameters p{c1, c2, α} are initialized to generate M bird nest positions, and the cost function corresponding to the position is calculated according to the bird nest position and step S31.

[0087] S322. Perform a secondary global search to obtain a new nest position, update the nest position and calculate the corresponding cost function; compare the cost function corresponding to the updated nest position with the optimal cost function, select the smallest cost function to update and save it as the optimal cost function, and globally update the optimal nest position and the corresponding cost function.

[0088] Specifically, the bird's nest position is updated according to the following formula;

[0089]

[0090] Where Sp = [Sp1Sp2Sp3] represents the step vector, represents the position of the g-th generation of the i-th bird's nest, represents the g-1 generation position of the i-th bird's nest, k (0<k<1) represents the weight of the i-th generation bird's nest position, 1-k represents the weight of the g-1 generation position of the contemporary bird's nest position, The position of the i-th nest in the g-th generation after global update. Sp1, Sp2, and SP3 correspond to the step size of b1, b2, and β parameter identification. Le' vy (λ) indicates that the step size follows Le' vy The random walk of the distribution. It means that each nest position randomly walks around the weighted position of the previous two generations.

[0091] The cost function corresponding to the new nest position is compared with the saved optimal cost function, the minimum cost function is selected for update, and the optimal nest position and corresponding cost function are globally updated.

[0092] S323. Locally search to obtain a new bird's nest position, update the bird's nest position for the second time and calculate the corresponding cost function; compare the cost function corresponding to the second updated nest position with the optimal cost function, select the smallest cost function to update and save it as the optimal cost function, and locally update the optimal bird's nest position and the corresponding cost function.

[0093] Specifically, generate a new bird's nest location:

[0094]

[0095] in, represents a new solution for local search, and represents two random bird nest positions in the g-th generation bird nest, r, γ are random numbers uniformly distributed in the interval [0,1], and H() represents the Heaviside function. The cost function corresponding to the position is calculated according to the bird nest position and step S31.

[0096] The cost function corresponding to the second updated bird's nest position is compared with the saved optimal cost function, the minimum cost function is selected for update, and the optimal bird's nest position and the corresponding cost function are locally updated.

[0097] S324. Repeat the above steps until the optimal cost function is less than a preset threshold, save the final bird's nest position as the optimal bird's nest position, and use the optimal bird's nest position parameters as model parameters.

[0098] S4. Based on the output of the sensor, the piezoelectric sensor input is calibrated using a short memory grey model.

[0099] For details, see Figure 6 According to formula (4), the pressure input inverse equation is obtained:

[0100]

[0101] in, Representation Matrix The inverse matrix of .

[0102] according to is a lower triangular matrix, Must be an upper triangular matrix, satisfying:

[0103]

[0104] Through the above formula (10), the dynamic measurement calibration formula of the piezoelectric sensor can be obtained:

[0105]

[0106] Among them, 1≤i<n. Indicates the dynamic calibration output of the piezoelectric sensor, and Ed indicates the end point of the short memory model output of the i-th pressure signal of the piezoelectric sensor. When i+L≤0, ED=i+L; when i+L>0, ED=n.

[0107] From the above, it can be seen that when i+L>n, due to the response process, the output of the pressure input signal has not yet fully responded or has not been fully measured. Therefore, there is a certain compensation error, but when i+L≤n, the compensation accuracy is higher. The faster the piezoelectric sensor responds, the smaller L can be selected, and the higher the measurement accuracy.

[0108] This application builds a model based on the dynamic response characteristics of the piezoelectric sensor, using the response characteristics of the pressure input signal in a certain period of time in the future, and conversely, using the output in a certain period of time in the future to calibrate the pressure input signal. This model is more in line with the dynamic response characteristics of the pressure signal, and the calibration is more accurate. This application uses the response truncation based on the rapidity of the sensor response to obtain a short memory model, which not only ensures the calibration accuracy, but also reduces the computational complexity and calculation time without significantly reducing the measurement rapidity. This application uses secondary learning to identify parameters based on the bionic principle, which is conducive to improving the identification convergence and avoiding local optimality.

[0109] The above descriptions are merely embodiments of the present application and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A piezoelectric sensor dynamic test calibration method based on short memory grey model, characterized in that: include: Construct a short memory grey model for dynamic testing of piezoelectric sensors; Converting the short memory grey model into an algebraic model; Based on the calibration of piezoelectric sensors, a model parameter identification algorithm is established; Based on the output of the sensor, the piezoelectric sensor input is calibrated by the short memory grey model.

2. The method according to claim 1, characterized in that The method for constructing a short memory grey model for dynamic testing of a piezoelectric sensor comprises: Based on the high-precision sensor sampling output as the nominal pressure value, a calibration grey model for the piezoelectric sensor input and output is established; Converting the calibrated grey model into an accumulation model; Based on the cumulative model and the memory length, a short memory grey model for dynamic test calibration of the piezoelectric sensor is obtained.

3. The method according to claim 2, characterized in that The method for obtaining a short memory grey model for dynamic test calibration of a piezoelectric sensor based on the cumulative model and the memory length includes: Based on formula (1), a calibration grey model of the input and output of the piezoelectric sensor is obtained; wherein formula (1) is: y(n)=(c1(nT) α +c2)*x(n) (1); Among them, (nT) α represents the sampling of tα at time nT, c1, c2 and α are the parameters to be identified, and the symbol * represents the convolution operation. The calibrated gray model represents the impulse response of the piezoelectric sensor as: c1(t) α +c2; where c1(nT) α +c2 is the discretization process of the impulse response.

4. The method according to claim 4, characterized in that: The method for obtaining a short memory grey model for dynamic test calibration of a piezoelectric sensor comprises: Based on formula (2), the short memory grey model is obtained; wherein formula (2) is: Among them, Sm represents the starting point of memory. When nL≥0, Sm=nL; when nL<0, Sm=0.

5. The method according to claim 2, characterized in that: The method for establishing a model parameter identification algorithm based on the calibration of a piezoelectric sensor comprises: Based on the algebraic model, construct a cost function; Based on the cuckoo optimization search algorithm and the cost function, the model parameters are obtained.

6. The method according to claim 5, characterized in that The method for obtaining model parameters based on the cuckoo optimization search algorithm and the cost function includes: Initialize the nest position and calculate the corresponding cost function, and save it as the optimal cost function; Global search to obtain a new bird's nest position, update the bird's nest position and calculate the corresponding cost function; compare the cost function corresponding to the updated nest position with the optimal cost function, select the minimum cost function to update and save it as the optimal cost function, and globally update the optimal bird's nest position and the corresponding cost function; Locally search to obtain a new bird's nest position, update the bird's nest position for the second time and calculate the corresponding cost function; compare the cost function corresponding to the nest position updated for the second time with the optimal cost function, select the minimum cost function to update and save it as the optimal cost function, and locally update the optimal bird's nest position and the corresponding cost function; Repeat the above steps until the optimal cost function is less than a preset threshold, save the final bird's nest position as the optimal bird's nest position, and use the optimal bird's nest position parameters as model parameters.

Images