CN105843780B - A kind of sparse deconvolution method of mechanical structure shock loading identification - Google Patents
A kind of sparse deconvolution method of mechanical structure shock loading identification Download PDFInfo
- Publication number
- CN105843780B CN105843780B CN201610222057.5A CN201610222057A CN105843780B CN 105843780 B CN105843780 B CN 105843780B CN 201610222057 A CN201610222057 A CN 201610222057A CN 105843780 B CN105843780 B CN 105843780B
- Authority
- CN
- China
- Prior art keywords
- impact load
- function
- sparse
- mechanical structure
- solution
- Prior art date
- Legal status (The legal status is an assumption and is not a legal conclusion. Google has not performed a legal analysis and makes no representation as to the accuracy of the status listed.)
- Active
Links
- 238000000034 method Methods 0.000 title claims abstract description 72
- 230000035939 shock Effects 0.000 title abstract 7
- 230000004044 response Effects 0.000 claims abstract description 45
- 239000011159 matrix material Substances 0.000 claims abstract description 32
- 238000012546 transfer Methods 0.000 claims abstract description 25
- 238000005316 response function Methods 0.000 claims abstract description 24
- 230000009977 dual effect Effects 0.000 claims abstract description 22
- 230000006870 function Effects 0.000 claims description 45
- 238000005457 optimization Methods 0.000 claims description 19
- 230000004888 barrier function Effects 0.000 claims description 16
- 230000009471 action Effects 0.000 claims description 9
- 230000008569 process Effects 0.000 claims description 7
- 238000012804 iterative process Methods 0.000 claims description 4
- 230000009466 transformation Effects 0.000 claims description 2
- 230000001133 acceleration Effects 0.000 abstract description 17
- 230000008901 benefit Effects 0.000 abstract description 5
- 238000005259 measurement Methods 0.000 abstract description 3
- 238000010276 construction Methods 0.000 abstract 1
- 238000005070 sampling Methods 0.000 description 4
- 238000012360 testing method Methods 0.000 description 4
- 239000002131 composite material Substances 0.000 description 3
- 238000000354 decomposition reaction Methods 0.000 description 3
- 238000012423 maintenance Methods 0.000 description 3
- 230000003321 amplification Effects 0.000 description 2
- 238000004364 calculation method Methods 0.000 description 2
- 235000009508 confectionery Nutrition 0.000 description 2
- 238000006073 displacement reaction Methods 0.000 description 2
- 230000005284 excitation Effects 0.000 description 2
- 238000012544 monitoring process Methods 0.000 description 2
- 238000003199 nucleic acid amplification method Methods 0.000 description 2
- 238000013459 approach Methods 0.000 description 1
- 238000013528 artificial neural network Methods 0.000 description 1
- 230000008859 change Effects 0.000 description 1
- 230000007423 decrease Effects 0.000 description 1
- 238000010586 diagram Methods 0.000 description 1
- 238000009792 diffusion process Methods 0.000 description 1
- 230000036541 health Effects 0.000 description 1
- 238000009863 impact test Methods 0.000 description 1
- 230000006872 improvement Effects 0.000 description 1
- 238000009434 installation Methods 0.000 description 1
- 238000012986 modification Methods 0.000 description 1
- 230000004048 modification Effects 0.000 description 1
- 238000010248 power generation Methods 0.000 description 1
- 230000002028 premature Effects 0.000 description 1
- 239000004576 sand Substances 0.000 description 1
- 230000002123 temporal effect Effects 0.000 description 1
- 238000010998 test method Methods 0.000 description 1
Classifications
-
- G—PHYSICS
- G06—COMPUTING; CALCULATING OR COUNTING
- G06F—ELECTRIC DIGITAL DATA PROCESSING
- G06F17/00—Digital computing or data processing equipment or methods, specially adapted for specific functions
- G06F17/10—Complex mathematical operations
- G06F17/15—Correlation function computation including computation of convolution operations
- G06F17/153—Multidimensional correlation or convolution
Landscapes
- Engineering & Computer Science (AREA)
- Physics & Mathematics (AREA)
- General Physics & Mathematics (AREA)
- Mathematical Physics (AREA)
- Computational Mathematics (AREA)
- Theoretical Computer Science (AREA)
- Mathematical Analysis (AREA)
- Mathematical Optimization (AREA)
- Pure & Applied Mathematics (AREA)
- Data Mining & Analysis (AREA)
- Algebra (AREA)
- Databases & Information Systems (AREA)
- Software Systems (AREA)
- General Engineering & Computer Science (AREA)
- Computing Systems (AREA)
- Management, Administration, Business Operations System, And Electronic Commerce (AREA)
Abstract
The present invention relates to a kind of sparse deconvolution method of mechanical structure shock loading identification, for solving the Ill-posed characteristic of shock loading identification indirect problem.This method includes the following steps：1) using the frequency response function between the mechanical structural impact load position of hammering method measurement and mechanical structure response measuring point, unit impulse response function is obtained, and then discretization obtains transfer matrix by inverse fast Fourier transform；2) acceleration signal generated using acceleration transducer measurement by mechanical structure shock loading；3) the convex Optimized model of sparse deconvolution of shock loading identification of the construction based on L1 norms；4) sparse deconvolution Optimized model is solved using prim al- dual interior point m ethod, obtains sparse deconvolution solution, i.e., shock loading to be identified.The present invention is suitable for shock loading of the recognition reaction in mechanical structure, compared with tradition is based on the Tikhonov regularization methods of L2 norms, has the advantages that accuracy of identification is high, computational efficiency is high and stability is strong.
Description
Technical Field
The invention belongs to the field of mechanical system state monitoring, and particularly relates to a sparse deconvolution method for identifying impact load of a mechanical structure.
Background
Impact loading is a very important type of dynamic loading, particularly in structural health monitoring of composite materials. For example, in the operation and maintenance process of a fan blade for wind power generation, the fan blade inevitably suffers from impact of wind sand, flying birds, hailstones, maintenance tools and other foreign objects, the occurrence frequency is high, and the impact damage is accumulated to cause potential safety hazards to the integrity and the bearing capacity of the fan blade; the impact of the sudden change airflow, the flying bird and the maintenance tool on the wings of the airplane. It is essential to monitor such impulse signals in real time, and it is very difficult to measure them directly.
The impact load identification method such as classical Tikhonov, truncated singular value decomposition and the like solves unknown load in an L2 norm space, relates to matrix inversion or decomposition operation, and is not suitable for large-scale inverse problem (the dimension of a transfer matrix is more than 10)4) The operation of (1); in recent years, function approximation (e.g., Db is small) has been based on the profile of the impact loadWaves, chebshiev polynomials, cubic B-splines, etc.) have been applied by many scholars to single impact load identification of small-scale data volumes. The method achieves the aim of regularizing approximate dynamic load by controlling the number of basis functions, and the biggest dilemma of the application is that the regularization parameter, namely the number of the basis functions is difficult to determine, and the result is invalid due to too much or too little number of the basis functions; the neural network approach around impact load recognition requires a large number of samples to learn various types of impact events, which is very limited in practical engineering applications. The traditional regularization method is difficult to cope with continuous impact load identification under large data scale, and the condition number of a transfer matrix is very large and the numerical stability is very poor; in addition, when the response noise level is high, the performance of the traditional regularization method is reduced or even can not be improved.
Disclosure of Invention
Based on the above, the invention discloses a sparse deconvolution method for impact load identification of a mechanical structure, which comprises the following steps:
s100, measuring a frequency response function between an impact load action point of the mechanical structure and a response measuring point of the mechanical structure and calculating a transfer matrix;
s200, applying impact load to the mechanical structure and measuring impact response;
s300, constructing a sparse solution convolution convex optimization model of impact load identification based on the L1 norm based on the steps S100 and S200;
s400, solving the sparse deconvolution convex optimization model to obtain the sparse deconvolution solution of the impact load.
Compared with the prior art, the invention has the following advantages:
1. different from the traditional truncated singular value decomposition and Tikhonov regularization method based on the L2 norm, the sparse deconvolution method based on the L1 norm for impact load identification fully utilizes the time domain sparse characteristic of the impact load, and greatly inhibits the amplification of response noise in the identified impact load;
2. compared with the traditional Tikhonov regularization algorithm, the sparse deconvolution iterative algorithm has high identification precision, high calculation efficiency and strong stability;
3. the adopted primal-dual interior point method has the advantages that the inversion operation of the transfer matrix is not involved, and the regularization parameter is not required to be determined, and the iteration process is the regularization process;
4. the sparse deconvolution model and the corresponding primal-dual interior point method provided by the invention solve the problem of large data scale (the transfer matrix dimension is more than 10)4) And identifying the problem of the lower impact load.
Drawings
FIG. 1 is a flow chart of a sparse deconvolution method of impact load identification of a mechanical structure in one embodiment of the present invention;
FIG. 2 is a schematic view of a 300W composite wind turbine blade impact load identification apparatus according to one embodiment;
3(a), 3(b), 3(c) are 300W wind turbine blade data measured by force sensors and acceleration sensors in one embodiment, wherein FIG. 3(a) is the impact load signal, FIG. 3(b) is the acceleration response at point R1; FIG. 3(c) acceleration response at point R2;
4(a), 4(b) are graphs of the PDIPM identifying the trend of the dual gap variation with fan blade impact load for one embodiment, wherein the response signal of FIG. 4(a) is R1; FIG. 4(b) the response signal is R2;
FIGS. 5(a), 5(b) are sparse deconvolution of fan blade impact loads for one embodiment, where the response signal of FIG. 5(a) is R1; FIG. 5(b) the response signal is R2;
6(a), 6(b) are Tikhonov regularization results of fan blade impact loading in one embodiment, wherein FIG. 6(a) response signal is R1; the response signal of fig. 6(b) is R2.
Detailed Description
The invention will be further described with reference to fig. 1-6 and a specific embodiment, it being emphasized that the following description is merely exemplary and the invention is not limited in its application to the examples described below.
In one embodiment, the invention discloses a sparse deconvolution method of mechanical structure impact load identification, the method comprising the steps of:
s100, measuring a frequency response function between an impact load action point of the mechanical structure and a response measuring point of the mechanical structure and calculating a transfer matrix;
s200, applying impact load to the mechanical structure and measuring impact response;
s300, constructing a sparse solution convolution convex optimization model of impact load identification based on the L1 norm based on the steps S100 and S200;
s400, solving the sparse deconvolution convex optimization model to obtain the sparse deconvolution solution of the impact load.
In the present embodiment, the impact load may be applied to any position of the mechanical structure in the step S200, and is not limited to the measurement point in the step S100.
The method is used for solving the difficulties of low precision, low efficiency and poor stability of the traditional impact load identification method, and solves the impact load identification problem under the large data scale with high precision and high efficiency by adopting the advanced primal-dual interior point method in the field of convex optimization. According to the method, the sparse theory based on the L1 norm, which is widely concerned by the current scientific and engineering fields, is applied to the field of load identification, and the sparse convolution model is solved by adopting the advanced interior point method optimization algorithm in the optimization field, so that the amplification of response noise in the identified impact load is greatly inhibited.
In one embodiment, the step S100 specifically includes the following steps:
s1001, measuring a frequency response function between an impact load action point of a mechanical structure and a response measuring point of the mechanical structure;
s1002, performing fast Fourier inverse transformation on the frequency response function to obtain a unit impulse response function, and further performing discretization to obtain a transfer matrix.
In this embodiment, the method for measuring the frequency response function mainly includes a hammering method and a vibration exciter excitation method, where the hammering method is relatively convenient, and in this embodiment, the hammering method is preferably selected to measure the frequency response function.
In one embodiment, the step S200 is implemented by measuring an impact response generated by an impact load applied to the mechanical structure using a sensor.
In this embodiment, acceleration sensors are used to measure the corresponding signals generated by the dynamic loads acting on the mechanical structure, and velocity, displacement or strain sensors may also be used to measure the vibrational response.
In one embodiment, the sparse deconvolution convex optimization model in step S300 is:
wherein | g | purple2Representing the L2 norm of the vector, | | g | | non-volatile memory1The L1 norm of the vector is represented, f represents the sparse deconvolution solution of the impact load, λ represents the regularization parameter, H system transfer matrix, and y is the impact load response vector.
In an embodiment, the sparse deconvolution convex optimization model in step S400 is solved by using a primal-dual interior point method (pdipmm), which specifically includes the following steps:
s401, constructing a dual gap function and a central path objective function by combining a sparse convolution convex optimization model, and initializing;
s402, calculating the searching direction of the central path target function;
s403, determining an iteration step length of the central path function;
s404, updating obstacle parameters in the central path function;
s405, updating the current solution based on the steps S401-404;
s406, setting a PDIPM iteration termination criterion, and if the current solution meets the iteration termination criterion, terminating the iteration process, wherein the current solution is a sparse deconvolution solution f of the impact load; otherwise, the iterative process returns to step S401 to continue the iterative computation until the pdipmm iteration termination criterion is satisfied.
In this embodiment, the dual gap function is used as a condition for determining the termination of the iteration of the dual interior point method, and the central path objective function is an objective function to be optimized by the dual interior point method.
In one embodiment, the dual gap function in step S401 is:
the center path function is:
wherein t ∈ (0, ∞) is barrier parameter, u ∈ RnFor barrier constrained variable, uiConstraining a variable u e R for a barriernPhi (f, u) is a logarithmic barrier function;
the initialization in step S401 specifically includes: initializing a non-negative initial solution f ═ 0]T∈RnBarrier constraint variable u ═ 1]T∈RnA termination threshold epsilon is more than 0, and a regularization parameter lambda is 0.02HTy||∞And the initial obstacle parameter t is 1/lambda.
In one embodiment, the step S402 calculates the search direction [ Δ f ] of the center path function by using the following formulaT，ΔuT]T：
Wherein,is a center path function phitA Hessian matrix of (f, u),is a center path function phitA gradient of (f, u);
setting the iteration step size in step S403 to S, and making S equal to βjWherein j represents the smallest integer satisfying the following formula:
wherein α ∈ (0, 1/2) and β ∈ (0, 1) are straight line search parameters.
In the present embodiment, more preferable parameters are set to α -0.01 and β -0.5.
In one embodiment, the step S404 is to update the barrier parameter t by using the following formula:
wherein n is the transfer matrix HDimension, constant μ ═ 2, smin＝0.5。
In one embodiment, the current solution in S405 comprises a current impact load sparse deconvolution solution fnewAnd the current solution u of the barrier constraint variablenewThe specific updating formula is as follows:
fnew＝fold+sΔf
unew＝uold+sΔu
wherein f isoldAnd uoldThe last PDIPM iteration result.
In one embodiment, the pdipmm iteration termination criteria in step S406 are:
where the termination threshold epsilon indicates an acceptable error.
In this embodiment, the value of the termination threshold value epsilon is continuously tried, and if the value is too small, although the precision is slightly improved, the iteration step number is more and the calculation time is longer; conversely, too large values of epsilon will cause premature termination of the iteration; typical values are e.g. 0.01.
In one embodiment, the invention discloses a sparse deconvolution method for impact load identification of a mechanical structure, which specifically comprises the following steps:
1) measuring the frequency response function and calculating the transfer matrix. Measuring a frequency response function H (omega) between an impact load action point of a mechanical structure and a response measuring point of the mechanical structure by adopting a hammering method, obtaining a unit impulse response function H (t) through Inverse Fast Fourier Transform (IFFT), and further discretizing to obtain a transfer matrix H, wherein omega represents a circular frequency variable, and t represents a time variable;
2) applying an impact load and measuring an acceleration impact response, and measuring a response signal y generated by the impact load acting on the mechanical structure using an acceleration sensor. Note that: the acceleration sensors in the step 1) and the step 2) can be replaced by speed, displacement and strain gauge sensors;
3) considering that the impact load signal is a sparse sequence in the time domain (in the test time, the impact force has a larger value only in the impact loading stage, and the non-loading region can be regarded as zero), constructing a sparse solution convolution convex optimization model based on the L1 norm:
wherein | g | purple2Representing the L2 norm of the vector, | | g | | non-volatile memory1An L2 norm representing the vector, f representing the impact load, and λ representing the regularization parameter; unlike the regularization model energy minimization criterion based on the L2 norm, the regularization model based on the L1 norm suppresses the diffusion of the learned energy at all time points, preserving the sparsity characteristics of the signal to be reconstructed.
4) Compared with the traditional Tikhonov method based on L2 regularization, the method has the advantages of explicit solution f ═ (H)TH+λI)-1HTy is different, the L1 regularization model has no explicit solution, and a primal-dual interior point method is used for solving the sparse deconvolution optimization model, which specifically comprises the following steps:
initialization 4.1): combining the sparse deconvolution model in the formula (1), constructing a dual gap function:
wherein the dual feasible variable v ═ 2(Af-y) and Lagrange dual problem g (v):
initialization 4.2): constructing a center path function:
wherein t ∈ (0, ∞) is barrier parameter, u ∈ RnConstraint variables for the obstacle and the logarithmic obstacle function Φ (f, u):
initialization 4.3): non-negative initial solution f ═ 0,.. 0, 0]T∈RnBarrier constraint variable u ═ 1]T∈RnA termination threshold epsilon is more than 0, and a regularization parameter lambda is 0.02HTy||∞The initial obstacle parameter t is 1/lambda; wherein | · | purple sweet∞Represents an infinite norm;
step 4.1): calculating the search direction [ Delta f ] of the center path functionT，ΔuT]T：
Wherein,is the Hessian matrix of the center path function,is the gradient of the central path function.
Step 4.2) calculating an iteration step s, and enabling s to be βjWherein j is the smallest integer satisfying the following formula:
wherein α ∈ (0, 1/2) and β ∈ (0, 1) are straight line search parameters, and typical values are α ═ 0.01 and β ═ 0.5.
Step 4.3): updating obstacle parameters:
where n is the dimension of the transfer matrix H, the constants μ 2 and smin＝0.5。
Step 4.4): and updating the current solution:
step 4.5): the ratio of the dual gap function and the dual objective function is taken as the PDIPM iteration termination criterion:
the termination threshold epsilon represents an acceptable error, and typically takes the value epsilon 0.01.
If the current solution fnewIf the above formula iteration termination criterion is met, terminating the iteration process to obtain a sparse deconvolution solution f of the impact load; otherwise, the iterative process returns to step 4.1) to continue the iterative computation until the above formula is satisfied.
FIG. 1 is a flow chart of a sparse deconvolution method for mechanical structure impact load identification, which is implemented by the present invention, and the method makes full use of the time domain sparsity of the impact load, constructs an impact load sparse deconvolution model according to the measured frequency response function and acceleration signal, and solves the problem by using an advanced primal-dual interior point method in the optimization field to realize the impact load identification, and comprises the following specific steps:
1) measuring the frequency response function and calculating the transfer matrix. Measuring a frequency response function H (omega) between a dynamic load application position point of a mechanical structure and a mechanical structure response measuring point by adopting a hammering method, obtaining a unit impulse response function H (t) through Inverse Fast Fourier Transform (IFFT), and further discretizing to obtain a transfer matrix H, wherein omega represents a circular frequency variable, and t represents a time variable; wherein, the hammering method is a test mode test method commonly used in the field;
11) the test schematic diagram is shown in FIG. 2, and the selected composite material fan blade has a length of 702mm, a maximum width of 112mm and a thickness of 11 mm. In order to simulate the real installation condition of the fan blade, the fixed support section of the cantilever beam support is used for clamping the position of 0-60 mm of the root of the fan blade, and two acceleration sensors with the models of PCB 333B50 are respectively arranged at the positions 120-160 mm away from the root and the end and are respectively marked as measuring points R1 and R2. The location of the simulated impact force is 70% from the blade root. The impact point is repeatedly knocked five times by adopting a pulse force hammer (a force sensor is embedded at the top of a hammer head) with the model of PCB 086C02, an impact force and an acceleration signal are synchronously recorded by a LMSSCADASIII data acquisition system, and a frequency response function from the impact load action point five times to an acceleration measuring point is H1(ω)、H2(ω)、H3(ω)、H4(omega) and H5(ω), the average value of which is H (ω) calculated by the module LMS IMPACT;
12) the sampling frequency when measuring the system frequency response function is 2048Hz, the sampling time is 1s, and the data length is 2050. The condition numbers of the high dimensional transfer matrices for excitation point F and response points R1 and R2 are 4.92E +17 and 2.66E +18, respectively (the condition numbers are an index for measuring the degree of matrix morbidity). It is known that the fan blade impact load identification problem is severely ill.
2) Applying an impact load and measuring acceleration impact response, and measuring a response signal y generated by the impact load acting on the mechanical structure by using an acceleration sensor;
21) the fan blade susceptible impact position is tapped five times continuously by using an impact force hammer, and an acceleration signal and an impact load signal are synchronously recorded at a sampling frequency of 2048Hz by LMS SCADASIII data acquisition (as shown in figures 3(a) and 3(b) and 3 (c)). And the actually measured force signal is used as a comparison object of the identification result of the impact load sparse convolution method. Note that the point of action of this step to apply the impact is consistent with the point of action of the step 1) to measure the frequency response function, while the acceleration position remains constant throughout.
22) In the impact test, the impact hammer strikes the fan blade five times in succession, and is marked as F1, F2, F3, F4 and F5 respectively, as shown in FIG. 3 (a). To verify the efficiency of the sparse deconvolution method of the present invention, four consecutive impact loads in fig. 3(a) would be identified simultaneously. The duration of the continuous impact was 14s, the sampling frequency was 2050Hz, and the response data length was 26638.
23) Because the continuous impact time history is reconstructed at the same time, the dimension of the solved problem becomes very large, the dimension of the original transfer function is far smaller than the length of the actually measured response data, and the load identification control equation at the moment is defined as:
wherein: m is the data length of the measured response, n is the unit impulse response function, and m > n. After discretization, the deconvolution model of equation (1) can be rewritten into a compact form of a matrix-vector:
y＝Hf； (2)
wherein: the new transfer matrix H ∈ Rm×mIs a truncated banded Toeplitz matrix. Under the sparse framework, the transfer matrix is referred to as the observation matrix H. In the present case, the response data dimension m for inverting the dynamic load is 26638, and the observation matrix H dimension is 26638 × 26638.
3) Considering that the impact load signal is a sparse sequence in the time domain (in the test time, the impact force has a larger value only in the impact loading stage, and the non-loading region can be regarded as zero), constructing a sparse solution convolution convex optimization model based on the L1 norm:
wherein | g | purple2Representing the L2 norm of the vector, | | g | | non-volatile memory1An L1 norm representing the vector, f represents a sparse deconvolution solution of the impact load, and λ represents a regularization parameter;
4) compared with the traditional Tikhonov method based on L2 regularization, the method has the advantages of explicit solution f ═ (H)TH+λI)-1HTy is different, the L1 regularization model has no explicit solution, and a primal-dual interior point method is used for solving the sparse deconvolution optimization model, which specifically comprises the following steps:
initialization 4.1): in combination with the sparse deconvolution model of claim 1, a dual gap function is constructed:
wherein the dual feasible variable v ═ 2(Af-y) and Lagrange dual problem g (v):
initialization 4.2): constructing a center path function:
wherein t ∈ (0, ∞) is a barrier parameter, and u ∈ RnConstraint variables for the obstacle and the logarithmic obstacle function Φ (f, u):
initialization 4.3): non-negative initial solution f ═ 0,.. 0, 0]T∈RnBarrier constraint variable u ═ 1]T∈RnA termination threshold epsilon is more than 0, and a regularization parameter lambda is 0.02HTy||∞The initial obstacle parameter t is 1/lambda; wherein | · | purple sweet∞Represents an infinite norm; .
In the case, the feasibility of calculating the high-dimensionality inverse problem by the Tikhonov method is considered, the computing environment is a workstation which is configured into 2 Intel Xeon E5580 CPUs and 1 memory of 48 GB;
step 4.1): calculating the search direction [ Delta f ] of the center path functionT，ΔuT]T：
Wherein,is the Hessian matrix of the center path function,is the gradient of the central path function.
Step 4.2) calculating an iteration step s, and enabling s to be βjWherein j is the smallest integer satisfying the following formula:
wherein α ∈ (0, 1/2) and β ∈ (0, 1) are straight line search parameters, and typical values are α ═ 0.01 and β ═ 0.5.
Step 4.3): updating obstacle parameters:
where n is the dimension of the transfer matrix H, the constants μ 2 and smin＝0.5。
Step 4.4): the updated current solution includes the current solution f of the impact loadnewAnd the current solution u of the barrier constraint variablenew：
The current solution includes a current solution f of the impact loadnewAnd the current solution u of the barrier constraint variablenew。
Step 4.5): the ratio of the dual gap function and the dual objective function is taken as the PDIPM iteration termination criterion:
the termination threshold epsilon represents an acceptable error, and typically takes the value epsilon 0.01.
If the current solution fnewIf the above formula iteration termination criterion is met, terminating the iteration process to obtain a sparse deconvolution solution f of the impact load; otherwise, the iterative process returns to step 4.1) to continue the iterative computation until the above formula is satisfied.
5) In order to quantitatively evaluate the accuracy of loads identified by sparse deconvolution algorithms PDIPM and a Tikhonov regularization method, respectively defining time domain global relative errors and impact load peak value relative errors as follows:
wherein f ismeasuredAnd fidentifiedThe measured impact load of the force sensor and the impact load reconstructed by applying the regularization method are respectively.
51) Fig. 4(a), 4(b) show that when the sparse deconvolution algorithm PDIPM identifies successive impact loads acting on the thin shell structure using response signals R1 and R2, respectively, the dual gap decreases rapidly and then gradually flattens as the number of iteration steps increases. The number of terminating iteration steps is 23 and 26, respectively.
52) Fig. 5(a), 5(b) are the continuous impact loads reconstructed by the sparse deconvolution algorithm pdippm using the response signals R1 and R2. It can be seen that the five impact loads reconstructed by the PDIPM using the response signals R1 and R2, respectively, are highly matched with the measured load, and the reconstructed impact loads are very sparse in the impact duration interval. Table 1 gives that the relative error of the continuous impact load reconstructed by the PDIPM with the response signals R1 and R2 is only 13.02% and 12.93%, respectively. The peak forces of the five measured impact loads were 11.19N, 36.24N, 23.88N, 38.90N, and 26.00N, respectively. The peak forces of the load inverted with the response signal R1 (see fig. 5(a)) were 11.43N, 36.81N, 24.61N, 39.22N, and 26.20N, respectively, and the relative errors were 2.14%, 1.51%, 3.06%, 0.82%, and 0.77%, respectively (see table 1).
53) Fig. 6(a), fig. (b) are the continuous impact loads reconstructed by the Tikhonov regularization method with response signals R1 and R2. It can be seen that the Tikhonov solution is amplified in the unloaded region of the impact load, particularly when the response point R2 is used to invert the dynamic load (see fig. 6 (b)). Table 1 shows that the relative error of the continuous impact load reconstructed by the Tikhonov method with response signals R1 and R2 is as high as 58.09% and 290.24%, respectively. In contrast, with the aid of the prior information of the temporal sparsity of the impact load, the continuous impact load reconstructed by the PDIPM is almost zero in the impact unloaded region (see fig. 5(a), 5 (b)). It is worth noting that: in this case, although the relative error of the Tikhonov method is large, the peak relative error is still acceptable (less than 10%) or even smaller than the PDIPM peak relative error. As for the time required for the continuous impact load reconstruction, Tikhonov takes much more time than pdippm. Therefore, the sparse deconvolution method can stably solve the inverse problem of high-dimensionality and serious-morbidity load identification with high precision and high efficiency.
Table 1 comparison of PDIPM and Tikhonov identification results for continuous impact loads of fan blades
The above description is only for the purpose of illustrating the preferred embodiments of the present invention and is not to be construed as limiting the invention, and any modifications, equivalents and improvements made within the spirit and principle of the present invention are intended to be included within the scope of the present invention.
Claims (8)
1. A sparse deconvolution method for impact load identification of a mechanical structure, the method comprising the steps of:
s100, measuring a frequency response function between an impact load action point of the mechanical structure and a response measuring point of the mechanical structure and calculating a transfer matrix;
s200, applying impact load to the mechanical structure and measuring impact response;
s300, constructing a sparse solution convolution convex optimization model based on the L1 norm impact load identification based on the steps S100 and S200, wherein the sparse solution convolution convex optimization model is as follows:
wherein | · | purple sweet2L2 norm representing vector, | · | | | non-volatile memory1Expressing L1 norm of the vector, f expressing an impact load sparse deconvolution solution, lambda expressing a regularization parameter, H expressing a transfer matrix, and y expressing an impact load response vector;
s400, solving a sparse deconvolution convex optimization model, and obtaining a sparse deconvolution solution of the impact load to be identified by using a primal-dual interior point method (PDIPM), wherein the sparse deconvolution method specifically comprises the following steps:
s401, constructing a dual gap function and a central path objective function by combining a sparse convolution convex optimization model, and initializing;
s402, calculating the searching direction of the central path target function;
s403, calculating the iteration step length of the central path function;
s404, updating obstacle parameters in the central path function;
s405, iteratively updating the current solution based on the steps S401-404;
s406, setting a PDIPM iteration termination criterion, and if the current solution meets the iteration termination criterion, terminating the iteration process, wherein the current solution is a sparse deconvolution solution of the impact load f; otherwise, the iterative process returns to step S401 to continue the iterative computation until the pdipmm iteration termination criterion is satisfied.
2. The method according to claim 1, wherein the step S100 specifically comprises the steps of:
s1001, measuring a frequency response function between an impact load action point of a mechanical structure and a response measuring point of the mechanical structure;
s1002, performing fast Fourier inverse transformation on the frequency response function to obtain a unit impulse response function, and further performing discretization to obtain a transfer matrix.
3. The method of claim 1, wherein: in step S200, an impact response generated by an impact load applied to the mechanical structure is measured by a sensor.
4. The method of claim 1,
the dual gap function in step S401 is:
wherein, the dual feasible variable v is 2(Hf-y), f is the impact load sparse deconvolution, λ represents the regularization parameter, H is the system transfer matrix, y is the impact load response vector, G (v) represents Lagrange dual function,
the center path objective function is:
wherein t ∈ (0, ∞) is barrier parameter, u ∈ RnFor barrier constrained variable, uiConstraining a variable u e R for a barriernPhi (f, u) is a logarithmic barrier function;
the initialization in step S401 specifically includes: initializing impact load sparse deconvolution solution f [ [0]T ∈ Rn, barrier constraint variable u ═ 1]T∈RnA termination threshold epsilon is more than 0, and a regularization parameter lambda is 0.02HTy||∞And the initial obstacle parameter t is 1/lambda.
5. The method of claim 4,
in step S402, the following formula is used to calculate the search direction [ Δ f ] of the center path functionT，ΔuT]T：
Wherein,is a center path function phitA Hessian matrix of (f, u),is a center path function phitA gradient of (f, u);
the iteration step size in step S403 is S, where S is βjWherein j represents the smallest integer satisfying the following formula:
wherein α ∈ (0, 1/2) and β ∈ (0, 1) are straight line search parameters.
6. The method of claim 5,
in step S404, the obstacle parameter t is updated by using the following formula:
where n is the dimension of the transfer matrix H, with the constant μ 2, Smmin＝0.5。
7. The method of claim 6,
the current solution in S405 comprises a current impact load sparse convolution solution fnewAnd the current solution u of the barrier constraint variablenewThe specific updating formula is as follows:
fnew＝fold+sΔf
unew＝uold+sΔu
wherein f isoldAnd uoldIterate the knot for the last PDIPMAnd (5) performing sparse deconvolution on the impact load in the results and performing obstacle constraint variable analysis.
8. The method of claim 7,
the PDIPM iteration termination criterion in step S406 is:
Priority Applications (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610222057.5A CN105843780B (en) | 2016-04-11 | 2016-04-11 | A kind of sparse deconvolution method of mechanical structure shock loading identification |
Applications Claiming Priority (1)
| Application Number | Priority Date | Filing Date | Title |
|---|---|---|---|
| CN201610222057.5A CN105843780B (en) | 2016-04-11 | 2016-04-11 | A kind of sparse deconvolution method of mechanical structure shock loading identification |
Publications (2)
| Publication Number | Publication Date |
|---|---|
| CN105843780A CN105843780A (en) | 2016-08-10 |
| CN105843780B true CN105843780B (en) | 2018-06-26 |
Family
ID=56597324
Family Applications (1)
| Application Number | Title | Priority Date | Filing Date |
|---|---|---|---|
| CN201610222057.5A Active CN105843780B (en) | 2016-04-11 | 2016-04-11 | A kind of sparse deconvolution method of mechanical structure shock loading identification |
Country Status (1)
| Country | Link |
|---|---|
| CN (1) | CN105843780B (en) |
Families Citing this family (13)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN108344547B (en) * | 2018-02-08 | 2023-06-16 | 天津大学 | Experimental system and verification method for identifying nonlinear stiffness of gap |
| CN109561036B (en) * | 2019-01-15 | 2021-06-18 | 哈尔滨工程大学 | Underwater acoustic channel blind deconvolution method based on convex optimization |
| CN109902386B (en) * | 2019-02-28 | 2021-07-06 | 西安交通大学 | Composite material structure impact load identification method and device based on group sparsity |
| CN109933871B (en) * | 2019-02-28 | 2021-04-13 | 西安交通大学 | Composite material structure impact load identification method and device based on iterative weighted sparsity |
| CN109933872B (en) * | 2019-02-28 | 2024-04-26 | 西安交通大学 | Reinforced sparsity-based composite material structure impact load identification method and device |
| CN113711143A (en) * | 2019-04-11 | 2021-11-26 | 三菱电机株式会社 | Numerical control device |
| CN110411757B (en) * | 2019-07-30 | 2021-10-29 | 安徽江淮汽车集团股份有限公司 | Shaft head dynamic load calculation method, device, equipment and storage medium |
| CN110889174A (en) * | 2019-10-17 | 2020-03-17 | 杭州电子科技大学 | Dynamic load identification method based on grouping sparsity |
| CN111651918B (en) * | 2020-05-27 | 2023-04-18 | 西安交通大学 | Impact load identification method and device based on generalized minimum and maximum concave penalty term |
| CN112052552B (en) * | 2020-07-13 | 2022-12-06 | 西安交通大学 | Identification method of gear local fault equivalent excitation force |
| CN112035966B (en) * | 2020-07-13 | 2024-04-19 | 西安交通大学 | Gear vibration source identification method based on endogenous excitation force of gear |
| CN112749688B (en) * | 2021-02-02 | 2023-05-16 | 北京信息科技大学 | Impact load sparse identification method and system based on MC penalty function |
| CN113343402B (en) * | 2021-07-07 | 2022-05-24 | 北京航空航天大学 | Pipeline corrosion grade evaluation method based on multilayer convolution sparse coding |
Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103852289A (en) * | 2014-03-10 | 2014-06-11 | 东南大学 | Problem cable load generalized displacement recognition method based on space coordinate monitoring |
| CN103954464A (en) * | 2014-04-29 | 2014-07-30 | 清华大学 | Dynamic load recognizing method based on wavelet multiresolution analysis |
| CN104075846A (en) * | 2014-07-11 | 2014-10-01 | 湖大海捷(湖南)工程技术研究有限公司 | Rotor unbalancedness identification method based on calculation of reverse seeking technology |
| CN104462862A (en) * | 2015-01-06 | 2015-03-25 | 西安交通大学 | Mechanical structure dynamic load identification method based on cubic b-spline scaling function |
| CN104537257A (en) * | 2015-01-12 | 2015-04-22 | 电子科技大学 | Distributed self-adaptation direct positioning method based on time difference |
| CN104732060A (en) * | 2015-01-19 | 2015-06-24 | 湖南科技大学 | Online identification method for multiple loads on blades of large wind power generation set |
| CN105136495A (en) * | 2015-07-23 | 2015-12-09 | 东南大学 | Simplified angular displacement strain monitoring damaged cable load identification method |
-
2016
- 2016-04-11 CN CN201610222057.5A patent/CN105843780B/en active Active
Patent Citations (7)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN103852289A (en) * | 2014-03-10 | 2014-06-11 | 东南大学 | Problem cable load generalized displacement recognition method based on space coordinate monitoring |
| CN103954464A (en) * | 2014-04-29 | 2014-07-30 | 清华大学 | Dynamic load recognizing method based on wavelet multiresolution analysis |
| CN104075846A (en) * | 2014-07-11 | 2014-10-01 | 湖大海捷(湖南)工程技术研究有限公司 | Rotor unbalancedness identification method based on calculation of reverse seeking technology |
| CN104462862A (en) * | 2015-01-06 | 2015-03-25 | 西安交通大学 | Mechanical structure dynamic load identification method based on cubic b-spline scaling function |
| CN104537257A (en) * | 2015-01-12 | 2015-04-22 | 电子科技大学 | Distributed self-adaptation direct positioning method based on time difference |
| CN104732060A (en) * | 2015-01-19 | 2015-06-24 | 湖南科技大学 | Online identification method for multiple loads on blades of large wind power generation set |
| CN105136495A (en) * | 2015-07-23 | 2015-12-09 | 东南大学 | Simplified angular displacement strain monitoring damaged cable load identification method |
Non-Patent Citations (1)
| Title |
|---|
| "不完备测点结构损伤与荷载的同步识别算法研究";张坤;《中国博士学位论文全文数据库 工程科技Ⅱ辑》;20110415(第4期);正文第14页，正文第60页 * |
Also Published As
| Publication number | Publication date |
|---|---|
| CN105843780A (en) | 2016-08-10 |
Similar Documents
| Publication | Publication Date | Title |
|---|---|---|
| CN105843780B (en) | A kind of sparse deconvolution method of mechanical structure shock loading identification | |
| CN106896156B (en) | The girder construction damnification recognition method of uniform load face curvature difference by cross | |
| CN111240268A (en) | Axle system thermal error modeling method and thermal error compensation system based on SLSTM neural network | |
| CN109558635B (en) | Structural interval uncertainty damage identification method based on unit modal strain energy sensitivity | |
| Pawar et al. | Damage detection in beams using spatial Fourier analysis and neural networks | |
| CN107729592B (en) | Time-varying structure modal parameter identification method based on generalized subspace tracking | |
| CN108038315A (en) | A kind of Random dynamic loads recognition methods based on spectrum stochastic finite meta-model | |
| CN112528411B (en) | Geometric nonlinear structure noise vibration response calculation method based on modal reduction | |
| Zhang et al. | A flutter prediction method with low cost and low risk from test data | |
| CN109902408B (en) | Load identification method based on numerical operation and improved regularization algorithm | |
| WO2018223774A1 (en) | Method for indirectly acquiring continuous distribution mechanical parameter field of non-homogeneous materials | |
| CN109933872B (en) | Reinforced sparsity-based composite material structure impact load identification method and device | |
| CN113534679B (en) | System monitoring model generation method, processor chip and industrial system | |
| CN106909738B (en) | Model parameter identification method | |
| JP6048358B2 (en) | Analysis device | |
| CN115292849A (en) | Mechanical structure residual life prediction method based on phase field method and BP neural network | |
| García-Fernández et al. | A review on fatigue monitoring of structures | |
| CN107844646A (en) | A kind of slender bodies distribution load-transfer mechanism reducing technique | |
| CN114861489B (en) | rPCK proxy model aided structure dynamic parameter identification method | |
| CN115455353A (en) | Online parameter identification method based on nonlinear time domain filtering | |
| CN111651918B (en) | Impact load identification method and device based on generalized minimum and maximum concave penalty term | |
| CN111931288A (en) | Method for measuring distribution similarity of time-frequency domain of fire impact response | |
| CN112016235A (en) | Impact load identification method and system of flexible antenna structure | |
| Kalyukh | Applicability of the Quasistatic Approach to the Calculation of the Characteristics of an Accelerating Towed System | |
| CN113155384A (en) | Sensor arrangement method for reducing uncertainty of structural damping ratio identification |
Legal Events
| Date | Code | Title | Description |
|---|---|---|---|
| C06 | Publication | ||
| PB01 | Publication | ||
| C10 | Entry into substantive examination | ||
| SE01 | Entry into force of request for substantive examination | ||
| GR01 | Patent grant | ||
| GR01 | Patent grant |