Method for determining power spectral density of random load of engineering structure and related equipment

Abstract

The invention provides an engineering structure random load power spectral density determination method and related equipment, and the method comprises the steps: obtaining a first power spectral density corresponding to an acceleration associated with an engineering structure, and carrying out the spectral decomposition of the first power spectral density, and obtaining a virtual acceleration response value; acquiring a transfer function matrix corresponding to each frequency point in the first power spectral density based on engineering parameters of the engineering structure; performing bilateral balance transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix; determining a virtual load based on the virtual acceleration response value and each improved transfer function matrix, and determining a second power spectral density corresponding to the random load based on the virtual load, the technical problem in the prior art that the identification error of the power spectrum density corresponding to the random load of the engineering structure under part of frequency points (especially the frequency points near the inherent frequency of the engineering structure) is large is solved, and the accuracy of determining the random load borne by the engineering structure is improved.

Description

Technical Field

[0001] The present application relates to the field of data processing technology, and in particular to a method for determining the power spectrum density of random loads on an engineering structure and related equipment. Background Art

[0002] A full understanding of the external loads borne by engineering structures during service is the basis for research in the fields of structural design and optimization, vibration control, and health monitoring. The actual external loads borne by engineering structures are very complex and have many influencing factors. It is usually difficult to describe the data at each moment with a deterministic functional relationship, such as the effects of earthquakes and wind on high-rise building structures, the buffeting loads received by aircraft during flight, and the effects of waves on ships and offshore platforms. Therefore, it is necessary to explore the identification method of such random loads from the perspective of probability statistics.

[0003] The prior art proposed the Inverse Pseudo-Excitation Method (IPEM), which conducted identification research on random loads based on power spectral density (PSD). However, due to the serious problem of function matrix ill-conditioning at the frequency points near the natural frequency of the structure, when there is measurement noise, there will be a large deviation between the load PSD identification result of IPEM at the corresponding frequency point and the actual load PSD, which will lead to a large deviation in the power spectral density of the determined random load. Summary of the invention

[0004] In view of this, the purpose of the present application is to propose a method for determining the power spectral density of random loads on an engineering structure and related equipment to overcome all or part of the deficiencies in the prior art.

[0005] Based on the above-mentioned purpose, the present application provides a method for determining the power spectral density of random loads on an engineering structure, including: obtaining a first power spectral density corresponding to the acceleration associated with the engineering structure, performing spectral decomposition on the first power spectral density, and obtaining a virtual acceleration response value; based on the engineering parameters of the engineering structure, obtaining a transfer function matrix corresponding to each frequency point in the first power spectral density; performing a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix; determining a virtual load based on the virtual acceleration response value and each improved transfer function matrix, and determining a second power spectral density corresponding to the random load based on the virtual load.

[0006] Optionally, performing spectral decomposition on the first power spectrum density to obtain a virtual acceleration response value includes: performing spectral decomposition on the first power spectrum density according to the following formula: in, is the first power spectral density, λ yj (ω) is the jth eigenvalue corresponding to the first power spectrum density, is the jth eigenvector corresponding to the first power spectral density, [] * represents taking the complex conjugate, [] T Indicates taking the transpose, r y is the rank corresponding to the first power spectral density, is the virtual acceleration response value, ω represents a frequency value.

[0007] Optionally, performing a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix includes: for each transfer function matrix, performing a first operator transformation on the transfer function matrix a predetermined number of times to obtain a first weighting matrix, and performing a second operator transformation on the first weighting matrix a predetermined number of times to obtain the improved transfer function matrix.

[0008] Optionally, determining the load based on the virtual acceleration response value and each improved transfer function matrix includes: determining a target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix; determining the virtual load based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix.

[0009] Optionally, determining a target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix includes: determining the target regularization parameter by the following formula: in, is the target regularization parameter, Represents the transfer matrix on the entire load identification band The condition number, max means to find the maximum value, λ Yj (ω)=P j λ yj (ω), P j is the jth diagonal element of the diagonal matrix P, λ yj (ω) is the eigenvalue corresponding to the first power spectrum density, max(λ Yj (ω)) represents the value for j = 1, 2, ..., r y The largest λ Yj (ω), P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, λ Tikh,j (ω) is a predetermined regularization parameter, and ω represents a frequency value.

[0010] Optionally, determining the virtual load based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix includes: determining the virtual load by the following formula: in, is the virtual load, Q(ω) is the second diagonal matrix used to adjust the matrix condition number, F j (ω) is the regularization parameter An approximate solution of i (ω) is determined using the i-th improved transfer function matrix The singular values ​​of is the target regularization parameter, u i(ω) is determined using the i-th improved transfer function matrix The left orthogonal singular value vector, v i(ω) is determined using the i-th improved transfer function matrix The right orthogonal singular value vectors of , P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, m f is the total number of all improved functions, and ω represents the frequency value.

[0011] Optionally, determining a second power spectrum density corresponding to the random load based on the virtual load includes: determining the second power spectrum density by using the following formula: Among them, S ff (ω) is the second power spectral density, is the virtual load, [] * represents taking the complex conjugate, [] T represents the transpose, ω represents the frequency value, r y is the rank corresponding to the first power spectral density.

[0012] Based on the same inventive concept, the present application also provides a device for determining the power spectral density of random loads on an engineering structure, comprising: a decomposition module, configured to obtain a first power spectral density corresponding to the acceleration associated with the engineering structure, and perform spectral decomposition on the first power spectral density to obtain a virtual acceleration response value; an acquisition module, configured to obtain a transfer function matrix corresponding to each frequency point in the first power spectral density based on the engineering parameters of the engineering structure; a transformation module, configured to perform a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix; a determination module, configured to determine a virtual load based on the virtual acceleration response value and each improved transfer function matrix, and determine a second power spectral density corresponding to the random load based on the virtual load.

[0013] Based on the same inventive concept, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable by the processor, wherein the processor implements the method as described above when executing the computer program.

[0014] Based on the same inventive concept, the present application also provides a non-transitory computer-readable storage medium, which stores computer instructions, and the computer instructions are used to enable a computer to execute the method as described above.

[0015] From the above, it can be seen that the method and related equipment for determining the power spectrum density of random loads of engineering structures provided by the present application include obtaining a first power spectrum density corresponding to the acceleration associated with the engineering structure, performing spectral decomposition on the first power spectrum density, obtaining a virtual acceleration response value, and analyzing the vibration characteristics of the engineering structure at different frequencies. Based on the engineering parameters of the engineering structure, the transfer function matrix corresponding to each frequency point in the first power spectrum density is obtained, so that multiple transfer function matrices are close to the actual engineering structure, which lays the foundation for accurately calculating the loads on the engineering structure. A bilateral balanced transformation is performed on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix, ensuring that there are relatively few matrix condition numbers in the transfer function matrix, so as to achieve the purpose of reducing the error of the transfer function matrix. Based on the virtual acceleration response value and each improved transfer function matrix, a virtual load is determined, and based on the virtual load, a second power spectrum density corresponding to the random load is determined, so as to achieve the purpose of accurately determining the virtual load and the second power spectrum density. BRIEF DESCRIPTION OF THE DRAWINGS

[0016] In order to more clearly illustrate the technical solutions in the present application or related technologies, the drawings required for use in the embodiments or related technical descriptions are briefly introduced below. Obviously, the drawings described below are only embodiments of the present application. For ordinary technicians in this field, other drawings can be obtained based on these drawings without creative work.

[0017] Figure 1 A schematic flow chart of a method for determining power spectral density of random loads on an engineering structure according to an embodiment of the present application;

[0018] Figure 2 A schematic diagram of a cantilever beam model according to an embodiment of the present application;

[0019] FIG3( a ) is a schematic diagram of the condition number after different balancing transformation times at a frequency of 5 Hz according to an embodiment of the present application;

[0020] FIG3( b ) is a schematic diagram of the condition number after different balanced transformation times at a frequency of 87 Hz according to an embodiment of the present application;

[0021] FIG4( a ) shows the first row and first column element S of the load power spectrum density when the measurement points are 4, 5, 6 and 10 in the embodiment of the present application. 11 Schematic diagram of recognition results;

[0022] FIG4( b ) shows the first row and second column element S of the load power spectrum density when the measurement points are 4, 5, 6 and 10 in the embodiment of the present application. 12 Schematic diagram of the recognition results of the real part changing with frequency;

[0023] FIG4( c ) shows the first row and second column element S of the load power spectrum density when the measurement points are 4, 5, 6 and 10 in the embodiment of the present application. 12 Schematic diagram of the recognition results of the imaginary part changing with frequency;

[0024] FIG4(d) shows the second row and second column element S of the load power spectrum density when the measurement points are 4, 5, 6 and 10 in the embodiment of the present application. 22 Schematic diagram of recognition results changing with frequency;

[0025] FIG5( a ) shows the first row and first column element S of the load power spectrum density when the measuring points are 2, 6, 7 and 10 in the embodiment of the present application. 11 Schematic diagram of recognition results changing with frequency;

[0026] FIG5( b ) shows the first row and second column element S of the load power spectrum density when the measuring points are 2, 6, 7 and 10 in the embodiment of the present application. 12 Schematic diagram of the recognition results of the real part changing with frequency;

[0027] FIG5(c) shows the first row and second column element S of the load power spectrum density when the measurement points are 2, 6, 7 and 10 in the embodiment of the present application. 12 Schematic diagram of the recognition results of the imaginary part changing with frequency;

[0028] FIG5(d) shows the second row and second column element S of the load power spectrum density when the measurement points are 2, 6, 7 and 10 in the embodiment of the present application. 22 Schematic diagram of recognition results changing with frequency;

[0029] Figure 6 A schematic diagram of the structure of a device for determining power spectrum density of random loads on an engineering structure according to an embodiment of the present application;

[0030] Figure 7 This is a schematic diagram of the hardware structure of an electronic device according to an embodiment of the present application. DETAILED DESCRIPTION

[0031] In order to make the objectives, technical solutions and advantages of the present application more clearly understood, the present application is further described in detail below in combination with specific embodiments and with reference to the accompanying drawings.

[0032] It should be noted that, unless otherwise defined, the technical terms or scientific terms used in the embodiments of the present application should be the usual meanings understood by people with ordinary skills in the field to which the present application belongs. The "first", "second" and similar words used in the embodiments of the present application do not represent any order, quantity or importance, but are only used to distinguish different components. "Including" or "comprising" and similar words mean that the elements or objects appearing in front of the word cover the elements or objects listed after the word and their equivalents, without excluding other elements or objects. "Connect" or "connected" and similar words are not limited to physical or mechanical connections, but can include electrical connections, whether direct or indirect. "Up", "down", "left", "right" and the like are only used to indicate relative positional relationships. When the absolute position of the described object changes, the relative positional relationship may also change accordingly.

[0033] As described in the background technology section, a full understanding of the external loads borne by engineering structures during service is the basis of research fields such as structural design and optimization, vibration control and health monitoring. On the one hand, structural design has gradually shifted from static design to dynamic design. The formulation of effective dynamic load standards can avoid the situation of "under / over design" or "under / over test" of the structure, which can directly affect the reliability, safety and design cost of the structure. On the other hand, for large engineering structures, by real-time monitoring of the external loads they are subjected to during service, identifying potential problems and anomalies, and taking preventive and remedial measures, it is possible to effectively avoid economic losses and casualties caused by major safety accidents and extend the service life of the structure. However, the external loads actually borne by engineering structures are very complex and have many influencing factors. It is usually difficult to describe the data at each moment with a deterministic functional relationship, such as the effects of earthquakes and wind on high-rise building structures, the buffeting loads received by aircraft during flight, and the effects of waves on ships and offshore platforms. Therefore, it is necessary to explore the identification method of such random loads from the perspective of probability statistics.

[0034] The existing technology proposes the inverse virtual excitation method and conducts identification research on random loads based on power spectrum density. However, due to the serious problem of frequency response function matrix ill-conditioning at the frequency points near the natural frequency of the structure. When there is measurement noise, there will be a large deviation between the power spectrum density identification result of the load at the corresponding frequency point of IPEM and the power spectrum density of the actual load. In view of the causes of the error, some scholars have conducted analysis and research, and proposed weighted averaging technology, improvement methods for frequency response function matrix ill-conditioning, and improved regularization methods, etc. However, the improvement of load identification accuracy is still limited, which leads to inaccurate power spectrum density determined based on load.

[0035] In view of this, the present application embodiment proposes a method for determining the power spectral density of random loads on an engineering structure, referring to Figure 1 , including the following steps:

[0036] Step 101: Obtain a first power spectrum density corresponding to the acceleration associated with the engineering structure, perform spectral decomposition on the first power spectrum density, and obtain a virtual acceleration response value.

[0037] In this step, the random load actually received by the engineering structure is very complex and has many influencing factors. Therefore, the second power spectrum density corresponding to the load directly obtained is not accurate. Among them, because the external force received by the engineering structure is uncertain, the uncertain external force received by the engineering structure is called a random load. When the engineering structure is subjected to an external force, acceleration will be generated. The load and the acceleration have a correlation relationship. It can be inferred that the first power spectrum density corresponding to the acceleration and the second power spectrum density corresponding to the random load also have a correlation relationship. Therefore, before determining the second power spectrum density, the first power spectrum density is first obtained. Among them, the power spectrum density (PSD) is a physical quantity that describes the distribution of signal power in the frequency domain. The first power spectrum density corresponding to the acceleration is associated with the engineering structure. Under the premise of the known engineering structure, the first power spectrum density can be relatively accurately inferred, and the second power spectrum density corresponding to the load can be calculated with the help of the first power spectrum density corresponding to the acceleration. In practical problems, the finite element method is usually used to model the engineering structure, and the first power spectrum density corresponding to the acceleration is derived with the help of the finite element method, and the first power spectrum density is obtained. Among them, the finite element method (FEM) is a numerical technique for finding approximate solutions to boundary value problems of partial differential equations. It decomposes the solution domain into several small subdomains, each of which is called a finite element. By assuming a simple approximate solution for each finite element and then deriving the total satisfaction condition for solving the entire domain, the solution to the problem is obtained. This solution is not an exact solution, but an approximate solution, because it is often difficult to get an exact solution to practical problems.

[0038] In practical engineering problems, the finite element method is used to model engineering structures. The differential equation of motion of a deterministic structure with N degrees of freedom can be expressed as:

[0039]

[0040] Among them, M, C and K are the mass, damping and stiffness matrices of the engineering structure respectively, y(t), and are the displacement, velocity and acceleration response vectors respectively, To include m f The corresponding power spectrum density is W is N×m f Load action position configuration matrix.

[0041] For multi-point stationary random loads acting on a linear system, virtual excitation can be used to solve the structural response. Since the transfer function matrix of the power spectral density can be a Hermitian matrix, S ff (ω) can be expressed as follows:

[0042]

[0043] in,[] * represents taking the complex conjugate, [] T represents the transpose, λ fj and S ff The eigenvalues ​​and eigenvectors of (ω), r f For S ff The rank of (ω),

[0044] Construct a dummy load:

[0045]

[0046] Among them, the virtual load is used to characterize the hypothetical external force on the engineering structure. The engineering structure is subject to multiple hypothetical external forces. Substituting formula (3) into formula (1), the virtual acceleration response of the structure under the action of the virtual load can be obtained:

[0047]

[0048] in, H(ω) is the transfer function matrix, t is the time, thus, the structure m y Acceleration response corresponding to degrees of freedom The PSD function is It can be written as:

[0049]

[0050] According to the virtual excitation method, Equation (5) establishes the relationship between the structural response PSD and the applied load PSD. Similarly, for the inverse problem, assuming that the structure m y The first power spectrum density corresponding to the acceleration response of degrees of freedom is In order to identify the second power spectrum density of the acting load, it is necessary to perform spectral decomposition on the first power spectrum density of the measured acceleration response of the known structure to obtain a virtual acceleration response value. The main purpose of spectral decomposition of acceleration is to analyze the vibration characteristics of the engineering structure at different frequencies. It should be noted that since the first power spectrum density corresponding to the acceleration is an estimated value determined based on work experience, the spectral decomposition of the first power spectrum density results in a virtual acceleration response value. The virtual acceleration response value reflects that the response value obtained is not the actual acceleration response value, but a hypothetical acceleration response value. Acceleration spectrum decomposition is the process of decomposing the acceleration signal into different frequency components. Through spectral decomposition, the energy distribution of the acceleration signal at different frequencies can be obtained, and then the vibration characteristics of the engineering structure at different frequencies can be analyzed.

[0051] Step 102: acquiring a transfer function matrix corresponding to each frequency point in the first power spectrum density based on the engineering parameters of the engineering structure.

[0052] In this step, the engineering structure has engineering parameters. Exemplarily, the engineering parameters may be parameters such as stiffness matrix, mass matrix, damping ratio, loading position, and response measurement position. According to the engineering parameters, a transfer function matrix suitable for the engineering structure can be selected in advance, and then accurate calculations can be performed based on the transfer function matrix. Since there are multiple frequency points in the power spectrum density, the frequency points in the first power spectrum density are the same as the frequency points in the second power spectrum density. Therefore, it is necessary to obtain the transfer function matrix corresponding to each frequency point in the first power spectrum density. By obtaining multiple transfer function matrices related to the engineering parameters, the multiple transfer function matrices are close to the actual engineering structure, which lays the foundation for accurately calculating the virtual loads on the engineering structure.

[0053] Step 103: perform bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix.

[0054] In this step, the transfer function matrix has a matrix condition number, which is widely used in numerical analysis. A problem with a low condition number is called well-conditioned, while a problem with a high condition number is called ill-conditioned. Ill-conditioned problems are prone to error amplification in numerical calculations. Therefore, in practical applications, it is necessary to avoid using ill-conditioned matrices as much as possible. In order to avoid using ill-conditioned matrices, a bilateral balanced transformation is performed on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix, ensuring that there are relatively few matrix condition numbers in the transfer function matrix, thereby achieving the purpose of reducing the error of the transfer function matrix.

[0055] Step 104: determining a virtual load based on the virtual acceleration response value and each improved transfer function matrix, and determining a second power spectrum density corresponding to the random load based on the virtual load.

[0056] In this step, since the engineering structure will generate acceleration when subjected to random load, the random load has a correlation with the acceleration. When determining the second power spectrum density corresponding to the random load, it is necessary to start from the first power spectrum density of the acceleration, perform spectrum decomposition through the first power spectrum density corresponding to the acceleration, obtain the virtual acceleration response value, and use the virtual acceleration response value to determine the virtual load. Since each improved transfer function matrix is ​​related to the engineering parameters of the engineering structure, each improved transfer function matrix can be close to the matrix required for calculating the virtual load of the actual engineering structure, and the improved transfer function matrix is ​​used to determine the virtual load. Therefore, based on the virtual acceleration response value and each improved transfer function matrix, the virtual load is determined to achieve the purpose of accurately determining the virtual load. The virtual load is used to characterize the assumed external force suffered by the engineering structure. When determining the random load of the engineering structure, it is necessary to determine all the assumed external forces suffered by the engineering structure. Therefore, multiple virtual loads can be regarded as random loads of the engineering structure. After determining the virtual load, the second power spectrum density corresponding to the random load can be determined using the virtual load. Since the determined virtual load has accuracy, the second power spectrum density determined using the virtual load is also accurate.

[0057] Through the above scheme, the first power spectrum density corresponding to the acceleration associated with the engineering structure is obtained, and the first power spectrum density is spectrally decomposed to obtain the virtual acceleration response value, and the vibration characteristics of the engineering structure at different frequencies are analyzed. Based on the engineering parameters of the engineering structure, the transfer function matrix corresponding to each frequency point in the first power spectrum density is obtained, so that multiple transfer function matrices are close to the actual engineering structure, which lays the foundation for accurately calculating the load on the engineering structure. A bilateral balanced transformation is performed on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix, ensuring that there are relatively few matrix condition numbers in the transfer function matrix, so as to achieve the purpose of reducing the error of the transfer function matrix. Based on the virtual acceleration response value and each improved transfer function matrix, the virtual load is determined, and based on the virtual load, the second power spectrum density corresponding to the random load is determined, so as to achieve the purpose of accurately determining the virtual load and the second power spectrum density.

[0058] In some embodiments, performing spectral decomposition on the first power spectrum density to obtain a virtual acceleration response value includes: performing spectral decomposition on the first power spectrum density using the following formula: in, is the first power spectral density, λ yj (ω) is the jth eigenvalue corresponding to the first power spectrum density, is the jth eigenvector corresponding to the first power spectral density, [] *represents taking the complex conjugate, [] T Indicates taking the transpose, r y is the rank corresponding to the first power spectral density, is the virtual acceleration response value, ω represents a frequency value.

[0059] In this embodiment, the first power spectrum density is spectrally decomposed to decompose relevant information from the first power spectrum density. The eigenvalue and eigenvector corresponding to the first power spectrum density can be decomposed, and the virtual acceleration response value can be obtained by calculation based on the eigenvalue and the eigenvector. The spectral decomposition of the first power spectrum density is converted into a formula calculation, and the virtual acceleration response value is digitized to achieve the purpose of accurately determining the virtual acceleration response value.

[0060] In some embodiments, performing a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix includes: for each transfer function matrix, performing a first operator transformation on the transfer function matrix a predetermined number of times to obtain a first weighting matrix, and performing a second operator transformation on the first weighting matrix the predetermined number of times to obtain the improved transfer function matrix.

[0061] In this embodiment, for each transfer function matrix, a first operator transformation is performed a predetermined number of times on the transfer function matrix to obtain a first weighting matrix. The first operator transformation may be an operator Transformation, Operator Transformation refers to the operator The process of transforming an object. It can be regarded as a special mapping, which performs a certain operation or transformation on the input object and outputs a new object. The first weighted matrix is ​​subjected to a predetermined number of second operator transformations to obtain an improved transfer function matrix. Wherein. The second operator change can be an operator Q transformation, and the operator Q transformation usually refers to the transformation of the position operator Q in quantum mechanics. The position operator Q is an unbounded self-adjoint linear operator with a dense domain. In quantum mechanics, the position operator is used to describe the position information of the particle, and its transformation usually involves the operation of the wave function to obtain the probability distribution of the particle's position. It should be noted that each transfer function can also be subjected to a predetermined number of first operator transformations and a predetermined number of second operator transformations alternately. By performing multiple operator transformations on the transfer function matrix, the matrix condition number of the transfer function matrix is ​​reduced, so that the error of the improved transfer function matrix is ​​reduced.

[0062] Considering that the transfer function matrix is ​​seriously ill-conditioned at some frequency points, when there is measurement noise, the virtual load There will be a large error in the solution of the power spectral density function S of the random excitation.ff (ω) is an error estimate. The condition number of a matrix is ​​used to describe the degree of ill-conditioning of the matrix. For the transfer function matrix If all its rows or columns have the same norm, the matrix is ​​balanced, and under this condition, the matrix has a better condition number. In the prior art, some techniques for random load identification reduce the frequency response function matrix condition number by selecting a left-multiplied diagonal weighting matrix Z(ω) to improve the accuracy of the solution:

[0063]

[0064] And satisfy:

[0065] cond[Z(ω)H(ω)] <cond[J(ω)] (7),

[0066] in cond[] represents the condition number of the matrix, but this method only balances each row vector of the transfer function matrix H(ω), that is, it ensures that all rows in the obtained matrix Z(ω)H(ω) have the same Euclidean norm.

[0067] Based on this, this embodiment further improves formula (6) based on the idea of ​​matrix balance:

[0068] P(ω)H(ω)Q(ω)F j (ω)=Y j (ω),j=1,2,…,r y (7)

[0069] in, P(ω) and Q(ω) are diagonal matrices used to adjust the matrix condition number. The improved transfer function is determined by the following process: First, for the transfer function matrix Defining Operators Sum Operator

[0070] in γ is the introduced magnification factor. When γ=1, the operator After the transformation, all rows of the resulting matrix will have the same Euclidean norm, and after the operator After the transformation, all columns of the obtained matrix will have the same Euclidean norm. Therefore, the transfer function matrix H is processed n times Transform and n times Transform To reduce the condition number of the matrix, it should be noted that each transfer function can also be subjected to a predetermined number of first operator transformations and a predetermined number of second operator transformations alternately, as shown below:

[0071]

[0072] Among them, H 2n =PHQ is regarded as the final transfer matrix after adjustment, and for convenience it is recorded as That is, the improved transfer function matrix. and is a diagonal matrix used to adjust the matrix condition number. Since the dimension of matrix H is generally not large for random load identification, the calculation of formula (10) is relatively simple and has high efficiency. In order to solve the problem that the transfer function matrix is ​​seriously ill-conditioned at the frequency point near the natural frequency of the structure, a double-sided balance method is adopted to effectively reduce the condition number of the ill-conditioned matrix by left-multiplying and right-multiplying the diagonal matrix, which has higher random load identification accuracy than the quasi-virtual excitation method and the traditional weighted matrix method. The idea of ​​double-sided matrix balance, through simple calculations, obtains the left-multiplied and right-multiplied diagonal weighted matrices of the transfer function matrix, effectively reduces the condition number of the transfer function matrix, and improves the ill-conditioned problem of solving the random load identification equation.

[0073] In some embodiments, determining the virtual load based on the virtual acceleration response value and each improved transfer function matrix includes: determining a target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix; determining the virtual load based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix.

[0074] In this embodiment, the regularization parameter λ Tikh,j (ω) can be determined by the generalized cross-validation criterion. The generalized cross-validation criterion can be expressed as:

[0075]

[0076] Among them, tr() represents the trace of the matrix, and the regularization parameter λ Tikh,j (ω) is G cv (λ) is the point at which it takes the minimum value.

[0077] When there is measurement noise, that is, Y j (ω) has errors. The corresponding formula for regularizing the problem can effectively improve the identification error caused by small singular values ​​in the matrix. However, in the process of random load PSD identification, two aspects still need to be considered. First, for The virtual acceleration response is obtained by decomposing the power spectrum density of the measured acceleration response Large eigenvalues yj (ω), a small regularization parameter is needed to ensure that more measurement response information is included. However, for small eigenvalues ​​λ yj (ω), but it is necessary to increase the regularization parameter to reduce the influence of measurement error. Secondly, in the low frequency band and near the natural frequency of the structure, the transfer matrix is ​​improved The condition number is large and the pathology is serious. If the same regularization method is still used for the frequency points with less pathological degree, overfitting problem may occur. Therefore, it is necessary to adjust the regularization parameter λ Tikh,j Improvements are made. Based on the virtual acceleration response value and each improved transfer function matrix, the target regularization parameter corresponding to each transfer function matrix is ​​determined. The target regularization parameter can eliminate the overfitting problem of the improved transfer function matrix. In the solution of the dynamic load identification equation, the Tikhonov regularization method is combined to propose an improved regularization parameter selection method, which fully considers the influence of the virtual acceleration response value and the condition number of the improved transfer function matrix after the measured response spectrum decomposition, effectively solves the ill-posed problem in the solution, and further improves the identification accuracy of the load PSD. Based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix, the virtual load is determined. The improved transfer function eliminates the overfitting problem through the target regularization parameter, further ensuring the accuracy of the determination of the virtual load.

[0078] In some embodiments, determining the target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix includes: determining the target regularization parameter by the following formula:

[0079] in, is the target regularization parameter, Represents the transfer matrix on the entire load identification band The condition number, max means to find the maximum value, λ Yj (ω)=P j λ yj (ω), P j is the jth diagonal element of the diagonal matrix P, λ yj (ω) is the eigenvalue corresponding to the first power spectrum density, max(λ Yj (ω)) represents the value for j = 1, 2, ..., r y The largest λ Yj (ω), P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, λ Tikh,j(ω) is a predetermined regularization parameter, and ω represents a frequency value.

[0080] In this embodiment, the regularization parameter λ Tikh,j (ω) can be determined by the generalized cross-validation criterion, but the regularization parameter λ Tikh,j (ω) may lead to overfitting problem in the improved transfer function matrix, so the regularization parameter λ needs to be adjusted. Tikh,j (ω) is improved. Get or calculate the regularization parameter λ Tikh,j (ω) improving multiple parameters related to the improvement, wherein the multiple parameters include a virtual acceleration response value and each improved transfer function matrix, and based on the multiple parameters, a target regularization parameter is calculated to eliminate the overfitting problem of the improved transfer function.

[0081] In some embodiments, determining the virtual load based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix includes: determining the virtual load by the following formula: in, is the virtual load, Q(ω) is the second diagonal matrix used to adjust the matrix condition number, F j (ω) is the regularization parameter An approximate solution of i (ω) is determined using the i-th improved transfer function matrix The singular values ​​of is the target regularization parameter, u i (ω) is determined using the i-th improved transfer function matrix The left orthogonal singular value vector, v i (ω) is determined using the i-th improved transfer function matrix The right orthogonal singular value vectors of , P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, m f is the total number of all improved functions, and ω represents the frequency value.

[0082] In this embodiment, the pseudo-inverse or regularization method can be used to Solve to obtain virtual loads The traditional IPEM can obtain the PSD S of the random excitation to be identified based on the measured response PSD. ff(ω). Since the frequency response function matrix is ​​severely ill-conditioned near the natural frequency of the structure, even if there is a small error in the measured structural response, the solution of equation (12) will cause a large deviation in the PSD of the load to be identified. Therefore, it is necessary to improve and optimize the original IPEM to obtain a more accurate load PSD at each frequency point. In addition, in order to ensure that the established equation (12) satisfies the virtual load To solve a positive or overdetermined system of equations, the number of measurement points generally needs to be greater than the number of loading points, i.e., m y ≥m f .

[0083] Through the operator of formula (10) The improved virtual load identification equation shown in equation (7) is obtained by transforming . Under the premise of considering the measurement response noise, according to the Tikhonov regularization method, the ill-conditioned equation (7) can be transformed into an optimization problem for solution:

[0084]

[0085] in λ Tikh,j (ω) represents the corresponding regularization parameter. The regular solution of the representation problem is combined with the singular value decomposition technique to achieve the purpose of accurately determining the virtual load. The solution can be expressed as:

[0086]

[0087] in, σ i (ω),u i (ω) and v i (ω) are The singular values ​​of and the orthogonal singular value vectors on the left and right,

[0088] In some embodiments, determining the second power spectrum density corresponding to the random load based on the virtual load includes: determining the second power spectrum density by the following formula: Among them, S ff (ω) is the second power spectral density, is the virtual load, [] * represents taking the complex conjugate, [] T represents the transpose, ω represents the frequency value, r y is the rank corresponding to the first power spectral density.

[0089] In this embodiment, the product of the load and the value after the load is subjected to complex conjugate processing and transposition processing is calculated to obtain the product value, and ry The product values ​​are added to obtain the second power spectrum density. After determining the virtual load, the second power spectrum density corresponding to the random load can be determined using the virtual load. Since the determined virtual load is accurate, the second power spectrum density determined using the virtual load is also accurate. Based on the traditional Tikhonov regularization and generalized cross-validation criterion, this embodiment fully considers the condition number of the transfer matrix and the virtual acceleration response value of the first power spectrum density, and proposes an improved regularization parameter selection strategy, which further alleviates the ill-posed problem in the identification process and improves the identification accuracy of the second power spectrum density of the random load. Among them, Tikhonov regularization is a method for preventing overfitting by introducing additional penalty terms in the optimization process. The generalized cross-validation criterion (GCV) is a method for selecting model parameters, especially in ridge regression and other regularization methods. GCV selects the optimal model parameters by minimizing the unbiased estimate of the test error, thereby avoiding the problems of overfitting and underfitting.

[0090] In another embodiment provided by the present application, after determining the second power spectrum density, a numerical example is performed to verify: in order to quantitatively check the accuracy of the load identification method, a 2-norm error over the entire frequency band is introduced:

[0091]

[0092] Among them, P id The identification result of the second power spectrum density representing the load over the entire frequency band, P b represents the corresponding benchmark solution.

[0093] A uniform Euler-Bernoulli cantilever beam loaded at two points is Figure 2 As shown, it is divided into 10 units, where the length of the beam is 1m and the elastic modulus is E = 2×10 11 Pa, the moment of inertia is I = 3 × 10 -6 m-4, density is ρ=7800kg / m3, damping ratio is 0.02. The first five natural frequencies of the structure are 4.91Hz, 30.76Hz, 86.11Hz, 168.77Hz, 278.98Hz, and the PSD function S of the real loads f1 and F2 ff for

[0094]

[0095] in,

[0096]

[0097] Based on the given real loads f1, f2, the random acceleration response of the cantilever beam structure is calculated, and noise is added to the calculated acceleration response to simulate the actual measurement data. The two loads to be identified f1, f2 and the 10 candidate acceleration response measurement point locations (1-10) are as follows: Figure 2 In order to improve the recognition accuracy, we can usually select a better combination of measurement positions according to the actual number of sensors to meet The condition number of the frequency response function matrix H(ω) in is low. Table 1 shows the measurement points when the number of sensors is 4 (the measurement points are 4, 5, 6, 10 and 2, 6, 7, 10 respectively). Figure 2 The position shown refers to the position where the sensor is placed on the cantilever beam, and the acceleration response of this position is measured). The frequency response function matrix condition numbers near the first 4 natural frequencies under different methods show that compared with the traditional transfer matrix (TTF) h(ω) and the traditional weighted transfer function (TWTF) matrix z(ω)h(ω) obtained by the single-sided balancing method, the improved weighted transfer function (MWTF) matrix P(ω)H(ω)Q(ω) obtained by the matrix double-sided balancing method proposed in this application has a better condition number. Figure 3 shows the condition numbers after different balancing transformations using the method of this application when the measuring points are 4, 5, 6 and 10: Figure 3(a) is when the frequency point is 5Hz; Figure 3(b) is when the frequency point is 87Hz. Combined with Figure 3, it can be found that after the first two balancing transformations (one Transform and once After the third balance transformation), the condition number of the matrix can be greatly reduced (the degree of 0 indicates the original condition number of the matrix), and the improvement effect of the condition number after the third balance transformation is very small. Figures 4 and 5 and Table 2 show the specific identification PSD curves and the corresponding relative errors at different measuring points. It can be found that when combined with traditional IPEM (using TTF), there will be large errors in the identification results at the frequency points near the natural frequency of the structure. When the balance matrix is ​​introduced (using TWTF), the identification results can be improved. Among them, Figure 4 shows the identification results of the power spectrum density of the load when the measuring points are 4, 5, 6 and 10: Figure 4 (a) is the first row and first column element S of the power spectrum density 11 The recognition result of the curve with frequency change; Figure 4(b) is the first row and second column element S of the power spectrum density 12 The recognition result of the curve of the real part changing with frequency; (c) The figure shows the first row and second column element S of the power spectrum density 12 The recognition result of the imaginary part changing with frequency; Figure 4(d) is the second row and second column element S of the power spectrum density 22 Figure 5 shows the identification results of the power spectrum density of the load when the measuring point positions are 2, 6, 7 and 10: Figure 5 (a) shows the first row and first column element S of the power spectrum density.11 The recognition result of the curve with frequency change; Figure 5(b) is the first row and second column element S of the power spectrum density 12 The recognition result of the curve of the real part changing with frequency; Figure 5(c) is the first row and second column element S of the power spectrum density 12 The recognition result of the imaginary part changing with frequency; Figure 5(d) is the second row and second column element S of the power spectrum density 22 The recognition result of the curve changing with frequency. It should be noted that the frequency point is a specific value in the frequency. This application further improves the introduced balance matrix (using MWTF) and obtains the best recognition result, especially the recognition accuracy at the frequency points near the natural frequency of the structure is improved, which fully verifies the effectiveness of the method proposed in this application.

[0098] Table 1 Condition numbers of the transfer function matrix at frequency points near the natural frequency

[0099]

[0100] Table 2 Relative error R of load PSD under different identification methods

[0101]

[0102] It should be explained that TTF in Table 1 is the abbreviation of the traditional transfer function matrix, TWTF is the abbreviation of the traditional weighted transfer function matrix obtained by the single-sided balancing method, and MWTF is the improved weighted transfer function matrix obtained by the matrix double-sided balancing method proposed in this application. 11 is the first row and first column element of the power spectrum density, Real(S 12 ) is the real part of the first row and second column element of the power spectrum density, Imag(S 12 ) is the imaginary part of the first row and second column element of the power spectrum density, S 22 It is the second row and second column element of the power spectral density.

[0103] It should be noted that the method of the embodiment of the present application can be performed by a single device, such as a computer or server. The method of this embodiment can also be applied to a distributed scenario and completed by multiple devices cooperating with each other. In the case of such a distributed scenario, one of the multiple devices can only perform one or more steps in the method of the embodiment of the present application, and the multiple devices will interact with each other to complete the described method.

[0104] It should be noted that the above describes some embodiments of the present application. Other embodiments are within the scope of the appended claims. In some cases, the actions or steps recorded in the claims can be performed in an order different from that in the above embodiments and still achieve the desired results. In addition, the processes depicted in the accompanying drawings do not necessarily require the specific order or continuous order shown to achieve the desired results. In some embodiments, multitasking and parallel processing are also possible or may be advantageous.

[0105] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a device for determining the power spectrum density of random loads on an engineering structure.

[0106] refer to Figure 6 , the power spectrum density determination device of the random load of the engineering structure comprises:

[0107] The decomposition module 10 is configured to obtain a first power spectrum density corresponding to the acceleration associated with the engineering structure, perform spectrum decomposition on the first power spectrum density, and obtain a virtual acceleration response value.

[0108] The acquisition module 20 is configured to acquire a transfer function matrix corresponding to each frequency point in the first power spectrum density based on the engineering parameters of the engineering structure.

[0109] The transformation module 30 is configured to perform a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix.

[0110] The determination module 40 is configured to determine a virtual load based on the virtual acceleration response value and each improved transfer function matrix, and determine a second power spectrum density corresponding to the random load based on the virtual load.

[0111] Through the above-mentioned device, the first power spectrum density corresponding to the acceleration associated with the engineering structure is obtained, and the first power spectrum density is spectrally decomposed to obtain a virtual acceleration response value, and the vibration characteristics of the engineering structure at different frequencies are analyzed. Based on the engineering parameters of the engineering structure, the transfer function matrix corresponding to each frequency point in the first power spectrum density is obtained, so that multiple transfer function matrices are close to the actual engineering structure, which lays the foundation for accurately calculating the load on the engineering structure. A bilateral balanced transformation is performed on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix, ensuring that there are relatively few matrix condition numbers in the transfer function matrix, so as to achieve the purpose of reducing the error of the transfer function matrix. Based on the virtual acceleration response value and each improved transfer function matrix, the virtual load is determined, and based on the virtual load, the second power spectrum density corresponding to the random load is determined, so as to achieve the purpose of accurately determining the virtual load and the second power spectrum density.

[0112] In some embodiments, the decomposition module 10 is further configured to perform spectral decomposition on the first power spectrum density by using the following formula: in, is the first power spectral density, λ yj (ω) is the jth eigenvalue corresponding to the first power spectrum density, is the jth eigenvector corresponding to the first power spectral density, [] * represents taking the complex conjugate, [] T Indicates taking the transpose, r y is the rank corresponding to the first power spectral density, is the virtual acceleration response value, ω represents a frequency value.

[0113] In some embodiments, the transformation module 30 is further configured to, for each transfer function matrix, perform a first operator transformation on the transfer function matrix a predetermined number of times to obtain a first weighting matrix, and perform a second operator transformation on the first weighting matrix a predetermined number of times to obtain the improved transfer function matrix.

[0114] In some embodiments, the determination module 40 is further configured to determine a target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix; and determine the virtual load based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix.

[0115] In some embodiments, the determination module 40 is further configured to determine the target regularization parameter by the following formula: in, is the target regularization parameter, Represents the transfer matrix on the entire load identification band The condition number, max means to find the maximum value, λ Yj (ω)=P j λ yj (ω), P j is the jth diagonal element of the diagonal matrix P, λ yj (ω) is the eigenvalue corresponding to the first power spectrum density, max(λ Yj (ω)) represents the value for j = 1, 2, ..., r y The largest λ Yj (ω), P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, λ Tikh,j(ω) is a predetermined regularization parameter, and ω represents a frequency value.

[0116] In some embodiments, the determination module 40 is further configured to determine the virtual load by the following formula: in, is the virtual load, Q(ω) is the second diagonal matrix used to adjust the matrix condition number, F j (ω) is the regularization parameter An approximate solution of i (ω) is determined using the i-th improved transfer function matrix The singular values ​​of is the target regularization parameter, u i (ω) is determined using the i-th improved transfer function matrix The left orthogonal singular value vector, v i (ω) is determined using the i-th improved transfer function matrix The right orthogonal singular value vectors of , P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, m f is the total number of all improved functions, and ω represents the frequency value.

[0117] In some embodiments, the determination module 40 is further configured to determine the second power spectrum density by the following formula: Among them, S ff (ω) is the second power spectral density, is the virtual load, [] * represents taking the complex conjugate, [] T represents the transpose, ω represents the frequency value, r y is the rank corresponding to the first power spectral density.

[0118] For the convenience of description, the above device is described in terms of functions divided into various modules. Of course, when implementing the present application, the functions of each module can be implemented in the same or multiple software and / or hardware.

[0119] The device of the above embodiment is used to implement the power spectrum density determination method of the random load of the engineering structure corresponding to any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be repeated here.

[0120] Based on the same inventive concept, corresponding to any of the above-mentioned embodiments and methods, the present application also provides an electronic device, including a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the program, the method for determining the power spectral density of random loads on an engineering structure as described in any of the above embodiments is implemented.

[0121] Figure 7 A more specific schematic diagram of the hardware structure of an electronic device provided in this embodiment is shown, and the device may include: a processor 1010, a memory 1020, an input / output interface 1030, a communication interface 1040, and a bus 1050. The processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040 are connected to each other through the bus 1050 in the device.

[0122] The processor 1010 can be implemented by a general-purpose CPU (Central Processing Unit), a microprocessor, an application-specific integrated circuit (ASIC), or one or more integrated circuits, and is used to execute relevant programs to implement the technical solutions provided in the embodiments of this specification.

[0123] The memory 1020 may be implemented in the form of ROM (Read Only Memory), RAM (Random Access Memory), static storage device, dynamic storage device, etc. The memory 1020 may store an operating system and other application programs. When the technical solutions provided in the embodiments of this specification are implemented by software or firmware, the relevant program codes are stored in the memory 1020 and are called and executed by the processor 1010.

[0124] The input / output interface 1030 is used to connect the input / output module to realize information input and output. The input / output module can be configured in the device as a component (not shown in the figure), or it can be externally connected to the device to provide corresponding functions. The input device may include a keyboard, a mouse, a touch screen, a microphone, various sensors, etc., and the output device may include a display, a speaker, a vibrator, an indicator light, etc.

[0125] The communication interface 1040 is used to connect a communication module (not shown) to realize communication interaction between the device and other devices. The communication module can realize communication through a wired mode (such as USB, network cable, etc.) or a wireless mode (such as mobile network, WIFI, Bluetooth, etc.).

[0126] The bus 1050 includes a path that transmits information between the various components of the device (eg, the processor 1010, the memory 1020, the input / output interface 1030, and the communication interface 1040).

[0127] It should be noted that, although the above device only shows the processor 1010, the memory 1020, the input / output interface 1030, the communication interface 1040 and the bus 1050, in the specific implementation process, the device may also include other components necessary for normal operation. In addition, it can be understood by those skilled in the art that the above device may also only include the components necessary for implementing the embodiments of the present specification, and does not necessarily include all the components shown in the figure.

[0128] The electronic device of the above embodiment is used to implement the corresponding method for determining the power spectrum density of the random load of the engineering structure in any of the above embodiments, and has the beneficial effects of the corresponding method embodiment, which will not be described in detail here.

[0129] Based on the same inventive concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a non-transitory computer-readable storage medium, wherein the non-transitory computer-readable storage medium stores computer instructions, and the computer instructions are used to enable the computer to execute the method for determining the power spectral density of random loads on engineering structures as described in any of the above embodiments.

[0130] The computer-readable medium of this embodiment includes permanent and non-permanent, removable and non-removable media, and information storage can be implemented by any method or technology. Information can be computer-readable instructions, data structures, modules of programs, or other data. Examples of computer storage media include, but are not limited to, phase change memory (PRAM), static random access memory (SRAM), dynamic random access memory (DRAM), other types of random access memory (RAM), read-only memory (ROM), electrically erasable programmable read-only memory (EEPROM), flash memory or other memory technology, read-only compact disk read-only memory (CD-ROM), digital versatile disk (DVD) or other optical storage, magnetic cassettes, tape disk storage or other magnetic storage devices or any other non-transmission media that can be used to store information that can be accessed by a computing device.

[0131] The computer instructions stored in the storage medium of the above embodiment are used to enable the computer to execute the method for determining the power spectral density of random loads on engineering structures as described in any of the above embodiments, and have the beneficial effects of the corresponding method embodiments, which will not be repeated here.

[0132] Based on the same concept, corresponding to any of the above-mentioned embodiment methods, the present application also provides a computer program product, including computer program instructions. When the computer program instructions are run on a computer, the computer executes the method for determining the power spectral density of random loads on engineering structures as described in any of the above embodiments, which has the beneficial effects of the corresponding method embodiments and will not be repeated here.

[0133] It should be noted that the embodiments of the present application can be further described in the following manner:

[0134] It is understandable that before using the technical solutions of each embodiment of the present disclosure, the type, scope of use, usage scenarios, etc. of the personal information involved will be informed to the user in an appropriate manner, and the user's authorization will be obtained.

[0135] For example, in response to receiving an active request from a user, a prompt message is sent to the user to clearly remind the user that the operation requested to be performed will require obtaining and using the user's personal information. Thus, the user can independently choose whether to provide personal information to software or hardware such as an electronic device, application, server, or storage medium that performs the operation of the technical solution of the present disclosure according to the prompt message.

[0136] As an optional but non-limiting implementation, in response to receiving the user's active request, the prompt information may be sent to the user in the form of a pop-up window, in which the prompt information may be presented in text form. In addition, the pop-up window may also carry a selection control for the user to choose "agree" or "disagree" to provide personal information to the electronic device.

[0137] It is understandable that the above notification and the process of obtaining user authorization are merely illustrative and do not constitute a limitation on the implementation of the present disclosure. Other methods that meet relevant laws and regulations may also be applied to the implementation of the present disclosure.

[0138] A person skilled in the art should understand that the discussion of any of the above embodiments is merely illustrative and is not intended to imply that the scope of the present application is limited to these examples. In line with the concept of the present application, the technical features in the above embodiments or different embodiments may be combined, the steps may be implemented in any order, and there are many other variations of the different aspects of the embodiments of the present application as described above, which are not provided in detail for the sake of simplicity.

[0139] In addition, to simplify the description and discussion, and in order not to make the embodiments of the present application difficult to understand, the known power supply / ground connection with the integrated circuit (IC) chip and other components may or may not be shown in the provided drawings. In addition, the device can be shown in the form of a block diagram to avoid making the embodiments of the present application difficult to understand, and this also takes into account the fact that the details of the implementation of these block diagram devices are highly dependent on the platform to be implemented in the embodiments of the present application (that is, these details should be fully within the scope of understanding of those skilled in the art). In the case of elaborating specific details (e.g., circuits) to describe exemplary embodiments of the present application, it is obvious to those skilled in the art that the embodiments of the present application can be implemented without these specific details or when these specific details are changed. Therefore, these descriptions should be considered to be illustrative rather than restrictive.

[0140] Although the present application has been described in conjunction with specific embodiments of the present application, many replacements, modifications and variations of these embodiments will be apparent to those skilled in the art from the foregoing description. For example, other memory architectures (e.g., dynamic RAM (DRAM)) may use the embodiments discussed.

[0141] The embodiments of the present application are intended to cover all such substitutions, modifications and variations that fall within the broad scope of the present application. Therefore, any omissions, modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the embodiments of the present application should be included in the protection scope of the present application.

Claims

1. A method for determining the power spectral density of random loads of an engineering structure, characterized in that: include: Acquiring a first power spectrum density corresponding to the acceleration associated with the engineering structure, and performing spectral decomposition on the first power spectrum density to obtain a virtual acceleration response value; Based on the engineering parameters of the engineering structure, obtaining a transfer function matrix corresponding to each frequency point in the first power spectrum density; Performing bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix; A virtual load is determined based on the virtual acceleration response value and each improved transfer function matrix, and a second power spectrum density corresponding to the random load is determined based on the virtual load.

2. The method according to claim 1, characterized in that The performing spectral decomposition on the first power spectrum density to obtain a virtual acceleration response value includes: The first power spectral density is spectrally decomposed by the following formula: in, is the first power spectral density, λ yj (ω) is the jth eigenvalue corresponding to the first power spectrum density, is the jth eigenvector corresponding to the first power spectral density, [] * represents taking the complex conjugate, [] T Indicates taking the transpose, r y is the rank corresponding to the first power spectral density, is the virtual acceleration response value, ω represents a frequency value.

3. The method according to claim 1, characterized in that The step of performing a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix includes: For each transfer function matrix, a first operator transformation is performed on the transfer function matrix a predetermined number of times to obtain a first weighting matrix, and a second operator transformation is performed on the first weighting matrix a predetermined number of times to obtain the improved transfer function matrix.

4. The method according to claim 1, characterized in that: The determining of the virtual load based on the virtual acceleration response value and each improved transfer function matrix comprises: Determining a target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix; The virtual load is determined based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix.

5. The method according to claim 4, characterized in that The step of determining a target regularization parameter corresponding to each transfer function matrix based on the virtual acceleration response value and each improved transfer function matrix comprises: The target regularization parameter is determined by the following formula: in, is the target regularization parameter, Represents the transfer matrix on the entire load identification band The condition number, max means to find the maximum value, λ Yj (ω)=P j λ yj (ω), P j is the jth diagonal element of the diagonal matrix P, λ yj (ω) is the eigenvalue corresponding to the first power spectrum density, max(λ Yj (ω)) represents the value for j=1,2,…,r y The largest λ Yj (ω), P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, λ Tikh,j (ω) is a predetermined regularization parameter, and ω represents a frequency value.

6. The method according to claim 4, characterized in that The determining the virtual load based on the target regularization parameter, the virtual acceleration response value and each improved transfer function matrix comprises: The virtual load is determined by the following formula: in, is the virtual load, Q(ω) is the second diagonal matrix used to adjust the matrix condition number, F j (ω) is the regularization parameter An approximate solution of i (ω) is determined using the i-th improved transfer function matrix The singular values ​​of is the target regularization parameter, u i (ω) is determined using the i-th improved transfer function matrix The left orthogonal singular value vector, v i (ω) is determined using the i-th improved transfer function matrix The right orthogonal singular value vectors of , P(ω) is the first diagonal matrix used to adjust the matrix condition number, is the virtual acceleration response value, m f is the total number of all improved functions, and ω represents the frequency value.

7. The method according to claim 1, characterized in that The determining, based on the virtual load, a second power spectrum density corresponding to the random load includes: The second power spectral density is determined by the following formula: Among them, S ff (ω) is the second power spectral density, is the virtual load, [] * represents taking the complex conjugate, [] T represents the transpose, ω represents the frequency value, r y is the rank corresponding to the first power spectral density.

8. A device for determining the power spectrum density of random loads of an engineering structure, characterized in that: include: a decomposition module configured to obtain a first power spectrum density corresponding to the acceleration associated with the engineering structure, perform spectrum decomposition on the first power spectrum density, and obtain a virtual acceleration response value; an acquisition module, configured to acquire a transfer function matrix corresponding to each frequency point in the first power spectrum density based on the engineering parameters of the engineering structure; A transformation module is configured to perform a bilateral balanced transformation on each transfer function matrix to obtain an improved transfer function matrix corresponding to each transfer function matrix; The determination module is configured to determine a virtual load based on the virtual acceleration response value and each improved transfer function matrix, and determine a second power spectrum density corresponding to the random load based on the virtual load.

9. An electronic device comprising a memory, a processor, and a computer program stored in the memory and running on the processor, characterized in that: When the processor executes the program, the method according to any one of claims 1 to 7 is implemented.

10. A non-transitory computer-readable storage medium storing computer instructions, characterized in that: The computer instructions are used to enable a computer to execute the method according to any one of claims 1 to 7.

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