A method for evaluating oil-paper insulation condition based on harmonic-discharge coupling analysis

Abstract

The present invention proposes a method and system for evaluating the state of oil-paper insulation based on harmonic-discharge coupling analysis, which relates to the technical field of transformer oil-paper insulation. The method comprises the following steps: configuring harmonic parameters, extracting the time-frequency energy distribution of each harmonic using a Morlet wavelet convolution kernel to construct a harmonic fingerprint matrix, collecting oil-paper insulation data to construct nonlinear cross features to generate an enhanced feature vector, calculating the dynamic attention weight of each harmonic component on the insulation state, and performing dual-channel degradation evaluation through the equivalent circuit equation of the physical channel and the attention LSTM network of the data channel to obtain the harmonic impact factor and state evaluation matrix. Finally, the HIF index is calculated by weighted fusion of the harmonic frequency offset and the amplitude exceeding the standard, and the evaluation result is output according to the HIF index. The present invention solves the problems of insufficient accuracy and poor interpretability of traditional methods in complex harmonic coupling scenarios, and significantly improves the accuracy and engineering applicability of oil-paper insulation state evaluation.

Description

Technical Field

[0001] The present invention relates to the technical field of transformer oil-paper insulation, and in particular to an oil-paper insulation state evaluation method based on harmonic-discharge coupling analysis. Background Art

[0002] With the rapid development of my country's power industry, power transmission and transformation equipment is moving towards larger capacity and higher voltage. 500kV AC and DC electrical equipment are widely used and have become a core component of power grid systems. Oil-immersed high-voltage transformers are one of the most critical components and, therefore, must offer high reliability to ensure safe and efficient operation of the power grid. This insulation system primarily consists of a composite insulating medium composed of oil and paper. Traditional oil-immersed high-voltage transformers use cellulose paper for insulation. Consequently, a growing number of high-voltage transformers are adopting new insulation papers to ensure optimal operation.

[0003] However, traditional oil-paper insulation condition assessment methods have significant limitations: First, existing technologies are mostly designed based on power frequency conditions and fail to effectively quantify the nonlinear coupling effect of harmonic frequency and content on discharge characteristics, resulting in assessment errors exceeding 35% under complex working conditions containing high-order harmonics (such as new energy grid-connected scenarios); second, although pure data-driven models (such as traditional LSTM and CNN) can extract discharge characteristics, they cannot establish the correlation between characteristic parameters and physical aging mechanisms such as electric field distortion and thermal stress, which violates the IEC 60599 standard's requirements for interpretability of insulation condition assessment; finally, existing methods rely on single indicators such as partial discharge inception voltage (PDIV) or dielectric loss tangent, which makes it difficult to characterize the synergistic degradation effects caused by the superposition of multiple harmonics (such as the coupling effect of high-frequency harmonics accelerating cellulose hydrolysis and low-frequency harmonics inducing local overheating). Summary of the Invention

[0004] The purpose of the present invention is to provide an oil-paper insulation status assessment method based on harmonic-discharge coupling analysis, which can accurately assess the oil-paper insulation status of the transformer, improve the insulation level of the water high-voltage transformer, and maintain the safe and stable operation of the high-voltage transformer.

[0005] The technical solution of the present invention is:

[0006] The present application provides a method for evaluating the state of oil-paper insulation based on harmonic-discharge coupling analysis, which comprises the following steps:

[0007] S1. Configure harmonic parameters and use Morlet wavelet convolution kernel to extract the time-frequency energy distribution of each harmonic according to the configured harmonic parameters to construct a harmonic fingerprint matrix;

[0008] S2, collecting oil-paper insulation data to construct nonlinear cross features to generate enhanced feature vectors;

[0009] S3, calculating the dynamic attention weight of each harmonic component on the insulation state according to the harmonic fingerprint matrix and the enhanced eigenvector;

[0010] S4. Based on the dynamic attention weight of each harmonic component on the insulation state, dual-channel degradation evaluation is performed through the equivalent circuit equation of the physical channel and the attention LSTM network of the data channel to obtain the harmonic impact factor and state evaluation matrix;

[0011] S5. Based on the harmonic impact factor and the state assessment matrix, the HIF index is calculated by weighted fusion of the harmonic frequency offset and the amplitude exceeding the standard, and the assessment result is output according to the HIF index.

[0012] Furthermore, in step S1, the harmonic parameters include harmonic frequency and harmonic content.

[0013] Furthermore, in step S1, the time-frequency energy distribution of each harmonic extracted by the Morlet wavelet convolution kernel satisfies:

[0014] ,

[0015] Where, g represents the time-frequency joint distribution function, t Indicates time, f k represents the kth frequency component, j represents the imaginary unit, s k Indicates the bandwidth parameter.

[0016] Furthermore, in step S2, the oil-paper insulation data include partial discharge inception voltage, average discharge capacity, maximum discharge capacity and discharge repetition rate.

[0017] Furthermore, in step S2, the calculation process of collecting oil-paper insulation data to construct nonlinear cross features to generate enhanced feature vectors includes:

[0018] Extract the local discharge characteristics and normalize them:

[0019] ,

[0020] ,

[0021] Generate nonlinear cross terms:

[0022] ,

[0023] Generate augmented feature vectors:

[0024] ,

[0025] Where X is the partial discharge characteristic vector, PDIV is the partial discharge inception voltage, Q max is the maximum discharge capacity, Q avg is the average discharge capacity, R discharge is the discharge repetition rate, X norm is the normalized partial discharge feature vector, is the characteristic mean of the unaged sample, is the standard deviation of the unaged sample, α is the nonlinear correlation term between discharge intensity and voltage, β is the nonlinear characteristic term of discharge quantity distribution, T represents the transpose of the matrix, is the enhanced feature vector.

[0026] Furthermore, in step S3, the calculation process of calculating the dynamic attention weight of each harmonic component on the insulation state based on the harmonic fingerprint matrix and the enhanced eigenvector includes:

[0027] Electric field distortion constraint calculation:

[0028] ,

[0029] PDIV decay rate calculation:

[0030] ,

[0031] Thermal stress constraint calculation:

[0032] ,

[0033] ,

[0034] Dynamic attention weight calculation:

[0035] ,

[0036] Where, E eff is the effective electric field distortion, n is the upper limit of harmonic order, h is the harmonic order, A h is the amplitude of the hth harmonic, f h is the frequency of the hth harmonic, ΔPDIV is the attenuation of the partial discharge inception voltage, k 1 is the attenuation proportional coefficient, k 2 is the thermal stress proportionality coefficient, E 0 is the reference electric field strength, ΔT is the temperature rise, τ agingis the aging time constant, A and B are the coefficients of the Arrhenius equation, T amb is the ambient temperature, w h is the dynamic attention weight of the h-th harmonic, σ is the Sigmoid function, A i is the amplitude of the i-th harmonic, f i is the frequency of the i-th harmonic, Q max is the maximum discharge capacity.

[0037] Furthermore, in step S4, the equivalent circuit equation of the above physical channel is:

[0038] ,

[0039] Where, Q theory is the theoretical charge, C is the equivalent capacitance, V harmontic is the harmonic voltage, t For time, R insul is the time-varying parameter of insulation resistance.

[0040] Furthermore, in step S4, the calculation formula of the attention LSTM network of the above data channel includes:

[0041] ,

[0042] ,

[0043] ,

[0044] Where, is the attention hidden state, w h is the dynamic attention weight of the hth harmonic, n is the upper limit of the harmonic order, h is the harmonic order, h t is the hth hidden state, L is the total loss function, L MSE is the mean square error loss, L SSIM is the structural similarity loss, L Phys is the physical constraint loss, is the fluctuation of the maximum discharge capacity, V is the voltage, t For time.

[0045] Furthermore, in step S5, the calculation formula of the above-mentioned state assessment matrix includes:

[0046] ,

[0047] Where, Sis the state evaluation matrix, ΔPDIV / PDIV is the rate of change of discharge starting voltage, is the fluctuation of the maximum discharge capacity, is the fluctuation of the average discharge amount, R is the current resistance value, R0 is the reference resistance value, H is the harmonic distortion rate, f is the frequency, A is the coefficient of the Arrhenius equation, t aging is the aging time constant, and HIF is the harmonic influence factor.

[0048] Furthermore, in step S5, the calculation formula for calculating the HIF index by weighted fusion of harmonic frequency offset and amplitude exceeding the standard degree includes:

[0049] ,

[0050] Where HIF is the harmonic impact factor, n is the upper limit of the harmonic order, h is the harmonic order, w h is the dynamic attention weight of the h-th harmonic, f h is the frequency of the hth harmonic, f 0 is the reference frequency, A h is the amplitude of the hth harmonic, A 0 is the reference amplitude.

[0051] Compared with the prior art, the present invention has at least the following advantages or beneficial effects:

[0052] The present invention proposes an oil-paper insulation condition assessment method based on harmonic-discharge coupling analysis. By constructing a harmonic fingerprint matrix to quantify harmonic frequency domain characteristics, the method combines a dynamic physical attention mechanism with a dual-channel degradation assessment model to achieve nonlinear mapping between harmonic parameters and partial discharge characteristics. Furthermore, the method innovatively introduces a differentiable physical constraint layer, embeds the electric field distortion model and thermal stress equation into a deep learning framework, and designs a harmonic influence factor (HIF) quantitative assessment indicator. This method addresses the problems of insufficient accuracy and poor interpretability of traditional methods in complex harmonic coupling scenarios, significantly improving the accuracy and engineering applicability of oil-paper insulation condition assessment. BRIEF DESCRIPTION OF THE DRAWINGS

[0053] In order to more clearly illustrate the technical solutions of the embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and therefore should not be regarded as limiting the scope. For ordinary technicians in this field, other relevant drawings can be obtained based on these drawings without paying any creative work.

[0054] Figure 1 This is a step diagram of a method for evaluating oil-paper insulation status based on harmonic-discharge coupling analysis of the present invention. DETAILED DESCRIPTION

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present application more clear, the technical solutions in the embodiments of the present application will be clearly and completely described below in conjunction with the accompanying drawings of the embodiments of the present application. Obviously, the described embodiments are only part of the embodiments of the present application, not all of the embodiments. Generally, the components of the embodiments of the present application described and shown in the drawings herein can be arranged and designed in various different configurations.

[0056] Therefore, the following detailed description of the embodiments of the present application provided in the accompanying drawings is not intended to limit the scope of the present application for protection, but merely represents selected embodiments of the present application. All other embodiments obtained by persons of ordinary skill in the art based on the embodiments in the present application without creative work are within the scope of protection of the present application.

[0057] It should be noted that similar reference numerals and letters denote similar items in the following drawings, and therefore, once an item is defined in one drawing, it does not need to be further defined or explained in subsequent drawings.

[0058] It should be noted that, in this document, the term "comprises" or any other variant thereof is intended to cover non-exclusive inclusion, so that a process, method, article, or apparatus that includes a series of elements includes not only those elements, but also includes other elements not explicitly listed, or also includes elements inherent to such process, method, article, or apparatus. In the absence of further limitations, the elements defined by the phrase "comprises..." do not exclude the presence of other identical elements in the process, method, article, or apparatus that includes the elements.

[0059] The following describes some embodiments of the present application in detail with reference to the accompanying drawings. In the absence of conflict, the following embodiments and features thereof may be combined with each other.

[0060] Example 1

[0061] See also Figure 1 , Figure 1 The figure shows a step diagram of an oil-paper insulation status assessment method based on harmonic-discharge coupling analysis provided in an embodiment of the present application.

[0062] The present application provides a method for evaluating the state of oil-paper insulation based on harmonic-discharge coupling analysis, which comprises the following steps:

[0063] S1. Configure harmonic parameters and use Morlet wavelet convolution kernel to extract the time-frequency energy distribution of each harmonic according to the configured harmonic parameters to construct a harmonic fingerprint matrix;

[0064] S2, collecting oil-paper insulation data to construct nonlinear cross features to generate enhanced feature vectors;

[0065] S3, calculating the dynamic attention weight of each harmonic component on the insulation state according to the harmonic fingerprint matrix and the enhanced eigenvector;

[0066] S4. Based on the dynamic attention weight of each harmonic component on the insulation state, dual-channel degradation evaluation is performed through the equivalent circuit equation of the physical channel and the attention LSTM network of the data channel to obtain the harmonic impact factor and state evaluation matrix;

[0067] S5. Based on the harmonic impact factor and the state assessment matrix, the HIF index is calculated by weighted fusion of the harmonic frequency offset and the amplitude exceeding the standard, and the assessment result is output according to the HIF index.

[0068] As a preferred implementation, in step S1, the harmonic parameters include harmonic frequency and harmonic content.

[0069] As a preferred embodiment, in step S1, the time-frequency energy distribution of each harmonic extracted by the Morlet wavelet convolution kernel satisfies:

[0070] ,

[0071] Where, g represents the time-frequency joint distribution function, t Indicates time, f k represents the kth frequency component, j represents the imaginary unit, s k Indicates the bandwidth parameter.

[0072] As a preferred embodiment, in step S2, the oil-paper insulation data includes partial discharge inception voltage, average discharge capacity, maximum discharge capacity and discharge repetition rate.

[0073] As a preferred embodiment, in step S2, the calculation process of collecting oil-paper insulation data to construct nonlinear cross features to generate enhanced feature vectors includes:

[0074] Extract the local discharge characteristics and normalize them:

[0075] ,

[0076] ,

[0077] Generate nonlinear cross terms:

[0078] ,

[0079] Generate augmented feature vectors:

[0080] ,

[0081] Where X is the partial discharge characteristic vector, PDIV is the partial discharge inception voltage, Q max is the maximum discharge capacity, Q avg is the average discharge capacity, R discharge is the discharge repetition rate, X norm is the normalized partial discharge feature vector, is the characteristic mean of the unaged sample, is the standard deviation of the unaged sample, α is the nonlinear correlation term between discharge intensity and voltage, β is the nonlinear characteristic term of discharge quantity distribution, T represents the transpose of the matrix, is the enhanced feature vector.

[0082] As a preferred embodiment, in step S3, the process of calculating the dynamic attention weight of each harmonic component on the insulation state according to the harmonic fingerprint matrix and the enhanced eigenvector includes:

[0083] Electric field distortion constraint calculation:

[0084] ,

[0085] PDIV decay rate calculation:

[0086] ,

[0087] Thermal stress constraint calculation:

[0088] ,

[0089] ,

[0090] Dynamic attention weight calculation:

[0091] ,

[0092] Where, E eff is the effective electric field distortion, n is the upper limit of harmonic order, h is the harmonic order, A h is the amplitude of the hth harmonic, f his the frequency of the hth harmonic, ΔPDIV is the attenuation of the partial discharge inception voltage, k 1 is the attenuation proportional coefficient, k 2 is the thermal stress proportionality coefficient, E 0 is the reference electric field strength, ΔT is the temperature rise, τ aging is the aging time constant, A and B are the coefficients of the Arrhenius equation, T amb is the ambient temperature, w h is the dynamic attention weight of the h-th harmonic, σ is the Sigmoid function, A i is the amplitude of the i-th harmonic, f i is the frequency of the i-th harmonic, Q max is the maximum discharge capacity.

[0093] As a preferred implementation, in step S4, the equivalent circuit equation of the physical channel is:

[0094] ,

[0095] Where, Q theory is the theoretical charge, C is the equivalent capacitance, V harmontic is the harmonic voltage, t For time, R insul is the time-varying parameter of insulation resistance.

[0096] As a preferred embodiment, in step S4, the calculation formula of the attention LSTM network of the data channel includes:

[0097] ,

[0098] ,

[0099] ,

[0100] Where, is the attention hidden state, w h is the dynamic attention weight of the hth harmonic, n is the upper limit of the harmonic order, h is the harmonic order, h t is the hth hidden state, L is the total loss function, L MSE is the mean square error loss, L SSIM is the structural similarity loss, L Phys is the physical constraint loss, is the fluctuation of the maximum discharge capacity, V is the voltage, t For time.

[0101] As a preferred embodiment, in step S5, the calculation formula of the state assessment matrix includes:

[0102] ,

[0103] Where, S is the state evaluation matrix, ΔPDIV / PDIV is the rate of change of discharge starting voltage, is the fluctuation of the maximum discharge capacity, is the fluctuation of the average discharge amount, R is the current resistance value, R0 is the reference resistance value, H is the harmonic distortion rate, f is the frequency, A is the coefficient of the Arrhenius equation, t aging is the aging time constant, and HIF is the harmonic influence factor.

[0104] As a preferred embodiment, in step S5, the calculation formula for calculating the HIF index by weighted fusion of harmonic frequency offset and amplitude exceeding the standard degree includes:

[0105] ,

[0106] Where HIF is the harmonic impact factor, n is the upper limit of the harmonic order, h is the harmonic order, w h is the dynamic attention weight of the h-th harmonic, f h is the frequency of the hth harmonic, f 0 is the reference frequency, A h is the amplitude of the hth harmonic, A 0 is the reference amplitude.

[0107] It should be understood that the structure shown in the figure is merely illustrative. A method for evaluating the oil-paper insulation condition based on harmonic-discharge coupling analysis may include more or fewer components than shown in the figure, or have a different configuration than that shown in the figure. Each component shown in the figure may be implemented using hardware, software, or a combination thereof.

[0108] In the embodiments provided in this application, it should be understood that the disclosed methods can also be implemented in other ways. The embodiments described above are merely illustrative. For example, the flowcharts or block diagrams in the accompanying drawings show the possible implementation architectures, functions and operations of the methods and computer program products according to multiple embodiments of the application. In this regard, each box in the flowchart or block diagram can represent a module, a program segment or a part of a code, and the module, program segment or a part of the code contains one or more executable instructions for implementing the specified logical functions. It should also be noted that in some alternative implementations, the functions marked in the box can also occur in an order different from that marked in the accompanying drawings. For example, two consecutive boxes can actually be executed substantially in parallel, and they can sometimes be executed in the opposite order, depending on the functions involved. It should also be noted that each box in the block diagram and / or flowchart, and the combination of boxes in the block diagram and / or flowchart, can be implemented using a dedicated hardware-based system that performs the specified function or action, or can be implemented using a combination of dedicated hardware and computer instructions.

[0109] In addition, the functional modules in each embodiment of the present application can be integrated together to form an independent part, or each module can exist independently, or two or more modules can be integrated to form an independent part.

[0110] If the functions are implemented in the form of software function modules and sold or used as independent products, they can be stored in a computer-readable storage medium. Based on this understanding, the technical solution of the present application, or the part that contributes to the prior art, or the part of the technical solution, can be embodied in the form of a software product. The computer software product is stored in a storage medium and includes a number of instructions for enabling a computer device (which can be a personal computer, server, or network device, etc.) to execute all or part of the steps of the method described in each embodiment of the present application. The aforementioned storage medium includes: various media that can store program codes, such as USB flash drives, mobile hard drives, read-only memories (ROM), random access memories (RAM), magnetic disks or optical disks.

[0111] The above description is merely a preferred embodiment of the present application and is not intended to limit the present application. Various modifications and variations are possible for those skilled in the art. Any modifications, equivalent substitutions, or improvements made within the spirit and principles of the present application shall be included within the scope of protection of the present application.

[0112] It will be apparent to those skilled in the art that the present application is not limited to the details of the exemplary embodiments described above and that the present application can be implemented in other specific forms without departing from the spirit or essential characteristics of the present application. Therefore, the embodiments should be considered in all respects as illustrative and non-restrictive, and the scope of the present application is defined by the appended claims, not the foregoing description, and all variations within the meaning and range of equivalents of the claims are intended to be included therein. Any reference sign in a claim should not be construed as limiting the claim to which it relates.

Claims

1. A method for evaluating the state of oil-paper insulation based on harmonic-discharge coupling analysis, characterized in that: The following steps are involved: S1. Configure harmonic parameters and use Morlet wavelet convolution kernel to extract the time-frequency energy distribution of each harmonic according to the configured harmonic parameters to construct a harmonic fingerprint matrix; S2, collecting oil-paper insulation data to construct nonlinear cross features to generate enhanced feature vectors; S3. Calculate the dynamic attention weight of each harmonic component on the insulation state based on the harmonic fingerprint matrix and the enhanced eigenvector. The calculation process includes: Electric field distortion constraint calculation: ， PDIV decay rate calculation: ， Thermal stress constraint calculation: ， ， Dynamic attention weight calculation: ， Where, E eff is the effective electric field distortion, n is the upper limit of harmonic order, h is the harmonic order, A h is the amplitude of the hth harmonic, f h is the frequency of the hth harmonic, ΔPDIV is the attenuation of the partial discharge inception voltage, k 1 is the attenuation proportional coefficient, k 2 is the thermal stress proportionality coefficient, E 0 is the reference electric field strength, ΔT is the temperature rise, τ aging is the aging time constant, A and B are the coefficients of the Arrhenius equation, T amb is the ambient temperature, w h is the dynamic attention weight of the h-th harmonic, σ is the Sigmoid function, A i is the amplitude of the i-th harmonic, f i is the frequency of the i-th harmonic, Q max is the maximum discharge capacity; S4. Based on the dynamic attention weight of each harmonic component on the insulation state, a dual-channel degradation assessment is performed using the equivalent circuit equation of the physical channel and the attention LSTM network of the data channel to obtain the harmonic impact factor and the state assessment matrix; wherein the calculation formula of the attention LSTM network of the data channel includes: ， ， ， Where, is the attention hidden state, For the h Dynamic attention weights for subharmonics, is the upper limit of harmonic order, is the harmonic order, For the hidden states, is the total loss function, is the mean square error loss, is the structural similarity loss, is the physical constraint loss, is the fluctuation of the maximum discharge capacity, is the voltage, For time; S5. Based on the harmonic impact factor and the state assessment matrix, the HIF index is calculated by weighted fusion of the harmonic frequency offset and the amplitude exceeding the standard, and the assessment result is output according to the HIF index.

2. The oil-paper insulation state assessment method based on harmonic-discharge coupling analysis according to claim 1, characterized in that: In step S1, the harmonic parameters include harmonic frequency and harmonic content.

3. The oil-paper insulation state evaluation method based on harmonic-discharge coupling analysis according to claim 1, characterized in that: In step S1, the time-frequency energy distribution of each harmonic extracted by the Morlet wavelet convolution kernel satisfies: Where, g represents the time-frequency joint distribution function, t Indicates time, f k represents the kth frequency component, j represents the imaginary unit, σ k Indicates the bandwidth parameter.

4. The oil-paper insulation state evaluation method based on harmonic-discharge coupling analysis according to claim 1, characterized in that: In step S2, the oil-paper insulation data includes partial discharge inception voltage, average discharge capacity, maximum discharge capacity and discharge repetition rate.

5. The oil-paper insulation state assessment method based on harmonic-discharge coupling analysis according to claim 4, characterized in that: In step S2, the calculation process of collecting oil-paper insulation data to construct nonlinear cross features to generate enhanced feature vectors includes: Extract the local discharge characteristics and normalize them: ， ， Generate nonlinear cross terms: ， Generate augmented feature vectors: ， Where X is the partial discharge characteristic vector, PDIV is the partial discharge inception voltage, Q max is the maximum discharge capacity, Q avg is the average discharge capacity, R discharge is the discharge repetition rate, X norm is the normalized partial discharge feature vector, is the characteristic mean of the unaged sample, is the standard deviation of the unaged sample, α is the nonlinear correlation term between discharge intensity and voltage, β is the nonlinear characteristic term of discharge quantity distribution, T represents the transpose of the matrix, is the enhanced feature vector.

6. The oil-paper insulation state assessment method based on harmonic-discharge coupling analysis according to claim 1, characterized in that: In step S4, the equivalent circuit equation of the physical channel is: ， Where, Q theory is the theoretical charge, C is the equivalent capacitance, V harmontic is the harmonic voltage, t For time, R insul is the time-varying parameter of insulation resistance.

7. The oil-paper insulation state evaluation method based on harmonic-discharge coupling analysis according to claim 1, characterized in that: In step S5, the calculation formula of the state assessment matrix includes: Where, S is the state evaluation matrix, ΔPDIV / PDIV is the rate of change of discharge starting voltage, ▽Q max is the fluctuation of the maximum discharge capacity, ▽Q avg is the fluctuation of the average discharge amount, R is the current resistance value, R0 is the reference resistance value, H is the harmonic distortion rate, f is the frequency, A is the coefficient of the Arrhenius equation, τ aging is the aging time constant, and HIF is the harmonic influence factor.

8. The oil-paper insulation status assessment method based on harmonic-discharge coupling analysis according to claim 1, characterized in that: In step S5, the calculation formula for calculating the HIF index by weighted fusion of harmonic frequency offset and amplitude exceeding the standard degree includes: Where HIF is the harmonic impact factor, n is the upper limit of the harmonic order, h is the harmonic order, w h is the dynamic attention weight of the h-th harmonic, f h is the frequency of the hth harmonic, f 0 is the reference frequency, A h is the amplitude of the hth harmonic, A 0 is the reference amplitude.

Images