Connecting rod neck contour error decomposition method based on VMD

Abstract

The invention discloses a VMD-based connecting rod neck contour error decomposition method, and relates to the field of connecting rod neck contour error analysis. The method comprises the following steps: inputting a crankshaft contour error, and pre-defining a crankshaft contour error convergence threshold value and the number of signal components needing to be separated; the signal component, the center frequency corresponding to the signal component and the Lagrange multiplier are updated; and judging whether decomposition is completed or not by using a convergence threshold. According to the method, the complex multi-component signal can be decomposed into amplitude modulation-frequency modulation components, and the noise is stable.

Description

Technical Field

[0001] The invention relates to the field of connecting rod neck profile error analysis, and more specifically to a connecting rod neck profile error decomposition method based on VMD. Background Art

[0002] Adaptive modal decomposition can adaptively extract single-component modal components that reflect the nature of signal fluctuations according to the local change characteristics of the signal, and represent the signal as a superposition of several single-component components. Since Huang et al. proposed the EMD method in 1998, a variety of adaptive modal decomposition methods such as EEMD, LMD, ITD, EWT, and ALIT have emerged in recent years, and have been applied in certain engineering practices. Under the understanding of the grinding process, the crankshaft connecting rod neck profile error is mainly caused by the motion control errors of the C-axis and X-axis during the follow-up grinding process. It is necessary to effectively separate these two components from the crankshaft connecting rod neck profile error. Compared with the above-mentioned adaptive modal decomposition methods, VMD has a rigorous mathematical theoretical foundation and is stable to noise and sampling. Therefore, how to use VMD to solve the problem of error decomposition is urgently needed for technicians in this field. Summary of the invention

[0003] In view of this, the present invention provides a connecting rod neck profile error decomposition method based on VMD.

[0004] In order to achieve the above object, the present invention adopts the following technical solution:

[0005] A connecting rod neck profile error decomposition method based on VMD includes the following steps:

[0006] Input crankshaft profile error, predefine crankshaft profile error convergence threshold and the number of signal components to be separated;

[0007] Update the signal components, the center frequencies corresponding to the signal components, and the Lagrange multiplier λ;

[0008] The convergence threshold is used to determine whether the decomposition is completed.

[0009] Optionally, when the VMD method is used to decompose the signal, the constrained variational optimization problem is

[0010]

[0011] In the formula, represents the kth IMF, ω k represents the corresponding center frequency, and K represents the number of decompositions.

[0012] Optionally, the constrained variational optimization problem is transformed into an unconstrained problem, and a quadratic penalty factor α and a Lagrange multiplier λ are introduced; by introducing the quadratic penalty factor α and the Lagrange multiplier λ, the augmented Lagrange expression is as follows:

[0013]

[0014] In the formula, <,> represents the inner product.

[0015] Optionally, updating the signal component, the center frequency corresponding to the signal component, and the Lagrange multiplier λ specifically includes:

[0016] For k = 1, 2, ... K and all ω ≥ 0, update as follows and λ n+1 :

[0017]

[0018] Where τ is the Lagrange multiplier update parameter.

[0019] Optionally, the specific formula for determining whether the decomposition is completed using the convergence threshold is as follows:

[0020]

[0021] Where ε is the convergence termination condition. If the condition is met, the decomposition is stopped, otherwise n=n+1 is set and the update step is returned.

[0022] It can be seen from the above technical solutions that, compared with the prior art, the present invention discloses a connecting rod neck profile error decomposition method based on VMD, which can decompose complex multi-component signals into amplitude modulation and frequency modulation components and is stable to noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the drawings required for use in the embodiments or the description of the prior art will be briefly introduced below. Obviously, the drawings described below are only embodiments of the present invention. For ordinary technicians in this field, other drawings can be obtained based on the provided drawings without paying creative work.

[0024] Figure 1 It is a schematic diagram of the process of the present invention;

[0025] Figure 2a is the crankshaft connecting rod neck profile error input in the embodiment of the present invention;

[0026] Figure 2bIt is the VMD decomposition result corresponding to the crankshaft connecting rod neck profile error input in the embodiment of the present invention. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0028] Example 1

[0029] The embodiment of the present invention discloses a connecting rod neck profile error decomposition method based on VMD, such as Figure 1 As shown, the following steps are included:

[0030] Input crankshaft profile error, predefine crankshaft profile error convergence threshold and the number of signal components to be separated;

[0031] Update the signal components, the center frequencies corresponding to the signal components, and the Lagrange multiplier λ;

[0032] The convergence threshold is used to determine whether the decomposition is completed.

[0033] The VMD method is an adaptive non-recursive decomposition method that can decompose complex multi-component signals into AM-FM components and is stable to noise. VMD defines IMF as an analytical AM-FM model and associates the AM-FM model parameters with the IMF bandwidth. According to the narrowband nature of the IMF, the AM-FM parameters are solved by minimizing the bandwidth to obtain the IMF. Compared with other adaptive modal decomposition methods, VMD has a rigorous mathematical theoretical foundation and is stable to noise and sampling. VMD decomposes the signal x(t) into a series of IMFs that have limited bandwidth near their respective center frequencies. When the VMD method is used to decompose the signal, the constrained variational optimization problem is

[0034]

[0035] In the formula, represents the kth IMF, ω k represents the corresponding center frequency, and K represents the number of decompositions.

[0036] In order to transform the constrained variational optimization problem of formula (1) into an unconstrained problem, it is necessary to introduce a quadratic penalty factor α and a Lagrange multiplier λ to achieve fast convergence and strengthen the constraints. By introducing these two parameters, the augmented Lagrange expression is as follows:

[0037]

[0038] In the formula, <,> represents the inner product. The Alternating Direction Method of Multipliers (ADMM) can be used to solve formula (2). and λ n+1 , and obtain the optimal solution. Finally, the signal x(t) is decomposed into a series of IMFs.

[0039] The complete algorithm of VMD is as follows:

[0040] (a) Initialization: λ 1 and n are set to 0, and the convergence threshold and the number K of IMFs to be separated are predefined.

[0041] (b) For k = 1, 2, ... K and all ω ≥ 0, update as follows and λ n+1 :

[0042]

[0043] Where τ is the Lagrange multiplier update parameter.

[0044] (c) Check the convergence conditions:

[0045]

[0046] Where ε is the convergence termination condition. If the condition is met, the decomposition is stopped; otherwise, n=n+1 is set and the process returns to step (b).

[0047] Example 2

[0048] Input preparation: Step 1.1: Input crankshaft profile error data. This is usually the measurement data obtained from the crankshaft machining process, including the position error of each measurement point.

[0049] Step 1.2: Predefine the crankshaft profile error convergence threshold. This threshold is used to determine whether the decomposition is accurate enough during the VMD (variational mode decomposition) process.

[0050] Step 1.3: Determine the number of signal components that need to be separated. This depends on the complexity of the contour error data and the desired analysis accuracy.

[0051] Variational Mode Decomposition (VMD): Step 2.1: Initialize the signal components, the center frequencies corresponding to the signal components, and the Lagrange multipliers. This usually involves setting initial guess values ​​for each component, which can be random or based on prior knowledge.

[0052] Step 2.2: Iteratively update the signal components, center frequencies, and Lagrange multipliers. In each iteration, these parameters are updated by minimizing the VMD objective function using an optimization algorithm (e.g., alternating direction method of multipliers ADMM).

[0053] Step 2.3: Use the convergence threshold to determine whether the decomposition is complete. Check whether the parameter change between adjacent iterations is less than the preset convergence threshold. If yes, the decomposition process ends; if not, continue the iteration.

[0054] Robust Gaussian regression filtering: Step 3.1: Use one (or some) key signal components obtained by VMD decomposition as a substitute for the original contour error and perform robust Gaussian regression filtering. This can reduce the influence of noise and outliers and obtain a smoother contour error curve.

[0055] Step 3.2: Calculate the difference between the original contour error and the filtered result. For each measurement point, calculate the absolute difference between its original error and the filtered error.

[0056] Step 3.3: Check whether the difference is greater than the set threshold. For each measurement point, if its difference is greater than the threshold, it is considered that there is a significant error or anomaly at the point.

[0057] Step 3.4: For points whose difference is greater than the threshold, use the filtering result as the first contour error instead of the original contour error. This can eliminate or reduce the errors of these points.

[0058] Low-pass filtering: Step 4.1: The first contour error is low-pass filtered again using a robust Gaussian regression filter. This can further smooth the data and remove high-frequency noise.

[0059] Step 4.2: Output the final contour error. The first contour error after low-pass filtering is the final contour error, which can be used for subsequent error analysis, quality control or optimization process.

[0060] When using VMD to decompose the crankshaft connecting rod neck profile error, the number of separated IMFs K must be determined in advance. The crankshaft connecting rod neck profile error is mainly affected by the C-axis and X-axis of the follow-up grinder, that is, the follow-up error source of the follow-up grinder. Therefore, the number K is set to 2, that is, the original profile error experimental data is decomposed into 2 components. The input crankshaft connecting rod neck profile error and its decomposition results are shown in Figure 2a and Figure 2b shown.

[0061] In this specification, each embodiment is described in a progressive manner, and each embodiment focuses on the differences from other embodiments. The same or similar parts between the embodiments can be referred to each other. For the device disclosed in the embodiment, since it corresponds to the method disclosed in the embodiment, the description is relatively simple, and the relevant parts can be referred to the method part.

[0062] The above description of the disclosed embodiments enables one skilled in the art to implement or use the present invention. Various modifications to these embodiments will be apparent to one skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the present invention. Therefore, the present invention will not be limited to the embodiments shown herein, but rather to the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A connecting rod neck profile error decomposition method based on VMD, characterized in that: The following steps are involved: Input crankshaft profile error, predefine crankshaft profile error convergence threshold and the number of signal components to be separated; Update the signal components, the center frequencies corresponding to the signal components, and the Lagrange multiplier λ; The convergence threshold is used to determine whether the decomposition is completed.

2. The connecting rod neck profile error decomposition method based on VMD according to claim 1, characterized in that: When the VMD method is used to decompose the signal, the constrained variational optimization problem is In the formula, u k (t) represents the kth IMF, ω k represents the corresponding center frequency, and K represents the number of decompositions.

3. The connecting rod neck profile error decomposition method based on VMD according to claim 2, characterized in that: The constrained variational optimization problem is transformed into an unconstrained problem, and the quadratic penalty factor α and the Lagrange multiplier λ are introduced. By introducing the quadratic penalty factor α and the Lagrange multiplier λ, the augmented Lagrange expression is as follows: In the formula, <,> represents the inner product.

4. The connecting rod neck profile error decomposition method based on VMD according to claim 1, characterized in that: The signal components, the center frequencies corresponding to the signal components, and the Lagrange multiplier λ are updated specifically including: For k = 1, 2, ... K and all ω ≥ 0, update as follows and λ n+1 : Where τ is the Lagrange multiplier update parameter.

5. The connecting rod neck profile error decomposition method based on VMD according to claim 1, characterized in that: The specific formula for using the convergence threshold to determine whether the decomposition is completed is as follows: Where ε is the convergence termination condition. If the condition is met, the decomposition is stopped, otherwise n=n+1 is set and the update step is returned.

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