Non-Gaussian noise pollution spiral shaft rod type part measurement signal processing method

Abstract

The invention discloses a non-Gaussian noise pollution spiral shaft rod type part measurement signal processing method, which can realize reliable purification of measurement signals, stable separation of bending deviation and spiral raceway morphology items and fitting reconstruction when pollution such as heavy tails, multiple peaks, burrs and sheet abnormal points exists. The method comprises the following steps: acquiring and synchronously registering measurement data of rotation and axial movement, establishing a joint fitting model for decomposing readings into deformation items and spiral raceway morphology items, and expressing the morphology items by multi-order harmonics, and a three-stage process is adopted to complete baseline establishment and coarse elimination, phase locking and fine filtering in sequence, and the harmonic order of the optimal spiral raceway morphology item is determined in a self-adaptive manner and finally reconstructed. The invention provides an effective solution for the problems that the continuous rotary scanning measurement signal of the spiral shaft rod type part is unstable in recovery and is easy to distort in reconstruction under the non-Gaussian noise pollution.

Description

Technical Field

[0001] This invention belongs to the field of signal processing, and in particular relates to a method for measuring the signal of a spiral shaft-type part contaminated by non-Gaussian noise. Background Technology

[0002] As key transmission or positioning components in high-end equipment, the surface morphology and geometric errors of helical shafts directly affect positioning accuracy, operational stability, and lifespan. To obtain surface contour information of these parts efficiently, continuous rotary scanning measurement is commonly used in engineering. This involves the part rotating continuously while the displacement sensor feeds linearly along the part's axis, creating a helical scanning trajectory on the part's surface. The sensor output signal is therefore a time-series or position-series synchronously integrating axial feed and rotation angle. It also incorporates various physical components, including slow variations caused by low-frequency geometric offsets such as clamping eccentricity and axis bending, periodic fluctuations caused by the periodic structure of the helical raceway, and measurement system noise and random disturbances.

[0003] During the aforementioned continuous rotary scanning measurement process, non-Gaussian noise contamination often occurs in the signal. Non-Gaussian noise contamination refers to noise contamination in the measurement signal that no longer follows a symmetrical, relatively light-tailed normal distribution near the mean, but instead exhibits obvious spikes, thick tails, skewed or mixed distribution characteristics. It often manifests as patches of outliers, abrupt spikes, local plateau drift, or a few extreme outliers. This type of contamination is more prominent on reflective metallic surfaces, in locally rough or defective areas, and can also be induced by rotary vibration, environmental interference, unstable optical echoes, acquisition saturation, or momentary loss of lock. Because outliers have large amplitudes, strong directions, and unstable distributions, they significantly skew the fitting benchmark and statistics, causing systematic distortion in subsequent threshold discrimination and morphology reconstruction.

[0004] Existing signal processing methods are mostly based on Gaussian noise assumptions or mild outlier scenarios, such as fixed threshold removal using the mean and standard deviation, traditional least-squares fitting, simple low-pass filtering, or smoothing. When faced with non-Gaussian noise contamination, these methods often suffer from three prominent problems: First, outlier-sensitive statistics such as the standard deviation can be amplified by spikes, leading to thresholds that are too wide to effectively remove outliers, or thresholds that are too narrow to mistakenly remove true structural information. Second, direct smoothing or low-passing can treat the high-frequency components of the helical raceway details as noise, resulting in the loss of contour details. Third, when bending offset and helical structure terms coexist, without robust separation and locking mechanisms, the fitted model is easily pulled by outliers, causing baseline drift and crosstalk between the bending and helical terms. This ultimately leads to inaccurate contour reconstruction and parameters that require repeated manual adjustment, resulting in insufficient robustness and repeatability.

[0005] To address the aforementioned problems, this invention tackles the technical challenges of non-Gaussian noise contamination in continuous rotary scanning measurement signals of helical shaft parts, including difficulty in removing outliers, baseline drift, accidental smoothing of structural details, and the difficulty in stably separating bending and helical structure terms. It proposes a robust three-stage denoising and reconstruction method for measurement signals to achieve effective recovery and stable reconstruction of continuous rotary scanning measurement signals under non-Gaussian noise contamination, providing a cleaner and more repeatable reconstructed signal foundation for evaluating the helical raceway morphology of parts and subsequent precision analysis. Summary of the Invention

[0006] The purpose of this invention is to provide a method for processing measurement signals of helical shaft parts contaminated by non-Gaussian noise. This invention addresses the technical problem of non-Gaussian noise contamination in measurement signals during continuous rotary scanning measurements of helical shaft parts. This contamination can manifest as a combination of heavy-tailed, light-tailed, and multi-peaked distributions, accompanied by anomalies caused by surface reflections, local defects, or momentary sensor lock-off. This invention achieves reliable purification and reconstructed fitting of the contaminated signal by performing staged signal modeling, combined with robust statistical thresholds and optimal harmonic order selection.

[0007] The specific operating steps of this invention are as follows:

[0008] (1) Obtain the continuous rotation scanning measurement data sequence of the helical shaft part to form a measurement dataset [x, φ, l], where x is the axial position vector, φ is the part rotation angle vector, and l is the sensor reading vector. Then, perform synchronous registration and equivalent sorting of the data by axial position.

[0009] (2) Establish a joint parameterized fitting model for the continuous rotary scanning measurement signal, decompose the observation readings into deformation terms and helical raceway morphology terms, wherein the helical raceway morphology terms are represented by Fourier series, and the harmonic order characterizes the number of harmonic terms contained in the Fourier expansion.

[0010] (3) In the first stage of coarse denoising and baseline establishment, the harmonic order of the spiral raceway morphology term is set to 0, the original dataset is fitted to obtain the initial baseline curve and an asymmetric two-sided elimination threshold is constructed. The negative large error points that have a significant effect on lowering the baseline curve are eliminated first to obtain the dataset after the first elimination.

[0011] (4) Second stage phase locking and fine filtering: On the dataset after the first removal, the harmonic order of the spiral raceway morphology term is set to 1, the residual is calculated and an adaptive two-sided threshold is constructed based on the median absolute deviation to remove the remaining non-Gaussian spikes and outliers, and a clean dataset is obtained.

[0012] (5) In the third stage, the optimal harmonic order of the spiral raceway morphology term is adaptively determined on the clean dataset. The harmonic order of the spiral raceway morphology term is gradually increased and the changes of adjacent fitting results are compared. When the change enters the plateau period, the harmonic order that is still significantly improved is taken as the optimal harmonic order of the spiral raceway morphology term.

[0013] (6) Based on the harmonic order of the optimal spiral raceway morphology term, the pure dataset is finally fitted and the measurement signal is reconstructed to achieve effective recovery and stable reconstruction of the original pollution signal.

[0014] In step (1), continuous rotary scanning measurement refers to the continuous rotation of the part and the continuous axial feed of the sensor to form a spiral scanning trajectory. The measurement dataset [x, φ, l] satisfies the condition that the elements x at the same sampling point satisfy the condition. i , φ i , l i One-to-one correspondence.

[0015] In step (2), the deformation term is used to characterize the offset of the geometric center of the cross section as the axial position changes, and the axial polynomial and multi-order harmonic coupling model is used; the helical raceway morphology term is used to characterize the periodic raceway undulations along the helical scanning trajectory, and the multi-order Fourier series approximation is used, and its fundamental frequency is determined by the mapping relationship between the lead and axial position of the helical shaft-type parts.

[0016] In step (3), the purpose of setting the harmonic order of the spiral raceway morphology term to 0 is to make the fitting result mainly characterize the low-frequency trend and angular gradual component related to the center line of the average cylindrical surface of the spiral shaft part, and to achieve the coarse screening and removal of most abnormal points through the asymmetric threshold.

[0017] In step (4), the adaptive two-sided threshold is constructed based on the absolute deviation of the median in order to avoid the residual nonnormal spurious points from significantly amplifying the standard deviation and causing the threshold to become too wide and ineffective. At the same time, outliers are robustly removed on both sides of the residual, so that the screening intensity is automatically adjusted according to the actual noise level, thereby improving the stability and accuracy of signal reconstruction.

[0018] In step (5), the change in adjacent fitting results refers to the degree of difference between the two fitting curves in the same data domain before and after the harmonic order of the spiral raceway morphology term is increased by one order. It is used to quantify the gain brought by the new harmonic to the reconstruction result, thereby determining whether the fitting has entered a plateau period and determining the optimal harmonic order.

[0019] The advantages of this invention are:

[0020] (1) In view of the problem that non-Gaussian noise pollution such as heavy tails and multi-peaks in continuous rotary scanning measurement can easily cause threshold failure and abnormal points to pull the fitting baseline, the present invention adopts a three-stage robust processing flow, first establishing a stable baseline and then gradually purifying the data, so that signal denoising and reconstruction still have reliability and reproducibility under strong pollution conditions.

[0021] (2) The present invention decomposes the observation signal into deformation terms and helical raceway morphology terms and performs joint parameterized fitting modeling. When anomalies exist, the deformation trend and the periodic fluctuations of the raceway can be effectively separated, significantly reducing baseline drift and contour distortion caused by crosstalk between the two types of components.

[0022] (3) Compared with existing methods that rely on Gaussian noise assumptions or are only applicable to mild outliers, this invention uses a robust scale estimation based on the absolute deviation of the median to construct an adaptive two-sided threshold, and combines it with the optimal harmonic order adaptive selection to make outlier identification and removal more stable, while taking into account the fidelity of the raceway details and the consistency of the reconstruction results. Attached Figure Description

[0023] Figure 1 This is a flowchart of the signal processing logic structure of the present invention.

[0024] Figure 2 Schematic diagram of continuous rotary scanning measurement process of lead screw

[0025] Figure 3 A schematic diagram for establishing the first-stage data fitting and threshold upper and lower bounds.

[0026] Figure 4 A schematic diagram for establishing data fitting and threshold upper and lower bounds in the second stage.

[0027] Figure 5 The optimal K for the third stage S Find the diagram

[0028] Figure 6 For optimal K S Final fitting diagram Detailed Implementation

[0029] The purpose of this invention is to provide a method for processing measurement signals of helical shaft parts contaminated by non-Gaussian noise. This invention addresses the common non-Gaussian noise contamination phenomenon in continuous rotary scanning measurement signals. This contamination can manifest as a combination of heavy-tailed, light-tailed, and multi-peaked distributions, accompanied by anomalies caused by surface reflections, local defects, or momentary sensor lock-off. This invention employs staged modeling, combined with robust statistical thresholds and optimal harmonic order selection, to achieve reliable purification and fitting reconstruction of the contaminated signal. The invention will be further described below with reference to the accompanying drawings.

[0030] Combination Figure 1 The logical flow diagram shows the specific operation steps of this invention as follows:

[0031] (1) Obtain the continuous rotation scanning measurement data sequence of the helical shaft part to form a measurement dataset [x, φ, l], where x is the axial position vector, φ is the part rotation angle vector, and l is the sensor reading vector. Then, perform synchronous registration and equivalent sorting of the data by axial position.

[0032] (2) Establish a joint parameterized fitting model for the continuous rotary scanning measurement signal, decompose the observation readings into deformation terms and helical raceway morphology terms, wherein the helical raceway morphology terms are represented by Fourier series, and the harmonic order characterizes the number of harmonic terms contained in the Fourier expansion.

[0033] (3) In the first stage of coarse denoising and baseline establishment, the harmonic order of the spiral raceway morphology term is set to 0, the original dataset is fitted to obtain the initial baseline curve and an asymmetric two-sided elimination threshold is constructed. The negative large error points that have a significant effect on lowering the baseline curve are eliminated first to obtain the dataset after the first elimination.

[0034] (4) Second stage phase locking and fine filtering: On the dataset after the first removal, the harmonic order of the spiral raceway morphology term is set to 1, the residual is calculated and an adaptive two-sided threshold is constructed based on the median absolute deviation to remove the remaining non-Gaussian spikes and outliers, and a clean dataset is obtained.

[0035] (5) In the third stage, the optimal harmonic order of the spiral raceway morphology term is adaptively determined on the clean dataset. The harmonic order of the spiral raceway morphology term is gradually increased and the changes of adjacent fitting results are compared. When the change enters the plateau period, the harmonic order that is still significantly improved is taken as the optimal harmonic order of the spiral raceway morphology term.

[0036] (6) Based on the harmonic order of the optimal spiral raceway morphology term, the pure dataset is finally fitted and the measurement signal is reconstructed to achieve effective recovery and stable reconstruction of the original pollution signal.

[0037] The detailed operations, formulas, and symbol explanations for steps (1) to (6) are as follows:

[0038] Ball screws are typical helical shaft components. Taking ball screws as an example... Figure 2 This describes the continuous rotary scanning measurement process for a leadscrew. After being clamped by a fixture, the leadscrew (the part being measured) undergoes continuous rotary motion. The displacement sensor is fed linearly along the leadcrew axis, causing the sensor's measuring point to form a helical scanning trajectory on the leadcrew surface. Therefore, the measurement signal output by the sensor is a position sequence that synchronously integrates the axial feed and rotation angle, where x represents the axial position, φ represents the part's rotation angle, and l represents the sensor reading.

[0039] Let N be the number of sampling points used in a single measurement. The discrete measurement sequence can be represented by a vector as follows:

[0040] (1)

[0041] Where x is the axial position vector, φ is the part rotation angle vector, and l is the sensor reading vector.

[0042] A ball screw can be considered as being formed by the helical motion of its single-section profile along its axis. For every lead movement, the profile also rotates by an angle of 2π rad. This results in a helical raceway on the screw's surface after forming. This helical structure is added to the measurement signal as a systematic geometric error during the measurement process. Let the nominal lead of the screw be p. h Since the sensor moves axially and the parts rotate synchronously, point measurement forms a helical sampling on the lead screw surface. The helical phase of the measuring point can be defined as:

[0043] (2)

[0044] in Used to be compatible with both left and right rotation.

[0045] The observed readings l from the superimposed local outlier point errors i To restore the normal surface profile signal, a joint parameterized fitting model is used, decomposing the readings into harmonic terms that vary with rotation angle and periodic terms that vary with helical phase, referred to as the deformation term and the helical raceway morphology term, respectively. The deformation term describes the offset of the cross-sectional geometric center as the axial position changes, and is modeled using a coupling form of polynomials and multiple harmonics. The helical raceway morphology term describes the periodic raceway undulations scanned by the sensor along the helical trajectory, and is approximated by multiple Fourier series expansions to approximate the true helical raceway profile.

[0046] Let P be the order of the axial polynomial, and K A For the angular harmonic order, K S For the harmonic order of the helical raceway morphology term, the fitting model for the sensor reading at the i-th sample point is... Written as:

[0047] (3)

[0048] Stack all unknown coefficients into a parameter vector with M elements:

[0049] (4)

[0050] Constructing a design matrix Let A i, : For the i-th row, its row vector is determined by the trigonometric functions of equation (3) in the data (x i , φ i, ψ i The value at position ) is concatenated with element 1, so that the overall regression form satisfies:

[0051] (5)

[0052] make = l, and by solving the above system of equations using the least squares method, the optimal coefficient estimate η describing the physical entity of the lead screw can be obtained. Substituting η into equation (5) again, the fitting and reconstruction of the measurement signal can be achieved.

[0053] When performing signal recovery and reconstruction based on a fitted model, the parameters P and K... A K S The setting of P directly affects the fitting results, therefore it needs to be selected and analyzed reasonably in conjunction with the measurement mechanism. P is used to describe the bending shape of the lead screw axis along the length direction, and usually a value of 4-5 is sufficient to balance expressiveness and stability. A This term describes the shape error of the lead screw cross-section. The shape error here mainly manifests as eccentricity, that is, the offset of the actual centroid of the part relative to the ideal centroid (center of rotation). When the lead screw is bent or misaligned during clamping, the sensor will observe an approximately sinusoidal change as the part rotates one revolution. Therefore, the cross-sectional eccentricity introduces a first-order harmonic component with the same frequency as rotation into the measurement signal, hence K... A Generally, it is taken as 1. K S The cross-sectional profile used to describe the helical raceway determines the model's ability to reproduce the details of the thread profile. The actual raceway shape is usually not an ideal sine wave, requiring higher-order harmonics to capture the details. If K... S If the value is too low, the raceway morphology will not fit accurately, and the residual error will be mistakenly identified as bending error. S If K is too large, the model may try to fit scratches or high-frequency electronic noise on the sensor surface, leading to a "ringing effect." Therefore, K... S Further analysis is needed to formulate reasonable selection principles, and the relevant methods will be provided in subsequent content.

[0054] Due to outliers introduced by factors such as spikes and sensor fluctuations in the actual measured data vector l, the fitting residuals exhibit non-Gaussian characteristics such as heavy tails or even multiple peaks. If the entire dataset is directly fitted, the least squares estimation is prone to oversensitivity to outliers, leading to parameter shifts and model distortion. Therefore, a three-stage iterative denoising and reconstruction algorithm from coarse to fine is proposed based on the fitting equation (5). During the iteration process, P is set to 4, and K... A Set to 1.

[0055] The first stage is used for coarse denoising and baseline establishment, such as Figure 3 As shown. Set K S= 0 Only the macroscopic profile term is retained for fitting, so that the fitting result mainly represents the low-frequency trend and angularly gradually varying component related to the centerline of the average cylindrical surface of the leadscrew. Asymmetric thresholding is used to coarsely screen out most outliers. Specifically, the basic fitting curve containing only bending and eccentricity terms is used as the judgment baseline, and then the leadscrew lead p is used as the benchmark. h Multiplying by a specific coefficient sets upper and lower boundaries on both sides, which are used to identify and delete outlier data outside the boundaries. The lead is chosen as the metric benchmark based on the empirical fact of the geometric similarity of ball screws, that is, the ball diameter and groove depth usually maintain a relatively fixed proportional relationship with the lead.

[0056] Since outliers often manifest as small negative fluctuations, these tiny anomalies can significantly lower the overall position of the fitted curve, causing the baseline to drop and deviate from the true geometric center. To avoid accidentally deleting valid data in this situation, the upper threshold needs to be sufficiently generous, ranging from 0.6 to 0.8 times the lead, to ensure that normal signals above the dropped baseline are fully preserved. Conversely, outliers causing baseline drop are usually concentrated not far below the baseline, so the lower threshold must be set very tightly, around 0.1 times the lead, to effectively remove outliers with a small downward bias, thus providing a cleaner data foundation for subsequent phase locking and fine filtering.

[0057] The second stage is used for phase locking and fine filtering, such as Figure 4 As shown. A fundamental spiral term is introduced into the dataset after the first stage of elimination, and K is set... S = 1 for secondary fitting. After the first stage of coarse denoising, the large negative error that lowered the baseline has been removed. Therefore, the fitted curve obtained after adding the spiral term will return to a reasonable position and be locked to the true geometric center of the spiral raceway. In this state, the residual, that is, the distance between the data point and the fitted curve, no longer shows a one-sided deviation, but fluctuates around the zero value, mainly reflecting random noise and a small number of local spikes.

[0058] Because non-normal spikes may still remain, directly estimating the fluctuation scale using ordinary standard deviation would significantly amplify the standard deviation, leading to an overly wide threshold and reduced screening effectiveness. Therefore, this stage no longer uses a fixed geometric scale as the threshold basis, but instead uses the median absolute deviation (MAD), which has a stronger ability to resist outliers, to estimate the noise level. Specifically, the MAD of the residuals is first calculated, which characterizes the typical width of the main residual distribution and is insensitive to marginal outliers. Then, the MAD is multiplied by 1.4826 to obtain the equivalent robust standard deviation. This coefficient ensures that it has a consistent scale with the standard deviation under normal noise conditions. Based on Construct a symmetrical envelope and shift it upwards by 3 ohms from the center of the fitted curve. As the upper bound, shift downwards by 3. This forms a tight statistical channel as a lower bound. Given that the residuals approximately follow a normal distribution, the vast majority of normal data should fall within this channel. Points falling outside the channel can be considered extremely low-probability events, typically corresponding to surface spikes or instantaneous measurement anomalies. Through this adaptive robust threshold, the algorithm can automatically adjust the filtering intensity based on the actual noise level of the signal, achieving precise removal of remaining minor anomalies and obtaining a clean dataset.

[0059] The third stage is used for high-order morphology reconstruction and optimal K-axis calculation. S Selection. On a clean dataset, integrate the optimal K. S The search process, combined with the optimal K S Perform the final parameter solution, such as Figure 5 As shown. For the same data, let K... S = 1, 2, ..., 20, calculate the order K for each... S Corresponding fitted vector To ensure that the evaluation focuses on the fitted curve itself rather than the magnitude of the residuals, the relative root mean square of the changes in two consecutive fitted curves is used as the convergence criterion. The difference fitting vector is defined as:

[0060] (6)

[0061] And define the relative change index as:

[0062] (7)

[0063] Where N′ is the length of the pure dataset.

[0064] Given a threshold ε > 0, the optimal order is determined using the principle of the last significant contribution, i.e., as K... S When the relative change in the fitted curve caused by increasing the order after a certain order is less than the threshold ε, the reconstruction result can be considered to have entered a stable stage. At this time, the last one that still satisfies δ(K) is considered to be stable. S The order of ε is used as the optimal K. S Set the optimal K S Perform a final fitting on the clean dataset, such as Figure 6 As shown. This enables effective fitting and recovery of measurement signals contaminated by anomalies, thus providing a reliable reconstructed signal basis for the evaluation of the lead screw surface morphology and subsequent analysis.

Claims

1. A method for processing measurement signals of helical shaft-type parts contaminated by non-Gaussian noise, characterized in that, Specifically, the steps include the following: (1) Obtain the continuous rotation scanning measurement data sequence of the helical shaft part to form a measurement dataset [x, φ, l], where x is the axial position vector, φ is the part rotation angle vector, and l is the sensor reading vector. Then, perform synchronous registration and equivalent sorting of the data by axial position. (2) Establish a joint parameterized fitting model for the continuous rotary scanning measurement signal, decompose the observation readings into deformation terms and helical raceway morphology terms, wherein the helical raceway morphology terms are represented by Fourier series, and the harmonic order characterizes the number of harmonic terms contained in the Fourier expansion. (3) In the first stage of coarse denoising and baseline establishment, the harmonic order of the spiral raceway morphology term is set to 0, the original dataset is fitted to obtain the initial baseline curve and an asymmetric two-sided elimination threshold is constructed. The negative large error points that have a significant effect on lowering the baseline curve are eliminated first to obtain the dataset after the first elimination. (4) Second stage phase locking and fine filtering: On the dataset after the first removal, the harmonic order of the spiral raceway morphology term is set to 1, the residual is calculated and an adaptive two-sided threshold is constructed based on the median absolute deviation to remove the remaining non-Gaussian spikes and outliers, and a clean dataset is obtained. (5) In the third stage, the optimal harmonic order of the spiral raceway morphology term is adaptively determined on the clean dataset. The harmonic order of the spiral raceway morphology term is gradually increased and the changes of adjacent fitting results are compared. When the change enters the plateau period, the harmonic order that is still significantly improved is taken as the optimal harmonic order of the spiral raceway morphology term. (6) Based on the harmonic order of the optimal spiral raceway morphology term, the pure dataset is finally fitted and the measurement signal is reconstructed to achieve effective recovery and stable reconstruction of the original pollution signal.

2. The method for processing measurement signals of non-Gaussian noise-contaminated helical shaft parts according to claim 1, characterized in that: Step (2) The process of establishing the joint parameterized fitting model for the continuous rotary scanning measurement signal is as follows: The number of sampling points for a single measurement is N, x is the axial position vector, φ is the part rotation angle vector, and l is the sensor reading vector. The discrete measurement sequence is represented by the following vector: (1) Let the nominal lead of the component be p. h , To accommodate both left and right rotation, the sensor moves axially while the part rotates synchronously. Point measurement forms a helical sampling on the part surface. The helical phase of the measurement point can be defined as: (2) For the sensor reading at the i-th sample point, its fitting model Written as: (3) Where P is the order of the axial polynomial, and K A For the angular harmonic order, K S The harmonic order of the spiral raceway morphology term is given.

3. The method for processing measurement signals of non-Gaussian noise-polluted helical shaft parts according to claim 1, characterized in that: The process of adaptively determining the order of the optimal helical raceway morphology in step (5) is as follows: On the clean dataset after the second stage of elimination, the harmonic order K of the optimal spiral raceway morphology term is integrated. S The search process, for the same data, lets K... S = 1, 2, …, 20, calculate the order K for each... S Corresponding fitted vector To evaluate the fitted curve itself rather than the magnitude of the residuals, the relative root mean square of the changes in two consecutive fitted curves is used as the convergence criterion. The difference fitting vector is defined as: (6) Let N′ be the length of the pure dataset, and define the relative change index as: (7) Given a threshold ε > 0, the optimal order is determined using the principle of the last significant contribution, i.e., as K... S When the relative change in the fitted curve caused by increasing the order after a certain order is less than the threshold ε, the reconstruction result can be considered to have entered a stable stage. At this time, the last one that still satisfies δ(K) is considered to be stable. S The order of ε is used as the optimal K. S .

Images