Adaptive tolerance envelope construction method for spectral curve and storage medium

Abstract

The application discloses a spectrum curve adaptive tolerance envelope construction method and a storage medium. The original envelope of a reference curve is extracted, and envelope points are differentiated and offset based on local slope characteristics (feature point longitudinal offset, non-feature point normal offset), so that the generated tolerance envelope can adapt to the local shape of the curve, reasonable tolerance width is maintained at peaks and valleys, and the tolerance envelope is expanded along the normal direction at the monotonic segment, thereby avoiding the problem that a traditional fixed tolerance band excessively contains or is insufficient in steep regions. A sliding window extreme value extraction method is used to construct the original envelope, which can effectively capture the fluctuation characteristics of the curve, and through normalization processing, the dimension influence is eliminated, so that the algorithm is applicable to spectrum curves of different frequency ranges and amplitude levels. A simplified removal algorithm based on slope extreme points is designed to eliminate abnormal ring structures in the envelope line.

Description

Technical Field

[0001] This invention relates to the field of spectrum analysis technology, specifically to a method for constructing an adaptive tolerance envelope of a spectrum curve and a storage medium thereon. Background Technology

[0002] In fault diagnosis and factory testing of rotating machinery such as motors and gearboxes, spectral analysis of vibration acceleration signals is a common method. The spectral curve of the device under test is typically compared with a standard spectrum, i.e., a pass / fail baseline curve, to determine product compliance. Traditional compliance determination methods often employ a unidirectional fixed tolerance band, i.e., a band-shaped region with a constant amplitude range above and below the baseline curve. However, in actual production, due to assembly tolerances, material differences, or changes in ambient temperature, the characteristic peak frequencies of qualified products often exhibit slight drifts, causing their spectral curves to exceed the amplitude range of the fixed tolerance band, leading to misjudgment. Furthermore, traditional methods do not consider the influence of local curve shapes (such as peaks and valleys) on tolerance adaptability; for steep resonance peaks in the spectrum, the fixed tolerance band is prone to over- or under-encapsulation. Summary of the Invention

[0003] To address the technical problem that fixed tolerance bands cannot adapt to frequency drift in the spectrum curve, resulting in a high misjudgment rate, this invention proposes an adaptive tolerance envelope construction method and storage medium for the spectrum curve. This method can generate dynamic, adaptive, and non-self-intersecting tolerance envelopes, significantly improving the accuracy and robustness of the judgment.

[0004] The technical solution adopted in this invention is as follows: an adaptive tolerance envelope construction method for a spectral curve, comprising the following steps:

[0005] S1. Input the qualified reference curve. The qualified reference curve is scaled with frequency as the horizontal axis X and amplitude as the vertical axis Y to obtain a normalized curve.

[0006] S2. Set the sliding window width according to the fluctuation period or spectral characteristics of the normalized curve, use the sliding window to traverse the curve, extract the maximum and minimum points in each window, connect all the extracted maximum points in order to form the original upper envelope curve, and connect all the extracted minimum points in order to form the original lower envelope curve.

[0007] S3. Traverse each data point on the original upper envelope curve and the original lower envelope curve as the current point. Based on the geometric relationship between the current point and its adjacent points, calculate the upper offset point and the lower offset point corresponding to the current point. Specifically, determine whether the current point is a feature point based on the product of the slopes of the line segments connecting the current point to its previous point and the line segments connecting the current point to its next point. If the current point is a feature point, then offset the current point longitudinally along the vertical axis to obtain the upper offset point and the lower offset point. If the current point is not a feature point, then offset the current point along the normal direction based on the local average slope to obtain the upper offset point and the lower offset point. For the starting point and ending point of the original upper envelope curve or the original lower envelope curve, offset the corresponding upper offset point and the lower offset point based on the slope of the connecting line on one side.

[0008] S4. Connect all the upper offset points in sequence to form the preliminary tolerance upper envelope, and connect all the lower offset points in sequence to form the preliminary tolerance lower envelope.

[0009] S5. For the upper envelope of the initial tolerance and the lower envelope of the initial tolerance, detect and remove the self-intersecting loops in the upper envelope of the initial tolerance and the self-intersecting loops in the lower envelope of the initial tolerance, respectively.

[0010] S6. Perform interpolation smoothing on the upper and lower envelopes after removing the self-intersecting loops to obtain smooth continuous curves.

[0011] S7. Perform inverse scaling on the smoothed upper and lower envelopes to restore them to their original frequency and amplitude, forming a dynamic tolerance envelope that encloses the qualified reference curve. Compare the curve to be tested with this dynamic tolerance envelope. If all data points of the curve to be tested are within the envelope range, it is considered qualified; otherwise, it is considered unqualified.

[0012] Optionally, the step in S3 of determining whether the current point is a feature point based on the slope product is as follows: calculate the slope k1 of the line connecting the current point and the previous point, and the slope k2 of the line connecting the current point and the next point; if the product of k1 and k2 is less than or equal to zero, then the current point is determined to be a feature point; if the product of k1 and k2 is greater than zero, then the current point is determined to be a non-feature point.

[0013] Optionally, the step of longitudinally offsetting the current point along the vertical axis in S3 is as follows: the upper offset point coordinate of the current point is taken as (Xi, Yi + Lu), and the lower offset point coordinate of the current point is taken as (Xi, Yi - Ld); where Lu is a preset upper tolerance offset amount, and Ld is a preset lower tolerance offset amount.

[0014] Optionally, the step of normal offsetting the current point along the normal direction based on the local average slope in S3 is as follows:

[0015] Calculate the average slope k = (k1 + k2) / 2;

[0016] Calculate the coordinates of the upper and lower offset points of the current point using the normal offset formula:

[0017] , ;

[0018] , .

[0019] Optionally, the step of normal offsetting the starting point or ending point based on the slope of the unilateral connecting line in S3 is as follows: for the starting point, take k = k2; for the ending point, take k = k1; calculate the coordinates of the upper offset point and the lower offset point of the starting point or ending point according to the normal offset formula.

[0020] Optionally, the step of detecting and removing self-intersecting loops in S5 includes: traversing the x-coordinate values ​​of each point on the upper or lower envelope of the initial tolerance, identifying continuous segments that satisfy the following pattern: first monotonically increasing, then monotonically decreasing, and then monotonically increasing again; marking each continuous segment as a potential self-intersecting loop, and recording the maximum value X of the x-coordinate within that segment. max and minimum value X min In the original point sequence of the upper or lower envelope of the initial tolerance, find the last x-coordinate value less than or equal to the minimum value X, starting from the starting point. min The point is denoted as the starting point Ps outside the loop; starting from the end point of the paragraph, find the first x-coordinate value greater than or equal to the maximum value X. max The point is denoted as the outer end point Pe; the self-intersecting loop is simplified and reconstructed based on the relationship between the tangent slopes at the outer start point Ps and the outer end point Pe.

[0021] Optionally, the simplified refactoring steps include:

[0022] Calculate the tangent slope Ks at Ps and the tangent slope Ke at Pe;

[0023] If Ks * Ke ≥ 0, then the original curve segment between Ps and Pe is simplified to a straight line segment connecting Ps and Pe;

[0024] If Ks * Ke < 0, then calculate the intersection point Pj of the line determined by Ps and its slope Ks and the line determined by Pe and its slope Ke, and simplify the original curve segment between Ps and Pe into a broken line segment connecting Ps, Pj and Pe in sequence.

[0025] Replace all points from Ps to Pe in the original point list of the initial tolerance upper envelope or initial tolerance lower envelope with the simplified reconstructed line segments.

[0026] Optionally, the scaling process in S1 may employ maximum / minimum scaling or standard deviation scaling.

[0027] Optionally, the sliding window width in step S2 is set according to the main frequency bandwidth of the qualified reference curve or an empirical formula; the upper tolerance offset Lu and the lower tolerance offset Ld in step S3 are set according to the product tolerance standard, and the two values ​​may be equal or unequal.

[0028] The present invention also discloses a computer-readable storage medium storing a computer program, which, when executed by a processor, implements the steps of the adaptive tolerance envelope construction method described above.

[0029] The beneficial effects of this invention are as follows: By extracting the original envelope of the reference curve and differentially shifting the envelope points based on local slope features (vertical shift of feature points and normal shift of non-feature points), the generated tolerance envelope can adapt to the local shape of the curve, maintaining a reasonable tolerance width at peaks and valleys, and expanding along the normal direction in monotonic segments, thus avoiding the problem of excessive or insufficient coverage in steep regions by traditional fixed tolerance bands; the original envelope is constructed using a sliding window extreme value extraction method, which can effectively capture the fluctuation characteristics of the curve, and the normalization process eliminates the influence of dimensions, making the algorithm applicable to spectral curves of different frequency ranges and amplitude levels; for self-intersecting loops that may be generated by normal shift, a simplified removal algorithm based on slope extreme points is designed, which can efficiently eliminate abnormal loop structures in the envelope, ensuring the geometric rationality and judgment reliability of the final tolerance envelope. Attached Figure Description

[0030] Figure 1 This is a schematic diagram of the overall process of the tolerance envelope construction method for determining the pass / failability of spectrum-type curves according to the present invention;

[0031] Figure 2 This is a schematic diagram comparing the effects of the traditional unidirectional tolerance band and the dynamic tolerance envelope of the present invention, where (a) is the traditional method and (b) is the method of the present invention.

[0032] Figure 3 This is a geometric schematic diagram of the dual-axis cooperative normal offset calculation in this invention;

[0033] Figure 4 This is a schematic diagram of the simplified self-intersecting loop removal algorithm in this invention, where (a) is the simplification when KsKe ≥ 0, and (b) is the simplification when KsKe < 0.

[0034] The labels in the attached figures are as follows: P, traditional unidirectional tolerance curve; S, qualified measured curve; T, measured curve of a certain item; C, tolerance curve of the present invention; O, original curve; F, processed curve. Detailed Implementation

[0035] The present application will now be described in further detail with reference to the accompanying drawings and embodiments.

[0036] like Figures 1 to 4 As shown, this embodiment discloses a tolerance envelope construction method for determining the pass / fail status of spectral curves. Using the vibration acceleration FFT spectral curve from a certain model of motor's factory test as the pass / fail benchmark curve, the complete implementation process of the method of this invention is described in detail. The testing system includes a data acquisition card, an industrial control computer, and testing software, with the algorithm module of the method of this invention embedded in the software. The motor runs at its rated speed, and the acceleration sensor picks up the vibration signal, which is then transformed by FFT to obtain the frequency range. Amplitude range The spectrum curve is used as a qualified reference curve (e.g.) Figure 2 (As shown by the solid line).

[0037] Step S1: Data Input and Preprocessing

[0038] Input N data points from the baseline curve into the system, each point consisting of a frequency value Xi and an amplitude Yi (i=1,…,N). To eliminate the influence of dimensions and stabilize subsequent calculations, the frequency and amplitude are normalized using a maximum-minimum method:

[0039] ,

[0040]

[0041] Where Xmin = 0 Hz, Xmax = 1000 Hz, Ymin = 0 m / s 2 Ymax = 10 m / s 2 After normalization, all coordinate values ​​are located in the [0,1] interval, resulting in the normalized curve Cnorm.

[0042] Step S2: Generate the original envelope

[0043] Observe the normalized curve Cnorm; its main resonance peak corresponds to a frequency bandwidth of approximately 0.05 (normalized units). To ensure the capture of local extrema, set the sliding window width W = 0.06 and the window step size Δ = 0.01 (usually taken as 1 / 5 to 1 / 2 of the window width). Starting from the curve's origin, slide the window to find the point with the largest and smallest y-coordinate within each window position and record their coordinates. After traversing the curve, connect all the maximum points in the original frequency order to obtain the original upper envelope curve Emax, and connect all the minimum points to obtain the original lower envelope curve Emin. These two curves roughly outline the fluctuation range of the baseline curve.

[0044] Step S3: Offset Point Calculation—Dual-Axis Cooperative Normal Offset

[0045] Set the upper tolerance offset Lu = 0.05 and the lower tolerance offset Ld = 0.05 (both in normalized units). These values ​​can be set according to the product tolerance standard; in this example, a symmetrical tolerance is used. For each data point Pi(Xi,Yi) on the original envelope curve (including points on Emax and Emin), based on its previous point... Calculate the offset point with the next point Pi+1. Figure 3 (a) is a feature point, and (b) is a non-feature point. The calculation process is divided into the following cases:

[0046] 1. Calculate the slope of adjacent line segments:

[0047]

[0048]

[0049] Since the frequency increases monotonically, the denominator is never zero.

[0050] 2. Feature point identification:

[0051] If k1×k2≤0, the determination point Pi is a feature point (such as a peak, valley, or inflection point), and a longitudinal offset (offset only in the Y direction) is used:

[0052] ,

[0053] If k1×k2>0, the determination point Pi is a non-feature point (located in a monotonic segment), and normal offset is used. First, calculate the average slope k=(k1+k2) / 2, and then calculate the normal offset point using the following formula:

[0054] ,

[0055] ,

[0056] The geometric meaning of this formula is: offset by a distance L along the normal direction of a straight line with a slope of k (i.e., the direction perpendicular to the tangent), thereby simultaneously changing the X and Y coordinates and forming a tolerance that adapts to the curve's direction.

[0057] 3. Endpoint processing:

[0058] Since it is not possible to obtain both the starting point (i=1) and the ending point (i=N) of the curve simultaneously, the normal offset is only performed using the slope of one side:

[0059] Starting point: Take k=k2 (i.e., the slope of the line connecting to the second point), and substitute it into the normal offset formula for calculation.

[0060] End point: Take k=k1 (i.e., the slope of the line connecting to the (N-1)th point) and substitute it into the normal offset formula for calculation.

[0061] Taking a point Pi(0.3, 0.4) on Emax as an example, its previous point (0.29, 0.38), then the next point Pi+1 (0.31, 0.41). Calculations show k1 = 2.0, k2 = 1.0, and the product k1k2 = 2.0 > 0, therefore it is a non-feature point. The average slope k = 1.5, and the upper offset point is:

[0062] ,

[0063]

[0064] Similarly, the lower offset point can be obtained.

[0065] For extreme points (e.g., at a peak where k1 is positive and k2 is negative, and the product is ≤0), the vertical offset is directly taken.

[0066] Perform the above operation on all points on Emax and Emin to obtain two sets of offset points respectively.

[0067] Step S4: Initial tolerance envelope generation

[0068] Connect all upper offset points (from Emax and Emin) in the original X order to obtain the initial tolerance upper envelope Uraw; connect all lower offset points to obtain the initial tolerance lower envelope Lraw. Due to curve curvature and normal offset, Uraw and Lraw may locally exhibit self-intersecting loops (see...). Figure 4 (a) Example).

[0069] Step S5: Self-intersecting loop detection and simplified removal

[0070] This step is one of the core improvements of the invention. Taking the initial upper envelope Uraw as an example, the same process is applied to Lraw.

[0071] 1. Positioning of self-intersecting loops:

[0072] Iterate through the x-coordinate array of all points in the Uraw array, checking if there exists a continuous sequence that follows a pattern of "first increasing, then decreasing, then increasing again". For example, in the x-sequence 1, 2, 3, 4, 5, 4.3, 4, 5.2, 6, 7, where 1 to 5 increase, 5, 4.3, and 4 decrease, and 4, 5.2, 6, and 7 increase. Therefore, extract the continuous sequence from the last increasing point before the first decreasing point (i.e., 5) to the first increasing point after the last decreasing point (i.e., 5.2), as a potential self-intersecting cycle. Record the maximum value Xmax and minimum value Xmin of x within this sequence.

[0073] 2. Determine the boundary points of the loop:

[0074] In the complete original point sequence, starting from the starting point, search backwards to find the last point whose X-coordinate value is less than or equal to Xmin, and denot it as the outer loop start point Ps; starting from the end point of the segment, search backwards to find the first point whose X-coordinate value is greater than or equal to Xmax, and denot it as the outer loop end point Pe. The curve segment between Ps and Pe is the self-intersecting segment to be processed.

[0075] 3. Slope Analysis and Simplified Reconstruction:

[0076] Calculate the tangent slope Ks at Ps and the tangent slope Ke at Pe. The tangent slope can be obtained through local difference or linear fitting: for example, take Ps and each point before and after it (if they exist) and perform least squares linear fitting; the slope of the fitted line is Ks.

[0077] If Ks×Ke≥0 (including those with the same sign or one of them being zero), it indicates that the ring structure is simple. All points between Ps and Pe can be deleted, and Ps and Pe can be directly connected by a straight line segment (see...). Figure 4 (a)).

[0078] If Ks×Ke<0, it indicates that the ring is teardrop-shaped, and the intersection point Pj of the two tangents needs to be introduced. Solve the system of equations:

[0079]

[0080] Find the intersection point Pj(Xj,Yj). Then delete all points between Ps and Pe, and insert Pj to form a new polyline segment Ps-Pj-Pe (see...). Figure 4 (b)).

[0081] 4. Line segment replacement:

[0082] Replace the portion from Ps to Pe (excluding Pe) in the original point list with the simplified and reconstructed new line segment to complete the removal of the current self-intersecting loop.

[0083] Repeat the above process until all self - intersecting loops are traversed. The processed envelope no longer has self - intersection phenomena and basically maintains the original tolerance shape.

[0084] Step S6: Post - processing of envelope - interpolation and smoothing

[0085] Perform cubic spline interpolation on the upper and lower envelopes after removing self - intersections respectively to obtain smooth continuous curves. Cubic spline interpolation can ensure second - order continuity of the curve, making the final tolerance envelope smooth and natural. The interpolation density can be set as needed. For example, 10 points are inserted between every two original points.

[0086] Step S7: Inverse scaling and output application

[0087] Inverse - scale the coordinate of each point on the smoothed upper and lower envelopes to restore to the original physical dimension:

[0088] ,

[0089]

[0090] Thus, the finally available dynamic tolerance envelope is obtained, as shown by the shaded area in Figure 2 (b). This envelope has adaptability in both the frequency and amplitude directions and can accommodate small drifts of characteristic peaks.

[0091] In automated testing, compare the frequency spectrum curve of the motor under test with this envelope: If all data points of the curve under test are located between the upper and lower envelopes, it is judged as qualified; otherwise, it is unqualified. For some occasions that only require unilateral limitation, the upper envelope or the lower envelope can also be used alone for judgment.

[0092] In actual testing, compare the frequency spectrum curve of the motor under test with this tolerance envelope to make an accurate judgment. Through experimental verification, the method of the present invention can reduce the misjudgment rate caused by frequency drift by about 70%, and the single - processing time consumption meets the real - time requirement of online detection (usually < 100ms).

[0093] The present invention also provides a storage medium. The storage medium can be any volatile or non - volatile storage device, including but not limited to: read - only memory (ROM), random access memory (RAM), flash memory, hard disk, optical disc, or USB storage device, etc. A computer program is stored on the storage medium, and when the computer program is executed by a processor, all or part of the steps of the foregoing method embodiments of the present invention are implemented.

[0094] It is understood that the specific embodiments described above are merely for explaining the relevant invention and not for limiting the invention. Furthermore, it should be noted that, for ease of description, only the parts relevant to the invention are shown in the accompanying drawings. Multiple technical solutions in the same embodiment, as well as multiple technical solutions in different embodiments, can be arranged and combined to form new technical solutions that do not contradict or conflict with each other. Any equivalent structural transformations made based on the content of this specification and drawings, whether directly or indirectly applied to other related technical fields, are similarly included within the scope of protection of this invention.

Claims

1. A method for constructing an adaptive tolerance envelope of a spectral curve, characterized in that, Includes the following steps: S1. Input the qualified reference curve. The qualified reference curve is scaled with frequency as the horizontal axis X and amplitude as the vertical axis Y to obtain a normalized curve. S2. Set the sliding window width according to the fluctuation period or spectral characteristics of the normalized curve, use the sliding window to traverse the curve, extract the maximum and minimum points in each window, connect all the extracted maximum points in order to form the original upper envelope curve, and connect all the extracted minimum points in order to form the original lower envelope curve. S3. Traverse each data point on the original upper envelope curve and the original lower envelope curve as the current point, and calculate the upper offset point and lower offset point corresponding to the current point based on the geometric relationship between the current point and the adjacent points before and after it. Specifically, the current point is determined to be a feature point based on the product of the slopes of the line segments connecting the current point to its previous point and the line segments connecting the current point to its next point. If the current point is a feature point, then the current point is offset longitudinally along the vertical axis to obtain the upper offset point and the lower offset point of the current point; If the current point is a non-feature point, then the current point is offset along the normal direction based on the local average slope to obtain the upper offset point and the lower offset point of the current point; For the starting point and ending point of the original upper envelope curve or the original lower envelope curve, the normal offset is performed based on the slope of the one-sided connecting line to obtain the corresponding upper offset point and lower offset point. S4. Connect all the upper offset points in sequence to form the preliminary tolerance upper envelope, and connect all the lower offset points in sequence to form the preliminary tolerance lower envelope. S5. For the upper envelope of the initial tolerance and the lower envelope of the initial tolerance, detect and remove the self-intersecting loops in the upper envelope of the initial tolerance and the self-intersecting loops in the lower envelope of the initial tolerance, respectively. S6. Perform interpolation smoothing on the upper and lower envelopes after removing the self-intersecting loops to obtain smooth continuous curves. S7. Perform inverse scaling on the smoothed upper and lower envelopes to restore them to their original frequency and amplitude, forming a dynamic tolerance envelope that encloses the qualified reference curve. Compare the curve to be tested with this dynamic tolerance envelope. If all data points of the curve to be tested are within the envelope range, it is considered qualified; otherwise, it is considered unqualified.

2. The adaptive tolerance envelope construction method for the spectrum curve according to claim 1, characterized in that, The step in S3 to determine whether the current point is a feature point based on the slope product is as follows: Calculate the slope k1 of the line connecting the current point and the previous point, and the slope k2 of the line connecting the current point and the next point; If the product of k1 and k2 is less than or equal to zero, then the current point is determined to be a feature point; If the product of k1 and k2 is greater than zero, then the current point is determined to be a non-feature point.

3. The adaptive tolerance envelope construction method for the spectral curve according to claim 1, characterized in that, The step of longitudinally offsetting the current point along the vertical axis in S3 is as follows: The coordinates of the upper offset point of the current point are taken as (Xi, Yi + Lu), and the coordinates of the lower offset point of the current point are taken as (Xi, Yi - Ld); Where Lu is the preset upper tolerance offset and Ld is the preset lower tolerance offset.

4. The adaptive tolerance envelope construction method for the spectrum curve according to claim 1, characterized in that, The step in S3 of offsetting the current point along the normal direction based on the local average slope is as follows: Calculate the average slope k = (k1 + k2) / 2; Calculate the coordinates of the upper and lower offset points of the current point using the normal offset formula: ， ； ， 。 5. The adaptive tolerance envelope construction method for the spectrum curve according to claim 1, characterized in that, The step in S3 of performing normal offset on the starting point or ending point based on the slope of the unilateral connecting line is as follows: For the starting point, take k = k2; for the ending point, take k = k1. The coordinates of the upper and lower offset points of the starting or ending point are calculated according to the normal offset formula.

6. The adaptive tolerance envelope construction method for the spectrum curve according to claim 1, characterized in that, The step of detecting and removing self-intersecting loops in S5 includes: Traverse the x-coordinate values ​​of each point on the upper or lower envelope of the initial tolerance to identify continuous segments that satisfy the condition of first monotonically increasing, then monotonically decreasing, and then monotonically increasing again. Each consecutive paragraph is labeled as a potential self-intersecting loop, and the maximum value of the x-coordinate X within that paragraph is recorded. max and minimum value X min ; In the original point sequence of the upper or lower envelope of the initial tolerance, find the last x-coordinate value less than or equal to the minimum value X, starting from the starting point. min The point is denoted as the outer starting point Ps; Find the first x-coordinate value greater than or equal to the maximum value X from the end point of the paragraph. max The point is denoted as Pe, the outer endpoint of the ring. The self-intersecting loop is simplified and reconstructed based on the relationship between the tangent slopes at the starting point Ps and the ending point Pe.

7. The adaptive tolerance envelope construction method for the spectrum curve according to claim 6, characterized in that, The simplified reconstruction steps include: Calculate the tangent slope Ks at Ps and the tangent slope Ke at Pe; If Ks * Ke ≥ 0, then the original curve segment between Ps and Pe is simplified to a straight line segment connecting Ps and Pe; If Ks * Ke < 0, then calculate the intersection point Pj of the line determined by Ps and its slope Ks and the line determined by Pe and its slope Ke, and simplify the original curve segment between Ps and Pe into a broken line segment connecting Ps, Pj and Pe in sequence. Replace all points from Ps to Pe in the original point list of the initial tolerance upper envelope or initial tolerance lower envelope with the simplified reconstructed line segments.

8. The adaptive tolerance envelope construction method for the spectrum curve according to claim 1, characterized in that, The scaling process in S1 uses either maximum / minimum scaling or standard deviation scaling.

9. The adaptive tolerance envelope construction method for the spectral curve according to claim 1, characterized in that, The width of the sliding window in S2 is set according to the main frequency bandwidth of the qualified reference curve or an empirical formula.

10. A storage medium storing a computer program, characterized in that, When the computer program is executed by the processor, it implements the steps of the adaptive tolerance envelope construction method as described in any one of claims 1 to 9.

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