A method for detecting deformation of a high-strength pipe threading machine head forging under dynamic load

Abstract

The present application relates to the technical field of on-line condition monitoring and fault diagnosis of metal plastic processing equipment, and discloses a deformation detection method of a high-strength pipe penetrating machine top head forging under dynamic load. A plurality of channel acceleration sensors are arranged circumferentially on the top head forging shell to collect vibration data, and a non-dimensional time sequence is used to average and standardize the data to construct a non-stationary index. Based on the fractional Fourier transform, a transform perspective is established according to the angle, the energy concentration degree of each angle is calculated, and the optimal angle is selected to obtain the amplitude spectrum and pulse intensity index. A plurality of groups of normal working condition historical data are used to generate a reference intensity and a threshold value, which are compared with the current index, and the standardized signal is divided into continuous time subintervals for local analysis and continuous determination, so that the top head forging micro-transient and stable structural deformation can be sensitively and reliably identified, and the shortcomings that the traditional single-point measurement and fixed threshold value are difficult to reflect the state and adapt to multiple working conditions are overcome.

Description

Technical Field

[0001] This invention relates to the field of online condition monitoring and fault diagnosis technology for metal plastic processing equipment, specifically a deformation detection method for high-strength tube threading machine mandrel forgings under dynamic load. Background Technology

[0002] High-strength tube-threading machines are widely used in the hot forming process of seamless steel pipes and other metal tubes. Their mandrel forgings undergo long-term service under high temperature, high load, and strong impact conditions, making them prone to plastic deformation and even local instability. In existing projects, monitoring the deformation of mandrel forgings often involves disassembly and measurement after the machine is stopped. This includes measuring the mandrel's external dimensions using gauges, calipers, templates, or coordinate measuring machines, or manually judging the results based on finite element static analysis. These methods rely on machine shutdown and disassembly, have long inspection cycles, cannot reflect the deformation evolution process under dynamic loads, and are difficult to detect early anomalies in a timely manner, often only being discovered after significant out-of-roundness, uneven wear, or fracture risk has occurred.

[0003] In terms of online monitoring, existing technologies mainly target the main drive system, bearing housing, or overall frame vibration of the pipe-piercing machine. A small number of vibration or acceleration sensors are deployed, and traditional frequency domain methods such as Fast Fourier Transform and frequency conversion analysis are used to provide a rough diagnosis of the equipment's operating status. These methods typically assume that the vibration signal is approximately stationary and focus on identifying speed-related periodic faults. They struggle to effectively separate the non-stationary, intermittent pulse characteristics generated by the mandrel forging under impact loads and thermo-mechanical coupling. Furthermore, because the measuring points are mostly located on the frame or support components, the signal contains a large amount of background vibration from components such as rolls, guides, and transmission chains, lacking directional sensitivity to local structural deformations of the mandrel forging. Some studies have also introduced time-frequency analysis methods such as Short-Time Fourier Transform, wavelet analysis, and Hilbert-Huang Transform to extract time-frequency features from the vibration signal during the piercing process. However, existing methods generally suffer from the following problems: First, parameters such as window length, wavelet basis, and number of decomposition levels largely depend on empirical selection, resulting in poor algorithm repeatability and engineering portability; second, time-frequency energy exhibits significant diffusion and cross-interference, making it difficult to clearly separate transient pulse components caused by top structure deformation amidst strong background noise and process fluctuations; third, most methods remain at the qualitative observation level of time-frequency spectra, lacking a unified method to quantify non-stationary impact characteristics into stable scalar indicators, and also lacking adaptive criteria for comparison with normal operating conditions, making it difficult to form threshold logic that can be directly used for online judgment.

[0004] Therefore, this case aims to propose a deformation detection method for high-strength pipe-threading machine mandrel forgings under dynamic loads. First, by deploying multi-channel accelerometers along the axial direction, the acceleration waveform of the forging under actual working conditions is collected. The original data is then averaged and standardized using dimensionless time sequence numbers to extract non-stationary indices, thereby obtaining the overall non-stationary characteristics of the signal. Subsequently, a bridge is built between the time domain and the fractional Fourier transform domain, dividing the angle candidate set and constructing a kernel function matrix. The transformation angle that best highlights the deformation signal is identified by calculating the energy concentration at each candidate angle. Next, the amplitude spectrum is extracted, and local peaks are detected on the spectrum to form a pulse peak set. The pulse intensity index of a single detection is further calculated based on statistics. Then, a reference intensity and judgment threshold are obtained by modeling historical data, and real-time indices are included in the comparison to give an overall deformation judgment. Finally, the signal is divided into multiple continuous intervals along the time axis, and the above transformation and judgment process is repeated to construct a sub-interval deformation sequence. Stable structural deformation trends are identified based on the continuous judgment length. Summary of the Invention

[0005] This invention provides a method for detecting deformation of high-strength tube-threading machine mandrel forgings under dynamic load, which helps to solve the problems mentioned in the background art.

[0006] This invention provides the following technical solution: a method for detecting the deformation of a high-strength tube-threading machine mandrel forging under dynamic load, comprising:

[0007] Accelerometers are installed circumferentially on the outer shell of the mandrel forging, and sampling parameters are set to collect multi-channel raw acceleration data along the axial direction.

[0008] Using the dimensionless time sequence as a reference, the average acceleration value is calculated for each sampling time to form a single-channel reference signal. The mean and standard deviation are calculated to generate a standardized signal, and the non-stationary index is constructed by the difference of the standardized signal.

[0009] Establish transform domain sampling points on the time-domain discrete sampling points corresponding to the standardized signal, divide the angle interval to obtain the candidate fractional Fourier angle set, and generate the fractional Fourier transform kernel function matrix for each angle.

[0010] Perform discrete transformation according to candidate angles to obtain a sequence of fractional Fourier transform results in complex form, and calculate the energy concentration index in the energy observation interval;

[0011] The candidate fractional Fourier angle with the largest energy concentration index is selected as the optimal fractional Fourier angle, and the complex modulus of the transformation result is extracted to form an amplitude spectrum sequence.

[0012] Local peaks are detected in the amplitude spectrum sequence to form a set of pulse peak positions, and the pulse intensity index is calculated based on the spectral statistics.

[0013] Multiple sets of historical acceleration data were collected under normal working conditions of the mandrel forging. Then, the following steps were performed in sequence: sensor deployment and acquisition, standardization and non-stationarity index construction, candidate angle and kernel function generation, fractional Fourier transform and energy concentration calculation, optimal angle identification and amplitude spectrum extraction, pulse peak detection and pulse intensity index calculation. A set of historical pulse intensity indices was obtained, a reference intensity index and a judgment threshold were calculated, and the deformation was determined by comparing them with the current pulse intensity index.

[0014] In the time domain, the standardized signal is divided into continuous time sub-intervals, and local fractional Fourier transform and pulse intensity index calculation are performed respectively. A deformation judgment sequence is constructed according to the sub-interval results, and structural deformation trends are identified based on the continuous judgment length.

[0015] Optionally, the step of circumferentially arranging acceleration sensors on the outer shell of the mandrel forging, setting sampling parameters, and collecting multi-channel raw acceleration data along the axial direction specifically includes:

[0016] Several accelerometers are symmetrically arranged in pairs or multiple pairs along the circumferential direction on the mandrel forging shell. Each accelerometer is assigned a unique number, and each accelerometer outputs the acceleration measurement value along the axial direction of the mandrel.

[0017] Set the total length of the dimensionless time series for the entire acquisition process and the dimensionless time step between two adjacent samples. Divide the total length of the dimensionless time series by the dimensionless time step to obtain the maximum sampling number. Increment the maximum sampling number by one to obtain the total number of sampling points. Then, starting from the initial dimensionless time number, add the numbers sequentially according to the dimensionless time step to calculate the dimensionless time number corresponding to each discrete sampling point.

[0018] At each discrete sampling point, the raw output values ​​of all accelerometers corresponding to the current discrete sampling point are collected to form a multi-channel raw acceleration data sequence indexed by the accelerometer number and the dimensionless time sequence number.

[0019] At each discrete sampling point, the original output values ​​of all accelerometers at the current discrete sampling point are summed, and the summation result is divided by the number of accelerometers to calculate the average acceleration value of the current discrete sampling point. All average acceleration values ​​are arranged in dimensionless time sequence to construct a single-channel reference signal sequence.

[0020] Optionally, the step of calculating the average acceleration value at each sampling time based on the dimensionless time sequence number to form a single-channel reference signal, calculating the mean and standard deviation to generate a standardized signal, and constructing a non-stationarity index using the difference of the standardized signal, specifically includes:

[0021] The mean of the reference signal sequence is calculated by summing the reference signal values ​​corresponding to all sampling points in the single-channel reference signal sequence and dividing the sum by the total number of sampling points.

[0022] At each sampling point, the difference between the reference signal value and the mean of the reference signal sequence is calculated. The difference is squared for all sampling points, and the sum of all squared results is calculated. The sum is then divided by the total number of sampling points to obtain the standard deviation of the reference signal sequence. When the standard deviation of the reference signal sequence is greater than zero, the mean of the reference signal sequence is subtracted from the reference signal value for each sampling point, and then the result is divided by the standard deviation of the reference signal sequence to generate a standardized signal sequence arranged in dimensionless time sequence. When the standard deviation of the reference signal sequence is zero, the standardized values ​​of all sampling points in the standardized signal sequence are uniformly set to zero.

[0023] In a standardized signal sequence, starting from the second sampling point to the penultimate sampling point, the second difference component formed by the standardized values ​​of three adjacent sampling points is calculated sequentially. Each second difference component is squared and summed. The coefficient relationship between the sum of squares and the constant 2 is then normalized to obtain the non-stationarity index.

[0024] Based on the total number of sampling points, a non-stationarity threshold is constructed by subtracting one from the total number of sampling points and multiplying by a constant two. The non-stationarity index is compared with the non-stationarity threshold. When the non-stationarity index is greater than the non-stationarity threshold, the standardized signal sequence is determined to have significant non-stationarity characteristics. When the non-stationarity index is not greater than the non-stationarity threshold, the standardized signal sequence is determined to be stationary.

[0025] Optionally, the step of establishing transform domain sampling points on the time-domain discrete sampling points corresponding to the standardized signal, dividing the angle interval to obtain a candidate fractional Fourier angle set, and generating the fractional Fourier transform kernel function matrix for each angle specifically includes:

[0026] Within the fractional Fourier transform domain, a transform domain sampling point sequence is constructed using the same total number of sampling points and dimensionless time step as the standardized signal sequence, so that each transform domain sampling point corresponds to a discrete time-domain sampling point in dimensionless time.

[0027] Within the preset angle range of zero to half a cycle, the angle range is evenly divided into several evenly spaced angles according to the preset division parameters. Each angle except the starting angle and the ending angle is taken as a candidate fractional Fourier angle to form a set of candidate fractional Fourier angles.

[0028] For each angle in the candidate fractional Fourier angle set, based on the sine and cosine function values ​​of the corresponding candidate fractional Fourier angle, a phase expression is constructed, which includes the dimensionless time index square term of the discrete time-domain sampling points, the dimensionless time index square term of the transform-domain sampling points, and the product term of the two. Substituting the phase expression into the complex exponential function and combining it with the angle-related amplitude adjustment coefficient, the kernel function value on all combinations of discrete time-domain sampling points and transform-domain sampling points is calculated, forming the fractional Fourier transform kernel function matrix corresponding to each candidate fractional Fourier angle.

[0029] Optionally, the step of performing a discrete transformation according to the candidate angle to obtain a sequence of complex-form fractional Fourier transform results, and calculating the energy concentration index within the energy observation interval, specifically includes:

[0030] For each angle in the candidate fractional Fourier angle set, multiply each sampling point value in the standardized signal sequence with the kernel function value at the corresponding row and column position in the fractional Fourier transform kernel function matrix of the corresponding candidate fractional Fourier angle, and sum them according to the dimensionless time sequence to obtain the complex form fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle at each transform domain sampling point.

[0031] In the transform domain sampling point sequence, a continuous transform domain sampling point interval at the middle position is selected as the energy observation interval, and the starting transform domain sampling point number and the ending transform domain sampling point number of the energy observation interval are kept within the range of transform domain sampling points.

[0032] For each candidate fractional Fourier angle, the complex modulus values ​​of all transform domain sampling points in the fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle are squared and summed to obtain the total energy of the corresponding candidate fractional Fourier angle. Within the energy observation interval, the complex modulus values ​​of the transform domain sampling points belonging to the energy observation interval in the fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle are squared and summed to obtain the energy within the energy observation interval. When the total energy is greater than zero, the energy within the energy observation interval is divided by the total energy to calculate the energy concentration index of the corresponding candidate fractional Fourier angle. When the total energy is zero, the energy concentration index of the corresponding candidate fractional Fourier angle is set to zero.

[0033] Optionally, the step of selecting the candidate fractional Fourier angle with the largest energy concentration index as the optimal fractional Fourier angle and extracting the complex modulus of the transformation result to form an amplitude spectrum sequence specifically includes:

[0034] In the set of candidate fractional Fourier angles, the energy concentration index corresponding to each candidate fractional Fourier angle is compared, and the candidate fractional Fourier angle with the largest energy concentration index is selected as the optimal fractional Fourier angle; when multiple energy concentration indices have the same maximum value, the one with the smallest angle value among these corresponding candidate fractional Fourier angles is selected as the optimal fractional Fourier angle.

[0035] In the sequence of fractional Fourier transform results in complex form corresponding to the optimal fractional Fourier angle, the complex modulus is calculated for the complex result of each sample point in the transform domain, and the complex modulus values ​​are arranged in order of the sample point number in the transform domain to construct the amplitude spectrum sequence under the optimal fractional Fourier angle.

[0036] Optionally, the step of detecting local peaks in the amplitude spectrum sequence, forming a set of pulse peak positions, and calculating the pulse intensity index based on spectral statistics specifically includes:

[0037] In the amplitude spectrum sequence, starting from the second transform domain sampling point to the second-to-last transform domain sampling point, the amplitude of the current transform domain sampling point is compared with the amplitude of the adjacent transform domain sampling point to its left and the amplitude of the adjacent transform domain sampling point to its right. When the amplitude of the current transform domain sampling point is greater than the amplitude of the adjacent transform domain sampling point to its left and the amplitude of the adjacent transform domain sampling point to its right, the current transform domain sampling point is marked as a pulse peak, the sequence number of the transform domain sampling point where the pulse peak is located is recorded, a set of pulse peak positions is constructed, and the number of pulse peaks is counted.

[0038] The amplitudes of all transform domain sampling points in the amplitude spectrum sequence are summed, and the summation result is divided by the total number of transform domain sampling points to obtain the mean of the amplitude spectrum. At each transform domain sampling point, the difference between the amplitude of the current transform domain sampling point and the mean of the amplitude spectrum is calculated. The differences of all transform domain sampling points are squared and summed. The summation result is divided by the total number of transform domain sampling points to obtain the standard deviation of the amplitude spectrum.

[0039] When the standard deviation of the amplitude spectrum is greater than zero and the number of pulse peaks is greater than zero, the ratio between the difference between the amplitude and the mean of the amplitude spectrum and the standard deviation of the amplitude spectrum is calculated for each pulse peak corresponding to the transform domain sampling point. The calculated ratio is squared and summed. The number of pulse peaks is used as the divisor to average the sum of squares to obtain the pulse intensity index. When the standard deviation of the amplitude spectrum is zero or the number of pulse peaks is zero, the pulse intensity index is set to zero.

[0040] Optionally, the step of collecting multiple sets of historical acceleration data under normal operating conditions of the mandrel forging, and sequentially performing sensor deployment and acquisition, standardization and non-stationarity index construction, candidate angle and kernel function generation, fractional Fourier transform and energy concentration calculation, optimal angle identification and amplitude spectrum extraction, pulse peak detection and pulse intensity index calculation, to obtain a set of historical pulse intensity indices, calculate a reference intensity index and a judgment threshold, and compare it with the current pulse intensity index to obtain a deformation judgment, specifically including:

[0041] When the mandrel forging is in normal working condition, multiple sets of historical acceleration data are collected. For each set of historical acceleration data, the following steps are performed in sequence: sensor deployment and multi-channel raw signal acquisition, standardization transformation and initial non-stationarity judgment, fractional Fourier transform kernel function matrix generation and candidate fractional Fourier angle set construction, fractional Fourier transform calculation and energy concentration index calculation, optimal fractional Fourier angle identification and amplitude spectrum extraction, and pulse peak detection and pulse intensity index calculation. The pulse intensity index corresponding to each set of historical acceleration data is obtained, forming a set of historical pulse intensity indices.

[0042] Summing up all pulse intensity indices in the historical pulse intensity index set, dividing the sum by the number of historical acceleration data sets, and calculating the reference intensity index, then adding a constant to the reference intensity index to construct the judgment threshold.

[0043] The same signal processing procedure as the historical acceleration data is performed on the current acceleration data to be detected to calculate the current pulse intensity index. The difference between the current pulse intensity index and the reference intensity index is calculated. The current difference is compared with the judgment threshold. When the current difference is greater than the judgment threshold, it is determined that the high-strength tube threading machine mandrel forging has deformed. When the current difference is not greater than the judgment threshold, it is determined that the high-strength tube threading machine mandrel forging has not deformed.

[0044] Optionally, the step of dividing the standardized signal into continuous-time sub-intervals in the time domain, performing local fractional Fourier transform and pulse intensity index calculation on each sub-interval, constructing a deformation judgment sequence based on the sub-interval results, and identifying structural deformation trends based on the continuous judgment length specifically includes:

[0045] The standardized signal sequence obtained from a single detection is uniformly divided into several continuous time sub-intervals in the time domain according to length. The number of sampling points in each time sub-interval is calculated by dividing the total number of sampling points in the standardized signal sequence by the number of time sub-intervals. The starting dimensionless time number and ending dimensionless time number of each time sub-interval are calculated in the order of dimensionless time number.

[0046] For each time sub-interval, select all sampling points belonging to the time sub-interval range between the starting dimensionless time index and the ending dimensionless time index of the time sub-interval, extract the standardized signal values ​​of these sampling points, perform local fractional Fourier transform using the optimal fractional Fourier angle, construct the local amplitude spectrum sequence of the corresponding time sub-interval, and calculate the local pulse intensity index of the corresponding time sub-interval according to the steps of pulse peak detection and pulse intensity index calculation.

[0047] For each time sub-interval, the local pulse intensity index of the corresponding time sub-interval is compared with the reference intensity index, the difference between the two is calculated, the current difference is compared with the judgment threshold, when the current difference is greater than the judgment threshold, the deformation judgment result of the corresponding time sub-interval is recorded as one, when the current difference is not greater than the judgment threshold, the deformation judgment result of the corresponding time sub-interval is recorded as zero, and the deformation judgment results of all time sub-intervals are arranged in order of the starting dimensionless time sequence number of the time sub-interval to construct a deformation judgment sequence;

[0048] Set the continuous judgment length, which does not exceed the total number of time sub-intervals. In the deformation judgment sequence, examine each continuous subsequence with the same length as the continuous judgment length in turn. When there is a continuous subsequence in which all deformation judgment results are one, it is determined that there is a stable structural deformation trend in the corresponding time range. When there is no continuous subsequence in which all deformation judgment results are one, it is determined that there is no stable structural deformation trend in the entire sampling time range.

[0049] The present invention has the following beneficial effects:

[0050] 1. This scheme uniformly deploys sensors circumferentially on the mandrel forging, offering spatial sampling advantages compared to traditional single-point measurements, enabling the capture of dynamic stress distribution along the circumference. Dimensionless time indices are used to synchronously index all channel data, effectively mitigating the drift issues of absolute time and sampling frequency. A single-channel reference signal is formed through point-by-point averaging, preserving overall deformation fluctuation information while reducing noise interference between channels. This preprocessing method allows subsequent standardization and differential calculations to focus more on genuine structural changes, rather than random interference or sensor bias. Unlike existing technologies that typically only perform denoising and filtering, this method introduces mean and standard deviation calculations from a statistical perspective, achieving adaptive normalization of the signal amplitude distribution and laying a solid foundation for non-stationary feature extraction.

[0051] 2. Given that signals under high-intensity dynamic loads often exhibit complex non-stationary characteristics, this scheme constructs a non-stationarity index through second-order difference variance normalization to quantitatively evaluate the fluctuation patterns of macroscopic signals. Unlike conventional time-frequency analysis or sliding window variance calculation, second-order difference operations can more sensitively capture local abrupt changes and micro-oscillations, giving the non-stationarity index both high time resolution and stability. A threshold criterion based on the total number of sampling points enables adaptive classification of stationary and non-stationary states without relying on empirical parameter tuning. This solves the problem of distinguishing between load changes and structural deformation signals in traditional detection methods, providing a strong reference for selecting appropriate calculation intervals for subsequent fractional Fourier transforms, thereby reducing false alarms and false negatives.

[0052] 3. Based on the need for multi-angle analysis of non-stationary signals, this scheme uniformly divides the fractional Fourier angle space, constructs an angle candidate set, and generates a kernel function matrix for the time-domain sequence based on each angle. This differs from traditional methods that use fixed transformation angles or empirically selected angles. It comprehensively covers all possible rotation bases from zero to half a period, making the transformation more flexible. The kernel function, during construction, includes the squared terms of the time domain and the squared terms of the frequency domain, as well as their product, effectively incorporating the time-frequency coupling information of the signal. This design increases the representational power of the fractional Fourier domain, enabling more accurate alignment of local energy concentrations in non-stationary signals. Compared to existing multi-resolution analysis methods, this scheme captures the multi-scale and multi-angle features of signals more deeply, improves detection sensitivity, and provides a more accurate benchmark for subsequent energy concentration calculations.

[0053] 4. This scheme obtains a complex fractional Fourier transform sequence at each candidate angle by performing an inner product operation between a kernel function and the standardized signal, and calculates the energy concentration index within a preset central energy observation interval. Unlike directly calculating the full-spectrum energy, this method focuses on the distribution ratio of signal energy in the key observation interval. The concentration index obtained after normalization clearly reflects local signal abrupt changes. The selection of the central interval and the calculation of the ratio have a significant effect on avoiding edge effects and reducing noise influence; at the same time, a safety zeroing is performed when the total energy is zero to ensure system stability. This index can quickly distinguish the differences in signal energy distribution at different angles, providing a quantitative basis for determining the optimal fractional Fourier angle, thereby improving the accuracy of identifying abnormally deformed signals.

[0054] 5. This scheme selects the angle with the largest energy concentration index from all candidate angles as the optimal angle, and prioritizes the angle with the smallest value when the indices are the same, to ensure the determinism of the output angle. This strategy avoids the instability caused by relying on manual thresholds or blind selection in traditional methods; through sorting and the small value priority rule, it achieves the repeatability and transparency of the algorithm. This gives the optimal transformation angle a clear and stable physical meaning and ensures the interpretability of amplitude spectrum information. In practical applications, it reduces the judgment fluctuations caused by angle jitter, enabling the detection system to maintain high consistency and reduce the false alarm rate during continuous operation.

[0055] 6. In the amplitude spectrum sequence extracted at the optimal angle, this scheme automatically identifies local peaks through neighbor-to-neighbor comparison and constructs a set of pulse peak positions. Then, it calculates the pulse intensity index based on the statistical relationship between the peak value, mean, and standard deviation. This method differs from simple peak counting or energy thresholding methods by combining peak information with full-spectrum statistics, enabling the pulse intensity to simultaneously reflect the prominence of the peak and the overall signal fluctuation characteristics. For signals with only noise or no structural changes, the intensity index is adaptively set to zero to reduce false alarms. For signals containing actual structural responses, the index can accurately reflect the deformation amplitude. This enhances the sensitivity to capturing weak deformation signals, which is crucial for improving the accuracy of structural health monitoring.

[0056] 7. This solution utilizes multiple sets of historical acceleration data under normal operating conditions, fully executing the aforementioned sensing, preprocessing, transformation, and pulse intensity calculation processes to obtain a set of historical pulse intensities. The average value of these intensities is used as a reference intensity index, and a unit constant is added to construct a judgment threshold. Compared to traditional fixed threshold or empirical threshold methods, this method automatically generates thresholds based on real historical data, more closely reflecting the actual operating condition fluctuation range and effectively adapting to the field environment. The addition of a constant bias enhances sensitivity to sudden anomalies. Therefore, comparing real-time pulse intensity with dynamic thresholds allows for flexible determination of structural deformation, adapting to multiple operating condition switching and reducing manual parameter tuning costs, achieving zero-benchmarking and self-learning structural health monitoring.

[0057] 8. To address the potential time-varying and continuous nature of deformation, this scheme divides the standardized signal into several continuous sub-intervals in the time domain. Local fractional Fourier transforms are performed on each sub-interval, and the pulse intensity is calculated to obtain the local judgment result for each sub-interval. Then, based on a preset continuous judgment length, stable deformation trends are identified. Unlike a one-time full-segment judgment, this segmented multi-scale strategy combines time-domain localization and trend analysis capabilities, accurately identifying the start and duration of deformation. The adjustable continuous sub-interval judgment length adapts to the monitoring needs of different structures and operating conditions, enabling early detection of sudden deformations while avoiding temporary false alarms caused by isolated anomalies. This innovation tightly integrates single-detection with trend judgment, achieving real-time, continuous, and reliable monitoring of structural deformation. Attached Figure Description

[0058] Figure 1 This is a schematic diagram of the process of the present invention. Detailed Implementation

[0059] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0060] Example, refer to Figure 1 A method for detecting deformation of a high-strength tube-threading machine mandrel forging under dynamic load, comprising:

[0061] Accelerometers are installed circumferentially on the outer shell of the mandrel forging, and sampling parameters are set to collect multi-channel raw acceleration data along the axial direction.

[0062] Using the dimensionless time sequence as a reference, the average acceleration value is calculated for each sampling time to form a single-channel reference signal. The mean and standard deviation are calculated to generate a standardized signal, and the non-stationary index is constructed by the difference of the standardized signal.

[0063] Establish transform domain sampling points on the time-domain discrete sampling points corresponding to the standardized signal, divide the angle interval to obtain the candidate fractional Fourier angle set, and generate the fractional Fourier transform kernel function matrix for each angle.

[0064] Perform discrete transformation according to candidate angles to obtain a sequence of fractional Fourier transform results in complex form, and calculate the energy concentration index in the energy observation interval;

[0065] The candidate fractional Fourier angle with the largest energy concentration index is selected as the optimal fractional Fourier angle, and the complex modulus of the transformation result is extracted to form an amplitude spectrum sequence.

[0066] Local peaks are detected in the amplitude spectrum sequence to form a set of pulse peak positions, and the pulse intensity index is calculated based on the spectral statistics.

[0067] Multiple sets of historical acceleration data were collected under normal working conditions of the mandrel forging. Then, the following steps were performed in sequence: sensor deployment and acquisition, standardization and non-stationarity index construction, candidate angle and kernel function generation, fractional Fourier transform and energy concentration calculation, optimal angle identification and amplitude spectrum extraction, pulse peak detection and pulse intensity index calculation. A set of historical pulse intensity indices was obtained, a reference intensity index and a judgment threshold were calculated, and the deformation was determined by comparing them with the current pulse intensity index.

[0068] In the time domain, the standardized signal is divided into continuous time sub-intervals, and local fractional Fourier transform and pulse intensity index calculation are performed respectively. A deformation judgment sequence is constructed according to the sub-interval results, and structural deformation trends are identified based on the continuous judgment length.

[0069] By circumferentially deploying multi-channel accelerometers on the forging shell and setting unified sampling parameters, this scheme achieves omnidirectional vibration signal acquisition of the pipe-threading machine's mandrel under dynamic loads, overcoming the limitations of traditional single-point or few-point measurements that cannot reflect the overall stress and deformation. Dimensionless time sequences are used to average, calculate the mean and standard deviation of the multi-channel raw data, and second-order difference is used to construct a non-stationary index, accurately extracting the global and local non-stationary characteristics of the signal and avoiding the problem of losing subtle signals in common filtering and denoising processes. Next, transform-domain sampling points are established on the time-domain sampling points, and the entire angle interval is divided into several candidate fractional Fourier angles. A kernel function matrix covers all possible time-frequency coupling relationships, enabling multi-angle fractional Fourier detection of different deformation modes. This step compensates for the blind spots caused by fixed or empirically selected angles in traditional Fourier transforms, improving the ability to capture minute, instantaneous deformation events. Subsequently, energy concentration indices are calculated based on candidate angles, and the angle with the highest concentration is selected to obtain the optimal transform domain viewpoint. Complex modulus values ​​are extracted to form an amplitude spectrum, and local peaks on the spectral lines are identified to construct a set of pulse peak positions. Furthermore, pulse intensity indices are calculated using spectral statistical characteristics to separate the structural deformation signal from the noise background. Finally, reference intensity and thresholds are automatically generated by combining multiple sets of historical data from normal operating conditions, and compared and judged in real-time detection, avoiding the risk of misjudgment caused by fixed thresholds. By dividing the standardized signal into continuous sub-intervals and performing multiple local judgments, a time-domain deformation trend sequence is established, enabling accurate positioning and trend identification of stable structural deformations.

[0070] The process of circumferentially arranging acceleration sensors on the outer shell of the mandrel forging, setting sampling parameters, and collecting multi-channel raw acceleration data along the axial direction specifically includes:

[0071] Several accelerometers are symmetrically arranged in pairs or multiple pairs along the circumferential direction on the mandrel forging shell. Each accelerometer is assigned a unique number, and each accelerometer outputs the acceleration measurement value along the axial direction of the mandrel.

[0072] Set the total length of the dimensionless time series for the entire acquisition process and the dimensionless time step between two adjacent samples. Divide the total length of the dimensionless time series by the dimensionless time step to obtain the maximum sampling number. Increment the maximum sampling number by one to obtain the total number of sampling points. Then, starting from the initial dimensionless time number, add the numbers sequentially according to the dimensionless time step to calculate the dimensionless time number corresponding to each discrete sampling point.

[0073] At each discrete sampling point, the raw output values ​​of all accelerometers corresponding to the current discrete sampling point are collected to form a multi-channel raw acceleration data sequence indexed by the accelerometer number and the dimensionless time sequence number.

[0074] At each discrete sampling point, the original output values ​​of all accelerometers at the current discrete sampling point are summed, and the summation result is divided by the number of accelerometers to calculate the average acceleration value of the current discrete sampling point. All average acceleration values ​​are arranged in dimensionless time sequence to construct a single-channel reference signal sequence.

[0075] Symmetrical arrangement of the outer shell of the high-strength pipe-threading machine top head There are one accelerometer sensor, sensor number is... Each sensor outputs a measurement of acceleration along the axial direction of the top head; where, This refers to the total number of acceleration sensors installed on the top of the high-strength pipe-driving machine; The number for the accelerometer;

[0076] Set the total length of the dimensionless time series for the entire acquisition process to be [value missing]. The dimensionless time step between two adjacent samplings is Let the maximum sampling index number be The total number of sampling points is ;

[0077] Calculate the first The serial numbers of the sampling points are: , ;in, For the index of discrete sampling points in the time domain; For the first The dimensionless time sequence number corresponding to each discrete sampling point;

[0078] The first The sensor at the first The original output value of each sampling point is denoted as: ;in, For the first An accelerometer in continuous dimensionless time variable The output function takes continuous dimensionless time as input. The output is the acceleration measurement value at the corresponding moment; It is a continuous dimensionless time variable; For the first The accelerometer sensor is at the first The time corresponding to each discrete sampling point The original acceleration output value;

[0079] Calculate in the first All at each discrete sampling point The average value of the raw outputs of the accelerometers Specifically: , ;

[0080] Constructing a single-channel reference signal sequence .

[0081] The process involves calculating the average acceleration value at each sampling time using a dimensionless time sequence as a reference to form a single-channel reference signal, calculating the mean and standard deviation to generate a standardized signal, and constructing a non-stationary index using the difference of the standardized signal. Specifically, this includes:

[0082] The mean of the reference signal sequence is calculated by summing the reference signal values ​​corresponding to all sampling points in the single-channel reference signal sequence and dividing the sum by the total number of sampling points.

[0083] At each sampling point, the difference between the reference signal value and the mean of the reference signal sequence is calculated. The difference is squared for all sampling points, and the sum of all squared results is calculated. The sum is then divided by the total number of sampling points to obtain the standard deviation of the reference signal sequence. When the standard deviation of the reference signal sequence is greater than zero, the mean of the reference signal sequence is subtracted from the reference signal value for each sampling point, and then the result is divided by the standard deviation of the reference signal sequence to generate a standardized signal sequence arranged in dimensionless time sequence. When the standard deviation of the reference signal sequence is zero, the standardized values ​​of all sampling points in the standardized signal sequence are uniformly set to zero.

[0084] In a standardized signal sequence, starting from the second sampling point to the penultimate sampling point, the second difference component formed by the standardized values ​​of three adjacent sampling points is calculated sequentially. Each second difference component is squared and summed. The coefficient relationship between the sum of squares and the constant 2 is then normalized to obtain the non-stationarity index.

[0085] Based on the total number of sampling points, a non-stationarity threshold is constructed by subtracting one from the total number of sampling points and multiplying by a constant two. The non-stationarity index is compared with the non-stationarity threshold. When the non-stationarity index is greater than the non-stationarity threshold, the standardized signal sequence is determined to have significant non-stationarity characteristics. When the non-stationarity index is not greater than the non-stationarity threshold, the standardized signal sequence is determined to be stationary.

[0086] Calculate the reference signal sequence The mean is ;

[0087] Calculate the reference signal sequence The standard deviation is ;

[0088] like Then the standardized signal sequence for: , ;in, In the first Standardized acceleration values ​​at each sampling point;

[0089] like Then for all ,make ;

[0090] Constructing a second-order difference nonstationarity index Specifically: ;

[0091] Set the non-stationarity threshold as follows: ;

[0092] like Then determine the standardized signal sequence. It exhibits significant non-stationary characteristics;

[0093] like Then determine the standardized signal sequence. smooth.

[0094] The step of establishing transform domain sampling points on the time-domain discrete sampling points corresponding to the standardized signal, dividing the angle interval to obtain the candidate fractional Fourier angle set, and generating the fractional Fourier transform kernel function matrix for each angle specifically includes:

[0095] Within the fractional Fourier transform domain, a transform domain sampling point sequence is constructed using the same total number of sampling points and dimensionless time step as the standardized signal sequence, so that each transform domain sampling point corresponds to a discrete time-domain sampling point in dimensionless time.

[0096] Within the preset angle range of zero to half a cycle, the angle range is evenly divided into several evenly spaced angles according to the preset division parameters. Each angle except the starting angle and the ending angle is taken as a candidate fractional Fourier angle to form a set of candidate fractional Fourier angles.

[0097] For each angle in the candidate fractional Fourier angle set, based on the sine and cosine function values ​​of the corresponding candidate fractional Fourier angle, a phase expression is constructed, which includes the dimensionless time index square term of the discrete time-domain sampling points, the dimensionless time index square term of the transform-domain sampling points, and the product term of the two. Substituting the phase expression into the complex exponential function and combining it with the angle-related amplitude adjustment coefficient, the kernel function value on all combinations of discrete time-domain sampling points and transform-domain sampling points is calculated, forming the fractional Fourier transform kernel function matrix corresponding to each candidate fractional Fourier angle.

[0098] The sampling point numbers for constructing the fractional Fourier transform domain are: , ;in, The fractional Fourier transform of the first... A sequence of dimensionless sampling points; For the discrete index of the fractional Fourier transform domain;

[0099] Construct the fractional Fourier angle set as follows: ;in, The set of Fourier angles for all candidate scores; For the first One candidate score Fourier angle; Number the angle index; To divide the angle range Evenly divided into The partitioning parameters used in the partitioning process, and satisfying the following conditions. ;

[0100] For sets Every angle in Generate the fractional Fourier kernel function, specifically: ;in, For fractional Fourier angles Below, from the discrete point in the time domain Transformation to discrete points in the transform domain The kernel function value; The imaginary unit; It is a natural exponential function.

[0101] The step of performing a discrete transformation according to candidate angles to obtain a sequence of complex-form fractional Fourier transform results, and calculating the energy concentration index within the energy observation interval, specifically includes:

[0102] For each angle in the candidate fractional Fourier angle set, multiply each sampling point value in the standardized signal sequence with the kernel function value at the corresponding row and column position in the fractional Fourier transform kernel function matrix of the corresponding candidate fractional Fourier angle, and sum them according to the dimensionless time sequence to obtain the complex form fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle at each transform domain sampling point.

[0103] In the transform domain sampling point sequence, a continuous transform domain sampling point interval at the middle position is selected as the energy observation interval, and the starting transform domain sampling point number and the ending transform domain sampling point number of the energy observation interval are kept within the range of transform domain sampling points.

[0104] For each candidate fractional Fourier angle, the complex modulus values ​​of all transform domain sampling points in the fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle are squared and summed to obtain the total energy of the corresponding candidate fractional Fourier angle. Within the energy observation interval, the complex modulus values ​​of the transform domain sampling points belonging to the energy observation interval in the fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle are squared and summed to obtain the energy within the energy observation interval. When the total energy is greater than zero, the energy within the energy observation interval is divided by the total energy to calculate the energy concentration index of the corresponding candidate fractional Fourier angle. When the total energy is zero, the energy concentration index of the corresponding candidate fractional Fourier angle is set to zero.

[0105] For each angle index, the fractional Fourier transform of the normalized signal is calculated as follows: , ;in, For fractional Fourier angle indexing Corresponding angle Lower Transform Domain Index The fractional Fourier transform result at the point;

[0106] The start and end points of the energy observation interval index are as follows: , ,satisfy: ;in, , These are the start and end indices of the energy observation interval in the transform domain, respectively;

[0107] Steps S401 to S402 are performed to calculate the energy concentration index for each angle index, specifically as follows:

[0108] S401, if Then let: ;in, Angle Index The corresponding energy concentration index; For complex numbers The model; In the angle The total energy within the entire transform domain; In the angle Lower observation interval Internal energy;

[0109] S402, if Then let: .

[0110] The process of selecting the candidate fractional Fourier angle with the largest energy concentration index as the optimal fractional Fourier angle and extracting the complex modulus of the transformation result to form an amplitude spectrum sequence specifically includes:

[0111] In the set of candidate fractional Fourier angles, the energy concentration index corresponding to each candidate fractional Fourier angle is compared, and the candidate fractional Fourier angle with the largest energy concentration index is selected as the optimal fractional Fourier angle; when multiple energy concentration indices have the same maximum value, the one with the smallest angle value among these corresponding candidate fractional Fourier angles is selected as the optimal fractional Fourier angle.

[0112] In the sequence of fractional Fourier transform results in complex form corresponding to the optimal fractional Fourier angle, the complex modulus is calculated for the complex result of each sample point in the transform domain, and the complex modulus values ​​are arranged in order of the sample point number in the transform domain to construct the amplitude spectrum sequence under the optimal fractional Fourier angle.

[0113] Selecting energy concentration Angle index for obtaining the maximum value When there are multiple angle indices, When the same maximum value is obtained, the smallest angle index is taken as the minimum value. : ;

[0114] Set in the candidate set The optimal fractional Fourier angle selected is ;

[0115] At the optimal angle From the corresponding transformation results, extract the amplitude spectrum sequence. Specifically: , ;in, To achieve the optimal angle Lower Transform Domain Index Amplitude spectral elements at; For angle indexing The fractional Fourier transform result.

[0116] The process of detecting local peaks in the amplitude spectrum sequence, forming a set of pulse peak positions, and calculating the pulse intensity index based on spectral statistics specifically includes:

[0117] In the amplitude spectrum sequence, starting from the second transform domain sampling point to the second-to-last transform domain sampling point, the amplitude of the current transform domain sampling point is compared with the amplitude of the adjacent transform domain sampling point to its left and the amplitude of the adjacent transform domain sampling point to its right. When the amplitude of the current transform domain sampling point is greater than the amplitude of the adjacent transform domain sampling point to its left and the amplitude of the adjacent transform domain sampling point to its right, the current transform domain sampling point is marked as a pulse peak, the sequence number of the transform domain sampling point where the pulse peak is located is recorded, a set of pulse peak positions is constructed, and the number of pulse peaks is counted.

[0118] The amplitudes of all transform domain sampling points in the amplitude spectrum sequence are summed, and the summation result is divided by the total number of transform domain sampling points to obtain the mean of the amplitude spectrum. At each transform domain sampling point, the difference between the amplitude of the current transform domain sampling point and the mean of the amplitude spectrum is calculated. The differences of all transform domain sampling points are squared and summed. The summation result is divided by the total number of transform domain sampling points to obtain the standard deviation of the amplitude spectrum.

[0119] When the standard deviation of the amplitude spectrum is greater than zero and the number of pulse peaks is greater than zero, the ratio between the difference between the amplitude and the mean of the amplitude spectrum and the standard deviation of the amplitude spectrum is calculated for each pulse peak corresponding to the transform domain sampling point. The calculated ratio is squared and summed. The number of pulse peaks is used as the divisor to average the sum of squares to obtain the pulse intensity index. When the standard deviation of the amplitude spectrum is zero or the number of pulse peaks is zero, the pulse intensity index is set to zero.

[0120] In index range Within, seeking fulfillment: , index The set of pulse peak positions is as follows: ;in, For the first The index position of each local pulse peak in the transform domain; Index the pulse peaks; Index all pulse peaks A set; The number of detected pulse peaks;

[0121] Calculate the amplitude spectrum sequence mean at all transform domain sampling points Specifically: ;

[0122] Calculate the amplitude spectrum sequence Standard deviation Specifically: ;

[0123] like and The pulse intensity index is then constructed as follows: ;in, This is a pulse intensity index based on the optimal angular amplitude spectrum;

[0124] like or Then let .

[0125] The process involves collecting multiple sets of historical acceleration data under normal operating conditions of the mandrel forging, and sequentially performing sensor deployment and acquisition, standardization and non-stationarity index construction, candidate angle and kernel function generation, fractional Fourier transform and energy concentration calculation, optimal angle identification and amplitude spectrum extraction, pulse peak detection and pulse intensity index calculation to obtain a set of historical pulse intensity indices. A reference intensity index and a judgment threshold are then calculated and compared with the current pulse intensity index to determine deformation. Specifically, this includes:

[0126] When the mandrel forging is in normal working condition, multiple sets of historical acceleration data are collected. For each set of historical acceleration data, the following steps are performed in sequence: sensor deployment and multi-channel raw signal acquisition, standardization transformation and initial non-stationarity judgment, fractional Fourier transform kernel function matrix generation and candidate fractional Fourier angle set construction, fractional Fourier transform calculation and energy concentration index calculation, optimal fractional Fourier angle identification and amplitude spectrum extraction, and pulse peak detection and pulse intensity index calculation. The pulse intensity index corresponding to each set of historical acceleration data is obtained, forming a set of historical pulse intensity indices.

[0127] Summing up all pulse intensity indices in the historical pulse intensity index set, dividing the sum by the number of historical acceleration data sets, and calculating the reference intensity index, then adding a constant to the reference intensity index to construct the judgment threshold.

[0128] The same signal processing procedure as the historical acceleration data is performed on the current acceleration data to be detected to calculate the current pulse intensity index. The difference between the current pulse intensity index and the reference intensity index is calculated. The current difference is compared with the judgment threshold. When the current difference is greater than the judgment threshold, it is determined that the high-strength tube threading machine mandrel forging has deformed. When the current difference is not greater than the judgment threshold, it is determined that the high-strength tube threading machine mandrel forging has not deformed.

[0129] When the forging is in normal working condition, collect data. Each set of historical data was used to calculate the corresponding pulse intensity index. , ;in, The number of historical data sets used to model the normal state; A numbered index for historical data; For the first The pulse intensity index of the group under historical data of normal operating conditions;

[0130] Construction reference strength index is ;

[0131] Construct the judgment threshold as ;

[0132] Pulse intensity index obtained from the current data to be detected If satisfied Then it is determined that the high-strength tube-threading machine mandrel forging has deformed; if the following conditions are met... Therefore, it is determined that the high-strength tube-threading machine mandrel forging has not deformed.

[0133] The process involves dividing the standardized signal into continuous-time sub-intervals in the time domain, performing local fractional Fourier transform and pulse intensity index calculations on each sub-interval, constructing a deformation judgment sequence based on the sub-interval results, and identifying structural deformation trends based on the continuous judgment length. Specifically, this includes:

[0134] The standardized signal sequence obtained from a single detection is uniformly divided into several continuous time sub-intervals in the time domain according to length. The number of sampling points in each time sub-interval is calculated by dividing the total number of sampling points in the standardized signal sequence by the number of time sub-intervals. The starting dimensionless time number and ending dimensionless time number of each time sub-interval are calculated in the order of dimensionless time number.

[0135] For each time sub-interval, select all sampling points belonging to the time sub-interval range between the starting dimensionless time index and the ending dimensionless time index of the time sub-interval, extract the standardized signal values ​​of these sampling points, perform local fractional Fourier transform using the optimal fractional Fourier angle, construct the local amplitude spectrum sequence of the corresponding time sub-interval, and calculate the local pulse intensity index of the corresponding time sub-interval according to the steps of pulse peak detection and pulse intensity index calculation.

[0136] For each time sub-interval, the local pulse intensity index of the corresponding time sub-interval is compared with the reference intensity index, the difference between the two is calculated, the current difference is compared with the judgment threshold, when the current difference is greater than the judgment threshold, the deformation judgment result of the corresponding time sub-interval is recorded as one, when the current difference is not greater than the judgment threshold, the deformation judgment result of the corresponding time sub-interval is recorded as zero, and the deformation judgment results of all time sub-intervals are arranged in order of the starting dimensionless time sequence number of the time sub-interval to construct a deformation judgment sequence;

[0137] Set the continuous judgment length, which does not exceed the total number of time sub-intervals. In the deformation judgment sequence, examine each continuous subsequence with the same length as the continuous judgment length in turn. When there is a continuous subsequence in which all deformation judgment results are one, it is determined that there is a stable structural deformation trend in the corresponding time range. When there is no continuous subsequence in which all deformation judgment results are one, it is determined that there is no stable structural deformation trend in the entire sampling time range.

[0138] Time series are sorted by length Evenly divided into Given subintervals, the length of a single subinterval is . ;in, This represents the number of sub-intervals into which the entire sampling time interval is divided;

[0139] Calculate the first The start and end numbers of each sub-interval are as follows: , , ;in, For the first The starting sequence number of each time sub-interval on the dimensionless time axis; For the first The termination number of each time sub-interval on the dimensionless time axis; This is the index of the time sub-interval;

[0140] For each sub-interval index, the corresponding sampling time range for that sub-interval Select sampling points within this range and normalize the signals from these sampling points. Use the optimal angle Perform a local fractional Fourier transform to construct the local amplitude spectrum of the sub-interval, and then apply the pulse intensity index... The pulse intensity index of this sub-interval is calculated by definition. ;in, For the first Local pulse intensity index obtained by calculating the spectrum of each time sub-interval;

[0141] For each The structural deformation determination result is as follows: ;in, For the first Deformation determination results for each time sub-interval;

[0142] The structural deformation trend sequence is as follows: ;in, It is a vector of deformed trend sequences composed of the determination results of all time sub-intervals;

[0143] Set the continuous deformation judgment length as: And satisfy ;

[0144] If a certain integer interval exists Make All within the corresponding interval If all conditions are met, it is determined that a stable structural deformation trend exists in the corresponding time interval; if no integer interval satisfies the above conditions, it is determined that no stable structural deformation trend exists within the entire sampling time range; where, To determine the starting index for examining continuous subintervals, the following condition must be met: ; It is a sub-interval index that is within a certain continuous interval.

[0145] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0146] The above description is only a preferred embodiment of the present invention. It should be noted that for those skilled in the art, several improvements and modifications can be made without departing from the technical principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for detecting the deformation of a high-strength tube-threading machine mandrel forging under dynamic load, characterized in that, include: Accelerometers are installed circumferentially on the outer shell of the mandrel forging, and sampling parameters are set to collect multi-channel raw acceleration data along the axial direction. Using the dimensionless time sequence as a reference, the average acceleration value is calculated for each sampling time to form a single-channel reference signal. The mean and standard deviation are calculated to generate a standardized signal, and the non-stationary index is constructed by the difference of the standardized signal. Establish transform domain sampling points on the time-domain discrete sampling points corresponding to the standardized signal, divide the angle interval to obtain the candidate fractional Fourier angle set, and generate the fractional Fourier transform kernel function matrix for each angle. Perform discrete transformation according to candidate angles to obtain a sequence of fractional Fourier transform results in complex form, and calculate the energy concentration index in the energy observation interval; The candidate fractional Fourier angle with the largest energy concentration index is selected as the optimal fractional Fourier angle, and the complex modulus of the transformation result is extracted to form an amplitude spectrum sequence. Local peaks are detected in the amplitude spectrum sequence to form a set of pulse peak positions, and the pulse intensity index is calculated based on the spectral statistics. Multiple sets of historical acceleration data were collected under normal working conditions of the mandrel forging. Then, the following steps were performed in sequence: sensor deployment and acquisition, standardization and non-stationarity index construction, candidate angle and kernel function generation, fractional Fourier transform and energy concentration calculation, optimal angle identification and amplitude spectrum extraction, pulse peak detection and pulse intensity index calculation. A set of historical pulse intensity indices was obtained, a reference intensity index and a judgment threshold were calculated, and the deformation was determined by comparing them with the current pulse intensity index. In the time domain, the standardized signal is divided into continuous time sub-intervals, and local fractional Fourier transform and pulse intensity index calculation are performed respectively. A deformation judgment sequence is constructed according to the sub-interval results, and structural deformation trends are identified based on the continuous judgment length.

2. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 1, characterized in that, The process of circumferentially arranging acceleration sensors on the outer shell of the mandrel forging, setting sampling parameters, and collecting multi-channel raw acceleration data along the axial direction specifically includes: Several accelerometers are symmetrically arranged in pairs or multiple pairs along the circumferential direction on the mandrel forging shell. Each accelerometer is assigned a unique number, and each accelerometer outputs the acceleration measurement value along the axial direction of the mandrel. Set the total length of the dimensionless time series for the entire acquisition process and the dimensionless time step between two adjacent samples. Divide the total length of the dimensionless time series by the dimensionless time step to obtain the maximum sampling number. Increment the maximum sampling number by one to obtain the total number of sampling points. Then, starting from the initial dimensionless time number, add the numbers sequentially according to the dimensionless time step to calculate the dimensionless time number corresponding to each discrete sampling point. At each discrete sampling point, the raw output values ​​of all accelerometers corresponding to the current discrete sampling point are collected to form a multi-channel raw acceleration data sequence indexed by the accelerometer number and the dimensionless time sequence number. At each discrete sampling point, the original output values ​​of all accelerometers at the current discrete sampling point are summed, and the summation result is divided by the number of accelerometers to calculate the average acceleration value of the current discrete sampling point. All average acceleration values ​​are arranged in dimensionless time sequence to construct a single-channel reference signal sequence.

3. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 2, characterized in that, The process involves calculating the average acceleration value at each sampling time using a dimensionless time sequence as a reference to form a single-channel reference signal, calculating the mean and standard deviation to generate a standardized signal, and constructing a non-stationary index using the difference of the standardized signal. Specifically, this includes: The mean of the reference signal sequence is calculated by summing the reference signal values ​​corresponding to all sampling points in the single-channel reference signal sequence and dividing the sum by the total number of sampling points. At each sampling point, the difference between the reference signal value and the mean of the reference signal sequence is calculated. The difference is squared for all sampling points, and the sum of all squared results is calculated. The sum is then divided by the total number of sampling points to obtain the standard deviation of the reference signal sequence. When the standard deviation of the reference signal sequence is greater than zero, the mean of the reference signal sequence is subtracted from the reference signal value for each sampling point, and then the result is divided by the standard deviation of the reference signal sequence to generate a standardized signal sequence arranged in dimensionless time sequence. When the standard deviation of the reference signal sequence is zero, the standardized values ​​of all sampling points in the standardized signal sequence are uniformly set to zero. In a standardized signal sequence, starting from the second sampling point to the penultimate sampling point, the second difference component formed by the standardized values ​​of three adjacent sampling points is calculated sequentially. Each second difference component is squared and summed. The coefficient relationship between the sum of squares and the constant 2 is then normalized to obtain the non-stationarity index. Based on the total number of sampling points, a non-stationarity threshold is constructed by subtracting one from the total number of sampling points and multiplying by a constant two. The non-stationarity index is compared with the non-stationarity threshold. When the non-stationarity index is greater than the non-stationarity threshold, the standardized signal sequence is determined to have significant non-stationarity characteristics. When the non-stationarity index is not greater than the non-stationarity threshold, the standardized signal sequence is determined to be stationary.

4. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 3, characterized in that, The step of establishing transform domain sampling points on the time-domain discrete sampling points corresponding to the standardized signal, dividing the angle interval to obtain the candidate fractional Fourier angle set, and generating the fractional Fourier transform kernel function matrix for each angle specifically includes: Within the fractional Fourier transform domain, a transform domain sampling point sequence is constructed using the same total number of sampling points and dimensionless time step as the standardized signal sequence, so that each transform domain sampling point corresponds to a discrete time-domain sampling point in dimensionless time. Within the preset angle range of zero to half a cycle, the angle range is evenly divided into several evenly spaced angles according to the preset division parameters. Each angle except the starting angle and the ending angle is taken as a candidate fractional Fourier angle to form a set of candidate fractional Fourier angles. For each angle in the candidate fractional Fourier angle set, based on the sine and cosine function values ​​of the corresponding candidate fractional Fourier angle, a phase expression is constructed, which includes the dimensionless time index square term of the discrete time-domain sampling points, the dimensionless time index square term of the transform-domain sampling points, and the product term of the two. Substituting the phase expression into the complex exponential function and combining it with the angle-related amplitude adjustment coefficient, the kernel function value on all combinations of discrete time-domain sampling points and transform-domain sampling points is calculated, forming the fractional Fourier transform kernel function matrix corresponding to each candidate fractional Fourier angle.

5. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 4, characterized in that, The step of performing a discrete transformation according to candidate angles to obtain a sequence of complex-form fractional Fourier transform results, and calculating the energy concentration index within the energy observation interval, specifically includes: For each angle in the candidate fractional Fourier angle set, multiply each sampling point value in the standardized signal sequence with the kernel function value at the corresponding row and column position in the fractional Fourier transform kernel function matrix of the corresponding candidate fractional Fourier angle, and sum them according to the dimensionless time sequence to obtain the complex form fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle at each transform domain sampling point. In the transform domain sampling point sequence, a continuous transform domain sampling point interval at the middle position is selected as the energy observation interval, and the starting transform domain sampling point number and the ending transform domain sampling point number of the energy observation interval are kept within the range of transform domain sampling points. For each candidate fractional Fourier angle, the complex modulus values ​​of all transform domain sampling points in the fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle are squared and summed to obtain the total energy of the corresponding candidate fractional Fourier angle. Within the energy observation interval, the complex modulus values ​​of the transform domain sampling points belonging to the energy observation interval in the fractional Fourier transform result sequence of the corresponding candidate fractional Fourier angle are squared and summed to obtain the energy within the energy observation interval. When the total energy is greater than zero, the energy within the energy observation interval is divided by the total energy to calculate the energy concentration index of the corresponding candidate fractional Fourier angle. When the total energy is zero, the energy concentration index of the corresponding candidate fractional Fourier angle is set to zero.

6. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 5, characterized in that, The process of selecting the candidate fractional Fourier angle with the largest energy concentration index as the optimal fractional Fourier angle and extracting the complex modulus of the transformation result to form an amplitude spectrum sequence specifically includes: In the set of candidate fractional Fourier angles, the energy concentration index corresponding to each candidate fractional Fourier angle is compared, and the candidate fractional Fourier angle with the largest energy concentration index is selected as the optimal fractional Fourier angle; when multiple energy concentration indices have the same maximum value, the one with the smallest angle value among these corresponding candidate fractional Fourier angles is selected as the optimal fractional Fourier angle. In the sequence of fractional Fourier transform results in complex form corresponding to the optimal fractional Fourier angle, the complex modulus is calculated for the complex result of each sample point in the transform domain, and the complex modulus values ​​are arranged in order of the sample point number in the transform domain to construct the amplitude spectrum sequence under the optimal fractional Fourier angle.

7. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 6, characterized in that, The process of detecting local peaks in the amplitude spectrum sequence, forming a set of pulse peak positions, and calculating the pulse intensity index based on spectral statistics specifically includes: In the amplitude spectrum sequence, starting from the second transform domain sampling point to the second-to-last transform domain sampling point, the amplitude of the current transform domain sampling point is compared with the amplitude of the adjacent transform domain sampling point to its left and the amplitude of the adjacent transform domain sampling point to its right. When the amplitude of the current transform domain sampling point is greater than the amplitude of the adjacent transform domain sampling point to its left and the amplitude of the adjacent transform domain sampling point to its right, the current transform domain sampling point is marked as a pulse peak, the sequence number of the transform domain sampling point where the pulse peak is located is recorded, a set of pulse peak positions is constructed, and the number of pulse peaks is counted. The amplitudes of all transform domain sampling points in the amplitude spectrum sequence are summed, and the summation result is divided by the total number of transform domain sampling points to obtain the mean of the amplitude spectrum. At each transform domain sampling point, the difference between the amplitude of the current transform domain sampling point and the mean of the amplitude spectrum is calculated. The differences of all transform domain sampling points are squared and summed. The summation result is divided by the total number of transform domain sampling points to obtain the standard deviation of the amplitude spectrum. When the standard deviation of the amplitude spectrum is greater than zero and the number of pulse peaks is greater than zero, the ratio between the difference between the amplitude and the mean of the amplitude spectrum and the standard deviation of the amplitude spectrum is calculated for each pulse peak corresponding to the transform domain sampling point. The calculated ratio is squared and summed. The number of pulse peaks is used as the divisor to average the sum of squares to obtain the pulse intensity index. When the standard deviation of the amplitude spectrum is zero or the number of pulse peaks is zero, the pulse intensity index is set to zero.

8. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 7, characterized in that, The process involves collecting multiple sets of historical acceleration data under normal operating conditions of the mandrel forging, and sequentially performing sensor deployment and acquisition, standardization and non-stationarity index construction, candidate angle and kernel function generation, fractional Fourier transform and energy concentration calculation, optimal angle identification and amplitude spectrum extraction, pulse peak detection and pulse intensity index calculation to obtain a set of historical pulse intensity indices. A reference intensity index and a judgment threshold are then calculated and compared with the current pulse intensity index to determine deformation. Specifically, this includes: When the mandrel forging is in normal working condition, multiple sets of historical acceleration data are collected. For each set of historical acceleration data, the following steps are performed in sequence: sensor deployment and multi-channel raw signal acquisition, standardization transformation and initial non-stationarity judgment, fractional Fourier transform kernel function matrix generation and candidate fractional Fourier angle set construction, fractional Fourier transform calculation and energy concentration index calculation, optimal fractional Fourier angle identification and amplitude spectrum extraction, and pulse peak detection and pulse intensity index calculation. The pulse intensity index corresponding to each set of historical acceleration data is obtained, forming a set of historical pulse intensity indices. Summing up all pulse intensity indices in the historical pulse intensity index set, dividing the summation result by the number of historical acceleration data sets, and calculating the reference intensity index, then adding a constant to the reference intensity index to construct the judgment threshold. The same signal processing procedure as the historical acceleration data is performed on the current acceleration data to be detected to calculate the current pulse intensity index. The difference between the current pulse intensity index and the reference intensity index is calculated. The current difference is compared with the judgment threshold. When the current difference is greater than the judgment threshold, it is determined that the high-strength tube threading machine mandrel forging has deformed. When the current difference is not greater than the judgment threshold, it is determined that the high-strength tube threading machine mandrel forging has not deformed.

9. The deformation detection method for a high-strength tube-threading machine mandrel forging under dynamic load according to claim 8, characterized in that, The process involves dividing the standardized signal into continuous-time sub-intervals in the time domain, performing local fractional Fourier transform and pulse intensity index calculations on each sub-interval, constructing a deformation judgment sequence based on the sub-interval results, and identifying structural deformation trends based on the continuous judgment length. Specifically, this includes: The standardized signal sequence obtained from a single detection is uniformly divided into several continuous time sub-intervals in the time domain according to length. The number of sampling points in each time sub-interval is calculated by dividing the total number of sampling points in the standardized signal sequence by the number of time sub-intervals. The starting dimensionless time number and ending dimensionless time number of each time sub-interval are calculated in the order of dimensionless time number. For each time sub-interval, select all sampling points belonging to the time sub-interval range between the starting dimensionless time index and the ending dimensionless time index of the time sub-interval, extract the standardized signal values ​​of these sampling points, perform local fractional Fourier transform using the optimal fractional Fourier angle, construct the local amplitude spectrum sequence of the corresponding time sub-interval, and calculate the local pulse intensity index of the corresponding time sub-interval according to the steps of pulse peak detection and pulse intensity index calculation. For each time sub-interval, the local pulse intensity index of the corresponding time sub-interval is compared with the reference intensity index, the difference between the two is calculated, the current difference is compared with the judgment threshold, when the current difference is greater than the judgment threshold, the deformation judgment result of the corresponding time sub-interval is recorded as one, when the current difference is not greater than the judgment threshold, the deformation judgment result of the corresponding time sub-interval is recorded as zero, and the deformation judgment results of all time sub-intervals are arranged in order of the starting dimensionless time sequence number of the time sub-interval to construct a deformation judgment sequence; Set the continuous judgment length, which does not exceed the total number of time sub-intervals. In the deformation judgment sequence, examine each continuous subsequence with the same length as the continuous judgment length in turn. When there is a continuous subsequence in which all deformation judgment results are one, it is determined that there is a stable structural deformation trend in the corresponding time range. When there is no continuous subsequence in which all deformation judgment results are one, it is determined that there is no stable structural deformation trend in the entire sampling time range.

Images