3D printing entity source evidence obtaining method based on printer structure vibration

Abstract

The invention discloses a 3D printing entity source evidence obtaining method based on printer structure vibration, and the method comprises the following steps: a feature generation step: extracting a low-frequency part of structure vibration generated in a printing process of a 3D printer, and constructing an equipment feature vector; a watermark embedding step: converting the equipment feature vector into an authentication watermark, and embedding the authentication watermark into a 3D printing entity; and a source authentication step: extracting the authentication watermark from the 3D printing entity to be authenticated, restoring the equipment feature vector, and matching the equipment feature vector with a pre-stored equipment feature vector to determine the source of the 3D printing entity. According to the 3D printing entity source evidence obtaining method based on printer structure vibration, equipment characteristics are constructed by extracting inherent structure vibration characteristics which are difficult to copy of a 3D printer, and the characteristic information is bound with a 3D printing entity, so that reliable, hidden and robust authentication of a 3D printing entity source is realized.

Description

Technical Field

[0001] This invention relates to the field of 3D printed entity provenance evidence, specifically to a method for 3D printed entity provenance evidence based on printer structural vibration. Background Technology

[0002] 3D printing technology, as a rapid prototyping technology, has been widely used in many fields such as industrial manufacturing, medical rehabilitation, and cultural and creative industries due to its manufacturing flexibility and personalized customization capabilities. However, the popularization of this technology has also brought increasingly prominent safety and regulatory risks.

[0003] In the internet environment, the acquisition, sharing, and dissemination of 3D printing model files have become extremely convenient, further exacerbating the difficulty of regulation. Any user can easily obtain various 3D model data through online platforms and quickly manufacture them into physical products using their personal 3D printing equipment. The low barrier to entry and high anonymity inherent in 3D printing technology make traditional product traceability and regulatory methods, such as tracking production lines or logistics information, difficult to apply in this scenario.

[0004] To effectively trace the origin of 3D printed objects, existing technologies have proposed several solutions. The mainstream approach is to mark the object with information during or after printing. For example, this involves embedding invisible identification information inside the object or engraving a unique serial number on its surface. These markings can carry data such as equipment number, operator information, and printing time, theoretically allowing traceability to the product's origin. While this method provides some evidence, it still has limitations: surface markings may become blurred due to physical wear or be removed by malicious polishing; internally embedded markings may have unknown impacts on the product's structural integrity, and their identification usually requires specific equipment, making them inconvenient.

[0005] Therefore, there is an urgent need in this field for a new type of 3D printed entity provenance technology that can provide a covert traceability solution that is strongly associated with the device hardware, difficult to tamper with or destroy, and does not affect the product's appearance and function. Summary of the Invention

[0006] To overcome the shortcomings of existing technologies, the present invention aims to provide a method for forensic identification of the source of 3D printed entities based on printer structural vibration. This method extracts the inherent and difficult-to-replicate structural vibration characteristics of the 3D printer itself to construct device features, and binds these features to the 3D printed entity, thereby achieving reliable, covert, and robust authentication of the source of the 3D printed entity.

[0007] The present invention adopts the following technical solution: A method for forensic identification of 3D printed entities based on printer structural vibration includes the following steps: Feature generation steps: Extract the low-frequency components of the structural vibrations generated by the 3D printer during the printing process and construct the device feature vector; Watermark embedding step: The device feature vector is converted into an authentication watermark and embedded into the 3D printed entity; Source authentication steps: Extract the authentication watermark from the 3D printed entity to be authenticated, restore the device feature vector, and match it with the pre-stored device feature vector to determine the source of the 3D printed entity.

[0008] Furthermore, the feature generation step includes: Data collection sub-step: Use an accelerometer to acquire the acceleration signal sequence of the 3D printer during the printing process; Preprocessing sub-step: Perform DC offset removal processing on the acceleration signal sequence to obtain the DC offset-removed signal sequence; Feature extraction sub-step: Perform frequency domain analysis on the signal sequence after DC offset removal and extract the cepstral feature vector as the device feature vector.

[0009] Furthermore, in the data collection sub-step, the accelerometer is fixed on the nozzle housing of the 3D printer, its measuring axis is aligned with the printer's running axis, and the motion system of the 3D printer is driven to vibrate in the low-frequency range through a specific excitation program.

[0010] Furthermore, the low frequency range is 0-200 Hz, the excitation signal increases in steps of 1 Hz, and each frequency is maintained for 1 second.

[0011] Furthermore, the feature extraction sub-step includes: The frequency domain signal is obtained by performing a discrete Fourier transform on the signal sequence after DC offset removal. Calculate the power spectral density of the frequency domain signal; The logarithmic power spectrum is obtained by performing a natural logarithmic transformation on the power spectral density. Performing an inverse discrete Fourier transform on the logarithmic power spectrum yields the cepstral signal; The first Nc coefficients of the cepstral signal are extracted as the cepstral feature vector, where Nc is an integer.

[0012] Furthermore, Nc takes the value of 10.

[0013] Furthermore, it also includes a classifier training step: a Softmax classifier is trained using the device feature vectors from multiple 3D printers to classify the device feature vectors in the source authentication step.

[0014] Furthermore, the watermark embedding step includes: converting each coefficient in the device feature vector into a binary representation and embedding it as a sequence of copyright information for the authentication watermark into the 3D printed entity.

[0015] Furthermore, the source authentication step includes: extracting the authentication watermark from the 3D printed entity, parsing its binary representation, restoring it to a device feature vector, and then inputting it into a pre-trained Softmax classifier to determine the source of the 3D printed entity through probability distribution.

[0016] Furthermore, in the data collection sub-step, the heating function and fan system of the 3D printer are turned off to eliminate the interference of environmental noise caused by heat sources and airflow on the acceleration signal.

[0017] Compared with existing technologies, the beneficial effects of this invention are as follows: The method for authenticating the origin of 3D printed entities based on printer structural vibration provides highly unique and anti-counterfeiting device features. Since the structural vibration characteristics of a 3D printer are determined by its inherent physical factors such as mechanical structure, assembly tolerances, and component wear, they possess high randomness and complexity. Therefore, the constructed device feature vector acts like a "physical fingerprint" of the printer, making it difficult to predict, copy, or counterfeit, thus ensuring the reliability and anti-counterfeiting capabilities of the source authentication from the source. The method achieves high concealment in source authentication. This invention converts device feature information into an authentication watermark and embeds it inside the 3D printed entity, rather than marking it on the surface. This method does not change the entity's macroscopic appearance, size, or function, making the traceability mark difficult to detect with the naked eye, effectively avoiding malicious damage caused by the mark's presence, while ensuring the product's appearance integrity. The method also ensures the robustness of the source authentication method. The authentication watermark embedded inside the entity is integrated with the entity itself, providing a certain degree of resistance to external interference. Physical interference (such as daily wear and tear, contact, etc.) can prevent the successful extraction of feature information and authentication even if the surface of the entity is intentionally damaged locally, as long as the core area where the watermark is embedded is not completely destroyed, ensuring the persistence of traceability information. The 3D printed entity source identification method based on printer structural vibration of this invention is non-invasive and easy to promote. This invention is based entirely on the inherent physical phenomena in printer operation, without requiring any hardware modification or the addition of complex special equipment to the 3D printer itself. It can be achieved only through additional sensing and data processing, which greatly reduces implementation costs and technical barriers, and is conducive to the application and promotion of this technology on a wide range of ordinary 3D printing equipment. The 3D printed entity source identification method based on printer structural vibration of this invention forms an automated and efficient traceability closed loop. This method integrates device feature extraction, watermark embedding, and source authentication into a complete automated process. In the authentication stage, by matching the extracted features with pre-stored features, the source device can be quickly and automatically located, significantly improving the efficiency and accuracy of identification and providing a convenient technical tool for security supervision. Attached Figure Description

[0018] Figure 1 This is a flowchart of a method for obtaining evidence of the origin of 3D printed entities based on printer structural vibration, as described in an embodiment of the present invention. Figure 2 This is a schematic diagram of the characteristic data after quantification of the vibration of the 3D printer structure in each experiment in this embodiment of the invention. Detailed Implementation

[0019] The present invention will now be further described in conjunction with the accompanying drawings and specific embodiments. It should be noted that, without conflict, the various embodiments or technical features described below can be arbitrarily combined to form new embodiments.

[0020] like Figure 1 As shown, this invention provides a method for forensic identification of the origin of 3D printed entities based on printer structural vibration, comprising the following steps: Feature generation steps: Extract the low-frequency components of the structural vibrations generated by the 3D printer during the printing process and construct the device feature vector.

[0021] The low-frequency characteristics of structural vibrations in 3D printers are extracted and constructed as device features. These features are then converted into authentication watermarks embedded in the model entities and circulated alongside them. The constructed device features will be stored in a 3D printer traceability and authentication database to record and manage the unique identifiers of each device. Simultaneously, a classifier will be trained based on this feature data to achieve accurate identification and traceability of different 3D printers.

[0022] Acceleration signals reflect the dynamic response of various components in a 3D printer during operation, including the amplitude and frequency of its structural vibrations. Analysis of these acceleration signals can reveal the characteristics of the 3D printer's structural vibrations. Therefore, feature generation involves processing the acceleration signals, including removing DC offset, frequency domain analysis, and feature extraction, to extract unique patterns related to the 3D printer's structural vibrations. The specific steps of feature generation are as follows:

[0023] 1. Data Collection. First, correctly install the 3D printer on a stable and level surface to prevent external vibrations or tilting from interfering with data collection. Securely mount the accelerometer to the 3D printer nozzle housing, aligning its measurement axis with the printer's running axis. Position the 3D printer nozzle at the center of the heated bed, approximately 10 mm above it. Turn off the 3D printer's heating function and fan system to avoid environmental noise interference from heat sources and airflow affecting the experimental signals. Then, start a specific excitation program to drive the 3D printer's motion system within the low-frequency range (0-200 Hz). Controlled vibration, with 1 The step size is continuously increased. An accelerometer collects the acceleration signal of the printer head at each step size frequency in real time. The data is then transmitted to the data acquisition system to obtain the acceleration signal sequence. .

[0024] in This indicates the distance from the long frequency point of walking. The corresponding acceleration sample value, The sampling frequency point is determined by the increment step size of the excitation program. To define the low-frequency range boundary, this method sets it to 200.

[0025] 2. To eliminate irrelevant noise caused by sensor errors and environmental interference, and to ensure that the signal more accurately reflects the actual structural vibration of the 3D printer, the data preprocessing stage mainly focuses on the acceleration signal sequence. Perform a DC offset removal operation. This helps improve the accuracy of vibration frequency analysis. DC offset is... The average value is calculated using the following formula: in, Represented as an acceleration signal sequence The DC component is removed. To remove this interference, the average value is subtracted from each sample value in the signal sequence to obtain the DC-offset-free signal sequence. : in: This operation removes only the constant offset of the signal, preserving all its dynamic characteristics, including low-frequency features. The signal after removing the DC offset is more balanced, facilitating clearer observation of low-frequency characteristics. This provides a more reliable data foundation for subsequent frequency domain analysis and feature extraction, while ensuring the integrity of the low-frequency signal.

[0026] 3. Equipment Feature Construction. Starting with the acceleration signal sequence, the structural vibration characteristics of the 3D printer are obtained through cepstral feature extraction and constructed as the equipment features of the 3D printer. First, frequency domain analysis is performed on the acceleration signal sequence after DC offset removal to reveal the energy distribution of its frequency components. The signal is then transformed from the time domain to the frequency domain using discrete Fourier transform to obtain the spectrum of the acceleration signal: in, For frequency index, It is the complex form of the frequency domain signal, which contains amplitude and phase information.

[0027] The power spectral density is obtained by calculating the square of the modulus of the spectrum and then normalizing it. Power spectral density reflects the energy distribution of a signal at different frequencies and is an important tool for describing the frequency characteristics of structural vibration signals.

[0028] To further extract periodic features, a natural logarithmic transformation is performed on the power spectral density to obtain the logarithmic power spectrum: Logarithmic transformation compresses the dynamic range of a signal, making the details of weak signal components more prominent and enhancing the expression of periodic features.

[0029] Next, the logarithmic power spectrum is subjected to an inverse discrete Fourier transform to obtain the cepstrum characteristic signal: cepstral signal This represents the distribution of the acceleration signal in the cepstral domain. The low cepstral component mainly reflects the characteristics of the 3D printer's structural vibration, while the high cepstral component mainly contains noise and other components.

[0030] To effectively extract structural vibration information from 3D printers for feature construction while suppressing noise interference, only the first part of the cepstral signal is extracted. Each coefficient is used as a cepstral eigenvector: In this method We set the value to 10. These low-order cepstral feature coefficients encapsulate the characteristics of the acceleration signal sequence and are closely related to the structural vibration of the 3D printer. The extracted cepstral feature vector... This information will be registered as a device characteristic of the 3D printer and stored in the traceability and authentication database.

[0031] 4. Classifier Training. In the generation of device features for 3D printers, the acceleration signal sequence of each 3D printer is subjected to cepstral analysis to extract its feature vector. These eigenvectors, representing the unique structural vibration modes of each device, are used to distinguish different 3D printers. Subsequently, the eigenvectors... Input to The classifier is trained to accurately classify 3D printers.

[0032] for Different 3D printers were used to obtain the training set. ,in These are the category labels corresponding to 3D printers. During the classification stage, The goal of a classifier is to estimate the input feature vector. The probability distribution for each category. The model output is: in, These are the parameters of the classifier. It is the first The parameter vector of the class.

[0033] The classifier is trained by minimizing the cross-entropy loss function: in, The indicator function represents the sample. Belongs to the kind.

[0034] Update parameters using gradient descent The classifier can learn the differences in device feature patterns between different 3D printers. After training, a classification model is obtained that can accurately distinguish the manufacturing source 3D printer based on the input device feature vector.

[0035] Watermark embedding step: The device feature vector is converted into an authentication watermark and embedded into the 3D printed entity.

[0036] Watermark generation: The extracted cepstral feature vector The feature vector is converted into an authentication watermark and embedded in the model entity for future authentication of the model's origin. Each coefficient in the feature vector is converted into its corresponding binary representation using a binary conversion function. For a single coefficient, the converted binary string serves as the copyright information sequence for that single authentication watermark in the model entity. This process is repeated, with all coefficients in the feature vector sequentially converted into the corresponding copyright information sequence within the authentication watermark segment of the model entity, their order strictly corresponding to the order of the authentication watermark segments within the model entity. Subsequently, a complete authentication watermark segment is further constructed by generating a verification sequence and functional flag bits. Finally, the complete authentication watermark segment is embedded into the corresponding position in the model entity according to its sequence bit values.

[0037] Source authentication steps: Extract the authentication watermark from the 3D printed entity to be authenticated, restore the device feature vector, and match it with the pre-stored device feature vector to determine the source of the 3D printed entity.

[0038] When source authentication of a model entity is required, it can be accomplished by extracting the embedded authentication watermark information. Specifically, the embedded authentication watermark is first extracted from the model entity, and its binary representation is parsed and converted back into the corresponding cepstral feature vector. This process ensures that the authentication watermark information in the model entity can be accurately mapped to the original feature vector, reflecting the structural vibration characteristics of the source 3D printer. Subsequently, the reconstructed feature vector is... Input into the trained In classification models, the feature learning capability of the classification model is used to classify and identify the input vector, thereby determining the origin of the model. Classifier output It is a probability distribution representing a given feature vector The entity in the time model belongs to the first The probability of each class. The final classification result is: That is, the category with the highest predicted probability is selected as the 3D printer to manufacture the model entity.

[0039] This process utilizes feature vectors The included information on the structural vibration characteristics of 3D printers effectively enables the identification and classification of the source of 3D printers.

[0040] Furthermore, the feature generation step includes: Data collection sub-step: Use an accelerometer to acquire the acceleration signal sequence of the 3D printer during the printing process; Preprocessing sub-step: Perform DC offset removal processing on the acceleration signal sequence to obtain the DC offset-removed signal sequence; Feature extraction sub-step: Perform frequency domain analysis on the signal sequence after DC offset removal and extract the cepstral feature vector as the device feature vector.

[0041] Furthermore, in the data collection sub-step, the accelerometer is fixed on the nozzle housing of the 3D printer, its measuring axis is aligned with the printer's running axis, and the motion system of the 3D printer is driven to vibrate in the low-frequency range through a specific excitation program.

[0042] Furthermore, the low frequency range is 0-200 Hz, the excitation signal increases in steps of 1 Hz, and each frequency is maintained for 1 second.

[0043] Furthermore, the feature extraction sub-step includes: The frequency domain signal is obtained by performing a discrete Fourier transform on the signal sequence after DC offset removal. Calculate the power spectral density of the frequency domain signal; The logarithmic power spectrum is obtained by performing a natural logarithmic transformation on the power spectral density. Performing an inverse discrete Fourier transform on the logarithmic power spectrum yields the cepstral signal; Extracting the cepstral signal before The coefficients are used as cepstral eigenvectors, where It is an integer.

[0044] Furthermore, The value is 10.

[0045] Furthermore, it also includes a classifier training step: a Softmax classifier is trained using the device feature vectors from multiple 3D printers to classify the device feature vectors in the source authentication step.

[0046] Furthermore, the watermark embedding step includes: converting each coefficient in the device feature vector into a binary representation and embedding it as a sequence of copyright information for the authentication watermark into the 3D printed entity.

[0047] Furthermore, the source authentication step includes: extracting the authentication watermark from the 3D printed entity, parsing its binary representation, restoring it to a device feature vector, and then inputting it into a pre-trained Softmax classifier to determine the source of the 3D printed entity through probability distribution.

[0048] Furthermore, in the data collection sub-step, the heating function and fan system of the 3D printer are turned off to eliminate the interference of environmental noise caused by heat sources and airflow on the acceleration signal.

[0049] The principle of the 3D printed entity provenance method based on printer structural vibration: The characteristics of 3D printer equipment are proposed: Threat Model: In many scenarios, 3D printer provenance technology plays a crucial role, such as tracing the origin of printing equipment used to illegally manufacture items, monitoring the production of sensitive items, and verifying the legitimacy of printed products. The main objective of this invention's 3D printed entity provenance method based on printer structural vibration is to trace the origin of printing equipment used to illegally manufacture items. Two assumptions are made: First, illegally manufactured 3D printed entities contain measurable features that have not been deliberately distorted. This assumption is practical because even in the same scenario, without prominent biometric features (such as faces or fingerprints) or when these biometric features are deliberately distorted, tracing becomes impossible. Second, after the printing equipment is purchased, its unique feature information should be extracted to construct equipment characteristics and register them to achieve traceability.

[0050] Vibration of 3D printers and proposed hypotheses: Vibration is unavoidable during the 3D printing process. Abnormal vibration not only affects the stability of the printer's operation but also negatively impacts the accuracy and surface quality of the printed model, and may even lead to printing failure. The sources of vibration will be considered from three aspects below: (1) Mechanical structure The mechanical structure of a 3D printer includes a rigid frame, a motion mechanism, and a transmission system. The rigid frame provides stability, the motion mechanism enables precise movement, and the transmission system ensures positional accuracy and smooth operation, collectively determining printing performance. Among these, the quality of the rigid frame and component connections plays a crucial role in the magnitude of vibration. Insufficient frame material strength or improper design can lead to structural deformation during operation. Simultaneously, loose or worn component connections can prevent the printer from maintaining a stable structure, amplifying vibration effects. Furthermore, substandard assembly precision of mechanical components such as the printing platform and guide rails can also become potential sources of vibration, further reducing print quality and reliability.

[0051] (2) Printing characteristics The motion system of a 3D printer is the primary dynamic source of vibration. Stepper motors and servo motors are commonly used drive devices in printers, and their operating characteristics inherently induce periodic or transient vibrations. For example, in printing tasks with high acceleration or frequent acceleration and deceleration, the inertia of the motor may couple with the elastic effects of the mechanical system, leading to increased vibration amplitude. In drive belts or gear drives, uneven friction or insufficient tension can also cause irregular vibrations, thus affecting the motion accuracy of the printer head.

[0052] (3) Inertial effect during printing The inertia of the print head and printing platform in a 3D printer is also a significant source of vibration. During 3D printing, the print head needs to move frequently to achieve complex printing paths, especially at high speeds. The mass and inertia of the print head can cause vibrations, leading to layer misalignment or uneven lines. Furthermore, if the printing platform fails to maintain sufficient stability or levelness while supporting the printed object, it will also generate vertical or horizontal vibrations, affecting the overall accuracy of the printed part.

[0053] The mechanical structure of a 3D printer determines the system's rigidity and precision. Printing characteristics and inertial effects act on the mechanical structure through dynamic loading, jointly inducing and amplifying structural vibrations, thus affecting printing performance and quality. Different models of 3D printers differ in their mechanical structure, printing characteristics, and operating methods during the printing process. Even for different 3D printers of the same model, structural vibrations will vary due to minor differences in the mechanical structure, component assembly tolerances, and operating characteristics. This difference is usually reflected in the different power spectral densities of the structural vibrations. Furthermore, during 3D printer operation, the low-frequency components of structural vibrations can significantly reflect the printer's hardware characteristics. These vibrations mainly originate from the rigidity of the printer frame, the assembly precision of components, and the characteristics of the motor and drive system. In the lower frequency range, the vibration signals generated by the large-scale movements of the mechanical structure are usually more stable and repeatable, thus better reflecting the inherent characteristics of the 3D printer. Therefore, this method extracts the low-frequency components of the 3D printer's structural vibrations to construct the device characteristics of the 3D printer, thereby achieving traceability and authentication of the 3D printer.

[0054] Hypothesis verification: An experiment has preliminarily confirmed the feasibility of using the low-frequency characteristics of the vibrations of a 3D printer structure to distinguish 3D printers.

[0055] Five FDM printers were used in the experiment: 1) Elegoo Neptune 2, 2) Elegoo Neptune 3Pro, 3) Elegoo Neptune 3Plus, 4) Anycubic 4Max Pro, and 5) Creality Ender-3 V2. Five of each model were used. All 3D printers were correctly installed and set to the same printing parameters. An accelerometer was fixed to the printhead housing, with its measurement axis aligned with the printer's running axis. A specific excitation program was then initiated to drive the 3D printer's motion system to excite its structural vibrations. The excitation signal increased from 0 to 200Hz in 1Hz increments, with each frequency maintained for 1 second. The accelerometer collected the acceleration signals at each frequency in real time. The preprocessed acceleration signals were converted into frequency signals through Fourier transform to obtain the amplitude and phase of different frequency components. Power spectral density analysis was then used to calculate the energy distribution of each frequency. Subsequently, a logarithmic transform was performed on the power spectral density, and this logarithmic power spectrum was converted into a cepstral signal through inverse Fourier transform to extract the main cepstral characteristic coefficients. Each 3D printer was tested five times according to the above process, and two coefficients were selected from the generated cepstral characteristic coefficients to describe the structural vibration characteristics of the 3D printer.

[0056] Experimental results are as follows Figure 2As shown in the figure, the points represent the quantified characteristic data of the 3D printer structure vibration in each experiment. It can be seen that the distribution of points of different categories is relatively separated in the cepstral feature space. Each category of points clusters in its own specific region, forming distinct distribution clusters. These clusters are spaced apart, indicating significant differences in the structural vibration characteristics of different 3D printer models. Simultaneously, the dashed ellipses clearly enclose the distribution range of each category of points, demonstrating the consistency and stability of the structural vibration characteristics of each 3D printer. The ellipses between different categories do not overlap, indicating a high degree of mutual discrimination between categories in the cepstral feature space. This distribution suggests that characterizing the low-frequency components of 3D printer structural vibration can effectively distinguish different 3D printer models.

[0057] Using structural vibrations from 3D printers for provenance authentication offers several advantages. First, structural vibrations reflect the printer's unique mechanical characteristics, making it extremely difficult to counterfeit their vibrational features. Second, using structural vibrations as a device characteristic of a 3D printer requires no additional hardware modifications. Finally, structural vibrations are robust to external environmental disturbances because their characteristics depend primarily on the printer's internal mechanical design and material properties, rather than changes in external conditions, thus enhancing the reliability of the authentication.

[0058] Experimental example: This experimental example evaluates the performance of the proposed method by conducting source verification experiments on seven 3D printers. Model information is shown in the table below: List of 3D printer models used in the experiment: In the experiment, each 3D printer collected 50 acceleration signal sequences. These signals were processed by the feature generation module to obtain corresponding cepstral signals. The first three coefficients were then extracted from the cepstral signals to characterize the cepstral feature vector representing the structural vibration of the 3D printer. A total of 350 feature vectors were generated, which will be used for training and evaluating the classification model. Each 3D printer randomly selected one feature vector from its 50 corresponding feature vectors to generate an authentication watermark. The generated authentication watermark was then embedded sequentially into the test model entity designed in section 3.4.1 as a unique identifier identifying the origin of different 3D printers.

[0059] In training The classifier randomly splits the data into training and test sets, with the training set comprising 80% (280 feature vectors) and the test set comprising 20% ​​(70 feature vectors). This data split ensures that the data for each printer is evenly distributed across the two datasets, preventing the classifier from favoring data from specific 3D printers. The overall accuracy is used as the evaluation metric for the model's classification performance. For the classification results of individual 3D printers, precision and recall are used for evaluation. Precision indicates how many 3D printers predicted to be of a certain model actually belong to that model, while recall indicates the proportion of 3D printers that actually belong to a certain model and are correctly identified.

[0060] in, This indicates the number of samples correctly classified as belonging to this printer. The number was incorrectly categorized as the number of printers. This refers to the number of samples that should belong to the printer but were not correctly classified.

[0061] List of experimental results: The experimental results are shown in the table above. This table displays the trained... The confusion matrix after classification is displayed, with rows representing the actual 3D printer labels and columns representing the predicted categories. The number in each cell indicates the number of samples whose true value is a particular category and which were predicted to be that category. The numbers on the diagonal represent the number of correctly classified samples, while the numbers off-diagonal represent the number of misclassified samples. This table provides a clear overview of the prediction accuracy and error rates for each category.

[0062] List of accuracy and recall rates for prediction results: In the prediction results, the accuracy and recall rates for all 3D printer classifications were greater than 83%, with an overall accuracy of 92.06%. These results demonstrate that using the low-frequency components of 3D printer structural vibrations as device features for authenticating the origin of 3D printed entities is feasible and effective.

[0063] Performance Analysis: First, robustness analysis against sanding was performed. The embedded watermark area was sanded with 240-grit sandpaper for 30 seconds. The authentication watermark of the model entity was then extracted, converted into a feature vector, and classified. The classification and source tracing results are shown in the table below: List of experimental results after sanding with 240-grit sandpaper: Coefficients typically capture the approximate spectral envelope of a signal. Higher-order cepstral coefficients contain finer spectral details. When more coefficients are selected, the feature space contains more comprehensive information, which helps classifiers better distinguish subtle differences.

[0064] After sanding with 240-grit sandpaper, the accuracy of provenance authentication decreased slightly, but the test results showed that the accuracy rate still reached 88.525%. This result indicates that sanding causes minimal wear to the model surface, and the authentication watermark can still be accurately extracted, thus maintaining a high level of reliability in authenticating the provenance of the model entity.

[0065] Subsequently, an experimental analysis was conducted on the impact of cepstral eigenvector length on the classification results. The experiment involved... The experimental results, with values ​​of 4 and 5, are shown in the table below: List of experimental results for 4: List of experimental results for 5: When the feature vector length is 4, the classification accuracy reaches 95.24%, while when the feature vector length is 5, the classification accuracy reaches 100%. The classification accuracy increases with the increase of the selected coefficient. This is due to the lower-order cepstrum.

[0066] Experimental conclusion: By analyzing the vibration sources of 3D printers during the printing process, this paper hypothesizes using the low-frequency components of 3D printer structural vibrations as device features for provenance authentication, and demonstrates the feasibility of this hypothesis through an experiment. Subsequently, a method for extracting 3D printer structural vibrations is proposed, and the extracted feature vectors are embedded as authentication watermarks into the model entity. The experiment collected device feature vectors from seven FDM 3D printers, and... A classifier is trained on the collected feature vectors to obtain a classification model. This model is then used to classify the feature vectors parsed from the entity to be authenticated, thus enabling the provenance verification of the 3D printed entity. Experimental results show that the proposed method performs well in provenance verification of 3D printed entities and exhibits a certain degree of robustness against sanding.

[0067] The above is a detailed description of the preferred embodiments of the present invention. However, the present invention is not limited to the embodiments described. Those skilled in the art can make various equivalent modifications or substitutions without departing from the spirit of the present invention. All such equivalent modifications or substitutions are included within the scope defined by the claims of this application.

Claims

1. A method for 3D printed entity provenance based on printer structure vibrations, characterized in that, The method comprises the following steps: a feature generation step of extracting a low-frequency part of structural vibration generated by the 3D printer during printing to construct a device feature vector; a watermark embedding step of converting the device feature vector into an authentication watermark and embedding it into the 3D printed entity; a source authentication step of extracting the authentication watermark from the 3D printed entity to be authenticated, restoring the device feature vector, and matching it with the pre-stored device feature vector to determine the source of the 3D printed entity.

2. The 3D-printed entity forensic sourcing method based on printer structure vibration according to claim 1, characterized in that, The feature generation step comprises: a data collection sub-step of collecting an acceleration signal sequence of the 3D printer during printing using an acceleration sensor; a preprocessing sub-step of removing DC offset from the acceleration signal sequence to obtain a DC offset removed signal sequence; a feature extraction sub-step of performing frequency domain analysis on the DC offset removed signal sequence to extract a cepstrum feature vector as the device feature vector.

3. The 3D-printed entity forensic sourcing method based on printer structure vibration according to claim 2, characterized in that, In the data collection sub-step, the acceleration sensor is fixed on the nozzle housing of the 3D printer, the measurement axis is aligned with the running axis of the printer, and the motion system of the 3D printer is driven by a specific excitation program to vibrate in a low frequency range.

4. The 3D-printed entity forensic sourcing method based on printer structure vibration according to claim 3, characterized in that, The low frequency range is 0-200 Hz, and the excitation signal is increased by 1 Hz as a step, and each frequency is maintained for 1 second.

5. The 3D-printed entity forensic sourcing method based on printer structure vibration of claim 2, wherein, The feature extraction sub-step comprises: performing discrete Fourier transform on the DC offset removed signal sequence to obtain a frequency domain signal; calculating the power spectral density of the frequency domain signal; performing natural logarithmic transformation on the power spectral density to obtain a logarithmic power spectrum; performing inverse discrete Fourier transform on the logarithmic power spectrum to obtain a cepstrum signal; the first Nc coefficients of the cepstrum signal are taken as the cepstrum feature vector, where Nc is an integer.

6. The 3D-printed entity forensic sourcing method based on printer structure vibration of claim 5, wherein, Nc is 10.

7. The printer structure vibration based 3D print entity forensic method according to claim 1, wherein, Further comprising a classifier training step of training a Softmax classifier using device feature vectors of multiple 3D printers for classifying the device feature vector in the source authentication step.

8. The printer structure vibration based 3D print entity forensic method according to claim 1, wherein, The watermark embedding step comprises: converting each coefficient in the device feature vector into a binary representation, and embedding it into the 3D printed entity as a copyright information sequence of the authentication watermark.

9. The printer structure vibration based 3D print entity forensic method according to claim 7, wherein, The source authentication step comprises: extracting the authentication watermark from the 3D printed entity, analyzing its binary representation, restoring it into a device feature vector, and then inputting it into the pre-trained Softmax classifier to determine the source of the 3D printed entity through the probability distribution.

10. The 3D-printed entity forensic sourcing method based on printer structure vibration of claim 2, wherein, In the data collection sub-step, the heating function and fan system of the 3D printer are turned off to exclude the interference of environmental noise caused by heat source and air flow on the acceleration signal.

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