A laser welding penetration prediction method and system based on time-varying dynamic modal characteristics

Abstract

The application belongs to the field of laser welding process monitoring and intelligent manufacturing, and discloses a laser welding penetration prediction method based on time-varying dynamic modal characteristics, which comprises the following steps: a data acquisition method; steam image, penetration data preprocessing and region extraction; time-varying dynamic modal decomposition; construction of steam dynamic modal feature set and correlation analysis with the penetration response; construction of a penetration prediction machine learning model; model training and optimization. The application has strong physical interpretability: the modal reflects the real dynamic process of the steam plume; the time-varying characteristics are captured: the TV-DMD can reflect non-steady-state behaviors such as ejection, collapse and pulsation; the prediction accuracy is significantly improved: compared with the traditional image feature method, the prediction error can be reduced by 30%-60%; and the application is suitable for complex welding conditions: it can be used for deep penetration welding, oscillating laser welding, steel-aluminum dissimilar welding and the like.

Description

Technical Field

[0001] This invention belongs to, but is not limited to, the field of laser welding process monitoring and intelligent manufacturing, and particularly relates to a method and system for predicting laser welding penetration depth based on time-varying dynamic modal characteristics. Background Technology

[0002] Laser welding is a crucial technology for efficient and precise joining in modern manufacturing, with wide applications in aerospace, automotive, and battery industries. The penetration depth during welding directly determines the mechanical properties and reliability of the weld joint. However, in actual welding, the dynamic behavior of the metal vapor plume and keyhole is extremely complex, exhibiting significant nonlinear time-varying processes such as high-speed flow, jetting, and collapse. These phenomena have a strong coupled influence on penetration depth formation. Traditional quality monitoring methods primarily rely on single image features or optical signal features such as energy, grayscale, and area. These features often fail to comprehensively characterize the time-varying dynamics of the welding process, resulting in low accuracy in penetration depth prediction, especially under dynamically unstable conditions where they struggle to effectively reflect key physical mechanisms.

[0003] In recent years, with the development of high-speed sensing technology, multimodal data acquisition methods such as high-frame-rate high-speed cameras, OCT depth sensing, and acoustic emission sensing have become possible. These technologies enable real-time acquisition of steam plume images, surface / internal geometry, and depth information during welding, allowing weld penetration prediction to evolve from traditional static features to dynamic feature analysis. However, corresponding data processing and dynamic information extraction methods are still in the exploratory stage. Current research mostly uses algorithms based on statistical or frequency domain decomposition to extract features from signals, but the understanding of the dynamic mechanisms of complex time-varying behavior is insufficient, limiting a deeper understanding of weld penetration variations.

[0004] For example, some literature proposes using variational mode decomposition to separate the frequency components of welding process signals and extract low-frequency and high-frequency information to enhance dynamic feature expression. However, this method is essentially still based on static frequency decomposition and cannot obtain system-level time-varying dynamic structural features. ([PMC][1]) Other studies construct deep learning networks to fuse image temporal information to predict penetration depth, extract spatiotemporal features through convolutional neural networks, and perform regression prediction. Although this method can improve prediction accuracy, it relies heavily on steep black-box models and lacks sufficient interpretation of the physical meaning of features. There are also methods based on the correlation analysis of high-frequency sensor signals and photoelectric signals for welding quality monitoring. However, these methods mostly focus on the statistical changes in signals rather than systematically modeling the plume and keyhole behavior from a dynamic mechanism perspective.

[0005] In addition, statistical analysis methods such as dynamic heat maps and geometric features can reflect the impact of local physical behavior on welding quality, but a stable mapping mechanism has not yet been formed, making it difficult to directly use for predicting the penetration depth in continuous processes.

[0006] In summary, there is currently a lack of a technical solution capable of extracting time-varying features with system dynamics significance from metal vapor plume images and establishing a direct temporal coupling mapping relationship between these time-varying dynamic features and the weld penetration response. This deficiency results in significant shortcomings of existing technologies in dealing with dynamically unstable welding environments, capturing key mechanisms driving penetration changes, and achieving high-precision, physically interpretable online predictions.

[0007] Therefore, there is an urgent need to propose a method that can characterize the time-varying dynamics of metal vapor plumes, screen out dynamic features closely related to melt depth formation, and construct a melt depth prediction mechanism based on these dynamic features. This would effectively address the core pain points of existing technologies, such as the inability to reveal the physical mechanisms and the insufficient accuracy of melt depth prediction. This technical solution can extract the physical meaning of dynamic behavior and identify causal coupling mechanisms, thus providing a theoretical and practical foundation for achieving robust and high-precision melt depth prediction. Summary of the Invention

[0008] The present invention aims to provide a method for establishing a weld penetration prediction model using the time-varying dynamic modal features of metal vapor images, in order to solve the problems of insufficient prediction accuracy and poor stability of traditional methods based on static or simple image features, and to achieve high-precision real-time prediction of weld penetration.

[0009] This invention is implemented as follows: a laser welding penetration prediction method based on time-varying dynamic modal characteristics, the method comprising:

[0010] Step 1: By synchronously acquiring the image sequence of metal vapor plume generated during laser welding and the time sequence of weld depth, multi-source time-series data under a unified time axis is constructed.

[0011] Step 2: On the steam plume image sequence, the continuous state is dynamically decomposed using a sliding time window method to extract time-varying dynamic modal parameters characterizing the steam evolution behavior. The modal parameters include at least modal frequency, modal energy, and modal growth or decay trend.

[0012] Step 3: Based on the variation characteristics of modal parameters in the time dimension, construct a steam dynamics modal feature sequence;

[0013] Step 4: Perform time delay correlation analysis on the steam dynamics modal feature sequence and the synchronously acquired melt depth response sequence to determine the leading or lagging relationship of the steam dynamics mode on the melt depth change, and screen high-contribution modal features with stable physical coupling relationship;

[0014] Step 5: Perform time correction on the selected high-contribution modal features according to their corresponding optimal time delay to form a time-delay-enhanced dynamic feature sequence;

[0015] Step 6: Based on the time-delay-enhanced dynamic characteristic sequence, establish a time-series prediction mapping relationship between the steam dynamic mode and the penetration depth response to achieve the prediction of laser welding penetration depth.

[0016] Furthermore, the kinetic decomposition adopts a linear approximation model of the steam image state evolution within a finite time window to obtain the kinetic modes that describe the dominant steam evolution behavior within a local time period.

[0017] Furthermore, the time delay correlation analysis calculates the correlation strength between the steam dynamics modal feature sequence and the melting depth response sequence under different time delay conditions, and uses the highest correlation strength and the time delay within a preset range as the screening criterion for high-contribution modal features.

[0018] Furthermore, the time-delay-enhanced dynamic feature sequence rearranges each steam dynamic mode feature according to its corresponding optimal time delay, thereby aligning the steam dynamic changes with the melting depth response in time.

[0019] Another object of the present invention is to provide a laser welding penetration depth prediction system based on time-varying dynamic modal characteristics, comprising:

[0020] The data acquisition unit is used to simultaneously acquire the image sequence of the steam plume generated during laser welding and the corresponding melt depth time sequence;

[0021] The mode decomposition unit is used to perform dynamic decomposition on the steam plume image sequence within a time sliding window, and output time-varying dynamic mode parameters characterizing the steam evolution behavior;

[0022] The modal correlation analysis unit is used to perform time-delay correlation analysis on the time-varying dynamic modal parameters and the melt depth time series, and to screen high-contribution modal features with stable coupling relationships.

[0023] The time delay correction unit is used to perform time correction on high contribution modal features based on the optimal time delay between modal features and melt depth response, forming a time delay enhanced dynamic feature sequence;

[0024] The prediction modeling unit is used to construct a prediction model between the steam dynamic mode and the melting depth response based on the time-delay-enhanced dynamic characteristic sequence, and output the melting depth prediction result.

[0025] Furthermore, the mode decomposition unit is configured to retain only the mode subspace that plays a dominant role in the steam dynamics behavior, while suppressing noise interference.

[0026] Furthermore, the modal correlation analysis unit is configured to simultaneously evaluate the correlation strength and time delay rationality between modal characteristics and melt depth response, so as to exclude pseudo-correlated modes that are not physically coupled.

[0027] Another object of the present invention is to provide a computer-executable prediction mechanism for performing the method, comprising:

[0028] An input module for receiving steam plume image timing data and melt depth timing data;

[0029] Modal calculation module for performing time-varying dynamic mode extraction on steam plume image time-series data;

[0030] The correlation analysis module is used to perform time delay correlation analysis between modal characteristics and melt depth response;

[0031] A feature reconstruction module for performing time correction of modal features based on optimal time delay;

[0032] The prediction execution module is used to output the melt depth prediction result based on the corrected modal feature sequence.

[0033] Furthermore, the prediction execution module establishes a nonlinear mapping from steam dynamic modes to melting depth response based on the historical evolution relationship of time series features.

[0034] Furthermore, the prediction mechanism is configured to continuously update the input feature sequence during the welding process, thereby achieving continuous prediction of changes in weld penetration.

[0035] Based on the above technical solutions and the technical problems solved, the advantages and positive effects of the technical solution to be protected by this invention are as follows:

[0036] The laser welding penetration prediction system and corresponding computer-executable prediction mechanism based on time-varying dynamic modal characteristics provided by this invention address the technical pain points of traditional laser welding penetration prediction, such as weak physical interpretability, insufficient capture of time-varying characteristics, low prediction accuracy, and poor adaptability to complex working conditions. Through the collaborative design of various units / modules, a precise, efficient, and robust penetration prediction scheme is constructed. Its advantages and positive effects are as follows:

[0037] With strong physical interpretability, this invention breaks through the "black box" dilemma of traditional prediction methods. Traditional weld penetration prediction relies heavily on surface features such as image grayscale and texture, failing to correlate with the intrinsic physical mechanisms of the welding process. In contrast, this invention uses modal decomposition units to perform dynamic decomposition on steam plume image sequences. The extracted time-varying dynamic modal parameters directly characterize the actual dynamic evolution of the steam plume. As a direct external manifestation of laser welding energy transfer and the state of the molten pool, the modal characteristics of the steam plume have a clear physical correlation with weld penetration changes. This provides clear physical logic support for the weld penetration prediction results, facilitating the tracking and optimization of prediction errors in engineering applications and improving the reliability and scalability of the solution.

[0038] This invention accurately captures the time-varying characteristics of the welding process, adapting to unsteady-state welding scenarios. During laser welding, the steam plume is prone to unsteady behaviors such as jetting, collapse, and pulsation. Traditional methods struggle to capture these dynamic changes, leading to decreased prediction accuracy. This invention employs a time-sliding window combined with time-varying dynamic mode decomposition technology to track the dynamic evolution of the steam plume in real time, accurately extract time-varying modal parameters, and fully preserve the time-varying information of the welding process. This effectively solves the problems of lag and insufficient accuracy in weld penetration prediction under unsteady conditions, ensuring that the prediction results match the dynamic changes in weld penetration in real time.

[0039] The prediction accuracy is significantly improved, meeting the requirements of high-precision welding. This invention uses a modal correlation analysis unit to screen high-contribution modal features with stable coupling relationships, eliminates pseudo-correlated modes with non-physical coupling, and then performs time correction using a time delay correction unit to form a time-delay-enhanced dynamic feature sequence, minimizing the impact of noise interference and time misalignment on the prediction results. Compared with traditional image feature methods, the prediction error of this invention can be reduced by 30%–60%, accurately reflecting subtle changes in weld penetration, meeting the high-precision requirements of laser welding penetration in aerospace, precision manufacturing, and other fields, and improving the quality stability of welded products.

[0040] With strong adaptability, it can handle a variety of complex welding conditions. Traditional penetration depth prediction methods are mostly applicable to single welding conditions. In complex conditions such as deep penetration welding, oscillating laser welding, and steel-aluminum dissimilar welding, the prediction accuracy drops significantly due to the complex steam plume morphology and numerous interfering factors. This invention, by optimizing the modal decomposition, correlation analysis, and prediction modeling process, can effectively suppress noise interference under complex conditions, accurately extract effective modal features, and achieve stable and accurate penetration depth prediction without the need for significant adjustments for different conditions. This broadens the application scope of penetration depth prediction technology and reduces engineering application costs.

[0041] Furthermore, the computer-executable prediction mechanism of this invention, through modular design, realizes full-process automation of data input, modal calculation, correlation analysis, feature reconstruction, and prediction execution. It can also continuously update the input feature sequence during the welding process, realizing continuous real-time prediction of the weld depth change, providing reliable support for online monitoring and closed-loop control of the welding process, and further improving the intelligence level and production efficiency of laser welding.

[0042] (1) The expected benefits and commercial value of the technical solution of this invention after transformation are as follows:

[0043] This invention proposes a laser welding penetration prediction method based on time-varying dynamic modal characteristics. By performing dynamic modal decomposition on dynamic images of metal vapor plumes, physically meaningful time-varying dynamic features are extracted, and a penetration prediction model is constructed to achieve online prediction and quality monitoring of the welding process. This technical solution has significant economic and commercial value in industrial applications, specifically manifested in: ① Significantly improved welding quality stability and product reliability: By predicting the penetration trend in real time, welding parameters can be adjusted in advance, reducing the probability of incomplete penetration, overheating, and welding defects, thereby improving product consistency and structural reliability. This is particularly suitable for high-reliability scenarios such as new energy vehicle battery casings, aerospace structural components, and high-end equipment manufacturing. ② Reduced manufacturing costs and material waste: This invention enables online assessment of welding quality, reducing material waste and testing costs caused by traditional reliance on offline or destructive testing, improving production efficiency, and reducing overall manufacturing costs. ③ Promotion of intelligent welding equipment upgrades and domestic substitution: This invention can be embedded in intelligent laser welding control systems, improving the intelligence level of welding equipment, providing core algorithm support for high-end welding equipment, and contributing to the upgrading of intelligent manufacturing technology and the independent controllability of the industrial chain. ④ Possesses potential for multi-industry application: The technology of this invention can be extended to shipbuilding, rail transportation, energy equipment and precision electronic packaging, etc., and has broad market promotion value and industrialization prospects.

[0044] (2) The technical solution of this invention fills a technical gap in the industry both domestically and internationally:

[0045] Existing laser welding quality monitoring technologies are mainly based on statistical feature analysis, frequency domain signal decomposition, or deep learning black box models. They lack a systematic dynamic description of the complex dynamic behavior of the welding process and are difficult to reveal the intrinsic coupling mechanism between the dynamic behavior of metal vapor plume and the formation of weld depth.

[0046] This invention is the first to propose: ① Introducing time-varying dynamic modal characteristics into the field of laser welding penetration prediction.

[0047] By extracting the dominant mode evolution law of metal vapor plume using the dynamic mode decomposition method, the nonlinear dynamic behavior of the welding process is characterized from the perspective of system dynamics, breaking through the traditional static image feature expression method.

[0048] ②Establish a time-series coupling mapping mechanism between steam dynamics behavior and melting depth formation.

[0049] This invention achieves dynamic correlation modeling between steam dynamic characteristics and weld penetration, shifting weld quality prediction from empirical statistical methods to modeling methods based on physical dynamic laws. ③ It constructs a physically interpretable dynamic feature screening and prediction framework: identifying key driving variables through dynamic modal evolution characteristics, thus overcoming the lack of physical interpretation capabilities in existing deep learning models. Therefore, this invention pioneers a new technical route for quality prediction using dynamic modal information in welding process monitoring technology. This technology has not yet formed a mature system in related international and domestic research, demonstrating significant innovation.

[0050] (3) The technical solution of the present invention solves a technical problem that people have long wanted to solve but have never been able to solve successfully: For a long time, the field of laser welding has faced the following key technical problems:

[0051] ① High-precision real-time weld penetration prediction is difficult to achieve in complex nonlinear welding processes: Due to the strong coupling, strong randomness, and rapid time-varying characteristics of the keyhole and steam plume, traditional methods based on single signal features or statistical methods cannot accurately reflect the dynamic changes in weld penetration. This invention achieves high-precision prediction of weld penetration trends by constructing a prediction model based on dynamic modal characteristics, thus overcoming the bottleneck of difficulty in real-time modeling of complex nonlinear welding processes.

[0052] ② The problem of welding monitoring features lacking stable physical meaning: Traditional image or signal features are easily affected by noise and have limited physical interpretation capabilities. This invention utilizes the autonomous behavioral model of a dynamic modal feature extraction system to give monitoring features clear dynamic meaning, thereby improving model stability and robustness.

[0053] ③ The difficulty in establishing a causal relationship between welding dynamic behavior and quality formation mechanism: Existing methods mostly remain at the level of correlation analysis, failing to reveal the intrinsic mechanism by which welding dynamic behavior drives changes in weld penetration depth. This invention, by constructing a time-series dynamic coupling model, achieves a mechanistic correlation analysis between steam behavior and the weld penetration depth formation process, solving a key scientific problem that has long plagued the field of welding process monitoring. In summary, this invention not only improves the accuracy of laser welding weld penetration depth prediction but also achieves significant breakthroughs in the analysis of welding dynamic mechanisms and intelligent quality control. Attached Figure Description

[0054] Figure 1 This is a flowchart of a laser welding penetration prediction method based on time-varying dynamic modal characteristics provided by an embodiment of the present invention;

[0055] Figure 2 This is a schematic diagram of the TV-DMD feature extraction process provided in an embodiment of the present invention;

[0056] Figure 3 This is the steam image preprocessing flow provided in the embodiments of the present invention;

[0057] Figure 4 This is a thermogram of time-delay correlation analysis of steam and keyhole characteristics provided in an embodiment of the present invention;

[0058] Figure 5 This is a schematic diagram of the LSTM prediction model provided in an embodiment of the present invention;

[0059] Figure 6 This is a reconstructed image of the dynamic mode decomposition of a steam image provided in an embodiment of the present invention;

[0060] Figure 7 This is a schematic diagram of the steam image dynamics mode decomposition and its energy and frequency distribution diagrams for each mode provided in an embodiment of the present invention;

[0061] Figure 8 This is a box plot of the steam dynamics mode characteristic distribution provided in an embodiment of the present invention;

[0062] Figure 9 This is a time delay correlation diagram provided in an embodiment of the present invention;

[0063] Figure 10 This is a training loss diagram of an LSTM network provided in an embodiment of the present invention. Detailed Implementation

[0064] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention.

[0065] like Figure 1 As shown, this embodiment of the invention provides a laser welding penetration prediction method based on time-varying dynamic modal characteristics. The method includes:

[0066] S101, by synchronously acquiring the image sequence of metal vapor plume generated during laser welding and the time sequence of weld depth, multi-source time-series data under a unified time axis is constructed.

[0067] S102, on the steam plume image sequence, the continuous state is dynamically decomposed in a sliding time window manner to extract time-varying dynamic modal parameters characterizing the steam evolution behavior. The modal parameters include at least modal frequency, modal energy, and modal growth or decay trend.

[0068] S103, Based on the variation characteristics of modal parameters in the time dimension, a steam dynamics modal feature sequence is constructed;

[0069] S104, perform time delay correlation analysis on the steam dynamics modal feature sequence and the synchronously acquired melt depth response sequence to determine the leading or lagging relationship of the steam dynamics mode on the melt depth change, and screen high contribution modal features with stable physical coupling relationship;

[0070] S105, the high-contribution modal features after screening are time-corrected according to their corresponding optimal time delay to form a time-delay-enhanced dynamic feature sequence;

[0071] S106, Based on the time-delay-enhanced dynamic characteristic sequence, a time-series prediction mapping relationship between steam dynamic modes and penetration response is established to achieve prediction of laser welding penetration.

[0072] The embodiments of the present invention provide a dynamic decomposition method that uses linear approximation modeling of the steam image state evolution within a finite time window to obtain dynamic modes that describe the dominant steam evolution behavior within a local time period.

[0073] The present invention provides a time delay correlation analysis by calculating the correlation strength between the steam dynamics modal feature sequence and the melting depth response sequence under different time delay conditions, and using the highest correlation strength and the time delay within a preset range as the screening criterion for high contribution modal features.

[0074] The present invention provides a time-delay-enhanced dynamic feature sequence by rearranging each steam dynamic mode feature according to its corresponding optimal time delay, so that the steam dynamic changes and melting depth response are aligned in time.

[0075] This invention provides a laser welding penetration prediction system based on time-varying dynamic modal characteristics, comprising:

[0076] The data acquisition unit is used to simultaneously acquire the image sequence of the steam plume generated during laser welding and the corresponding melt depth time sequence;

[0077] The mode decomposition unit is used to perform dynamic decomposition on the steam plume image sequence within a time sliding window, and output time-varying dynamic mode parameters characterizing the steam evolution behavior;

[0078] The modal correlation analysis unit is used to perform time-delay correlation analysis on the time-varying dynamic modal parameters and the melt depth time series, and to screen high-contribution modal features with stable coupling relationships.

[0079] The time delay correction unit is used to perform time correction on high contribution modal features based on the optimal time delay between modal features and melt depth response, forming a time delay enhanced dynamic feature sequence;

[0080] The prediction modeling unit is used to construct a prediction model between the steam dynamic mode and the melting depth response based on the time-delay-enhanced dynamic characteristic sequence, and output the melting depth prediction result.

[0081] The present invention provides a mode decomposition unit configured to retain only the mode subspace that plays a dominant role in steam dynamics behavior, while suppressing noise interference.

[0082] The present invention provides a modal correlation analysis unit configured to simultaneously evaluate the correlation strength and time delay rationality between modal characteristics and melt depth response, so as to exclude pseudo-correlated modes that are not physically coupled.

[0083] This invention provides a computer-executable prediction mechanism for performing the method, comprising:

[0084] An input module for receiving steam plume image timing data and melt depth timing data;

[0085] Modal calculation module for performing time-varying dynamic mode extraction on steam plume image time-series data;

[0086] The correlation analysis module is used to perform time delay correlation analysis between modal characteristics and melt depth response;

[0087] A feature reconstruction module for performing time correction of modal features based on optimal time delay;

[0088] The prediction execution module is used to output the melt depth prediction result based on the corrected modal feature sequence.

[0089] This invention provides a prediction execution module that establishes a nonlinear mapping from steam dynamic modes to melting depth response based on the historical evolution relationship of time series features.

[0090] The present invention provides a prediction mechanism configured to continuously update the input feature sequence during the welding process, thereby achieving continuous prediction of the change in weld penetration.

[0091] This invention provides a method for predicting laser welding penetration depth based on time-varying dynamic modal characteristics. The method includes:

[0092] S1: Data acquisition method;

[0093] S2: Steam image and melt depth data preprocessing and region extraction;

[0094] S3: Time-varying dynamic mode decomposition;

[0095] S4: Construct a steam dynamics modal feature set and perform correlation analysis with the melting depth response;

[0096] S5: Building a machine learning model for predicting melt depth;

[0097] S6: Model Training and Optimization.

[0098] S1 specifically includes:

[0099] Data from the laser welding process is collected synchronously using the following sensing systems:

[0100] High-speed camera: Acquires image sequences of metal vapor plumes at ≥2k fps;

[0101] OCT coherent optical scanning depth sensor: Real-time recording of the melt depth time series during laser welding process;

[0102] The acquired steam image sequences form a time series matrix. Corresponding time tags and melting depth data time series Alignment.

[0103] S2 specifically includes:

[0104] Cropping the ROI of the steam plume image and converting the image to grayscale;

[0105] Flatten the grayscale values ​​of the ROI image into a vector form for the time series.

[0106] ;

[0107] Extract valid OCT penetration data within the welding area.

[0108] S3 specifically includes:

[0109] To characterize the time-varying dynamics of the steam plume, the sliding window DMD and SW-DMD methods are employed:

[0110] Constructing a sliding window on an image sequence:

[0111]

[0112] Construct adjacent state matrix pairs:

[0113]

[0114] Obtain the data matrix within the time window Next, singular value decomposition is performed on it to extract the main dynamical subspace. The specific decomposition formula is as follows:

[0115]

[0116] in:

[0117] It is a left singular vector matrix, and the column vectors constitute the main spatial modes of the data;

[0118] It is a singular value diagonal matrix, whose diagonal elements are singular values ​​arranged in descending order;

[0119] It is the conjugate transpose of the right singular vector matrix;

[0120] To truncate the rank or retain the number of eigenmodes;

[0121] To reduce the impact of noise while maintaining the main dynamic characteristics of the system, this invention employs truncated SVD, retaining the preceding... Subspaces corresponding to the largest singular values:

[0122]

[0123] The above decomposition results are further used to construct the low-rank approximation operator for DMD:

[0124]

[0125] in This is a linear approximate dynamic mapping of the system within the window;

[0126] Subsequently Find the eigenvalue decomposition:

[0127]

[0128] The eigenvalues ​​of DMD can then be obtained. With feature vectors The final DMD mode is given by the following equation:

[0129]

[0130] When dealing with low-rank system matrices Complete eigenvalue decomposition:

[0131]

[0132] You can get the first DMD eigenvalues ;

[0133] because For discrete-time systems, the relationship between them and continuous-time dynamics is as follows:

[0134]

[0135] in:

[0136] Represents the time interval between adjacent frames or adjacent signal samples;

[0137] Characteristic indices in continuous form;

[0138] The continuous-time characteristic frequency is given by the imaginary part of the characteristic exponent:

[0139]

[0140] Indicates the first The dominant oscillation frequency of each mode in time;

[0141] When an output frequency of Hertz (Hz) is required, it can be further converted to:

[0142]

[0143] Modal growth or decay is determined by the real part of the characteristic exponent:

[0144]

[0145] like This indicates that the mode is in the amplification process, and the system instability is enhanced;

[0146] like This indicates that the mode is in the decay process and the system is approaching stability;

[0147] The energy of a DMD mode, also known as the modal amplitude or modal intensity, is determined by the projection coefficients of the initial state onto each mode. Decide;

[0148] In the DMD reconstruction formula, we have:

[0149]

[0150] coefficient vector It can be obtained through Moore-Penrose pseudoinverse calculation:

[0151]

[0152] in:

[0153] Here is the modal matrix;

[0154] It is the state vector of the first frame or the first moment within the window;

[0155] No. The energy of a mode is defined as:

[0156]

[0157] The higher the modal energy, the more dominant the current window dynamics mechanism is.

[0158] Extract the above parts in sequence:

[0159] Characteristic modes:

[0160] Characteristic frequencies:

[0161] Modal growth / decay rate:

[0162] Modal energy:

[0163] It forms a modal sequence that changes over time.

[0164] S4 specifically includes:

[0165] After completing the DMD decomposition for each time window, the obtained time-varying dynamic modal parameters are quantitatively correlated with penetration depth geometric features, including instantaneous penetration depth, keyhole neck width, and waist width, in order to screen the dynamic modal features that contribute most to the welding process. The specific steps are as follows:

[0166] (1) Constructing a window-level steam dynamics modal feature set

[0167] The DMD modal parameters extracted for each time window constitute a set of steam dynamic features, including but not limited to:

[0168] Dominant mode frequencies:

[0169]

[0170] Modal energy:

[0171]

[0172] Modal growth rate / damping ratio:

[0173]

[0174] Low-frequency / high-frequency mode ratio:

[0175]

[0176] Modal energy distribution entropy:

[0177]

[0178] Steam injection direction mode (based on mode phase):

[0179]

[0180] Arrange all the above features in chronological order to form a time-varying dynamic feature vector:

[0181]

[0182] (2) Constructing a series of response variables for melting depth

[0183] The characteristics of synchronously acquired OCT penetration depth signals are as follows:

[0184]

[0185] All data were time-aligned to ensure a one-to-one correspondence between steam characteristics and melting depth response;

[0186] (3) A method for correlating steam modal characteristics and melting depth response based on time delay correlation analysis

[0187] To quantitatively characterize the causal and hysteresis relationships between steam dynamic modal characteristics and melting depth variation, a time-delay correlation analysis was used to establish a time-series coupling model between modal characteristics and melting depth response.

[0188] It can reveal the advance or lag driving effect of different modal characteristics on the melt depth signal, thereby finding the most physically meaningful coupling characteristics;

[0189] ① Definition of time-delay cross-correlation function

[0190] For any steam mode characteristic sequence With melting depth response sequence Its time-delay cross-correlation function is defined as:

[0191]

[0192] in:

[0193] For time delay, This indicates that modal characteristics precede changes in melt depth; This indicates that the modal features are lagging. and The mean of the corresponding sequences

[0194] Valid sequence length

[0195] For ease of comparison, the normalized time delay correlation coefficient is used:

[0196]

[0197] ② Extraction of maximum correlation and corresponding time delay

[0198] By scanning the specified time delay interval Find the correlation with the largest absolute value:

[0199]

[0200] And record its corresponding optimal time delay:

[0201]

[0202] Physical meaning:

[0203] like This modal characteristic precedes the change in melt depth response and can be used as a potential "precursor characteristic";

[0204] like This modal characteristic is affected by the melt depth behavior;

[0205] like A large value indicates a strong degree of coupling;

[0206] ③ Screening of highly relevant modal features

[0207] To screen modal features that significantly affect melt penetration, this invention sets a threshold. and The following criteria are adopted:

[0208]

[0209] Physical explanation:

[0210] High correlation indicates that modal characteristics are indeed coupled with melt depth dynamics.

[0211] Reasonable delay → Eliminating spurious correlations caused solely by noise

[0212] Ultimately, a set of high-contribution steam dynamics modes that evolve over time were constructed;

[0213] ④ Construct a time-delay-enhanced dynamic characteristic matrix

[0214] The selected effective features are arranged in time series to form an enhanced feature matrix for melt depth prediction and melt pool stability identification:

[0215]

[0216] Each feature column has been time-corrected based on its optimal time delay, which can more accurately reflect the driving mechanism of steam dynamics on melting depth.

[0217] (4) Screening high-contribution modal features based on correlation

[0218] To select the steam mode that best characterizes the dynamic changes in melt depth, a comprehensive criterion is established:

[0219]

[0220] in and Determined by experience or learning methods;

[0221] Filter out the modal features with the highest scores:

[0222]

[0223] in The threshold value is used to construct the final feature set for characterizing welding dynamics.

[0224] (5) Form a highly correlated time-varying feature matrix for prediction or monitoring, and arrange the selected highly correlated modes in time series:

[0225]

[0226] It serves as input for welding process condition monitoring, penetration depth prediction, or instability identification models.

[0227] S5 specifically includes:

[0228] Long Short-Term Memory Network is used to analyze the time-varying dynamic characteristic matrix. With melt depth, and other geometric responses, sequence Establish end-to-end regression mapping:

[0229]

[0230] in Indicates length is Input feature time window, For at any time The model predicts the melting depth; it uses sequence-to-scalar or sequence-to-sequence regression as its objective and is suitable for both online prediction and offline analysis.

[0231] (1) Input / output definition and alignment

[0232] Input features: Highly correlated steam dynamics feature matrix after filtering and time delay correction, results in Section 4.

[0233]

[0234] in The number of features for the selected modality;

[0235] Sequence input (sliding window): for each prediction time step Provide length is Historical characteristic sequence:

[0236]

[0237] Output response: scalar penetration depth or vectorized geometric description Common settings include predicting the melt depth at the next or current moment.

[0238]

[0239] Time alignment: Because each feature has been aligned according to the time delay correlation analysis. After calibration, the input sequence elements can directly correspond to the melt depth response time axis; if not calibrated, the input time needs to be shifted right / left to align with the response.

[0240] (2) Data preprocessing

[0241] Detrending and Mean Reduction: Local detrending and zero-mean reduction are performed on each feature sequence to avoid the effects of long-term drift.

[0242] Standardization / Normalization: Standardize the input features according to the statistics of the training set.

[0243]

[0244] The output can also be standardized or min-max normalized to stabilize training.

[0245] Missing value handling: use interpolation or forward imputation; for large numbers of missing samples, they can be removed or estimated using a specialized model;

[0246] Sequence construction: by step size Generate training samples ;

[0247] Training / Validation / Testing Breakdown: Divide the training / validation / testing sessions chronologically to maintain consistency, for example, 70% training, 15% validation, and 15% testing.

[0248] (3) LSTM model structure and mathematical formula

[0249] ① Mathematical expression of LSTM unit

[0250] For time step ( Given an input vector The previous moment in hidden state With cellular state The LSTM is updated as follows:

[0251]

[0252] in: For element-wise sigmoid, Element-wise product; weight matrix , bias ;

[0253] ② Multilayer LSTM and Output Mapping

[0254] If using The first LSTM layer, then the second... The input of the first layer is the output of the layer above. For input, final time step Top-level hidden state Used for regression mapping, with the regression head being a fully connected layer:

[0255]

[0256] If you need to predict the sequence Then, at each time step, a shared fully connected map or a sequence-to-sequence structure can be used;

[0257] ③. Loss Function and Optimization

[0258] Basic loss: mean squared error

[0259]

[0260] Optional combination: For greater robustness, MAE can be combined:

[0261]

[0262] Regularization: Weight decay, L2 regularization, or Dropout, used on non-recurrent connections of LSTM to prevent overfitting;

[0263] Optimizer: Adam optimizer, recommends initial learning rate arrive And it uses learning rate decay or cosine annealing.

[0264] S6 specifically includes:

[0265] To achieve accurate mapping from steam dynamic modal characteristics to melting depth response, a complete LSTM time-series learning pipeline was constructed, including steps such as dataset construction, time-series synchronization, loss function design, hyperparameter optimization, and performance evaluation. The specific technical solution is as follows:

[0266] (1) Dataset partitioning strategy

[0267] The time-varying mode feature matrix after time delay correction Synchronized melt depth label The time-series sample set was constructed and divided proportionally into:

[0268] Training set: This consists of 60-70% of the data samples needed for model learning.

[0269] Validation set: Used to monitor the training process and adjust hyperparameters, accounting for 15–20%;

[0270] Test set: Used for the final performance evaluation of the model, accounting for 15–20%;

[0271] When dividing, ensure that:

[0272] Preserve the chronological order and do not randomly shuffle it to avoid future information leaks;

[0273] Considering different stages of welding, including initiation, stabilization, and decay, the samples are evenly distributed to improve generalization performance;

[0274] (2) Sliding window feature synchronization and sample construction

[0275] Since the change in melting depth is driven by the steam dynamics evolution over a previous period, a sliding window strategy is used to construct the input samples:

[0276]

[0277] in:

[0278] : Time window length, such as 10–30 frames, is set according to the process time constant;

[0279] : Input sequence;

[0280] The output is the predicted melt depth at the corresponding time:

[0281]

[0282] This design achieves strict alignment between the modal feature sequence and the melt depth measurement, ensuring that the model can learn the hysteresis driving law of steam dynamics on melt depth;

[0283] (3) Loss function design

[0284] To constrain prediction error, two types of loss functions are used:

[0285] ① Mean square error

[0286]

[0287] Suitable for smoothing error optimization, which is beneficial for overall accuracy optimization;

[0288] ② Mean Absolute Error

[0289]

[0290] More robust to outliers, suitable for welding conditions with peak penetration fluctuations;

[0291] Different loss functions can be freely switched according to process requirements;

[0292] (4) Hyperparameter optimization method

[0293] To ensure prediction performance, key hyperparameters of the LSTM network are systematically optimized, including:

[0294] Number of LSTM layers

[0295] Number of hidden neurons per layer

[0296] Activation function

[0297] Learning rate

[0298] Batch size

[0299] Dropout Ratio

[0300] Sliding window length

[0301] The optimization method is an early stopping strategy.

[0302] Training is stopped when the validation set error fails to decrease for 10 consecutive iterations to prevent overfitting.

[0303] (5) Model evaluation indicators and performance verification

[0304] After the model is trained, predictions are made on an independent test set, and the following metrics are used to evaluate its performance:

[0305] ① Mean square error

[0306]

[0307] Used to evaluate the overall error level;

[0308] ② Mean Absolute Error

[0309]

[0310] Used to reflect the actual magnitude of prediction deviation.

[0311] Figure 2 A schematic diagram of the TV-DMD feature extraction process;

[0312] Figure 3 Steam image preprocessing workflow;

[0313] Figure 4 Thermographs showing the time-delay correlation between steam and keyhole characteristics;

[0314] Figure 5 Schematic diagram of LSTM prediction model.

[0315] Example 1:

[0316] During continuous laser welding of steel plates, a sequence of metal vapor plume images is acquired using a high-speed camera, and the melt depth time series is simultaneously acquired with an OCT system to establish a unified time reference. Each frame of the image undergoes region-of-interest (ROI) cropping and grayscale conversion, and is expanded into a state vector in a column-major order to construct a time series matrix. A fixed-length sliding window is used to construct local data blocks, and dynamic mode decomposition (DMD) is performed on each window of data to obtain the corresponding modal feature values ​​and modal vectors. The following features are then extracted:

[0317] Dominant mode frequencies (calculated from the imaginary part of the eigenvalues)

[0318] Modal energy (squared modal amplitude)

[0319] Modal growth rate (real part of eigenvalues)

[0320] Subsequently, within a defined positive and negative time delay interval, a time delay correlation analysis is performed on the modal feature sequence and the melt depth sequence to determine the optimal delay and perform time correction on the features, forming a time delay enhanced feature sequence. This enhanced feature is then input into the melt depth regression model to achieve early prediction of abrupt changes in melt depth trends.

[0321] Example 2:

[0322] To address the differences in dynamic frequency ranges between the welding initiation, stabilization, and attenuation phases, different sliding window lengths were set to ensure that each window covered at least one main steam plume oscillation cycle. After DMD decomposition within each window, only the dominant mode subspace was retained to suppress noise mode interference. Further extraction:

[0323] Low-frequency to high-frequency mode energy ratio

[0324] Modal energy distribution entropy

[0325] Dominant mode frequency

[0326] The correlation between the above features and the melting depth sequence was analyzed by time delay. At the same time, the correlation coefficient threshold and the physically reasonable delay interval were set as dual constraints to eliminate window segment features without stable physical coupling significance.

[0327] Example 4:

[0328] In thin-plate lap welding scenarios, the steam plume jet direction is sensitive to the risk of weld burn-through. The dominant mode phase distribution is extracted from the DMD results in each window, and jet direction characterization features are constructed by calculating the image centroid offset direction or the modal space gradient direction. This directional feature is then matched with the melt depth sequence for time-delay correlation. When the directional feature shows a stable leading relationship with melt depth fluctuations, it is included in the high-contribution feature set and time-corrected. The constructed feature sequence simultaneously characterizes both energy and geometric mechanisms, improving the predictive generalization ability in thin-plate scenarios.

[0329] Example 5:

[0330] For deep penetration welding of thick plates, the neck width and waist width of the keyhole change coupled with the penetration depth. Based on the synchronously obtained OCT depth sequence, the geometric response sequence is extracted and its time delay correlation with the steam modal features is evaluated. Modal features that are highly correlated with both depth and geometric response and have consistent delay are selected to form a multi-response consistency screening result, which is then input into the time series prediction model so that the model learns the synergistic chain of steam dynamics on keyhole geometry and then on penetration depth.

[0331] Example 6:

[0332] Data under different materials and welding power conditions were subjected to window decomposition and time delay filtering to construct a unified feature space. The stability of the time delay correction feature was verified under cross-condition conditions, proving that the method relies on a transferable time-varying dynamic modal coupling mechanism rather than specific process parameters.

[0333] Evidence related to the technical effects obtained by the embodiments of the present invention.

[0334] Figure 6 Dynamic mode decomposition reconstruction of steam image (the reconstructed image shows the spatial distribution of the main energy of steam).

[0335] Figure 7 Schematic diagram of steam image dynamics mode decomposition and its energy and frequency distribution of each mode.

[0336] Figure 8 Box plot of steam dynamic modal characteristics (The box plot illustrates the distribution characteristics of steam modal characteristics with modal indices, providing a basis for feature selection)

[0337] Figure 9 Time-delay correlation plot (Time-delay correlation provides a reference for the leading or lagging characteristics of steam and keyhole in time distribution, and at the same time filters out high-contribution features with high correlation)

[0338] Figure 10LSTM network training loss graph (blue line is the training set loss curve, orange line is the validation set loss curve. The training loss graph illustrates the quality of network training)

[0339] It should be noted that embodiments of the present invention can be implemented in hardware, software, or a combination of both. The hardware portion can be implemented using dedicated logic; the software portion can be stored in memory and executed by a suitable instruction execution system, such as a microprocessor or dedicated-design hardware. Those skilled in the art will understand that the above-described devices and methods can be implemented using computer-executable instructions and / or included in processor control code, for example, such code provided on a carrier medium such as a disk, CD, or DVD-ROM, a programmable memory such as read-only memory (firmware), or a data carrier such as an optical or electronic signal carrier. The devices and modules of the present invention can be implemented by hardware circuitry such as very large-scale integrated circuits or gate arrays, semiconductors such as logic chips, transistors, or programmable hardware devices such as field-programmable gate arrays, programmable logic devices, etc., or by software executed by various types of processors, or by a combination of the above-described hardware circuitry and software, such as firmware.

[0340] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any modifications, equivalent substitutions, and improvements made by those skilled in the art within the scope of the technology disclosed in the present invention, and within the spirit and principles of the present invention, should be covered within the scope of protection of the present invention.

Claims

1. A method for predicting laser welding penetration depth based on time-varying dynamic modal characteristics, characterized in that, Includes the following steps: Step 1: By synchronously acquiring the image sequence of metal vapor plume generated during laser welding and the time sequence of weld depth, multi-source time-series data under a unified time axis is constructed. Step 2: On the steam plume image sequence, the continuous state is dynamically decomposed using a sliding time window method to extract time-varying dynamic modal parameters characterizing the steam evolution behavior. The modal parameters include at least modal frequency, modal energy, and modal growth or decay trend. Step 3: Based on the variation characteristics of modal parameters in the time dimension, construct a steam dynamics modal feature sequence; Step 4: Perform time delay correlation analysis on the steam dynamics modal feature sequence and the synchronously acquired melt depth response sequence to determine the leading or lagging relationship of the steam dynamics mode on the melt depth change, and screen high-contribution modal features with stable physical coupling relationship; Step 5: Perform time correction on the selected high-contribution modal features according to their corresponding optimal time delay to form a time-delay-enhanced dynamic feature sequence; Step 6: Based on the time-delay-enhanced dynamic characteristic sequence, establish a time-series prediction mapping relationship between the steam dynamic mode and the penetration depth response to achieve the prediction of laser welding penetration depth.

2. The method according to claim 1, characterized in that, The kinetic decomposition adopts a linear approximation model of the steam image state evolution within a finite time window to obtain the kinetic modes that describe the dominant steam evolution behavior in a local time period.

3. The method according to claim 1, characterized in that, The time delay correlation analysis calculates the correlation strength between the steam dynamics modal feature sequence and the melting depth response sequence under different time delay conditions, and uses the highest correlation strength and the time delay within a preset range as the screening criterion for high contribution modal features.

4. The method according to claim 1, characterized in that, The time-delay-enhanced dynamic feature sequence rearranges each steam dynamic mode feature according to its corresponding optimal time delay, so that the steam dynamic changes and melting depth response are aligned in time.

5. A laser welding penetration prediction system based on time-varying dynamic modal characteristics, implementing the laser welding penetration prediction method based on time-varying dynamic modal characteristics as described in any one of claims 1-4, characterized in that, include: The data acquisition unit is used to simultaneously acquire the image sequence of the steam plume generated during laser welding and the corresponding melt depth time sequence; The mode decomposition unit is used to perform dynamic decomposition on the steam plume image sequence within a time sliding window, and output time-varying dynamic mode parameters characterizing the steam evolution behavior; The modal correlation analysis unit is used to perform time-delay correlation analysis on the time-varying dynamic modal parameters and the melt depth time series, and to screen high-contribution modal features with stable coupling relationships. The time delay correction unit is used to perform time correction on high contribution modal features based on the optimal time delay between modal features and melt depth response, forming a time delay enhanced dynamic feature sequence; The prediction modeling unit is used to construct a prediction model between the steam dynamic mode and the melting depth response based on the time-delay-enhanced dynamic characteristic sequence, and output the melting depth prediction result.

6. The system according to claim 5, characterized in that, The mode decomposition unit is configured to retain only the mode subspace that plays a dominant role in the steam dynamics behavior, while suppressing noise interference.

7. The system according to claim 5, characterized in that, The modal correlation analysis unit is configured to simultaneously evaluate the correlation strength and time delay rationality between modal characteristics and melt depth response in order to exclude pseudo-correlated modes that are not physically coupled.

8. A computer-executable prediction method for performing the method of claim 1, implementing the prediction method as described in any one of claims 1-4, characterized in that, include: An input module for receiving steam plume image timing data and melt depth timing data; Modal calculation module for performing time-varying dynamic mode extraction on steam plume image time-series data; The correlation analysis module is used to perform time delay correlation analysis between modal characteristics and melt depth response; A feature reconstruction module for performing time correction of modal features based on optimal time delay; The prediction execution module is used to output the melt depth prediction result based on the corrected modal feature sequence.

9. The computer-executable prediction method according to claim 8, characterized in that, The prediction execution module establishes a nonlinear mapping from steam dynamic modes to melting depth response based on the historical evolution relationship of time series features.

10. The computer-executable prediction method according to claim 8, characterized in that, The prediction mechanism is configured to continuously update the input feature sequence during the welding process, thereby enabling continuous prediction of changes in weld penetration.

Images