Identifying the direction of weld path deviations in laser deep penetration welding of hidden T-joints by means of OCT

Over the past decade, optical coherence tomography (OCT) has emerged as a useful tool for online monitoring the keyhole depth in deep penetration laser welding¹ that is overall in good agreement with the weld depth.² OCT is an interferometric measuring method that allows for determining absolute distances of surfaces inside the measuring spot.³ However, due to the challenging measuring environment, the OCT signal often exhibits a small signal-to-noise-ratio due to the pronounced keyhole dynamics and impaired accessibility of the keyhole bottom, thus raising the demand for statistical filtering to extract the actual keyhole depth from the raw signal. For this purpose, different filtering approaches were introduced. Boley et al. separated the noise from the significant data by assuming a Poisson distribution of the noise and combined it with a percentile filter to extract reliable values for the weld depth.⁴ A different approach was introduced by Mittelstädt et al., who analyzed the frequency distribution of the OCT data point cloud by means of a histographic analysis and found that the last significant local peak corresponds well with the actual weld depth obtained from metallographic cross sections.⁵ This approach yields the advantage of reducing the demand for experimental calibration and heuristic parameters of the filter. The method of histographic analysis of the OCT data point frequency was further investigated by Mattulat et al.⁶ as well as by Pordzik et al.⁷ who applied the method to OCT data acquired from weldings at reduced ambient pressure in a stationary as well as in a time-resolved manner. In further research, Pordzik et al. derived certain characteristics from the histographic analysis as measures for the ambiguity of the depth measurement as well as a measure for the process dynamics or the keyhole fluctuations.⁸ Besides probing the inside of the keyhole, OCT was used for the prediction of quality characteristics of the weld seam. Stadter et al. investigated correlations between OCT signals and topographic features of the resulting weld seams by means of artificial neural networks and thus were able to predict quality characteristics in-line.⁹ An in-line depth control based on OCT measurements was successfully implemented by Schmoeller et al. who managed to drastically reduce the weld depth fluctuations for weld seams in different aluminum alloys.¹⁰ Recently, OCT has been employed in the surveillance of laser welding processes to distinguish between full and partial penetration of the laser beam when welding sufficiently thin materials. Different characteristics of the OCT signal when welding hidden T-joints were analyzed by Ahlers et al. to detect misalignments between the web sheet and the laser beam path as a basic requirement for setting up a beam path control.¹¹ 

In this research, the potential of OCT to capture averaged topological features of an opaque surface like the keyhole wall is exploited to identify the direction of lateral weld path deviations (LWPD) when welding hidden T-joints from pure nickel. When the lateral weld path deviation is sufficiently high, the melt pool reaches the edge of the web sheet, altering the mechanical constraints exerted on the melt pool boundaries by the surrounding solid substrate material. This change of mechanical constraints influences the melt pool dynamics, leading to an asymmetry in the process zone as illustrated in Fig. 1. As the keyhole is formed by the evaporation pressure acting on the surface of the molten material, the asymmetry of the melt pool constraints is likely to also affect the keyhole shape. If such an asymmetry of the process zone also manifests in the keyhole shape, it should be detectable by characteristics in the OCT signal when the OCT probe beam is shifted laterally in relation to the axis of the processing laser beam, thus probing the keyhole shape for anisotropic geometrical features. The sensitivity of the OCT signal toward the positioning of the OCT beam inside the keyhole was already demonstrated by Dorsch et al. who recorded OCT signals for different medial and lateral OCT beam shifts.¹² A mapping of the keyhole shape by OCT measurements was used by Sokolov et al. who introduced multimodality of the OCT signal as an indicator for different reflection depths or pronounced features of the keyhole shape, respectively.¹³ By shifting the OCT probe beam relatively to the processing laser beam axis, a 3D keyhole shape could be reconstructed, revealing characteristic features. Changes in the OCT signal when welding hidden T-joints from pure nickel were already investigated by Mattulat who used the extracted keyhole depth value as well as the OCT sampling efficiency as measures for changes in the keyhole dynamics related to misalignments between the web sheet and the laser beam path.¹⁴ However, in this approach, only changes in the OCT signals related to the proximity of the process zone to the edge of the web sheet were investigated while potential asymmetries indicating the direction of the beam path deviations were not considered. The detectability of potential asymmetrical features of the keyhole and the process zone depends on

• The lateral weld path deviation, determining how pronounced the asymmetry will be. The higher the deviation, the more pronounced the asymmetry should become.

• The lateral shift of the OCT probe beam, probing the keyhole walls for asymmetrical geometric features.

A schematic of the experimental setup including the applied process parameters is shown in Fig. 2. The weld experiments were performed on hidden T-joints consisting of pure nickel (Ni 2.4068). The face sheet had a thickness of $0.8mm$ while the thickness of the web sheet was $1.5mm$⁠. The metal sheets were positioned in a clamping device ensuring a positioning accuracy conforming to industrial standards. To ensure full and even contact between the upper edge of the web sheet to the face sheet, the edges of the web sheets were milled after cutting. As laser beam source the spot-in-spot laser IPG AMB 6000/9000 operating at a wavelength of $1070nm$ was used in combination with the processing optics Precitec YW52 that was equipped with an OCT module. The processing head allowed for coaxially coupling the OCT beam into the laser beam path of the processing laser. For the processing laser beam, spot diameters of 187  $μ$m for the core spot and 540  $μ$m for the ring spot were measured. The overall laser power was set to 3800 W and split equally onto the core and the ring component of the laser spot. The weldings were performed at a constant process velocity of $8 m min$ at a length of 115 mm. The applied process parameters resulted in an average weld depth of approximately 2 mm.

The OCT system operates at a central wavelength of 1550 nm with a spectral width of 35 nm (full width at half maximum). The power of the superluminescent diode was 40 mW while the diameter of the OCT measuring spot was approximately 70  $μ$m. During the experiments, the systems maximum measuring frequency of 70 kHz was used. Given the process velocity and the length of the weld path, a total number of approximately 50 000 OCT data points per weld seam was recorded. In accordance with previous investigations by Pordzik et al., from the depth spectrum resulting for each OCT measurement the highest maxima up to the fifth order along with their corresponding intensity values, also referred to as qualities, were recorded in order to enhance the scope of detectable geometric features inside the OCT measuring spot.⁸ For the quality values, indicating the peak heights and thus the strength of the OCT beam reflection from a certain depth, ranging between values of 0 and 999, a threshold of 25 was applied to filter out noisy signals and to reduce the data transfer rate. This way, for each OCT measurement, a feature vector of length 10 was obtained consisting of the five depth values and five quality values. In order to investigate the detectability of potential asymmetric shape features of the keyhole induced by asymmetric boundary conditions acting on the melt pool, different combinations of lateral weld path deviations and lateral OCT spot deflections were investigated as shown in Fig. 3.

It was assumed that on average, on a sufficiently long time interval, the process zone exhibits a symmetry with respect to the plane defined by the laser beam axis and the weld direction. Under this assumption, the lateral weld path deviations were only investigated in one lateral direction, namely, to the right side of the process direction while the OCT probe beam was deflected to both sides of the keyhole, thus all unique cases of equivalent combinations were considered. The equivalence of certain parameter combinations due to symmetry considerations is illustrated in Fig. 4, showing the pairwise equivalence of combining different directions of the LWPD and the LOSD. The LWPD was varied between 200 and $450μ m$ in steps of $50μ m$ while the LOSD was varied between $±50$ and $±200μ m$ in steps of $50μ m$ resulting in a total number of 48 different parameter combinations. Each experiment was carried out two times for validation. Prior to the experiments, the central OCT spot positions were adjusted. The lateral OCT spot center position was determined by scanning the OCT probe beam over a small laser shot hole in an aluminum foil with a diameter of approximately $200μ m$ similar to the focus diameter of the laser core beam. The medial OCT spot position was determined by longitudinal scanning of the OCT beam during the welding process, applying the process parameters described above. The optimal medial OCT position was associated with the OCT signal exhibiting the highest signal-to-noise ratio as well as the most pronounced OCT data point accumulation in the region of the expected weld depth. Additionally, the process zone including the melt pool and the keyhole opening was observed via high-speed videography. The recordings were executed using the high-speed camera Photron Nova S-12 in combination with an illumination laser CAVILUX HF. The recordings were executed at a frame rate of $40kHz$ and a resolution of $384\,px×512\,px$⁠.

Prior to the actual OCT analyses, the recorded raw data were preprocessed. For this purpose, the time interval in which the welding process was located was chosen manually from the raw data. Additionally, an offset correction was applied to the data, removing the ground from the depth measurement, as small inaccuracies during the clamping of the T-joint can lead to minor tilting of the specimen. Furthermore, time intervals including disruptions of the OCT signal due to joint defects or process phenomena were labeled manually and excluded from further analyses, as those disruptions were assumed not to be characteristic for the lateral weld path deviation and therefore to negatively affect the results. To exclude potential deviations of the OCT signal from the start or the end of the processes, for each experiment only the inner 90% of the data points belonging to the weld process were used for further analysis. In this research, two approaches for data analysis were chosen, namely, a classical approach using the histographic analysis of the OCT data point distribution as well as a machine learning approach employing artificial neural networks (ANNs) for binary classification of the direction of the LWPD.

The classical approach for the OCT data analysis is based on the investigations by Pordzik et al.⁸ A catalog of characteristics describing the histographic OCT data point distributions is derived to identify differences in the OCT signals depending on the tested combinations of LWPD and LOSD (see Fig. 4). For this analysis, the complete OCT signal of a weld is used for generating the OCT frequency distribution, thus resulting in a static analysis of the process. Figure 5(a) illustrates how the OCT data point distribution is generated from the pre-processed OCT signal while Fig. 5(b) shows how the relevant characteristics are derived from it. For the histographic analyses, a bin size of $50μ m$ was selected while the significance threshold for LLP evaluation was chosen as the $1σ$-environment above the mean bin population of the histogram.

The machine learning approach employs ANNs in order to distinguish between the directions of the LWPDs by means of binary classification. The ANNs were built in the framework TensorFlow that is an open source program library developed by the Google Brain Team. As network architecture, a standard network consisting of 10 fully connected hidden layers each populated with 20 nodes and an input layer with 10 nodes according to the 10 features obtained from the OCT measurements was chosen. For the nodes of the hidden layers, ReLU functions (rectified linear unit) were chosen as activation function whereas for classification in the output layer sigmoid functions were used. Figure 6 shows the principal architecture of the employed ANNs as well as the applied parameters for the architecture and for the training instance.

For the training of the neural network, each OCT feature vector requires a data label corresponding to the respective directional combination of LWPD and LOSD applied in the experiments. The data label is attributed to the feature vector according to the sign of the value for the LOSD. As the OCT measurements exhibit a significant amount of noise, it would be futile to feed every single feature vector as a data point into the neural network. Instead, an evaluation window is chosen, containing a defined number of consecutive OCT feature vectors with the same data label, which are stacked to a 2D feature map with each row corresponding to the time series of a certain OCT feature. Averaging each row of this OCT feature map results in an averaged feature vector according to Fig. 7 that is forwarded to the neural network. Using evaluation windows of a certain size reduces the amount of data points for training the neural network; thus, an overlap of 80% between adjacent windows is chosen to compensate for this detrimental effect.

To mitigate short-term-memory effects during the training stage of the ANN, the sequence of the averaged and labeled feature vectors is shuffled to provide an alternation of the training labels as random as possible. The prepared input data for the training are split into a training and a test data set by a ratio of 4 to 1. The test data set is required to evaluate the performance of the network and to diagnose potential overfitting. The training of the neural network was performed with a cross-entropy loss function at a learning rate of 0.001 over 200 epochs. A higher number of epochs did not lead to any further improvement of the training accuracy. The performance of the networks and, therefore, their capability of distinguishing the directions of the LWPDs is evaluated by the value of the test accuracy ranging between 0 and 1, where 0 means that all data points were misclassified, whereas a value of 1 indicates that all predictions were in total agreement with the data labels. It is worth mentioning that in contrast to the conventional approach, the machine learning approach already constitutes a time-resolved analysis of the OCT signal.

The high-speed recordings of the process zone including the melt pool and the keyhole opening were averaged into a single image from which three characteristics were derived, namely, the maximum melt pool width, the melt pool width at the position of the keyhole center, as well as the maximum keyhole width, as shown in Fig. 8 on the left side. The melt pool exhibits a maximum width of 1.2 mm, thus, with a thickness of 1.5 mm of the web sheet, leaving a margin of $150μ m$ to each side of the ideal weld path. At the keyhole center position, the melt pool width was measured to be $0.9mm$⁠, leaving a margin of $300μ m$ to each side. Based on these findings, the lowest value for the lateral weld path deviation was chosen as $200μ m$ because at lower deviations no changes in the mechanical boundary conditions acting on the melt pool as stated in the hypothesis are to be expected. The lateral weld path deviation was varied between $200$ and $500μ m$ in steps of $50μ m$⁠. To evaluate the influence of the weld path deviation on the melt pool shape, metallographic cross sections were generated as shown in Fig. 8 on the right side. It can be seen that at an LWPD of $250μ m$ the melt pool reaches the edge of the web sheet so that at higher values influences on the OCT signal are to be expected depending on the direction of the LOSD, while for lower values the process zone should remain symmetrical on average so that the LOSD direction is not expected to yield any significant differences between the OCT signals. For an LWPD of $400μ m$ and higher values, a significant bulging of the melt pool becomes visible, indicating the induced asymmetry of the process zone. At an LWPD of $500μ m$⁠, it was observed that the welding alternated between full and partial penetration due to the proximity to the web sheet edge the keyhole temporarily developed a second opening causing a complete disruption of the OCT signal.

For each LWPD, pairs of opposite LOSDs sharing the same absolute value were compared to each other. Hereby, the positive sign of the LOSDs corresponds to the combination R-R being equivalent to the combination L-L belonging to the equilateral configuration (see Fig. 4). Accordingly, the negative sign corresponds to the combination R-L being equivalent to the combination L-R, both belonging to the inequilateral configuration.

The results for the histographic analysis of the OCT data point distribution are shown in Fig. 9.

The pixel plot shows the absolute value of the relative score deviation depending on the LWPD and the LOSD. For the peak prominence, the scores range from 1% to 850%. All values from Fig. 9 colored in dark red exceed the 100% relative score deviation. The RPSAT yields less significant values for the relative score deviation ranging from 4% to 97%; however, the highest and lowest values for the RPSAT qualitatively match the results from the peak prominences. The best accordances between the scores derived on the basis of both histogram characteristics regarding the most and the least significant parameter combinations for distinguishing the direction of the LWPD are highlighted in the score plots from Fig. 9 as A and B. To get an impression of the overall influence of the LWPD on the keyhole symmetry, for the parameter combinations A and B the histograms of the OCT measurements are compared in Fig. 10.

It can be seen that for the parameter combination A, yielding a high relative score deviation, the shapes of the OCT frequency distributions differ noticeably as the equilateral LOSD yields an additional peak in the distribution. Therefore, the equilateral and inequilateral deflections refer to different LLPs leading to a high directional distinctiveness. On the other hand, the OCT frequency distributions for parameter combination B, yielding one of the lowest relative score deviations, exhibit very similar shapes with LLPs at almost the same height and depth locations. Thus, no distinction between the directions of the LWPD is possible in this case. From the pixel plots in Fig. 9, it is noticeable that for an LOSD of $200μ m$ there is a pronounced drop in both scores for all LWPD values.

The results of this analysis are shown in Fig. 11.

When only the features of the first OCT peak are analyzed, prediction accuracies ranging from 60% to 82% can be observed with an outlier of $87μ m$ in the lower left corner. Including the second peak order additionally to the first order significantly raises the prediction accuracies by up to 8% to values around 90% at best. Further increasing the highest peak order from the second to the fifth order has no significant impact on the top scoring parameter combinations. Two lines stick out from the plots, namely, those with LWPD values of $200$ and $350μ m$⁠, which exhibit the highest prediction accuracies regardless of the LOSD setting.

Besides these two lines, the block in the lower right corner ranging from LOSD values between $150$ and $200μ m$ and LWPD values between $200$ and $400μ m$ exhibits slightly elevated prediction accuracies. Besides the OCT data scope, the influence of the evaluation window size on the prediction accuracies was investigated. Including all five peak orders, resulting in a feature vector of length 10 (see Fig. 7), three different evaluation windows were tested spanning 200, 400, and 800 data points with an overlap between adjacent windows of 80%. The results are shown in Fig. 12.

For a window size spanning 200 data points, maximum prediction accuracies of around 80% can be achieved. Doubling the window size to 400 results in maximum accuracies of around 90%, while further increasing it to 800 data points yields maximum prediction values around 95%. Similar to the variation of the OCT data scope, the same patterns of elevated prediction accuracies can be recognized in the pixel plots for the different evaluation windows.

It is worth emphasizing that each pixel in the given plots represents a separately trained ANN based on the underlying experimental data for the parameter combination of LOSD and LWPD. To provide a better understanding of the training process, selected examples of training curves are shown in Fig. 13 for an evaluation window including 400 data points and an OCT data scope spanning the five highest feature orders resulting in a total of ten features per data point. The exemplary ANNs exhibit very different final test accuracies ranging from 50% up to almost 90% so that different learning curve progressions can be expected.

The learning curves show the prediction accuracies of each ANN on the training data set at a given training epoch. The quadratic markers at the right hand side of the plot indicate the final test accuracies as they are represented in Figs. 11 and 12. All learning curves start at an accuracy of around 50%, which represents the ratio of data points belonging to each binary class and hence is equivalent to a random guess. The highest scoring ANN marked as B drastically improves its accuracy after only a few epochs to values around 85% and from there on shows a flat and degressive progression reaching a final training accuracy of 98%. The lowest scoring ANN marked as A almost remains constantly at an accuracy of 50% despite some minor fluctuations indicating that the network was not able to detect meaningful patterns in the provided data. It is noticeable that both, the lowest and the highest scoring ANN, exhibit the least pronounced fluctuations. The learning curve corresponding to the parameter combinations marked as C shows a delayed response to the training at around 25 epochs but a rather steep learning progress increasing from 60% to values above 80%. The learning curve D only shows an overall accuracy improvement of 10% throughout the learning stage while exhibiting very strong fluctuations of around the same order of magnitude. With higher training epochs, the initial fluctuations decrease but still remain the most pronounced compared to the other learning curve progressions. The test accuracies for the ANNs belonging to the parameter combinations denoted as B, C, and D exhibit final test accuracies that are around 5%–10% lower than the training accuracies obtained from the last training epoch. Despite the depicted learning curves C and D from Fig. 13 do not show signs of saturation at 200 training epochs, further investigations on the ANN parameters have shown that using a greater number of epochs and thus further improving the training accuracies does not result in any significant improvements in the test accuracies. Therefore, a total of 200 training epochs was found to be sufficient.

As can be seen from the metallographic cross sections, the melt pool reaches the edge of the web sheet at an LWPD of $250μ m$⁠; thus, at lower path deviations, no influence of the process zone by asymmetric boundary conditions acting on the melt pool is to be expected. However, both the statistical approach and the machine learning approach yield significant scores for the distinctiveness of the deviation direction for an LWPD of $200μ m$⁠. For the histographic analysis of the OCT data point distribution, all OCT data points from the weld were used, thus giving a distribution that should be less prone to detrimental effects stemming from noise. This means that characteristics of the frequency distributions of the OCT data points cannot be attributed to random fluctuations but are rather representative of frequently occurring geometric properties of the keyhole shape probed by the OCT probe beam. It is therefore not plausible how the frequency distributions yield significant differences for opposite LOSDs at low LWPDs as the symmetry of the process zone should be conserved on a time scale beyond spontaneous keyhole fluctuations that are likely to exhibit asymmetries momentarily on short time scales of a few microseconds.

Although the center position of the OCT spot relative to the laser beam has been adjusted carefully, it can be theorized that small remaining deviations in the positioning can lead to differences in the frequency distributions especially at low LOSDs. OCT measurements taken at low LOSDs are likely to stem predominately from the keyhole bottom. At the keyhole bottom, the surface normals of the reflective keyhole walls tend to be directed more parallelly toward the OCT beam axis, therefore collecting reflections from a narrow depth range. The more the OCT beam is shifted toward the keyhole walls the surface normals of the irradiated keyhole walls tilt with respect to the OCT beam axis, thus collecting reflections from a rather broad depth range as schematically depicted in Fig. 14. The simulated OCT depth spectrum corresponding to each beam position shows how much power of the OCT measuring beam is reflected at each depth. A short probed depth range with the OCT beam probing the center of the keyhole results in a high, narrow, and asymmetric peak while the OCT beam position covering the keyhole wall exhibits a flatter and more broadened depth spectrum with a less pronounced asymmetry. This means that the closer the OCT beam is located toward the keyhole center the more pronounced even small local geometric deviations can appear in the measurement. By this reasoning, OCT measurements taken at small LOSDs are more prone to positioning errors by capturing positioning-related asymmetries. Therefore, measurements located more in the direction of the upper right corner of the pixel plot with high values for the LOSD as well as for the LWPD are more reliably related to actual asymmetric keyhole deformations.

The histograms showing the OCT data point distributions for parameter combinations with a significantly high and low score as depicted in Fig. 10 reveal a pronounced difference for the high scoring parameter combination. As the highest five peaks from the OCT depth spectrum are considered, the histograms also capture multimodal features of the OCT signal as described by Sokolov et al.;¹³ thus, more complex geometric properties of the keyhole walls are contained in the OCT data point distributions. The distribution from the equilateral LOSD exhibits an additional significant peak, indicating an asymmetric keyhole wall feature due to the melt pool deformation. Despite this asymmetric feature, both distributions for both directions of the LOSD show strong similarities as they share the positions of their global maximum peaks. For the histograms of the low scoring parameter combination, it is not clear why they do not differ from one another in any significant manner. This seems especially peculiar as the same parameter combination is among the highest scoring parameters for the neural network analysis, indicating that the neural network uses OCT features that are lost in the histographic analysis due to summation and a lack of distinction between the different peak orders.

The drop in the scores from the histographic analysis for LOSDs of $200μ m$ can possibly be explained by the presence of the face sheet. The asymmetric melt pool boundary conditions are only present at a depth below the thickness of the face sheet. At smaller depths, the symmetry is preserved as the melt pool is surrounded by the face sheet material. The higher the LOSD the lower the depth of the keyhole walls probed by the OCT beam; thus, at lower depths, it is plausible that symmetry between the OCT data point distribution belonging to opposite LOSDs is restored. However, this does not explain which features the neural network uses to still achieve prediction accuracies of up to 87% in those cases.

Comparing the scores from the histographic analysis to the scores from the neural network predictions for an evaluation window size of 800 at an LOSD of $200μ m$⁠, the results appear to be contradictory. However, it lies in the nature of ANNs and furthermore constitutes a main reason for their application that the complexity of abstracted patterns in the input data is not easily comprehensible for a human observer. Thus, the seeming contradiction is not necessarily profound and rather indicates a demand for further investigations.

The results presented in this research are based on welding experiments carried out under well controlled environmental conditions and for the basic case of a straight weld path at a constant velocity. However, it is of great interest how the presented methods would perform under more challenging conditions. The question of robustness is directly related to the response of the keyhole shape to altered boundary conditions or environmental influences. Curved weld paths are usually accompanied by a change in the process velocity due to the reorientation of the processing head. As the adjustment of the relative positioning between the OCT measuring beam and the laser processing beam is crucial for the detectability of misalignments and furthermore highly dependent on the process veloctiy, it is unlikely that the same ANN or set of feature characteristics would be applicable in both cases. However, it would be a viable solution to segment the weld path into different regions and apply customized detection criteria based on the current weld path position. The question of generality of the proposed method furthermore implies the demand for testing different materials and their influence on the detectability of misalignments and the performance of the weld path control. It is commonly known that different materials yield different keyhole dynamics as the absorption properties, viscosity and surface tension vary drastically from one another. Additionally, the OCT measuring process is directly influenced by the materials absorption properties in the given OCT spectrum. It is known that these effects lead to fundamentally different OCT data point distributions and different characteristic features. Therefore, the ANNs would need to be trained separately for each set of materials and parameter combinations. The question of whether or not the presented distinctive features in the OCT data point distributions for different combinations of LOSDs and LWPDs can be found for different materials remains a topic for further investigations. However, the hypothesis underlying the presented investigations does not rely on any assumptions concerning the used materials so it is reasonable to assume that the proposed principles also apply for different experimental parameters and materials.

In this research, it has been investigated whether it is possible to employ OCT measurements in order to distinguish between the directions of lateral weld path deviations in laser deep penetration welding of hidden T-joints consisting of pure nickel (Ni 2.4068). The underlying assumption states that the keyhole deforms asymmetrically when the melt pool reaches the edge of the web sheet so that these asymmetric features of the resulting keyhole shape can be detected by an OCT measurement. To explore this hypothesis, different combinations of lateral weld path deviations and lateral OCT spot deflections were tested and the results were analyzed statistically by means of histographic analyses of the OCT data point frequency distributions as well as by means of machine learning by employing artificial neural networks. Based on the findings, the following conclusions can be drawn:

• The OCT frequency distribution shows a significant dependence on the direction of the lateral OCT spot deflection regarding the peak prominence and the relative peak size above threshold of the last local peak in the distributions.

• For the parameter combinations exhibiting the most significant directional distinctiveness, the histographic OCT analyses show pronounced differences affirming the postulated keyhole asymmetry caused by the lateral weld path deviation.

• Inaccuracies in the initial calibration of the OCT spot center position can lead to ambiguous results and thus false predictions of the direction of the lateral weld path deviation.

• Artificial neural networks have been proven to be suitable for a time-resolved prediction of the direction of the lateral weld path deviation based on OCT measurements raising maximum prediction accuracies between 80% and 95%.

• The larger the size of the evaluation windows, the higher the prediction accuracies from the neural network; thus, the time resolution of the prediction and the accuracy are competing parameters that must be adjusted according to the individual requirements.

• Employing OCT in combination with artificial neural networks has been proven capable of distinguishing between the directions of lateral weld path deviations, thus raising the potential of improving the performance of OCT-based weld path controllers.

• It has been shown that it is possible to detect the beam path deviation before the laser beam leaves the web sheet position of the hidden T-joint, hence indicating the possibility of preventing weld seam defects caused by misalignments.

ANN

artificial neural network

LLP

last local peak

LOSD

lateral OCT spot deflection

LWPD

lateral weld path deviation

OCT

optical coherence tomography

RPSAT

relative peak size above threshold

The project on which this publication is based was funded by the German Federal Ministry of Education and Research under Grant No. 03HY119F. The responsibility for the contents of the publication lies with the authors.

The authors have no conflicts to disclose.

Ronald Pordzik: Conceptualization (lead); Data curation (lead); Formal analysis (lead); Investigation (lead); Methodology (lead); Resources (lead); Software (lead); Validation (lead); Visualization (lead); Writing – original draft (lead); Writing – review & editing (equal). Thomas Seefeld: Supervision (lead); Writing – review & editing (equal).