# Temporal Resolution of Acoustic Process Emissions for Monitoring Joint Gap Formation in Laser Beam Butt Welding

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## Abstract

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## 1. Introduction

## 2. Materials and Methods

#### 2.1. Specimen Configuration

#### 2.2. Weld and Measurement Setup

## 3. Dataset and Cluster Analysis

#### 3.1. Signal Analysis

#### 3.2. Dataset Preparation

#### 3.3. Clustering Technique

## 4. Results and Discussions

#### 4.1. Validation Setup and Parameters

#### 4.2. Scenario I: Gap Detection

#### 4.3. Scenario II: Identification of Gap Size

#### 4.3.1. Classification Accuracy

#### 4.3.2. Separability Analysis Using Relative Recall

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

kNN | k-nearest neighbors algorithm |

NCA | Neighborhood components analysis |

RLT | Repeated learning-testing validation |

T | Duration of signal segments |

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**Figure 1.**Specimen configuration including patch segmentation according to [14]: (

**a**) schematic illustration, (

**b**) the photograph of an exemplary pre-welding sample, (

**c**) the photograph of an exemplary post-welding sample. The gap size of (

**b**,

**c**) is $0.2$ $\mathrm{m}$$\mathrm{m}$.

**Figure 3.**Exemplary measurement results of a specimen with $0.3$ $\mathrm{m}$$\mathrm{m}$ gaps. Top row (

**a**,

**b**): the spectrograms of the structure-borne sensor signal placed at the beginning of the specimen (SB1), bottom row (

**c**,

**d**): the spectrograms of the airborne sensor signal (AB). For both rows, the entire frequency range (approximately $3.125$ $\mathrm{M}$$\mathrm{Hz}$) is shown in the left column, whereas the lower frequency range (<760$\mathrm{k}$$\mathrm{Hz}$) is presented in the right column. Here, the measurement data up to $1.3$ $\mathrm{s}$ are shown for the sake of presentation.

**Figure 4.**Illustration of the validation procedure. (1) Signals are segmented with the given duration T in the time domain. (2) The segments are preprocessed in the frequency domain. (3) The preprocessed segments are clustered via NCA. (4) The test segments are classified via kNN.

**Figure 5.**Illustration of how the gap detection accuracy changes depending on the segment duration T. The equivalent weld seam length is provided on top (in purple), which indicates that the weld seam is progressed for $0.2$ $\mathrm{m}$$\mathrm{m}$ in 1 $\mathrm{m}$$\mathrm{s}$. The results are obtained by conducting repeated learning-testing validations for 50 iterations based on Scenario I, where the segments are classified into three classes (Zero Gap, Gap, and Noise). Top row (

**a**): average accuracy with error bars (standard deviation) and bottom row (

**b**): average confusion matrices for selected segment duration. The channels mentioned in the results are the structure-borne ultrasound sensor at the beginning (SB1) and the airborne ultrasound sensor (AB).

**Figure 6.**Exemplary illustration of segments separability for different segment durations T. Since the dimension of the input vectors $\mathbf{x}$ $\in {\mathbb{R}}^{2048}$ is reduced to 2 (=number of classes minus one) after NCA clustering, the results shown here are the output vectors $\mathbf{y}={\left[{c}_{1},{c}_{2}\right]}^{T}$$\in {\mathbb{R}}^{2}$ in two dimensional images. The cluster regions are represented by different colors (purple for Zero Gap, blue for Gap and yellow for Noise). For exemplary purpose, these results are obtained by running a single training-test split for each duration. The channels mentioned in the results are the structure-borne ultrasound sensor at the beginning (SB1) and the airborne ultrasound sensor (AB).

**Figure 7.**Illustration of how the classification accuracy of gap size changes depending on the segment duration T. The equivalent weld seam length is provided on top (in purple), which indicates that weld seam is progressed for $0.2$ $\mathrm{m}$$\mathrm{m}$ in 1 $\mathrm{m}$$\mathrm{s}$. The results are obtained by conducting repeated learning-testing validations for 50 iterations based on Scenario II, where the segments are classified into five classes (Zero Gap, Gap 0.1, Gap 0.2, Gap 0.3 and Noise). Top row (

**a**): average accuracy with error bars (standard deviation) and bottom row (

**b**): average confusion matrices for selected segment duration. The channels mentioned in the results are the structure-borne ultrasound sensor at the beginning (SB1) and the airborne ultrasound sensor (AB).

**Figure 8.**Average relative recall with regard to the Zero Gap class (top row (

**a**)) and the Noise class (bottom row (

**b**)) over varying duration T after 50 realizations. The results show how easy (high recall) or difficult (low recall) it is to distinguish between the reference class and another class. This serves as an indicator of how separable the cluster of the reference class is from that of another class. The results show how the relative recall changes depending on the segment duration for each channel: SB1 is a structure-borne sensor at the start of a specimen, and AB is an airborne sensor.

Name | Type | Specifications | Distance |
---|---|---|---|

IZFP RI-MA71RC | Airborne | Center frequency: 520 $\mathrm{k}$$\mathrm{Hz}$ | |

(AB) | ultrasound | Transducer diameter: 23 $\mathrm{m}$$\mathrm{m}$ | ${a}_{mic}$ = 297 $\mathrm{m}$$\mathrm{m}$ |

sensor | Focal point: 50 $\mathrm{m}$$\mathrm{m}$ | ||

QASS QWT sensors | Structure borne | ||

(SB1: at the start, | ultrasound | Max frequency: 100 $\mathrm{M}$$\mathrm{Hz}$ | ${a}_{sensor}$ = 114 $\mathrm{m}$$\mathrm{m}$ |

SB2: at the end) | sensor |

File Type | File Count |
---|---|

Gap 0.1 + Zero Gap + Noise | 15 |

Gap 0.2 + Zero Gap + Noise | 22 |

Gap 0.3 + Zero Gap + Noise | 23 |

Operation | Parameter | Value |
---|---|---|

RLT validation | Number of iterations | 50 |

Segment durations | 1… 100 $\mathrm{m}$$\mathrm{s}$ | |

Scenario I | 120 segments per class | |

Scenario II | 30 segments per class | |

Data split ratio | 67% training | |

33% test | ||

STFT | Sampling frequency | 6$\mathrm{M}$$\mathrm{Hz}$ |

Frequency bins | 2048 | |

Time window | 2048 samples (≈ $0.341$ $\mathrm{m}$$\mathrm{s}$) | |

Window type | Hanning window | |

Overlap | 50% | |

NCA | Initialization | linear discriminant analysis |

Input size | 2048 | |

Output size | ${N}_{class}-1$ | |

kNN | k | 3 |

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**MDPI and ACS Style**

Kodera, S.; Schmidt, L.; Römer, F.; Schricker, K.; Gourishetti, S.; Böttger, D.; Krüger, T.; Kátai, A.; Straß, B.; Wolter, B.;
et al. Temporal Resolution of Acoustic Process Emissions for Monitoring Joint Gap Formation in Laser Beam Butt Welding. *Appl. Sci.* **2023**, *13*, 10548.
https://doi.org/10.3390/app131810548

**AMA Style**

Kodera S, Schmidt L, Römer F, Schricker K, Gourishetti S, Böttger D, Krüger T, Kátai A, Straß B, Wolter B,
et al. Temporal Resolution of Acoustic Process Emissions for Monitoring Joint Gap Formation in Laser Beam Butt Welding. *Applied Sciences*. 2023; 13(18):10548.
https://doi.org/10.3390/app131810548

**Chicago/Turabian Style**

Kodera, Sayako, Leander Schmidt, Florian Römer, Klaus Schricker, Saichand Gourishetti, David Böttger, Tanja Krüger, András Kátai, Benjamin Straß, Bernd Wolter,
and et al. 2023. "Temporal Resolution of Acoustic Process Emissions for Monitoring Joint Gap Formation in Laser Beam Butt Welding" *Applied Sciences* 13, no. 18: 10548.
https://doi.org/10.3390/app131810548