# A Weld Defects Detection System Based on a Spectrometer

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Plasma Spectroscopy

## 3. Change Detection

_{t+1}is the transition matrix from the state θ

_{t}to θ

_{t+1}; θ, in this work, is the radiation intensity; and w is the noise, represented as a random variable with normal distribution with zero mean and variance Q.

_{t}) is the radiation emitted by the plasma (θ

_{t}) with an added noise (ν

_{t}). The noise also is a random variable with normal distribution with zero mean, but variance R. With this model it is presented a diagram flux of the change detection, given by Figure 1.

_{t}) is filtered. The filter estimates the radiation intensity (θ

_{t}). The residual (ε

_{t}) is calculated and, from this information, the distance measure is done. This value measures the difference between the sensor reading and the estimation given by the filter. The residual itself is an example of this distance. Then, it is done a statistic test (g

_{t}) based on the distance. Finally, g

_{t}is compared to a threshold (h) to decide if there is a defect in the weld. If the value is lower than the reference, it is assumed that the welding process is normal. But, if the statistical test value is greater than the threshold, it is possible that a defect occurred. There are many change detection algorithms. This work presents a widely used one, the Cusum LS Filter [16] and another is proposed, which applies steps from different algorithms.

_{a}, is recorded, the statistics tests are reset and t

_{0}becomes t. With the values of the alarm instants, it is possible to indicate the defect’s position once the weld speed is constant:

_{1}and θ̂

_{2}with variances P

_{1}and P

_{2}, are obtained. If there is no abrupt change in the data, these estimates will be consistent. Otherwise, an alarm is set.

## 4. Experimental Issues

## 5. Results and Discussion

## 6. Conclusions

## References and Notes

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**MDPI and ACS Style**

Bebiano, D.; Alfaro, S.C.A.
A Weld Defects Detection System Based on a Spectrometer. *Sensors* **2009**, *9*, 2851-2861.
https://doi.org/10.3390/s90402851

**AMA Style**

Bebiano D, Alfaro SCA.
A Weld Defects Detection System Based on a Spectrometer. *Sensors*. 2009; 9(4):2851-2861.
https://doi.org/10.3390/s90402851

**Chicago/Turabian Style**

Bebiano, Daniel, and Sadek C. A. Alfaro.
2009. "A Weld Defects Detection System Based on a Spectrometer" *Sensors* 9, no. 4: 2851-2861.
https://doi.org/10.3390/s90402851