4.4.1. Evaluation Procedures

In this work, to employ the FCE method to evaluate the quality of weld bead, some steps were taken as follows.

Step1: Confirm the evaluation indexes elements set *U* for this work.

The most intuitive evaluation method for the weld bead is the appearance. In general, experienced welders can justify whether the process operational parameters are proper or not according to the appearance of the weld bead, and then make corresponding optimizations. Hence, the appearance was an important evaluation index element. In addition, the grain structure and size can determine the microstructure properties of the weld bead, therefore, the grain size was also an important index element. Moreover, some abnormal phenomena, such as short-circuiting, arc interruption and splashes, can induce the instability of the electrical signals, so the stability of the electrical signals can also be helpful for evaluating the quality of weld bead. Furthermore, the key shape measurement parameters of the weld bead were bead width, bead height and penetration. The bead height and penetration should follow a certain relation, hence, a new variable, which was bead height coefficient, was introduced to assist the evaluation, the bead height coefficient can be derived using a quotient between bead width and bead height (*B*/*h*). Also, the penetration and bead width should be individual evaluation

index elements. Hence, a comprehensive evaluation index element set can be confirmed as shown in Equation (5):

> *U* = {Appearance, grain size, stability of electrical signal, bead height coefficient, penetration, bead width} (5)

Step2: Establish the evaluation indexes weights set *W*.

Considering the different levels of importance of above confirmed evaluation index elements, after consulting experienced experts and examined relative materials, corresponding weights set was shown in Equation (6):

$$\mathcal{W} = \{0.3, 0.3, 0.2, 0.06, 0.07, 0.07\} \tag{6}$$

Step3: Establish the evaluation results set *V*.

According to the experience of welding researches, hierarchy was used in this work, the quality evaluation of the weld bead can be divided into four grades, which are shown in Equation (7).

$$V = \langle \text{Excellert, Good, Median, Poor} \rangle \tag{7}$$

To provide accurate qualitative evaluation results, the four grades can correspond to mathematical values, as shown in Table 8.

**Table 8.** Mapping from grades to mathematical values.


In addition, the fuzzy operator used in this work was M (·,+) [21].

4.4.2. The Foundation and Evaluation Results of FCE

The foundation of quality evaluation for weld bead in this work can be seen in:


Hence, all of these five evaluation index elements should be divided into four grades, which used the division described in Equation (7) as shown in Step 4. Then using FCE algorithm, quantitative evaluation scores can be obtained. Corresponding evaluation for each criterion and final quantitative evaluation scores can be seen in Table 9.


**Table 9.** Evaluation results of FCE.

As shown in Table 9, not only the individual evaluate criterion for weld bead was provided, but also the overall quality of weld bead can also be qualitatively presented, these results can also be used in the orthogonal experimental analyses in the following part.
