Prediction of martensite start temperature of steel combined with expert experience and machine learning

Figures & data

Table 1. Empirical equation of M_S calculation.

No.	Equation	Ref.
1	$M_S{(}^o\mathit{C})=(930-570\mathit{C}-60\mathit{Mn}-20\mathit{Si}-30\mathit{Ni}-50\mathit{Cr}-20\mathit{Mo}-20\mathit{W}-32)/1.8$	[5]
2	$M_S{(}^o\mathit{C})=(930-600\mathit{C}-60\mathit{Mn}-20\mathit{Si}-30\mathit{Ni}-50\mathit{Cr}-20\mathit{Mo}-20\mathit{W}-32)/1.8$	[6]
3	$M_S{(}^o\mathit{C})=(1000-650\mathit{C}-70\mathit{Mn}-35\mathit{Ni}-70\mathit{Cr}-50\mathit{Mo}-32)/1.8$	[7]
4	$M_S{(}^o\mathit{C})=(930-540\mathit{C}-60\mathit{Mn}-20\mathit{Si}-30\mathit{Ni}-40\mathit{Cr}-20\mathit{Mo}-32)/1.8$	[8]
5	$M_S{(}^o\mathit{C})=561-474\mathit{C}-33\mathit{Mn}-17\mathit{Ni}-17\mathit{Cr}-21\mathit{Mo}$	[9]
6	$M_S{(}^o\mathit{C})=539-423\mathit{C}-30.4\mathit{Mn}-17.7\mathit{Ni}-12.1\mathit{Cr}-7.5\mathit{Mo}$	[10]
7	$M_S{(}^o\mathit{C})=512-453\mathit{C}-71.5\mathit{CMn}-16.9\mathit{Ni}+15\mathit{Cr}-9.5\mathit{Mo}+217C^2-67.6\mathit{C}\bullet \mathit{Cr}$	[10]
8	$M_S{(}^o\mathit{C})=539-423\mathit{C}-30.4\mathit{Mn}-7.5\mathit{Si}-17.7\mathit{Ni}-12.1\mathit{Cr}-7.5\mathit{Mo}+10\mathit{Co}$	[11]
9	$M_S{(}^o\mathit{C})=545-330\mathit{C}-23\mathit{Mn}-7\mathit{Si}-13\mathit{Ni}-14\mathit{Cr}-5\mathit{Mo}-13\mathit{Cu}+4\mathit{V}+7\mathit{Co}$	[12]
10	$M_S{(}^o\mathit{C})=520-320\mathit{C}-50\mathit{Mn}-5\mathit{Si}-20\mathit{Ni}-30\mathit{Cr}-20\mathit{Mo}-5\mathit{Cu}$	[13]
11	$M_S{(}^o\mathit{C})=491.2-302.6\mathit{C}-30.6\mathit{Mn}-14.5\mathit{Si}-16.6\mathit{Ni}-8.9\mathit{Cr}+2.4\mathit{Mo}+7.4\mathit{W}-11.3\mathit{Cu}+8.6\mathit{Co}$	[14]
12	$M_S{(}^o\mathit{C})=565-600(1-exp(-0.96\mathit{C}))-31\mathit{Mn}-13\mathit{Si}-8\mathit{Ni}-10\mathit{Cr}-12\mathit{Mo}$	[15]
13	$\begin{array}{rl}& M_S{(}^o\mathit{C})=545-601.2(1-exp(-0.868\mathit{C}))-34.4\mathit{Mn}-13.7\mathit{Si}-17.3\mathit{Ni}-9.2\mathit{Cr}-15.4\mathit{Mo}+10.8\mathit{V}\\ & +4.7\mathit{Co}-16.3\mathit{Cu}\end{array}$	[16]
14	$M_S{(}^o\mathit{C})=(2381.3-3000\mathit{C}-60\mathit{Mn}-50\mathit{Si}-110\mathit{Ni}-75\mathit{Cr}-32)/1.8$	[17]
15	$\begin{array}{rl}& M_S{(}^o\mathit{C})=635-474\left[\mathit{C}+0.86(\mathit{N}-0.15(\mathit{Nb}+\mathit{Zr}))-0.066(\mathit{Ta}+\mathit{Hf})\right]-(17\mathit{Cr}\\ & +33\mathit{Mn}+21\mathit{Mo}+17\mathit{Ni}+39\mathit{V}+\mathit{W})\end{array}$	[18]
16	$M_S{(}^o\mathit{C})=692-37\mathit{Mn}-14\mathit{Si}+20\mathit{Al}-11\mathit{Cr}-502\sqrt{\mathit{C}+0.86\mathit{N}}$	[19]
17	$\begin{array}{rl}& M_S{(}^o\mathit{C})=523.73-521.33\mathit{C}-23.18\mathit{Mn}+20.65\mathit{Si}-11.93\mathit{Ni}-11.56\mathit{Cr}\\ & -7.49\mathit{Mo}-102.20\mathit{Cu}-21.80\mathit{V}+8.47\mathit{W}+1.75\mathit{Co}+169.53C^2+14.33\mathit{C}\bullet \mathit{Cr}\\ & +2.06\mathit{C}\bullet \mathit{Mo}+36.53\mathit{C}\bullet \mathit{V}-13.69\mathit{C}\bullet \mathit{W}\end{array}$	[20]
18	$\begin{array}{rl}& M_S{(}^o\mathit{C})=475.9-335.1\mathit{C}-34.5\mathit{Mn}-1.3\mathit{Si}-15.5\mathit{Ni}-13.1\mathit{Cr}-10.7\mathit{Mo}\\ & -9.6\mathit{Cu}+11.67ln(d_{\gamma })\end{array}$	[21]

Figure 1. Distribution of normalized features.

Figure 2. Distribution of M_S in data set.

Table 2. Spatial distribution range of data set.

Feature	Description	Max	Min	Mean
TAust	Austenitizing temperature (K)	1673	1023	1256.94
C	wt.% of C	2.25	0.01	0.37
Si	wt.% of Si	3.8	0	0.33
Mn	wt.% of Mn	8	0	0.80
Ni	wt.% of Ni	10	0	0.83
Cr	wt.% of Cr	17	0	1.24
Mo	wt.% of Mo	5.75	0	0.26
V	wt.% of V	5.05	0	0.11
Cu	wt.% of Cu	1.49	0	0.054
W	wt.% of W	19.2	0	0.46
Al	wt.% of Al	1.26	0	0.013
Ti	wt.% of Ti	0.2	0	0.0018
Nb	wt.% of Nb	0.167	0	0.0015
N	wt.% of N	0.287	0	0.0020
Co	wt.% of Co	11.35	0	0.081
MS	Martensite start temperature (K)	819	335	613.26

Table 3. Parameters used in equation (2)(2) $-\mathrm{\Delta }{G}_c(\mathit{J}/\mathit{mol})=K_1+\sqrt{\sum _i{(K_i{X}_i^{0.5})}^2}+\sqrt{\sum _j{(K_j{X}_j^{0.5})}^2}+\sqrt{\sum _k{(K_k{X}_k^{0.5})}^2}+K_{\mathit{Co}}{X}_{Co}^{0.5}$(2) .

Parameter	Value (J/mol)	Parameter	Parameter
KC	4009	KAl	280
KN	3097	KCu	752
KCr	1868	KNi	172
KMn	1980	KW	714
KMo	1418	KCo	352
KNb	1653	KTi	1473
KSi	1979	KV	1618

Table 4. Atomic feature.

Abb.	Description
mAW	mean Atomic Weight
mC	mean Column
mR	mean Row
rN	range Number
mN	mean Number
rAR	range Atomic Radius
mAR	mean Atomic Radius
rE	range Electronegativity
mE	mean Electronegativity
asve	avg s valence electrons
apve	avg p valence electrons
adve	avg d valence electrons
fsve	frac s valence electrons
fpve	frac p valence electrons
fdve	frac d valence electrons
FCC	FCC lattice parameters
BCC	BCC lattice parameters

Table 5. Hyperparametric adjustment.

Model	Hyperparameter	Search range	Optimal hyperparameter
LSO	alpha	[0.1,50]	0.1
ETR	n_estimators	[6], 8000]	1494
	max_depth	[2], 100]	74
	min_samples_split	[2], 100]	2
	min_samples_leaf	[1], 100]	1
	max_features	[0.1,1]	0.82
SVR	C	[1000,8000]	5000
	gamma	[0.1,20]	0.1
GBT	n_estimators	[22], 8000]	3321
	learning_rate	[0.001,1]	0.1
	max_depth	[2,48]	22
	subsample	[0.5,1.0]	0.5
	min_samples_split	[2,48]	19
	min_samples_leaf	[1,16]	1

Figure 3. Comparison of predicted and measured values of four machine learning models with original feature input (a) ETR(b) GBT(c) SVR(d) LOS.

Figure 4. Comparison between the predicted value of the model and the measured value after adding atomic feature.

Figure 5. PCC heat map between features.

Figure 6. VIF value of multicollinearity feature.

Figure 7. MIC analysis of features and target variables.

Figure 8. Comparison between predicted values and measured values of the model after feature selection.

Figure 9. Difference between M_S measured value and calculated value.

Figure 10. Summary chart of characteristic SHAP values (a) average SHAP(b) SHAP of each sample.

Figure 11. Distribution of SHAP values corresponding to features (a) C (b) gc (c) Ni (d) taust (e) mE (f) Cr (g) BCC (h) adve.

Figure 12. The difference between the calculated value and the measured value of the model and the corresponding C content and element content.

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