Process optimization of quenching and partitioning by machine learning aided with orthogonal experimental design

Owing to a balance between toughness and strength, quenching and partitioning (Q&P) is promising in steel industry. However, for a new material or a new process, it remains challenging how to get the best parameters in low cost way. Here, a novel workflow combining orthogonal experimental design with artificial neural network and particle swarm optimization, was adopted to explore the relationship between quenching and partitioning process parameters and properties in Fe-0.65 wt%C-1.50 wt%Si-0.91 wt%Mn-1.08 wt%W steel. By using this method, the workload is reduced significantly. Compared with traditional process, the elongation of the steel increases by 146% times without loss in yield strength and a little improvement in ultimate tensile strength by quenching at 167 °C followed by partitioning at 367 °C for 5.0 min.


Introduction
The trade-off between strength and toughness has been given the most attention by researchers of structural materials [1].Recently, the quenching and partitioning (Q&P) is proposed to overcome the trade-off in the highstrength steel by stabilizing retained austenite [2].According to quenching temperature(QT) and partitioning temperature(PT), it can be divided into two classes: single-step Q&P(PT = QT) and two-step Q&P(PT≠QT) [3].Last decades, most effort was donated to improve the combination of strength and ductility for different steels including low or medium carbon steel designed in labs [4], some commercial steels [5], and some cast irons [6].
Here comes a problem how to build the model speedily and efficiently for Q&P steel to enhance the performance.
In Q&P process, the microstructure is governed by process parameters, which mean QT, PT and Pt for Q&P, and they are easy to control.As a result, it is more practicable to build a bridge between process parameters and properties.However, the relationship between process and properties is complex and nonlinear [7].The artificial neural network (ANN) provides a solution for such problem.In past, ANN has been applied to build relationship between properties and compositions [8,9], parameters [10,11], and to design new alloys [12].When combined with some optimization algorithm, such as particle swarm optimization (PSO) [13], ANN can optimize the input by output.The ANN model, as a data-driving computational model, need sufficient data.The input data is very important.Nevertheless, on the one hand, most researchers just collect the data from documents, which often fill the experimental space with several lines, causing uncertainty in the empty area.On the other hand, there is no experimental data for a new material or new process.In addition, in considering the economics, the number of experiments should be as little as possible.
In this paper, we chose Fe-0.65 wt%C-1.50wt%Si-0.91 wt%Mn-1.08 wt%W as steel alloy and established the ANN model between heat treatment parameters and mechanical properties, finally, optimized process by combining the ANN model and particle swarm optimization (PSO).The purpose of this study is to provide a workflow of optimizing process parameter for new material or process in a low-cost way.

Experimental data sources
The data set used in this paper is from the research results of Liao et al [14] In their study, The steel was handled by Q&P process and bainite process [15], and the corresponding mechanical properties and process parameters are shown in table 1.The process was designed by orthogonal experimental design (OED) (L 16 ) and all the data got by OED was used for training the ANN model in current work.In addition, there are four additional experiments (as table 1) were conducted, which were used as validation set in current work.

Optimization workflow 2.2.1. The workflow
To optimize the parameters of Q&P heat-treatment in a low-cost way, a comprehensive method, which combines orthogonal experimental design (OED) with artificial neural network (ANN) and particle swarm optimization (PSO), is proposed.The schematic representation is shown as figure 1. OED provides experimental data for ANN model, including the inputs (here is QT, PT and Pt) and outputs (here means total elongation (El t ), reduction of area (RA), yield strength (YS) and ultimate tensile strength (UTS)).Then ANN model is trained by back propagation algorithm.After training, the ANN model will be used to predict mechanical properties by inputting heat-treatment parameters.When combined with some optimization algorithm (here is PSO), the trained ANN model can be used to optimize heat-treatment parameters by properties to reach some particular purpose, such as highest YS.

Artificial neural network
ANN model has been proved mathematically to be able to mapping between any nonlinear object [16], and it is suitable to solve problems with unknown inner mechanism.On the other hand, the data obtained by OED is irredundant, which is quite suitable for ANN model.
The ANN model used in current work is illustrated in figure 1, which was implemented in MATLAB software.There are four layers: an input layer with three nodes, two hidden layers with three and four nodes respectively, and an output layer with four nodes.To guarantee the capability of generalization, the Bayesian Regulation (trainbr) was used as training algorithm.The transfer function was chosen as symmetric sigmoid (tansig).The mean square error (MSE) was used to evaluate the performance of the network.The training process would stop when MSE < 0.0005 or iteration times > 2000.Before training, the input and output value was normalized to [0.1, 0.9] by equation (1).
Where V norm is the normalized value, V is the actual value, V min is the minimum of V and V max is the maximum of V.
The data got by orthogonal experiments were all used for training, and four additional experiments were used for validation.

Particle swarm optimization
After training the ANN model, mechanical properties of the steel can be predicted easily according to Q&P process parameters.To get the best parameters of particular purpose, such as highest elongation without loss in strength compared with traditional treatment, multi-objective optimization algorithm (such as particle swarm optimization (PSO) [17], and artificial bee colony (ABC) algorithm [18]) can be applied to the trained ANN model.In present work, PSO method was used.PSO is a population-based stochastic optimization technique inspired by the foraging of a bird flock, and it searches the 'food' by the following equations.
Where v i t is the velocity of particle i at iteration t; x i t is current position of particle i at iteration t; x , pbest t x t gbest are the personal and global best position, respectively; w is weighting factor; c 1 , c 2 are learning rate; rand 1 , and rand 2 are tow random number, ranging from 0 to 1.In current work, 30 particles were used, and w, c 1 , c 2 were set as 0.4, 0.3 and 0.6 respectively.The tolerance was 10 −6 .

ANN performance analysis
The result of training and validation of the network is illustrated as figure 2(a).It is obvious that the slope and the correlation coefficients between outputs and targets are 0.87, 0.957 for training, 0.795, and 0.879 for validation.From the diagram, it is clear that the mechanical performance between predicted and experimental matches well.The relative error is less than 10% except No.8 experiment, and the average relative error is 3.53%.The highly consistent between experimental and predicted mechanical properties shows that the trained ANN model is reasonable for current work.increase of all heat treatment parameters.YS decreases with QT, while it has a peak with PT (1633 MPa at 314 °C) and Pt (1631 MPa at 17.8 min).RA exists as an extremum for all parameters, specifically, maximum of 46% for QT 179 °C and 46.1% for PT 338 °C, minimum of 39.5% for Pt 7.1 min.El t increases with QT and has a maximum 17.1% at 370 °C, a minimum 15.5% at 10.2 min.

Prediction of mechanical properties by ANN model
However, the influence of single factor is studied by fixing other two parameters.To observe the influence of multi-parameters on properties, the mechanical performance around 180-330-20 is illustrated in figure 4. As we can see from figure, the relationship between parameters and properties is very complex, in addition, the toughness and strength cannot reach maximum simultaneously.The maximal El t (20.9%) happened at 180-400-5 while UTS is a minimum at this condition.RA's maximum is 46.8% at 180-375-5, in addition, there exist another peak around 176-348-20, reaching about 46.2%.The maximum of YS is 1804 MPa at 140-306-20 and 2290 MPa at 180-300-5 for UTS.Compared with the result of single parameter, the properties' maximum of multi-factors is obviously higher.

Parameters optimization
By using the trained ANN model [19], the mechanical properties and ultra-high temperature ceramics melting temperature in different conditions can be predicted easily [20].However, it remains a problem how to get the maximum properties in whole parameter space.To get the global optimum and corresponding parameters, PSO algorithm [21], was applied in the trained ANN model in current work.
Here, the parameters of highest single mechanical property with and without loss of other properties compared with traditional treatment are searched by PSO algorithm.With regard to elongation, figure 5(a)   shows the searching procedure by 30 particles without any constrain, and all particles reached global maximum by quenching at 200 °C followed by partitioning at 400 °C for 5.3 min after 65 iterations.The other optimal processer and corresponding properties are shown in table 2. The steel will achieve diverse goals by different processes.For high toughness, the El t is about 3 times of traditional heat treatment when handed by 200-400-5.3.For high strength application, the UTS increases from 1814 MPa to 2073 MPa along with 26.3% increase in elongation at 145-313-11.1.For co-ordination of toughness and strength without loss in mechanical properties, the 167-367-5 is the best choice, UTS•El t of which is about 2.4 times of traditional.The application potential of steel is expanded by parameter optimization.

Conclusion
By combining ANN model and PSO algorithm, parameters optimization of Q&P heat treatment in Fe-0.65 wt% C-1.50 wt%Si-0.91 wt%Mn-1.08 wt%W were explored.The following conclusion can be made: (1) This method provides a solution for parameters optimization of Q&P heat treatment in a cost-conserving way.On one hand, it takes full use of orthogonality, which ensures the non-redundant data for ANN model.On the other hand, ANN can fill the gap among the orthogonal table, and the parameters can be searched when trained ANN is combined with PSO algorithm.
(2) The relationship between heat treatment parameters and mechanical properties is established by ANN model, and the average relative error is 3.53%.Using the trained ANN model, the effect of single and multiparameters on mechanical performance is studied.
(3) The best parameters are designed by searching the trained ANN model using PSO algorithm.Compared with traditional heat treatment, the elongation of 167-367-5.0increases by 146% times with no loss in YS and a little improvement in UTS.As a result, the UTS • El t is about 2.4 times of traditional.

Figures 2 (
b) and (c) show the difference of mechanical properties between ANN model and experiments.No.1 to No.16 experiments are the training data and the others are used for validation.
Owing to the properties at 180-330-20 achieve acceptable strength-ductility trade-off, the influence of heat treatment parameters around 180-330-20 on mechanical properties is investigated by trained ANN model, and the results are shown in figure 3 and figure 4. Around 180-330-20, UTS decreases monotonously with the

Figure 1 .
Figure 1.Schematic representation of the comprehensive method used in this work.

Figure 2 .
Figure 2. The training and validation of ANN model in this study.(a) The training and validation for ANN; The predicted and experimental (b) El t , RA (c) YS, UTS and relative error.

Figure 3 .
Figure 3.The effect of single heat treatment parameter (a) QT; (b) PT; (c) Pt on mechanical properties.

Figure 4 .
Figure 4.The effect of multi heat treatment parameters on mechanical properties (a) El t ; (b) RA; (c) YS; (d) UTS.

Figure 5 (
b) illustrates the properties varying with processes around the best parameters for elongation, and it is clear that the elongation reaches a peak at 200-400-5.3(figure5(b 1 )) while the UTS gets its minimum (figure 5(b 4 )).

Table 2 .
The processes and corresponding mechanical properties optimized by PSO.Objective function is the target that need to be optimized, and constrain means all of the four properties are greater than those handled by traditional process.