A Soft Sensing Method of Billet Surface Temperature Based on ILGSSA-LSSVM

doi:10.21203/rs.3.rs-1842747/v2

Download PDF

Article

A Soft Sensing Method of Billet Surface Temperature Based on ILGSSA-LSSVM

https://doi.org/10.21203/rs.3.rs-1842747/v2

This work is licensed under a CC BY 4.0 License

You are reading this latest preprint version

It is difficult to measure the surface temperature of continuous casting billet, which results in the lack of important feedback parameters for further scientific control of billet quality. This paper proposes a sparrow search algorithm(SSA) to optimize the least square support vector machine(LSSVM) model for surface temperature prediction of billet, which is improved by Logistic chaotic mapping and Golden sine algorithm (Improve Logistic Golden Sine Sparrow Search Algorithm LSSVM, ILGSSA-LSSVM). Based on LSSVM, the optimal solution of sparrow population is improved by improved Logistic chaos mapping and Golden sine algorithm as the value of penalty factor $\gamma$and kernel parameter$\sigma$. Global optimization method is adopted to find the optimal parameter combination, which reduces the influence of blindly determining parameters on the prediction accuracy. The results show that the maximum error of ILGSA-LSSVM soft Sensing model is 3.85733℃, the minimum error is 0.0174℃, and the average error is 0.05805℃. The performance of ILGSA-LSSVM soft Sensing model is better than that of traditional least square support vector machine, BP neural network and gray Wolf optimized least square support vector machine.

surface temperature

billet

Logistic chaotic map

Golden sine algorithm

Sparrow search algorithm

LSSVM

In continuous casting, secondary cooling control is the core of billet solidification process, and it largely determines structure and quality of billet. Therefore, adopting a reasonable secondary cooling system to obtain appropriate solidification rate is the key problem to ensure quality and yield of billet in efficient continuous casting. As an important feedback parameter reflecting the secondary cooling intensity, surface temperature of billet is the premise to realize the dynamic control of secondary cooling water. Unreasonable pouring process and secondary cooling water distribution system will often cause billet internal quality defects. In order to eliminate the billet defects, the solidification process must be controlled. If the surface temperature of billet could be accurately obtained and fed back to the secondary cooling control system for process optimization, the dynamic optimization of the secondary cooling water distribution and closed-loop control of the temperature of billet can be realized. So, it does great benefits to secondary cooling control, improving quality of the billet, reducing the internal cracks of the billet, and meanwhile it improves the automatic level of continuous casting process.

Due to the influence of high temperature of secondary cooling zone and its water mist environment, contact temperature measurement methods are difficult to measure temperature of moving billet^[1]. Moreover, the existence of water film on the surface of billet and the randomly stripped iron oxide sheet make the surface emissivity of billet uncertain and change frequently. Therefore, making the thermometer and thermal imager which are based on infrared temperature measurement mechanism unable to achieve long-term accurate application^[2–4]. The temperature field based on mechanism model is an important research direction of billet temperature analysis. N. K. Nath, et al^[5–10] achieved the acquisition of billet temperature by establishing the heat transfer mechanism models of billet in metallurgical process. However, continuous casting process is a complex process, physically and chemically, and it is difficult to obtain model parameters in actual production. Therefore, the theoretical models are complex and their accuracy cannot be guaranteed. Shu Fuhua, et al^[11] used the Least Squares Support Vector Machine(LSSVM) to predict the billet temperature, though the prediction accuracy needs to be improved. Sun Jie, et al^[12] established the billet surface temperature prediction model with the Ant Colony Algorithm, but it was easy to fall into the local optimal.

In the view of the applicability and accuracy of billet surface temperature analysis and prediction, we propose a billet surface temperature prediction model based on ILGSSA-LSSVM in this paper. Firstly, we established the least square support vector machine regression model to predict the surface temperature of billet. Secondly, the Sparrow search algorithm (SSA) was adopted to optimize initial weights and thresholds of the model. Thirdly, an improved Logistic chaotic mapping was used to improve the initialization quality of SSA, and the Golden sine algorithm was used to improve the global search ability of SSA. Finally, the accurate prediction of surface temperature of billet was realized.

2.1 LSSVM regression prediction model of billet surface temperature

The support vector machine (SVM) theory proposed by C. Cortes^[13] in 1995 is a machine learning model that seeks the best compromise between the learning accuracy of training samples and the ability to identify arbitrary samples based on the VC dimension theory and the principle of minimum structural risk. SVM has strong generalization ability, can solve nonlinear problems and can avoid local minima in solving small sample training set.

In 1999, J.A.K. Suykens^[14] proposed the least squares support vector machine (LSSVM). Based on the original method, the two norm was used and the inequality constraint was changed into equality constraint, so that solving the convex quadratic programming problem was transformed into solving linear equations, and the solving efficiency was improved.

The mathematical description of LSSVM is as follows: Suppose there is a training data set composed of samples,$D=\left\{ {\left( {{I_i},{Y_i}} \right)\left| {i=1,2,3,...,N} \right.} \right\}$,${I_i}$is the input va, ue,${Y_i}$ is the output value. LSSVM regression model can be expressed as:

$$Y(I)={\omega ^T}\varphi ({I_i})+b$$

Where, $\omega$ is the weight vector, $\varphi ({I_i})$ is a nonlinear mapping function that maps ${I_i}$ to a higher dimensional space, and is an offset quantity. In the prediction model of this paper $N=12$. ${I_1}$ to ${I_{12}}$ are molten steel temperature in Tundish, inlet temperature of crystallizer, outlet temperature of crystallizer, water flow rate of crystallizer, casting billet pulling speed, temperature of secondary cooling water, water pressure of valve port from section #0 to #2, valve opening from section #0 to #2 respectively.

In order to solve the problem of partial specific points, the error variable ${e_i}$ is introduced into each sample, and the ${L_2}$-norm of the error variable is added into the original function. The LSSVM optimization problem can be translated into:

$$\left\{ \begin{gathered} {\hbox{min} _{\omega ,b,e}}J(\omega ,e)=\frac{1}{2}{\omega ^T}\omega +\gamma \frac{1}{2}\sum\limits_{{i=1}}^{n} {{e_i}^{2}} \hfill \\ s.t.{Y_i}({\omega ^T}{I_i}+b)=1 - {e_i},i=1,......,N \hfill \\ \end{gathered} \right.$$

Where, $\gamma$ is the penalty factor to adjust the relationship between output ${Y_i}$ and error variable ${e_i}$.

Lagrange multiplier is introduced to solve the optimization problem:

$$L(\omega ,b,e;\alpha )=J(\omega ,e) - \sum\limits_{{i=1}}^{n} {{\alpha _i}[{Y_i}({\omega ^T}{x_i}+b) - 1+{e_i}]}$$

Where, ${\alpha _i}$ represents the Lagrange multiplier corresponding to ${I_i}$.

According to the KKT Conditions (Karush-Kuhn-Tucker Conditions), take the derivative of each variable to solve the values of ${\alpha _i}$ and :

$$\left\{ \begin{gathered} \frac{{\partial L}}{{\partial \omega }}=0 \to \omega =\sum\limits_{{i=1}}^{n} {{\alpha _i}{Y_i}{I_i}} \hfill \\ \frac{{\partial L}}{{\partial b}}=0 \to 0=\sum\limits_{{i=1}}^{n} {{\alpha _i}{Y_i}} \hfill \\ \frac{{\partial L}}{{\partial {e_i}}}=0 \to {\alpha _i}=\gamma {e_k},k=1,2,...,N \hfill \\ \frac{{\partial L}}{{\partial {\alpha _i}}}=0 \to {y_i}({\omega ^T}{I_i}+b) - 1+{e_k},k=1,2,...,N \hfill \\ \end{gathered} \right.$$

For the new sample , the output of the LSSVM nonlinear regression model is:

$$Y(I)=\sum\limits_{{i=1}}^{n} {{\alpha _i}{K_{ij}}+b}$$

Where, ${K_{ij}}$ is the kernel function matrix. Radial basis function (RBF) has the advantages of strong adaptability and wide application, so RBF is chosen as the kernel function of this model. So, ${K_{ij}}=\exp \left\{ {\left. { - \frac{{{{\left\| {{I_i} - {I_j}} \right\|}^2}}}{{2{\sigma ^2}}}} \right\}} \right.$,$\sigma$ is the kernel parameter.

In LSSVM regression modeling, the prediction accuracy depends on the value of penalty factor $\gamma$ and kernel parameter $\sigma$. The penalty factor $\gamma$is used to balance accuracy and error. The larger $\gamma$ is, the smaller the error is. However, the more complex the model decision function is, the more parameters it contains, and overfitting is easy to occur. The kernel parameter $\sigma$ represents the refinement of the partition between the value and the sample. The smaller $\sigma$ is, the more complex the curves selected in the low-dimensional space are, the finer the categories are, and the overfitting is easy to occur. Therefore, this paper adopts the sparrow search algorithm improved by Logistic chaos mapping and golden sine to carry out global optimization and select appropriate values of $\gamma$ and $\sigma$.

2.2 Hybrid improved ILGSSA algorithm

Sparrow search algorithm is a population optimization algorithm based on swarm intelligence, foraging behavior and anti-predation behavior of sparrows ^[15]. In foraging behavior, the population of sparrows is divided into the finder population and follower population. After foraging, those randomly selected individuals in the population turn to be the guard population. The finder population is responsible for finding the feeding area and direction, and the follower population forages with the finder population. Each sparrow is likely to be a finder, but the ratio of finders to followers remains constant throughout the population. When the alarm value is greater than the safe value, the sparrow population will give up the current position and fly to the safe area.

In this paper, SSA is adopted to optimize the penalty factor value and kernel parameters of LSSVM, which solves the problem of low prediction accuracy due to the limitation of parameter selection.

Assume that there is a sparrow population with a number of $n~$, and position of the sparrows in $~m~$ dimensional solution space is expressed as:

$$X=\left[ {\begin{array}{*{20}{c}} {{x_{1,1}}}&{{x_{1,2}}}& \cdots & \cdots &{{x_{1,m}}} \\ {{x_{2,1}}}&{{x_{2,2}}}& \cdots & \cdots &{{x_{2,m}}} \\ \vdots & \vdots & \vdots & \vdots & \vdots \\ {{x_{n,1}}}&{{x_{n,2}}}& \cdots & \cdots &{{x_{n,m}}} \end{array}} \right]$$

where, is the optimal dimension of the billet surface temperature prediction model. In this model,$m=2$.

The fitness of the sparrows can be expressed as:

$${F_X}={\left[ {{f_1},{f_2},...,{f_n}} \right]^T}~$$

where, ${f_i}$ is the fitness of each sparrow, which is the sum of the mean square error of the training set and the mean square error of the test set of the model (that is, total error).

Because the initial solution is randomly generated in SSA, which takes aggregation to the initial solution, and cause ununiform distribution of solution space. Logistic chaotic map has advantage of good randomicity, so we adopt Logistic chaotic map to generate initial solution ^[16–21]. However, in practice, Logistic map points distribution tends to relatively cluster in the upper half, and rare in the lower one as it is shown in Fig. 1(a). In order to make the map points more uniformly distributed and enhance the ergodicity of the chaotic map, we propose an improved Logistic chaotic map, its formula is given as:

$${x_{i,j+2}}=\mu {x_{i,j+1}}(1 - {x_{i,j+1}})+(4 - \mu ){x_{i,j}}(1 - {x_{i,j}})$$

where, ${x_{i,j}}$$\in \left( {0,1} \right)$, is the position of the th individual in the th dimension of the initial generation of sparrow population; ${x_{i,1}}$ and ${x_{i,2}}$ are random numbers uniformly distributed on (0,1); $\mu$ is the coefficient of chaos. If $\mu$ is closer to 4, the system is more uniformly distributed on (0, 1). In this paper, $\mu$ is chosen to be 3.99.

In order to compare the improvement effect clearly and intuitively, we set the number of iteration times to 2000, the map points distribution after improvement is shown in Fig. 1(b), and the histogram of the points distributions before and after the improvement are shown in Fig. 3.

It can be seen from the comparison in Fig. 2, the bigger the chaotic value which is before the improvement, the more the map points will be clustered, and the number of map points will reach maximum when the chaotic value reaches maximum. While the number of the improved Logistic chaotic map points with a higher ergodicity is more uniform. Therefore, the sparrow population diversity is improved by initializing the population with the improved Logistic chaotic map.

According to Golden sine algorithm simulate the searching process of unit circle by sine function ^[22–25] can obtain high quality area. In this paper, the update rule of finders' position of sparrow population is defined as:

$$\left\{ {\begin{array}{*{20}{c}} {x_{{i,j}}^{{t+1}}=\left\{ {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {x_{{i,j}}^{t}\cdot \left| {\sin \left( {{r_1}} \right)} \right| - {r_2}\sin \left( {{r_1}} \right)\cdot \left| {{c_1}x_{{best}}^{t} - {c_2}x_{{i,j}}^{t}} \right|}&{\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}if}&{{R_2}<ST} \end{array}} \end{array}} \\ {\begin{array}{*{20}{c}} {x_{{i,j}}^{t}+Q}&{\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{}&{otherwise} \end{array}} \end{array}} \end{array}} \right.} \\ {{c_1}= - \pi \left( {1 - \pi } \right)+\pi \tau \begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{}&{} \end{array}}&{}&{} \end{array}}&{}&{} \end{array}}&{}&{}&{} \end{array}}&{} \end{array}\begin{array}{*{20}{c}} {}&{} \end{array}} \\ {{c_2}= - \pi \tau +\pi \left( {1 - \tau } \right)\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{}&{} \end{array}}&{}&{} \end{array}}&{}&{} \end{array}}&{}&{}&{} \end{array}}&{} \end{array}\begin{array}{*{20}{c}} {}&{} \end{array}} \\ {\tau =\frac{{\sqrt 5 - 1}}{2}\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{}&{} \end{array}}&{}&{} \end{array}}&{}&{} \end{array}}&{}&{}&{} \end{array}}&{} \end{array}\begin{array}{*{20}{c}} {}&{} \end{array}\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{} \end{array}} \end{array}} \right.$$

where, $x_{{i,j}}^{t}$ is the position of the th individual in the th dimension of sparrow population in the th generation; ${x_{best}}$ is the global optimal position; is a random number that obeys standard normal distribution; ${r_1}$and ${r_2}$ are random numbers obeying uniform distribution on $\left[ {0,2\pi } \right]$ and $\left[ {0,\pi } \right]$ respectively; ${c_1}$and ${c_2}$ are partition coefficients; $\tau$ is golden ratio; ${R_2}$ is the early warning value obeying the random number of uniform distribution on $\left[ {0,1} \right]$; $ST$$\in \left[ {0.5,1} \right]$ is the safe value.

While ${R_2}<~ST$, the early warning value is less than the safety value, the finder population is in a safe state and it searches for food in a wide area around the current location; while $~~{R_2} \geqslant ~ST$, the early warning value exceeds the safe value, the finder population leaves the current location and flies to another place randomly obeying standard normal distribution.

The follower population position update rule in the population is defined as:

$$x_{{i,j}}^{{t+1}}=\left\{ {\begin{array}{*{20}{c}} {Q\cdot \left| {\sin \left( {{r_1}} \right)} \right| - {r_2}\sin \left( {{r_1}} \right)\cdot \left| {{c_1}x_{{worst}}^{t} - {c_2}x_{{i,j}}^{t}} \right|\begin{array}{*{20}{c}} {}&{\begin{array}{*{20}{c}} {if}&{i>\frac{n}{2}} \end{array}} \end{array}} \\ {x_{{i,j}}^{{t+1}}+\left| {x_{{i,,j}}^{t} - x_{p}^{t}} \right|\cdot {A^+}\cdot L\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{} \end{array}}&{} \end{array}}&{} \end{array}}&{}&{otherwise} \end{array}} \end{array}} \right.$$

Where, ${\text{~}}{{\text{x}}_{worst}}$ is the global worst position; $x_{p}^{t}$ is the current best position of the finder population; is a$1 \times m$ matrix in which each element is randomly assigned a value of 1 or -1, ${A^+}=A{~^T}{\left( {A{A^T}} \right)^{ - 1}}$.

When $~i>\frac{n}{2}$, it means that the current position of the finder population is not good, there is not enough food, and the follower population will fly to another region. When $~i \leqslant \frac{n}{2}$, the follower population forages near the finder population.

The initial population randomly selects 10–20% of individuals as guards who are responsible for early warning and detection of the surrounding environment:

$$x_{{i,j}}^{{t+1}}=\left\{ {\begin{array}{*{20}{c}} {x_{{best}}^{t}+\beta \cdot \left| {x_{{i,j}}^{t} - x_{{best}}^{t}} \right|\begin{array}{*{20}{c}} {\begin{array}{*{20}{c}} {}&{if} \end{array}}&{{f_i}>{f_g}} \end{array}} \\ {x_{{i,j}}^{t}+K\cdot \frac{{\left| {x_{{i,j}}^{t} - x_{{worst}}^{t}} \right|}}{{\left( {{f_i} - {f_w}} \right)+\varepsilon }}\begin{array}{*{20}{c}} {}&{if}&{{f_i}={f_g}} \end{array}} \end{array}} \right.$$

Where, $\beta$ is a random number that obeys standard normal distribution; is a random number that obeys the uniform distribution on [-1,1]; ${f_i}$ is the fitness of the current individual sparrow; ${f_w}$ and ${f_g}$ are the current global worst fitness and best fitness respectively. ε is an infinitesimal constant.

If ${f_i}>{f_g}$, the population felt danger and approached to the safe position, and if ${f_i}={f_g}$, the population stays in a safe position and moving around it.

When the sparrow population reaches the minimum fitness or the maximum number of iterations, the population stops updating.

2.3 ILGSSA-LSSVM algorithm flow

In this paper, the fitness (i.e. the total error) was used to evaluate the global optimization results. When the sparrow population reaches the minimum fitness or the maximum number of iterations, the population stops updating, and the optimal position information output is the optimal value of $\gamma$ and $\sigma$ of the LSSVM surface temperature prediction model. The flow of ILGSSA-LSSVM algorithm is shown in Fig. 3, which includes the following 6 steps:

1) The improved Logistic chaotic mapping initializes sparrow population.

2) Calculate and sort the individual fitness of the population, and mark the best fitness and the worst fitness.

3) Update the position of the finder population, follower population and guard population.

4) Determine whether the minimum fitness or the maximum number of iterations has been achieved. If not, go to Step 2).

5) Assign the optimal individual position of output to the $\gamma$ and $\sigma$ values of the LSSVM.

6) Predict the billet surface temperature by LSSVM regression model.

A comparison of the fitness curves between ILGSSA-LSSVM model and SSA-LSSVM model in this paper under the number of 20 iterations is shown in Fig. 4. The fitness of ILGSSA tends to be stable and converges to 0.01273 at 12th generation, while the SSA tends to be stable and converges to 0.01467 at 18th generation. Compared with SSA-LSSVM model, ILGSSA-LSSVM model not only converges faster, but also has smaller fitness.

Figure 5 shows the infrared colorimetric thermometer used in the filed at secondary cooling outlet. The measurement results of the thermometer are regarded as the final temperature of the billet surface after emissivity correction and data filtering. In this paper, the temperature measured by the thermometer is used to verify the calculation results of the soft sensing method.

The soft sensing method in this paper is tested in the field of Fujian Sanming Steel Co., Ltd with steel grade Q235 where the size of billet is 150mm × 150mm. There were 300 groups of continuous production parameters of the secondary system which were taken as the data sample set. Where, 200 groups were randomly selected as the training set, and the remaining 100 groups were the test set.

Gray wolf optimizer (GWO)^[26] and SSA are both emerging biological heuristic algorithms in recent years. GWO algorithm is introduced to compare with ILGSSA algorithm. And BP network is one of the most widely used neural network models, which can learn and store a large number of mapping relations. Similarly, BP neural network is introduced to compare with LSSVM. In order to verify the accuracy of this soft sensing method for billet surface temperature, five soft sensing methods including ILGSSA-BP model, SSA-LSSVM model, LSSVM model, GMO-LSSVM model and BP model are compared with ILGSSA-LSSVM model.

The parameters of ILGSSA-LSSVM model, ILGSSA-BP model and SSA-LSSVM model were set to be consistent. Suppose the warning value of sparrow population is 0.6, the finders take 70% of the population, the followers take 30%, and the guards take 40%. The optimization range of parameters $\gamma$ and $\sigma$ to be optimized is $\gamma \in \left[ {0.01,500} \right]$,$\sigma \in \left[ {0.01,100} \right]$.The optimization result is: $\gamma =7.9982$,${\sigma ^2}=6.6038$.

Table 1

Comparison table of soft sensing results
Model	Maximum error/℃	Minimum error/℃	Mean error/℃
ILGSSA-LSSVM	3.85733	0.01740	0.05805
ILGSSA-BP	6.39868	0.86509	3.67250
SSA-LSSVM	5.02431	0.00585	1.05740
GWO-LSSVM	5.318245	0.07711	0.64137
LSSVM	9.47212	0.28742	4.17160
BP	9.26264	0.36246	4.79316

The comparison results of the above six soft sensing method models are shown in Table 1. ILGSSA-LSSVM model has the minimum maximum error and mean error, and the minimum error is larger than SSA-LSSVM model but smaller than other models. Figure 6 and Fig. 7 show the comparison of results and errors in test sets of six soft sensing methods. On the whole, the maximum error, minimum error and average error of LSSVM optimization model are all smaller than that of BP neural network optimization model. ILGSSA-LSSVM model has the smallest relative error and the smallest error fluctuation, so this soft sensing method is relatively robust.

The mean square deviation ($MSE$) and root mean square error ($RMSE$) are generally used to characterize the degree of dispersion between the predicted value and the true value. The decision coefficient ${R^2}$ is used to express the goodness of fitting between the predicted value and the true value, when ${R^2}$ is closer to 1, predicted value is closer to the true value. The mean absolute error ($MAE$) is used to evaluate the fitting accuracy and avoid the deviations cancelling each other out.

$$\left\{ \begin{gathered} MSE=\frac{1}{n}{\sum\limits_{{i=1}}^{n} {\left( {{y_i} - \widehat {{{y_i}}}} \right)} ^2} \hfill \\ RMSE=\sqrt {\frac{1}{n}{{\sum\limits_{{i=1}}^{n} {\left( {{y_i} - \widehat {{{y_i}}}} \right)} }^2}} \hfill \\ {R^2}=1 - \frac{{{{\sum\limits_{{i=1}}^{n} {\left( {{y_i} - \widehat {{{y_i}}}} \right)} }^2}}}{{{{\sum\limits_{{i=1}}^{n} {\left( {{y_i} - \overline {y} } \right)} }^2}}} \hfill \\ MAE=\frac{1}{n}\sum\limits_{{i=1}}^{n} {\left| {{y_i} - \widehat {{{y_i}}}} \right|} \hfill \\ \end{gathered} \right.$$

Where, is the number of members of the test set; ${y_i}$ is the th predicting value; and $\widehat {{{y_i}}}$ is the real predicted value of ${y_i}$.

Table 2

Comparison table of evaluation indexes of various soft sensing methods
Model	MSE	RMSE	${R^2}$	MAE
ILGSSA-LSSVM	1.381	1.1752	0.900	0.93262
ILGSSA-BP	15.5271	3.9404	0.41206	3.6725
SSA-LSSVM	2.0631	1.4364	0.68821	1.2684
GWO-LSSVM	1.4147	1.1894	0.6484	1.0173
LSSVM	19.884	4.4591	0.82718	4.1716
BP	29.0398	5.3889	0.56141	5.1217

Evaluation indexes of different models are shown in Table 2. Compared with the other five models, ILGSSA-LSSVM model has the smallest $MSE$, $RMSE$,$MAE$ and error values, and the value of ${R^2}$ is closest to 1.

To sum up, ILGSA-LSSVM soft sensing method has the highest accuracy, the best fitting degree and the smallest error fluctuation. In the actual production process, the soft temperature sensing method and infrared colorimetric thermometer verify each other, which is beneficial to temperature measurement calibration, and provides reference for the actual production of steel mills.

In this paper, we proposed a hybrid improved billet surface temperature soft sensing method based on ILGSSA-LSSVM, which achieved good prediction for the surface temperature of billet and provided accurate parameter feedback for secondary cooling water distribution process of continuous casting. The main conclusions are as follows:

With the improved Logistic chaotic mapping, the stability and uniformity of the initial solution distribution of sparrow population was improved. Golden sine algorithm was adopted to obtain better high-quality solution region of sparrow population scanning, which improved the global searching ability of ILGSSA-LSSVM.

Global optimization method was adopted to find the optimal parameter combination of $\gamma$ and $\sigma$, which reduced the influence of blindly determining parameters on the prediction accuracy.

Compared with ILGSSA-BP model, SSA-LSSVM model, LSSVM model, GMO-LSSVM model and BP model, ILGSSA- LSSVM model had the advantages of fewer iterations and higher convergence accuracy, and could obtain the surface temperature of billet more quickly and accurately. The results show that the maximum error of ILGSA-LSSVM soft Sensing model is 3.85733℃, the minimum error is 0.0174℃, and the average error is 0.05805℃.

The soft sensing method lays a reliable foundation for the control and optimization of secondary cooling water distribution in continuous casting.

Acknowledgements

This paper is supported by National Natural Science Foundation of China (No. 61963002, No. 61866001), Natural Science Foundation of Jiangxi Province China (No. 20202BABL203034). We thank the editor, and the anonymous reviewers for their work improving this manuscript for publication.

Author contributions

J.L. and L.Y. wrote the manuscript. J.F. and Q.H. were in charge of the field experiment. F.Y. analyzed the data. All authors discussed the results and reviewed the manuscript.

Data availability

The datasets used and analyzed during the current study are available from the corresponding author on reasonable request.

Competing interests

The authors declare no competing interests.

Liu Jun, Ma Jiaocheng, Yang Feng, et al. New Solution to Surface Temperature of Casting Billet Measurement Based on Preceded Reflector and Multi-Wavelength[J]. Journal of Iron and Steel Research(International), 2012, 19(8): 12-16.
Zang Yuzhong. Research on Method and Application of Vision-based Temperature Field Measurement for Continuous Casting Billet[D], Northeastern University, 2014.
Ma Jiaocheng, Liu Jun, Yang Qing, et al. The Temperature Field Measurement of Billet Based on Multi-information Fusion, Materials Transaction, 2014, 55(8): 1319-1323.
Ma Jiaocheng, Liu Jun, Wang Biao. Based on Multi-information Fusion Casting Billet Temperature Field Measurement Method and Analysis of Influencing Factors, Acta Electronica Sinica, 2015, 43(8): 1616-1620(EI).
N. K. Nath, K. Mandal, A. K. Singh, et al. Ladle furnace online reckoner for prediction and control of steel temperature and composition[J]. Ironmaking & Steelmaking, 2006, 33(2): 140-150.
Hardin, R. A., Liu, K., Beckermann, C., et al. A transient simulation and dynamic spray cooling control model for continuous steel casting[J]. Metall Mater Trans B, 2003, 34: 297–306.
Ge Jianhua, Wang Minglin, Zhao Wenbo, et al. Numerical Simulation of Temperature Field During Slow Cooling Process of Continuous Casting Billet Stacking[J]. Hot Working Technology, 2017, 46(13): 105-108+114.
Dang Aiguo, Cui Juan, Li Yongchao, et al. Numerical Simulation of Temperature Change of Cast Billet of 325 mm × 280 mm Bearing Steel[J]. Special Steel, 2015, 36(2): 17-20.
J. R. S. Zabadal, M. T. M. B. Vilhena, S. Q. B. Leite. Heat transfer process simulation by finite differences for online control of ladle furnaces[J], Ironmaking & Steelmaking, 2004, 31(3): 227-234.
Fredman, T. P., Torrkulla, J., Saxén, H. Two-dimensional dynamic simulation of the thermal state of ladles[J]. Metall Mater Trans B, 1999, 30: 323–330.
Shu Fuhua, Ding Jiangang. Surface Temperature Prediction of Continuous Casting Billet Based on Support Vector Machine[J]. Steelmaking, 2009, 25(1): 55-59.
Sun Jie, Yu Menghan. Prediction Model of Billet Temperature in Rolling Furnace by Neural Network[J]. Foreign Electronic Measurement Technology, 2021, 40(9): 24-28.
Corinna Cortes, Vladimir Vapnik. Support-Vector Networks.[J]. Machine Learning, 1995, 20(3).
J.A.K. Suykens,J. Vandewalle. Least Squares Support Vector Machine Classifiers.[J]. Neural Processing Letters,1999,9(3).
Jiankai Xue, Bo Shen. A novel swarm intelligence optimization approach: sparrow search algorithm, Systems Science & Control Engineering[J]. 2020, 8(1): 22-34.
WANG Mingxin. The diffusive Logistic equation with a free boundary and sign-changing coefficient [J]. Journal of Differential Equations, 2015, 258(4): 1252-1266.
Xu Guangxian, Cui Junjie. Safety network coding design based on improved Logistic chaotic sequence[J]. Journal of Chongqing University of Posts and Telecommunications (Natural Science Edition), 2021, 33(01): 94-104.
Xu Hongli, Qian Xu, Yue Xun, et al. New ant colony optimization algorithm based on Logistic chaotic image to resolve VRP problem[J]. Application Research of Computers, 2012, 29(06): 2058-2060.
Chen Zhigang, Liang Diqing, Deng Xiaohong, et al. Performance Analysis and Improvement of Logistic Chaos Mapping[J]. Journal of Electronics & Information Technology, 2016, 38(06): 1547-1551.
Wan Youhong, Li Jungang. An Improved Chaotic Map Based on Logistic and Its Performance Analysis[J]. Information and Control, 2012, 41(6): 675-680.
Lu Qing, Lin Xiaohui, Li Jun, et al. Improved Method for Chaotic Frequency Hopping Sequence[J]. Journal of Data Acquisition and Processing, 2010, 25(1): 122-125.
Tanyildizi E, Demir G. Golden sine algorithm: a novel math-inspired algorithm[J]. Advances in Electrical and Computer Engineering, 2017, 17(2): 71-78.
TANYILDIZI E. A novel optimization method for solving constrained and unconstrained problems: modified golden sine algorithm[J]. Turkish journal of electrical engineering and computer sciences, 2018, 26: 3288-3305.
Yu Jianfang, Liu Sheng, Wang Junjie,et al. Ant lion optimization algorithm integrating with Levy flight and golden sine[J]. Application Research of Computers, 2020, 37(8): 2349-2353.
Gao Fanfan, Ding Zhengsheng. Flower Pollination Algorithm Combining Dynamic Convergence Factor and Golden Sine[J]. Journal of Henan University of Science and Technology(Natural Science), 2022, 43(2): 47-53+7.
Seyedali Mirjalili, Mohammad Mirjalili, Andrew Lewis. Grey Wolf Optimizer[J]. Advances in Engineering Software,2014,69.

No competing interests reported.

Download PDF

Editorial decision: Major revision
17 Oct, 2022
Reviews received at journal
11 Sep, 2022
Reviewers agreed at journal
09 Aug, 2022
Reviewers invited by journal
25 Jul, 2022
Editor assigned by journal
25 Jul, 2022
Editor invited by journal
21 Jul, 2022
Submission checks completed at journal
21 Jul, 2022
First submitted to journal
20 Jul, 2022

You are reading this latest preprint version

A Soft Sensing Method of Billet Surface Temperature Based on ILGSSA-LSSVM

Status:

Version 2

Abstract

Figures

1. Introduction

2. Prediction Model Of Billet Surface Temperature Ilgssa-lssvm

2.1 LSSVM regression prediction model of billet surface temperature

2.2 Hybrid improved ILGSSA algorithm

2.3 ILGSSA-LSSVM algorithm flow

3. Test And Analysis

4. Conclusion

Declarations

References

Additional Declarations

Status:

Version 2