A novel quantum genetic algorithm with the application in LS-SVR

The characteristics of LS-SVR are analyzed. LS-SVR is fitted for modeling small samples and high dimensional data, but the performance of LS-SVR is related to the specific data distribution, the kind of kernel function, its related kernel parameter, and the penalty coefficient. In this paper, the radial basis function is applied as the kernel function of LS-SVR, and the real double-chain coding target gradient quantum genetic algorithm (DCQGA) is applied to optimize the kernel parameter and penalty item coefficient of LS-SVR, then the regression prediction model DCQGALSSVR is proposed. It is of great significance to build an accurate and reliable fault prediction model for the health monitoring and fault diagnosis of liquid rocket engines. The thrust of a liquid rocket engine is an important factor in its health monitoring. By predicting the thrust change value and comparing the predicted value with the engine thrust threshold, it can be predicted whether the engine will fail at a certain time. In this paper, the proposed DCQGALSSVR model is used to model the thrust of a liquid rocket engine. The simulation results show that the average relative error is 0.37% using LSSVR for modeling on 12 test samples, and is 0.3186% using DCQGALSSVR on the same samples. It can be seen that DCQGALSSVR is effective for the health monitoring of liquid rocket engines, so it has a certain promotion significance.


Introduction
Recently, artificial neural networks have been widely used [1][2][3], although their optimization processes have a great relationship with the selection of the initial points.At the same time, the performance of artificial neural networks is associated with the number of training samples.The birth of the Support Vector Machine (SVM) provides a new method to solve these problems.It is a new learning algorithm presented by Vapnik et al. [4].SVM can improve its generalization ability and overcome neural network shortcomings.Therefore, SVM has been widely used [5].[6] used intelligent algorithms to optimize the key parameters of SVM.Inspired by [6], this paper uses the real number double-chain coding target gradient quantum genetic algorithm (DCQGA) for optimizing the key parameters of LS-SVR and proposes a hybrid non-parametric model DCQGALSSVR based on DCQGA and LS-SVR.Then the proposed DCQGALSSVR model is applied to predict the thrust of a liquid rocket engine.The simulation results show that the method works well.[7] presented DCQGA Algorithm.SVM was proposed by Vapnik et al. [4].[5] introduced SVR.[6][7][8][9][10] introduced the applications of SVR or SVM in different research fields.

DCQGALSSVR Model
The performance of LS-SVR is related to the type of kernel function, the relevant kernel parameters, and the penalty coefficient C. The type of kernel function has little effect on LS-SVR, while the kernel parameters and penalty item coefficient have a great influence on the performance of LS-SVR.In this paper, the radial basis function is applied as the kernel function of LS-SVR.
The expression of radial basis kernel function is expressed as:  where  is its width.It can be seen from [9] that the performance of LS-SVR obtained by the cross-validation method is not higher than that of LS-SVR optimized by an intelligent algorithm.Therefore, the DCQGA algorithm is used to optimize the parameters of LS-SVR so as to establish the DCQGALSSVR model.The flowchart of DCQGALSSVR is shown in Figure 1.

Application
The thrust of a rocket engine is a leading indicator.By predicting its change value and comparing the predicted value with the engine thrust threshold, it can be predicted whether the engine will fail at a certain time.The parameters of DCQGA are set by this: the population size 20, the maximum number of iterations 100, the mutation probability 0.05, and the stepsize of rotation angle 0.001*pi.Because the performance of LS-SVR is very sensitive to its key parameters of 2   and C, the ranges of 2  and C are determined to be [0.01,1000] and [0.01, 10000] respectively [9][10].
In the DCQGALSSVR model, the experimental method is as follows: Firstly, the training samples are applied to train LS-SVR to obtain the trained LS-SVR.Then, the test samples are inputted into the trained LS-SVR to obtain the forecast values of these test samples.The negative value of the root mean square error between the predicted values of test samples and their true values, -RMSE is used as the fitness function of DCQGA.Obviously, in order to make LS-SVR have good generalization ability, the larger -RMSE is preferred.Using the above experimental method can obtain the best 2  and best C; then, the best 2   and best C are substituted into the LS-SVR, and the training samples are trained to obtain the fitting values of the training samples.At the same time, the time consumed by the training process is recorded, and then the tested samples are input into the LS-SVR trained by the training samples under the condition of best 2   and best C to obtain the predicted values of the test samples.
Through the above experiments, the fitting curve of training samples of the liquid rocket engine thrust, the prediction curve of test samples, the change curve of the fitness function and the prediction values are obtained respectively.The results of these simulations are as follows.It can be seen from Figure 2 that the DCQGALSSVR model can fit the training samples well.At the same time, it can be seen from Figure 3 that DCQGALSSVR can also predict the test samples well, indicating that the DCQGALSSVR model has good generalization performance.From Figure 4, it can be seen that after 36 iterations of the DCQGALSSVR model, the fitness function tends to a stable value of -0.004246.
From Table 2, the prediction results of test samples show that the average relative error of testing samples is 0.3186%; if the intelligent algorithm is not applied to optimize the key parameters of LS-SVR, the average relative error of the testing samples is 0.37%.
It can be seen from the above that the model proposed in this paper is effective.

Conclusion
Because the performance of LS-SVR is extremely sensitive to its kernel parameters and the penalty coefficient, this paper combines DCQGA algorithm with LS-SVR to optimize the key parameters of LS-SVR, thus proposing a new hybrid non-parametric regression prediction model DCQGALSSVR.This proposed model is applied to monitor the thrust of a rocket engine.The simulation shows that the model is effective in the field of health status monitor of the liquid rocket engine.

Figure 2 Figure 3 Figure 4
Figure 2 The fitted curve of the training samples using DCQGA

Table 1 .
In this paper, the DCQGALSSVR model proposed above is used to build the thrust model of a liquid rocket engine.The training and test samples of the model are from the firing test data (Table1) and normalized.In this experiment, the first 13 rows of data are used as training samples for modeling.The last 12 rows of data are test samples to test the effect of prediction.Each independent variable of the function F=f( o m  , f m  ,p c ,t) is applied as the model input, and F is used as the model output.The table of firing test data The thrust F of the engine is closely associated with the parameters such as the oxidant flow rate o m  , the combustion agent flow rate f m  , the combustion chamber pressure p c , and the time interval t.This relationship can be summarized as F=f( o m  , f m  ,p c ,t), so F can be predicted by these parameters.

Table 2 .
The prediction results of testing samples