支持向量回归机及其在智能航空发动机参数估计中的应用
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摘要
智能发动机控制作为航空发动机最值得发展的先进控制概念,它包括的内容非常丰富。因而,本文重点研究了智能发动机控制中的推力估计器设计和解析余度技术。推力估计器在智能发动机控制中的直接推力控制和性能退化缓解控制中都有重要应用;智能发动机控制中的高可靠性控制就是针对传感器故障而提出的,而要保证传感器工作的可靠性,发展先进的解析余度技术是一种有效的途径。在设计推力估计器和发展解析余度技术的过程当中,作者利用了机器学习中具有统计学基础和优良泛化能力的支持向量回归技术,并针对原有算法的一些缺点和不足之处提出了许多有价值的算法和观点,更重要的是,作者将自己提出的算法应用到了推力估计器设计和解析余度技术当中并取得了满意的效果。本文的主要研究内容如下:
首先针对经典支持向量回归机不能抑制系统中存在的奇异点问题提出了截尾ε-不敏感损失函数,并进而提出了截尾支持向量回归机。截尾支持向量回归机不仅能抑制系统中存在的奇异点而提高回归机的泛化能力,还减少了支持向量的数目,提高了实时性。由于截尾支持向量回归机涉及到非凸优化问题,因而作者利用CCCP技巧,将非凸优化问题转化为一系列凸优化问题,才使这个非凸优化问题得以解决。作者在实现截尾支持向量回归机的过程当中从两个角度出发:一是对偶空间;二是原空间。虽然角度不同,但达到的效果基本相同。
在分析了硬支持向量回归机产生过拟合现象的原因后,作者提出了利用Greedy Stagewise策略来近似训练硬支持向量回归机,即GS-HSVR算法。这主要是由于Greedy Stagewise策略产生的“早停”现象阻止了硬支持向量回归机过拟合现象的发生,这其实相当于一种正则化策略。和经典的软支持向量回归机比较起来,笔者提出的近似训练算法在泛化能力上和软支持向量回归机相当,但在训练时间和支持向量数目上都有一定的优势。
和经典支持向量回归机比较起来,最小二乘支持向量回归机虽然能减轻训练代价,但其解缺乏稀疏性。为了实现其解的稀疏性,作者在介绍FSA-LSSVR算法的基础上,首先提出了LS2SVR算法。这种算法和FSA-LSSVR算法以及一些现存的算法比较起来,无论在训练时间和支持向量数目上都占有一定的优势。和FSA-LSSVR算法比较起来,LS2SVR考虑到了整个训练样本集产生的约束对目标函数的影响,因而在较少支持向量数目的情况下,能取得和FSA-LSSVR一样的泛化能力,并进行了证明。为了进一步实现LSSVR的稀疏性,作者将约简技术和迭代策略结合起来提出了RR-LSSVR算法。与FSA-LSSVR、RLSSVR和LS2SVR相比较,RR-LSSVR算法有更优秀的稀疏性,但这种算法的训练代价也是最大的。
为了改善局部变化差异比较大的系统的学习效果,同时也为了利用先验知识和多核学习的优势,作者将半参数技术和多核学习结合起来,提出了两种多核半参数支持向量回归机:一种是多核半参数线性规划支持向量回归机(MSLP-SVR),另一种是稀疏多核半参数最小二乘支持向量回归机(稀疏MSLSSVR)。这两种多核半参数回归机有一个特性,那就是经典的单核回归机是其特例,这也就意味着多核半参数回归机的学习效果不会比经典的单核回归机差。另外,和其他多核学习算法比较起来,作者提出的多核学习算法在泛化能力或者训练时间上占有优势。
作者研究和提出这些算法的目的就是为了应用它们。这主要包括两个方面:一是利用RR-LSSVR算法进行推力估计器设计;二是基于GS-HSVR算法提出了一种在线进行传感器故障诊断的解析余度技术。
实现直接推力控制和性能退化缓解控制的一个重要环节就是进行推力估计器设计。首先作者基于用于模型选择的留一法来进行推力估计器输入量的选择。在确定完推力估计器的输入量后,用RR-LSSVR算法进行了全包线推力估计器的设计。为了在全包线内设计高精度和高实时性的推力估计器,作者将包线按高度进行分块。紧接着,提出了更合理的对全包线进行分块的方法,那就是将全包线内的点进行聚类。一般来说,每一类中的数据点都是相似的,推力不会相差太大,这就避免了在推力绝对误差基本相同的情况,由于推力相差太多而导致相对误差较大现象的发生。针对航空发动机在服役过程中发生的性能退化现象,在训练过程中加入退化样本后使这个问题得以解决。为了实时地估计出航空发动机运行时的推力值,作者修改了RR-LSSVR算法,在输入端引入反馈的推力值来模拟航空发动机的动态过程而设计了动态过程推力估计器。
在智能发动机控制概念中有一种高可靠性控制。所谓高可靠性控制,就是要保证提供给控制器的信号是正确可靠的。针对这个问题,作者将离线GS-HSVR算法进行了适当的改进。改进后的算法即FOAHSVR算法不仅能获得和GS-HSVR相当的泛化能力,更重要的是FOAHSVR是一种在线学习算法。利用FOAHSVR的在线学习性,提出了一种在线进行航空发动机传感器故障诊断的方案,并能对航空发动机的单传感器或者多传感器的偏置故障进行很好的检测、隔离和自适应重构而形成了解析余度技术。为了应对传感器的漂移故障,作者还提出了一种修正策略,实验表明,此修正策略能对航空发动机传感器发生的漂移故障进行有效的检测和自适应重构。
As an advanced control concept worthiest of developing in aeroengines, intelligent engine control possesses plentiful contents. Hence, in this dissertation, thrust estimator design and analytical redun-dacy technique for intelligent engine control attract more attentions. The thrust estimator plays a paramount role in direct thrust control and performance deterioration mitigation control, while ad-vanced analytical redundancy technique is always referred as a powerful and effective tool to cope with sensor fault in high reliability control emphasized in intelligent engine control. During the proc-ess of designing thrust estimator and developing analytical redundancy, based on support vector re-gression (SVR) owning statistical learning foundation and excellent generlization performance, to circumvent the shortcomings existing in the original algorithms, many valuable algorithms and view-points are proposed. To be more important, the proposed algorithms are applied to thrust estimator design and analytical redundancy technique, and the satisfactory results are obtained.
The classical SVR does not oppress outliers in the system. To this end, the truncated support vector regression (TSVR) with truncatedε-insensitive loss function is proposed, which not only oppreses outliers in the system and enhances generalization performance but also reduces the number of sup-port vectors and improves the real time. To solve the non-convex optimization problem in TSVR, the concave-convex procedure (CCCP) is utilized to transform the non-convex optimization to a series of convex ones so that this problem is settled successfully. In the process of realizing TSVR, there are two different perspectives, one of which is the dual; another is the primal. Although perspectives are different, the similar results can be achieved.
After analyzing the overfitting phenomenon in hard support vector regression (HSVR), the greedy stagewise strategy is employed to approximately train HSVR, viz. GS-HSVR. In effect, the presented GS-HSVR uses the early stopping rule, which is equivalent to an implicit regularization technique, to block the overfitting phenomenon. Compared with the classical SVR, GS-HSVR takes advantages to a certain extent in the training time and the number of support vectors.
In comparison with classical SVR, the solution of least squares support vector regression (LSSVR) is lack of sparseness. To sidestep this problem, on the basis of fast sparse approximation for LSSVR (FSA-LSSVR), a novel algorithm, viz. LS2SVR, is proposed. By contrast with FSA-LSSVR and other pruning algorithms, LS2SVR takes advantages of the training time and the number of support vectors. Due to consideration of generating constraints for the target function from the ensemble training set, LS2SVR can gain the comparable generalization performance with FSA-LSSVR using less number of support vectors, which is proved. Furthermore, after combining reduced technique with iterative strat-egy, recursive reduced LSSVR (RR-LSSVR) is proposed. Compared with FSA-LSSVR, RLSSVR (random LSSVR), and LS2SVR, with the exception of the training cost, RR-LSSVR holds better sparseness.
To improve many unkown systems owning different data trends in different regrions, i.e., some parts are steep variations while other parts are smooth variations, after combining semiparametric technique with multikernel learning, two multikernel semiparametric predictors, i.e., multikernel semiparametric linear programming support vector regression (MSLP-SVR) and sparse multikernel semiparametric least squares support vector regression (sparse MSLSSVR), are proposed. The com-mon characteristic of the two predictors above is that the classical predictors are their special cases, which signifies the learning effectiveness of the two proposed predictors not worse than the classical ones. In addition, compared with other multikernel learning algorithms, the two proposed multikernel learning algorithms take advantages in generalization performance or training time.
The main purpose of researches on these algorithms above is to exploit them, which includes two aspects. One is that RR-LSSVR is utilized to design thrust estimator for intelligent aeroengine. An-other is that based on GS-HSVR, an online analytical redundancy technique for sensor fault in intel-ligent aeroengine is proposed.
The design of thrust estimator is significant for direct thrust control and performance deterioration mitigation control in telligent engine control. Hence, firstly, the input parameters of thrust estimator are determined by leave-one-out strategy which is commonly-used to select model. In order to design thrust estimator with high accuracy and real time, according to the fight altitude, the full flight enve-lope is divided. Subsequently, a more reasonable method is presented to divide the flight envelope, i.e., the whole samples in the full flight envelope are grouped using the clustering method. In general, during each group, the thrust does not fluctuate steeply, which guarantees to avoid the phenomenon that the relative errors are obviously different with the almost same thrust errors due to the sharply fluctuant thrust. To mitigate the deterioration phenomenon, after adding deterioration samples to the training set, this problem is solved. Finally, to simulate the dynamic process in intelligent aeroengines, the modified RR-LSSVR, which uses the feedback thrust as the input parameter, is exploited to design dynamic thrust estimator.
As a concept in intelligent engine control, high reliability control is to supply correct signals for aeroengine controller. To this problem, the improved GS-HSVR, viz. fast online approximation for hard support vector (FOAHSVR), can get the similar generalization performance to GS-HSVR. More importantly, FOAHSVR is an online learning algorithm. Hence, an online analytical redundancy scheme for sensor fault in telligent aeroengines is proposed, which can be used to detect, isolate and accommodate sensor failure fault. To deal with sensor drift fault, a correction strategy is proposed, and the experimental results demonstrate that the presented correction strategy is capable of detecting, isolating and accommodating the sensor drift fault effectively.
首先针对经典支持向量回归机不能抑制系统中存在的奇异点问题提出了截尾ε-不敏感损失函数,并进而提出了截尾支持向量回归机。截尾支持向量回归机不仅能抑制系统中存在的奇异点而提高回归机的泛化能力,还减少了支持向量的数目,提高了实时性。由于截尾支持向量回归机涉及到非凸优化问题,因而作者利用CCCP技巧,将非凸优化问题转化为一系列凸优化问题,才使这个非凸优化问题得以解决。作者在实现截尾支持向量回归机的过程当中从两个角度出发:一是对偶空间;二是原空间。虽然角度不同,但达到的效果基本相同。
在分析了硬支持向量回归机产生过拟合现象的原因后,作者提出了利用Greedy Stagewise策略来近似训练硬支持向量回归机,即GS-HSVR算法。这主要是由于Greedy Stagewise策略产生的“早停”现象阻止了硬支持向量回归机过拟合现象的发生,这其实相当于一种正则化策略。和经典的软支持向量回归机比较起来,笔者提出的近似训练算法在泛化能力上和软支持向量回归机相当,但在训练时间和支持向量数目上都有一定的优势。
和经典支持向量回归机比较起来,最小二乘支持向量回归机虽然能减轻训练代价,但其解缺乏稀疏性。为了实现其解的稀疏性,作者在介绍FSA-LSSVR算法的基础上,首先提出了LS2SVR算法。这种算法和FSA-LSSVR算法以及一些现存的算法比较起来,无论在训练时间和支持向量数目上都占有一定的优势。和FSA-LSSVR算法比较起来,LS2SVR考虑到了整个训练样本集产生的约束对目标函数的影响,因而在较少支持向量数目的情况下,能取得和FSA-LSSVR一样的泛化能力,并进行了证明。为了进一步实现LSSVR的稀疏性,作者将约简技术和迭代策略结合起来提出了RR-LSSVR算法。与FSA-LSSVR、RLSSVR和LS2SVR相比较,RR-LSSVR算法有更优秀的稀疏性,但这种算法的训练代价也是最大的。
为了改善局部变化差异比较大的系统的学习效果,同时也为了利用先验知识和多核学习的优势,作者将半参数技术和多核学习结合起来,提出了两种多核半参数支持向量回归机:一种是多核半参数线性规划支持向量回归机(MSLP-SVR),另一种是稀疏多核半参数最小二乘支持向量回归机(稀疏MSLSSVR)。这两种多核半参数回归机有一个特性,那就是经典的单核回归机是其特例,这也就意味着多核半参数回归机的学习效果不会比经典的单核回归机差。另外,和其他多核学习算法比较起来,作者提出的多核学习算法在泛化能力或者训练时间上占有优势。
作者研究和提出这些算法的目的就是为了应用它们。这主要包括两个方面:一是利用RR-LSSVR算法进行推力估计器设计;二是基于GS-HSVR算法提出了一种在线进行传感器故障诊断的解析余度技术。
实现直接推力控制和性能退化缓解控制的一个重要环节就是进行推力估计器设计。首先作者基于用于模型选择的留一法来进行推力估计器输入量的选择。在确定完推力估计器的输入量后,用RR-LSSVR算法进行了全包线推力估计器的设计。为了在全包线内设计高精度和高实时性的推力估计器,作者将包线按高度进行分块。紧接着,提出了更合理的对全包线进行分块的方法,那就是将全包线内的点进行聚类。一般来说,每一类中的数据点都是相似的,推力不会相差太大,这就避免了在推力绝对误差基本相同的情况,由于推力相差太多而导致相对误差较大现象的发生。针对航空发动机在服役过程中发生的性能退化现象,在训练过程中加入退化样本后使这个问题得以解决。为了实时地估计出航空发动机运行时的推力值,作者修改了RR-LSSVR算法,在输入端引入反馈的推力值来模拟航空发动机的动态过程而设计了动态过程推力估计器。
在智能发动机控制概念中有一种高可靠性控制。所谓高可靠性控制,就是要保证提供给控制器的信号是正确可靠的。针对这个问题,作者将离线GS-HSVR算法进行了适当的改进。改进后的算法即FOAHSVR算法不仅能获得和GS-HSVR相当的泛化能力,更重要的是FOAHSVR是一种在线学习算法。利用FOAHSVR的在线学习性,提出了一种在线进行航空发动机传感器故障诊断的方案,并能对航空发动机的单传感器或者多传感器的偏置故障进行很好的检测、隔离和自适应重构而形成了解析余度技术。为了应对传感器的漂移故障,作者还提出了一种修正策略,实验表明,此修正策略能对航空发动机传感器发生的漂移故障进行有效的检测和自适应重构。
As an advanced control concept worthiest of developing in aeroengines, intelligent engine control possesses plentiful contents. Hence, in this dissertation, thrust estimator design and analytical redun-dacy technique for intelligent engine control attract more attentions. The thrust estimator plays a paramount role in direct thrust control and performance deterioration mitigation control, while ad-vanced analytical redundancy technique is always referred as a powerful and effective tool to cope with sensor fault in high reliability control emphasized in intelligent engine control. During the proc-ess of designing thrust estimator and developing analytical redundancy, based on support vector re-gression (SVR) owning statistical learning foundation and excellent generlization performance, to circumvent the shortcomings existing in the original algorithms, many valuable algorithms and view-points are proposed. To be more important, the proposed algorithms are applied to thrust estimator design and analytical redundancy technique, and the satisfactory results are obtained.
The classical SVR does not oppress outliers in the system. To this end, the truncated support vector regression (TSVR) with truncatedε-insensitive loss function is proposed, which not only oppreses outliers in the system and enhances generalization performance but also reduces the number of sup-port vectors and improves the real time. To solve the non-convex optimization problem in TSVR, the concave-convex procedure (CCCP) is utilized to transform the non-convex optimization to a series of convex ones so that this problem is settled successfully. In the process of realizing TSVR, there are two different perspectives, one of which is the dual; another is the primal. Although perspectives are different, the similar results can be achieved.
After analyzing the overfitting phenomenon in hard support vector regression (HSVR), the greedy stagewise strategy is employed to approximately train HSVR, viz. GS-HSVR. In effect, the presented GS-HSVR uses the early stopping rule, which is equivalent to an implicit regularization technique, to block the overfitting phenomenon. Compared with the classical SVR, GS-HSVR takes advantages to a certain extent in the training time and the number of support vectors.
In comparison with classical SVR, the solution of least squares support vector regression (LSSVR) is lack of sparseness. To sidestep this problem, on the basis of fast sparse approximation for LSSVR (FSA-LSSVR), a novel algorithm, viz. LS2SVR, is proposed. By contrast with FSA-LSSVR and other pruning algorithms, LS2SVR takes advantages of the training time and the number of support vectors. Due to consideration of generating constraints for the target function from the ensemble training set, LS2SVR can gain the comparable generalization performance with FSA-LSSVR using less number of support vectors, which is proved. Furthermore, after combining reduced technique with iterative strat-egy, recursive reduced LSSVR (RR-LSSVR) is proposed. Compared with FSA-LSSVR, RLSSVR (random LSSVR), and LS2SVR, with the exception of the training cost, RR-LSSVR holds better sparseness.
To improve many unkown systems owning different data trends in different regrions, i.e., some parts are steep variations while other parts are smooth variations, after combining semiparametric technique with multikernel learning, two multikernel semiparametric predictors, i.e., multikernel semiparametric linear programming support vector regression (MSLP-SVR) and sparse multikernel semiparametric least squares support vector regression (sparse MSLSSVR), are proposed. The com-mon characteristic of the two predictors above is that the classical predictors are their special cases, which signifies the learning effectiveness of the two proposed predictors not worse than the classical ones. In addition, compared with other multikernel learning algorithms, the two proposed multikernel learning algorithms take advantages in generalization performance or training time.
The main purpose of researches on these algorithms above is to exploit them, which includes two aspects. One is that RR-LSSVR is utilized to design thrust estimator for intelligent aeroengine. An-other is that based on GS-HSVR, an online analytical redundancy technique for sensor fault in intel-ligent aeroengine is proposed.
The design of thrust estimator is significant for direct thrust control and performance deterioration mitigation control in telligent engine control. Hence, firstly, the input parameters of thrust estimator are determined by leave-one-out strategy which is commonly-used to select model. In order to design thrust estimator with high accuracy and real time, according to the fight altitude, the full flight enve-lope is divided. Subsequently, a more reasonable method is presented to divide the flight envelope, i.e., the whole samples in the full flight envelope are grouped using the clustering method. In general, during each group, the thrust does not fluctuate steeply, which guarantees to avoid the phenomenon that the relative errors are obviously different with the almost same thrust errors due to the sharply fluctuant thrust. To mitigate the deterioration phenomenon, after adding deterioration samples to the training set, this problem is solved. Finally, to simulate the dynamic process in intelligent aeroengines, the modified RR-LSSVR, which uses the feedback thrust as the input parameter, is exploited to design dynamic thrust estimator.
As a concept in intelligent engine control, high reliability control is to supply correct signals for aeroengine controller. To this problem, the improved GS-HSVR, viz. fast online approximation for hard support vector (FOAHSVR), can get the similar generalization performance to GS-HSVR. More importantly, FOAHSVR is an online learning algorithm. Hence, an online analytical redundancy scheme for sensor fault in telligent aeroengines is proposed, which can be used to detect, isolate and accommodate sensor failure fault. To deal with sensor drift fault, a correction strategy is proposed, and the experimental results demonstrate that the presented correction strategy is capable of detecting, isolating and accommodating the sensor drift fault effectively.
引文
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