支持向量机算法及其在雷达干扰效果评估中的应用研究
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摘要
随着电子技术的发展,雷达对抗在战争中发挥着越来越重要的作用。雷达干扰是雷达对抗的主要组成部分,干扰效果是反映干扰装备作战能力的一项重要的综合性指标,它表现为干扰前后雷达工作性能的下降程度,是雷达方、干扰方以及对抗环境等方面的众多因素共同作用的结果。干扰效果评估要解决的是根据影响因素估计干扰效果的问题,科学合理地评估干扰效果对雷达干扰/抗干扰技术的研究、雷达及干扰装备的研制都具有重要的意义。
雷达干扰效果评估方法主要有早期的评估因子法,后来的模糊综合评估法,以及近几年出现的基于人工神经网络(ANN)等机器学习理论的智能评估法。智能评估法是利用机器学习理论对干扰实验所得到的实验样本进行学习,得到干扰效果与影响因素之间对应关系,并由此实现对特定影响因素下干扰效果的评估。因为具有以实验数据为基础、受人为影响小等特点,智能评估法已被认为是一种非常有前景的干扰效果评估方法。从智能评估角度,干扰效果评估问题可以看作是一个有限样本的学习问题,神经网络在有限样本情况下容易出现因过学习而导致的推广能力下降,而在统计学习理论基础上发展起来的支持向量机(SVM)是专门针对有限样本问题的机器学习方法,所以利用SVM解决干扰效果评估问题会更有优势。由于干扰技术的多样性,本文仅针对舰载有源干扰设备对反舰导弹末制导雷达进行的自卫式干扰进行研究。针对雷达干扰效果评估及战时预测问题研究合适的支持向量机算法,并解决其在该领域的相关应用问题是本文的主要研究内容,具体如下:
1.在支持向量机算法方面,对计算复杂度低的最小二乘支持向量机(LS-SVM)进行了研究。针对干扰效果评估中的离线学习以及干扰效果战时预测中需要对预测误差较大的样本进行在线学习的需求,并且为了克服标准LS-SVM解的非稀疏性的缺点,研究了两种在线式的LS-SVM:基于更新逆核矩阵的在线式LS-SVM和基于序列最小优化(SMO)的在线式LS-SVM,并分别研究了它们的分类算法和回归算法。它们均采用“预测→增量学习→逆学习”的思想迭代完成学习过程,能够根据具体问题自适应地得到稀疏的解,不但能够快速地完成离线学习,而且能够用于在线学习问题。
2.对SVM相关的参数选择及特征选择问题进行了研究。在SVM参数选择方面,针对SVM的性能一般是参数的多峰函数的特点,研究了利用全局优化能力强的微分进化算法(DE)解决SVM的参数选择问题。另外,针对机器学习领域有些问题的输入维数很高,需要进行特征选择的问题,研究了利用DE算法同步选择SVM的参数和特征的方法。仿真实验表明,与基于微粒群算法(PSO)的类似方法相比,基于DE的参数选择方法和同步选择方法不但具有更快的寻优速度,而且具有更强的参数选择和特征选择能力。
3.为了得到智能评估方法用以学习的实验样本,针对实验中的干扰效果度量问题进行了研究。通过分析末制导雷达的工作过程及其面临的有源干扰的特点,结合“时间准则”和“效率准则”,提出了以搜索时间比和跟踪误差比为指标的、综合定量的干扰效果度量方法。利用海军某电子对抗仿真中心的半实物仿真系统进行了干扰实验,实验结果表明度量的干扰效果符合理论及工程实践规律,度量方法有效。
4.根据干扰效果评估定量化的要求,将其看作一个回归问题,在分析末制导雷达有源干扰效果的主要影响因素基础上,研究了基于LS-SVM回归的干扰效果评估方法。半实物仿真实验表明,该方法能够根据影响因素较为准确地评估出的干扰效果,比基于ANN的评估方法具有更高的评估精度;此外,对干扰效果的战时预测问题进行了尝试性研究,根据战时影响因素不完全可知、预测精度不需要太高的特点,将干扰效果的战时预测看作一个分类问题,研究了基于LS-SVM分类的干扰效果战时预测方法。
With the development of electronic technology, radar confrontation is playing an important role in modern warfare. Radar jamming is the main component of radar confrontation, and jamming effect is an important index of jamming equipment, which is showed as the decline degree of radar’s performance before and after jamming. Jamming effect is influenced by many factors of radar, jamming and confrontation environment, and jamming effect evaluation is estimating the possible jamming effect according to influence factors. Scientific and rational evaluation of jamming effect takes great significance on the research of radar jamming/anti-jamming technology, and the development of radar and jamming equipment.
The main evaluation methods of radar jamming effect include early evaluation factor methods, subsequent fuzzy synthetic evaluation methods and intelligent evaluation methods based on machine learning theory, such as artificial neural network (ANN). In intelligent evaluation methods, machine learning theories are used to get the relationship between jamming effect and influence factors by learning on samples get in radar jamming experiment. Because the intelligent evaluation is based on experiment samples and slightly influenced by artificial factors, it has been considered to be a very promising approach to solve radar jamming effect evaluation. From the perspective of intelligent evaluation, the evaluation of radar jamming effect can be considered as learning problem with limited samples, in this case the generalization ability of ANN would decline because of overfitting, while support vector machine (SVM) based on statistical learning theory is developed to solve the learning problem with limited samples, so it will be more superior that SVM is used to solve jamming effect evaluation problem. Because of the diversity of radar jamming, in this dissertation researches are focused on self-screening jamming of shipbased active jamming equipment to terminal guidance radar of anti-ship missile. Researches on proper SVM algorithms for the evaluation and prediction at wartime of radar jamming effect, and solving the relevant application problems of SVM are the main contents of this dissertation, detailed as follows:
1. In support vector machine algorithm, the least squares support vector machine (LS-SVM) with low computational complexity was studied. To satisfy the offline learning requirement of jamming effect evaluation and online learning requirement to the samples with larger predicting error in jamming effect prediction at wartime, and avoid the shortcoming of standard LS-SVM that solution is nonsparse, two kinds of online LS-SVM were studied: the online LS-SVM based on refreshing inverse kernel matrix and the online LS-SVM based on sequence minimal optimization (SMO), the classification and regression algorithms of them were proposed. Both of them iteratively accomplish learning process by use of "predicting→incremental learning→decremental learning" idea. They can adaptively get sparse solution according to specific learning problem, not only can learn rapidly at offline problem, but also can be used in online learning problem.
2. The relevant parameters selection and features selection of SVM were studied in succession. In parameters selection of SVM, according to the character that SVM’s performance is multi-peak function of parameters, the differential evolution (DE) algorithm with strong global optimization ability was used to solve the parameters selection of SVM. Moreover, in machine learning area there are matters with high dimension inputs (features) and the features need to be selected. According to this case, parameters and features simultaneous selection based on DE algorithm was studied. Compared with the similar methods based on PSO, the DE-based parameters selection method and the DE-based simultaneous selection method not only is more rapid at optimization speed, but also have more powerful parameters and features selection ability.
3. To get the training samples for intelligent evaluation, the measurement method of jamming effect in experiment was studied. On the base of analysis of terminal guidance radar’s working process and the countering active jamming, and the combination of "time norms" and "efficiency norms", a comprehensive quantitative measurement method was proposed which use searching-time ratio and tracking-error ratio as measurement indexes. Jamming experiments were implemented by use of semi-physical simulation system at one of naval electronic warfare simulation center, results show that the measured jamming effect accords with theory and practice engineering rule, and the measurement method of radar jamming effect is effective.
4. According to the quantitative requirement of radar jamming effect evaluation, it was regarded as a regression problem, and the jamming effect evaluation method based on LS-SVM regression was studied on the base of analyzing main influence factors of terminal guidance radar’s active jamming effect. Semi-physical simulation experiments show that the proposed evaluation method can accurately evaluate jamming effect according to specific influence factors. Compared with the evaluation method based on ANN, the LS-SVM regression-based method has higher evaluation accuracy. In addition, the jamming effect prediction at wartime was tentatively studied. According to the fact that influence factors are not all knowable and predicting results aren’t need very accuracy, jamming effect prediction at wartime was regarded as a classification problem, and the jamming effect prediction method at wartime based on LS-SVM classification was studied.
雷达干扰效果评估方法主要有早期的评估因子法,后来的模糊综合评估法,以及近几年出现的基于人工神经网络(ANN)等机器学习理论的智能评估法。智能评估法是利用机器学习理论对干扰实验所得到的实验样本进行学习,得到干扰效果与影响因素之间对应关系,并由此实现对特定影响因素下干扰效果的评估。因为具有以实验数据为基础、受人为影响小等特点,智能评估法已被认为是一种非常有前景的干扰效果评估方法。从智能评估角度,干扰效果评估问题可以看作是一个有限样本的学习问题,神经网络在有限样本情况下容易出现因过学习而导致的推广能力下降,而在统计学习理论基础上发展起来的支持向量机(SVM)是专门针对有限样本问题的机器学习方法,所以利用SVM解决干扰效果评估问题会更有优势。由于干扰技术的多样性,本文仅针对舰载有源干扰设备对反舰导弹末制导雷达进行的自卫式干扰进行研究。针对雷达干扰效果评估及战时预测问题研究合适的支持向量机算法,并解决其在该领域的相关应用问题是本文的主要研究内容,具体如下:
1.在支持向量机算法方面,对计算复杂度低的最小二乘支持向量机(LS-SVM)进行了研究。针对干扰效果评估中的离线学习以及干扰效果战时预测中需要对预测误差较大的样本进行在线学习的需求,并且为了克服标准LS-SVM解的非稀疏性的缺点,研究了两种在线式的LS-SVM:基于更新逆核矩阵的在线式LS-SVM和基于序列最小优化(SMO)的在线式LS-SVM,并分别研究了它们的分类算法和回归算法。它们均采用“预测→增量学习→逆学习”的思想迭代完成学习过程,能够根据具体问题自适应地得到稀疏的解,不但能够快速地完成离线学习,而且能够用于在线学习问题。
2.对SVM相关的参数选择及特征选择问题进行了研究。在SVM参数选择方面,针对SVM的性能一般是参数的多峰函数的特点,研究了利用全局优化能力强的微分进化算法(DE)解决SVM的参数选择问题。另外,针对机器学习领域有些问题的输入维数很高,需要进行特征选择的问题,研究了利用DE算法同步选择SVM的参数和特征的方法。仿真实验表明,与基于微粒群算法(PSO)的类似方法相比,基于DE的参数选择方法和同步选择方法不但具有更快的寻优速度,而且具有更强的参数选择和特征选择能力。
3.为了得到智能评估方法用以学习的实验样本,针对实验中的干扰效果度量问题进行了研究。通过分析末制导雷达的工作过程及其面临的有源干扰的特点,结合“时间准则”和“效率准则”,提出了以搜索时间比和跟踪误差比为指标的、综合定量的干扰效果度量方法。利用海军某电子对抗仿真中心的半实物仿真系统进行了干扰实验,实验结果表明度量的干扰效果符合理论及工程实践规律,度量方法有效。
4.根据干扰效果评估定量化的要求,将其看作一个回归问题,在分析末制导雷达有源干扰效果的主要影响因素基础上,研究了基于LS-SVM回归的干扰效果评估方法。半实物仿真实验表明,该方法能够根据影响因素较为准确地评估出的干扰效果,比基于ANN的评估方法具有更高的评估精度;此外,对干扰效果的战时预测问题进行了尝试性研究,根据战时影响因素不完全可知、预测精度不需要太高的特点,将干扰效果的战时预测看作一个分类问题,研究了基于LS-SVM分类的干扰效果战时预测方法。
With the development of electronic technology, radar confrontation is playing an important role in modern warfare. Radar jamming is the main component of radar confrontation, and jamming effect is an important index of jamming equipment, which is showed as the decline degree of radar’s performance before and after jamming. Jamming effect is influenced by many factors of radar, jamming and confrontation environment, and jamming effect evaluation is estimating the possible jamming effect according to influence factors. Scientific and rational evaluation of jamming effect takes great significance on the research of radar jamming/anti-jamming technology, and the development of radar and jamming equipment.
The main evaluation methods of radar jamming effect include early evaluation factor methods, subsequent fuzzy synthetic evaluation methods and intelligent evaluation methods based on machine learning theory, such as artificial neural network (ANN). In intelligent evaluation methods, machine learning theories are used to get the relationship between jamming effect and influence factors by learning on samples get in radar jamming experiment. Because the intelligent evaluation is based on experiment samples and slightly influenced by artificial factors, it has been considered to be a very promising approach to solve radar jamming effect evaluation. From the perspective of intelligent evaluation, the evaluation of radar jamming effect can be considered as learning problem with limited samples, in this case the generalization ability of ANN would decline because of overfitting, while support vector machine (SVM) based on statistical learning theory is developed to solve the learning problem with limited samples, so it will be more superior that SVM is used to solve jamming effect evaluation problem. Because of the diversity of radar jamming, in this dissertation researches are focused on self-screening jamming of shipbased active jamming equipment to terminal guidance radar of anti-ship missile. Researches on proper SVM algorithms for the evaluation and prediction at wartime of radar jamming effect, and solving the relevant application problems of SVM are the main contents of this dissertation, detailed as follows:
1. In support vector machine algorithm, the least squares support vector machine (LS-SVM) with low computational complexity was studied. To satisfy the offline learning requirement of jamming effect evaluation and online learning requirement to the samples with larger predicting error in jamming effect prediction at wartime, and avoid the shortcoming of standard LS-SVM that solution is nonsparse, two kinds of online LS-SVM were studied: the online LS-SVM based on refreshing inverse kernel matrix and the online LS-SVM based on sequence minimal optimization (SMO), the classification and regression algorithms of them were proposed. Both of them iteratively accomplish learning process by use of "predicting→incremental learning→decremental learning" idea. They can adaptively get sparse solution according to specific learning problem, not only can learn rapidly at offline problem, but also can be used in online learning problem.
2. The relevant parameters selection and features selection of SVM were studied in succession. In parameters selection of SVM, according to the character that SVM’s performance is multi-peak function of parameters, the differential evolution (DE) algorithm with strong global optimization ability was used to solve the parameters selection of SVM. Moreover, in machine learning area there are matters with high dimension inputs (features) and the features need to be selected. According to this case, parameters and features simultaneous selection based on DE algorithm was studied. Compared with the similar methods based on PSO, the DE-based parameters selection method and the DE-based simultaneous selection method not only is more rapid at optimization speed, but also have more powerful parameters and features selection ability.
3. To get the training samples for intelligent evaluation, the measurement method of jamming effect in experiment was studied. On the base of analysis of terminal guidance radar’s working process and the countering active jamming, and the combination of "time norms" and "efficiency norms", a comprehensive quantitative measurement method was proposed which use searching-time ratio and tracking-error ratio as measurement indexes. Jamming experiments were implemented by use of semi-physical simulation system at one of naval electronic warfare simulation center, results show that the measured jamming effect accords with theory and practice engineering rule, and the measurement method of radar jamming effect is effective.
4. According to the quantitative requirement of radar jamming effect evaluation, it was regarded as a regression problem, and the jamming effect evaluation method based on LS-SVM regression was studied on the base of analyzing main influence factors of terminal guidance radar’s active jamming effect. Semi-physical simulation experiments show that the proposed evaluation method can accurately evaluate jamming effect according to specific influence factors. Compared with the evaluation method based on ANN, the LS-SVM regression-based method has higher evaluation accuracy. In addition, the jamming effect prediction at wartime was tentatively studied. According to the fact that influence factors are not all knowable and predicting results aren’t need very accuracy, jamming effect prediction at wartime was regarded as a classification problem, and the jamming effect prediction method at wartime based on LS-SVM classification was studied.
引文
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