基于EMD的机械振动分析与诊断方法研究
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摘要
本论文结合“机械振动本底源信号半盲分离与重建方法的研究”(国家自然科学基金项目(50675194))和“超临界、超超临界大型汽轮发电机组状态监测与故障诊断技术及其系统研究”(国家高技术研究发展计划项目(863计划,2008AA04Z410)),针对复杂机械系统振动信号的非平稳特征,本文将经验模式分解(Empirical Mode Decomposition,EMD)方法引入到机械系统振动分析及故障诊断中,对其在机械振动信号中存在的物理应用基础、端点效应及虚假模式等问题展开研究,给出了机械有效振动模式分析的解决方案及对应典型故障特征的提取方法,在此基础上建立了EMD—2D-HMM的诊断级联模型,并结合实验进行了验证。
本文主要工作包括:
第1章概述了旋转机械振动分析与故障诊断技术的国内外研究现状,分析了现有振动信号处理技术存在的问题,论证了将经验模式分解方法引入到机械振动系统故障诊断的可行性和迫切性,通过对经验模式分解方法在不同领域的国内外研究分析,总结了该方法存在的不足和进一步的研究趋势。最后根据机械系统故障诊断所涉及的信号检测、预处理、特征提取及模式分类等环节,系统地给出了论文的选题背景、研究内容、技术路线和创新点。
第2章从机械系统振动特性的角度研究了EMD方法处理振动信号的物理意义,提出了基于EMD的机械系统振动模式分析方法。论述了振动信号EMD处理的基本原理和算法流程,建立了机械系统振动的理论模型,研究了单自由度和多自由度机械系统的振动响应特性及其EMD分析,研究发现了机械振动模式与固有模式函数(Intrinsic Mode Function,IMF)之间存在高相关性对应关系的现象,并以简支梁横向振动响应为例,结合大量仿真与实验,验证了基于EMD的机械系统振动模式分析方法的有效性,破解了EMD方法在机械系统振动信号处理中存在的物理解释难题,为后续的机械振动模式特征二次提取和故障诊断工作提供指导。
第3章综述了国际国内关于端点效应抑制方法的前沿研究,分析了EMD方法中端点效应产生的机理及其在振动信号分析中引起的数据失真等不良影响与给后续诊断工作带来的困难,针对大型旋转机械振动信号的特点,指出现有抑制端点效应的信号延拓方法存在的不足,提出了一种基于端点优化对称延拓(End Optimization Symmetric Extension,EOSE)的抑制EMD端点效应新方法,该方法通过对信号和其包络线的偏差评价函数的最小化计算,获取最佳的信号端点值,使原始信号的上、下包络线最大化地逼近原始信号两端点,达到从源头上抑制端点效应的目的,使分解得到的振动模式能够较好地反映设备的振动特性。仿真和实验研究验证了该方法的有效性。
第4章主要针对旋转机械振动信号经EMD分解产生高频噪声模式及低频虚假模式的缺陷,重点研究了白噪声在EMD分解中具有的统计特性,在此基础上提出了一种基于白噪声统计特性的机械振动模式有效性检验方法。该方法是对EMD方法的一种发展,可以自适应地消除机械振动信号经EMD分解产生的高频噪声模式及低频虚假模式,得到反映信号实际物理意义的振动模式分量集,整个处理过程不需要构造任何参数表达的基函数及相关滤波函数,也无需有关信号的任何先验知识,因而在实际应用中具有更好的适用性。采用大量实验验证了该方法能够有效识别出反映系统振动特性的振动模式,提高了特征提取的精度。
第5章从机械非平稳振动信号的降噪要求着手,分别描述了数字滤波、Kalman滤波、小波降噪及EMD降噪等四种现有常用降噪方法,给出了各降噪方法的降噪原理和适用情况,明确了这四种降噪方法对于旋转机械非平稳振动信号的降噪存在的不足,重点研究了EMD降噪给非平稳振动信号带来的模式混叠现象,利用正态分布白噪声在经验模式分解中具有的二进尺度分解特性,提出了一种非平稳振动信号的集成EMD降噪方法。通过仿真和转子启动过程试验振动信号对该降噪方法、EMD降噪方法及小波降噪方法的性能进行了比较测试。结果表明,该降噪方法具有更高的信噪比,不仅能够消除高斯噪声,而且能够有效抑制脉冲干扰,较好地降低了噪声对机械振动模式的影响。
第6章对瞬时能量与机械系统结构状态变化的物理联系展开了理论研究,在机械运行过程中,其振动信号的瞬时能量分布会随着结构异常的产生发生变化,不同的瞬时能量分布即代表了不同故障类型。利用EMD和Hilbert变换方法,给出了振动模式瞬时能量的概念,提出了一种基于EMD-HT的瞬时能量分布特征提取方法。从时-频域描述信号的角度出发,提取了机械振动信号的瞬时能量分布和Hilbert边际谱特征,转子实验系统振动信号的分析结果表明,基于瞬时能量分布和Hilbert边际谱的二维特征向量对于识别不同故障类型的有效性。
第7章论述了2D-HMM诊断方法在大型旋转机械非平稳振动信号时序模式分类方面具有的优越性,阐述了2D-HMM的基本概念和诊断原理,分析了EMD和2D-HMM在故障诊断中结合的必要性和可行性,建立了EMD—2D-HMM的诊断模型,提出了一种基于EMD—2D-HMM级联模型的故障诊断方法,该方法利用EMD方法提取的有效振动模式的瞬时能量分布及Hilbert边际谱特征进构造2D-HMM的时频域观测序列,并以此作为输入建立2D-HMM分类器,进而训练出对应各种故障类型的2D-HMM诊断模型库,通过求其最大似然概率值来判断机器的运行状态和故障类型。以转子实验台为基础构建了试验系统,试验研究结果表明,该方法相比HMM和小波包—2D-HMM诊断方法表现出更高的分类性能和诊断适用性。
第8章在基于EMD—2D-HMM的故障诊断方法研究的基础上,分析了设计和开发相应故障诊断系统的具体需求。设计了基于EMD—2D-HMM故障诊断系统总体框架,重点研究了数据采集及预处理单元和故障诊断软件包的结构组成及设计方案。研发了基于EMD—2D-HMM故障诊断软件系统;利用实验台实测数据对系统的可行性进行了测试。
第9章总结了全文的研究成果和创新之处,并对今后的工作提出了展望。
Based on the "Research on method for mechanical vibration source semi-blind source separation and reconstruction" (National Nature Science Fund Project, No: 50675194), and the "Research on the condition monitoring and fault diagnosis techniques and its application system of supercritical and ultra-supercritical steam turbines and pressure generating units" (High Technology Research and Development Program of China, No: 2008AA04Z410), aiming at nonstable charateristics of vibration signals of mechanical system, introduced empirical mode decomposition (EMD) method into vibration analysis and fault diagnosis for mechanical system, research on phsical application basis, end effect and false modes of EMD, presented solution scheme for mechanical vibration mode effective analysis and fault feature extraction method, set up EMD—2D-HMM diagnosis model, and carried out a large number of simulation and experiment. The details were as follows:
In Chapter one: The method of the situation monitoring and fault diagnosis of the rotating machine which uses vibration signals and the techniques were discussed. The problems existed in the techniques of vibration information operation were analyzed. Feasibility and importance of introducing EMD into fault diagnosis of rotating machines were disputed. Through the study and analysis applicaition of EMD in the different fields, concluded the next research development of EMD method. Finally, according to signal detection, pretreatment, feature extraction and mode classification related to meachanical fault diagnosis, described the background to carry out this research and its details, the scheme and the innovation points of this dissertation.
In Chapter two: Researched the phsical meaning of vibration signal analysis with EMD on view of mechanical vibration characteristics, presented an analysis method of vibrating mode of mechanical system based on EMD. The fundamental principle and algorithm procedure of EMD method were discussed in detail. The vibration model of mechanical system was established, studied the vibrating characteristics and its EMD analysis of single-freedom-degree and multi-degree-of-freedom system, the relationship discussion between mechanical vibrating mode and intrinsic mode function (IMF) was introduced. Using transverse vibration response of beam supported of both ends as an example. An important phenomenon that the existence of corresponding relation between system vibrating mode and IMF which obtained by EMD for vibating signal with experimental results, which established substantial theoretical foundation for EMD method in the application of condition monitoring and fault diagnosis for rotating machines, solved phsical difficult problem of EMD for vibration mode analysis for mechanical sysytem.
In Chapter three: The origin of EMD method's end effect and its harmful influence in vibration signal analysis, the front research at home and abroad about restraining end effect methods were summarized. Aiming at vibrating characteristic of rotating machine, drawbacks of the available signal extension methods for restraining end effect were pointed out. A new method of restraining end effect based on end optimization symmetric extension (EOSE) was presented. Firstly, assumed two ends of original signal as unknown value, and extended in a point-symmetrical manner with end-point as its center. Secondly, constituted deviation error evaluation function concerning original signal, and minimized the function, so that obtained the two optimization end-points value. Extended in a point symmetrical manner with new end-point value, the obtained up and down envelops maximally approached original signal end-point, which restrained the envelops divergence in EMD algorithm. Finally, in the process of filtering intrinsic mode function (IMF) discard the extended data, which release end effect to original signal outside and maximally reduced distortion of original signal. Simulation and experiment show that the proposed method could restrain end effect effectively and precisely extract classic fault feature of vibration signal of rotating machine.
In Chapter four: Aiming at the defect of bring high-frequency nosie mode and low-frequency false mode by EMD for mechanical vibration signals, stastistic charactistics of white nosie with EMD method were researched. A method based on the characteristics of white noise is presented to test the validity of mechanical vibrating mode. This method is a developed algorithm of empirical mode decomposition (EMD), which adaptively eliminated high frequency noise components and low frequency false components by applying the characteristics of normalized white noise under EMD, so the intrinsic mode set reflecting actual physical process of vibration signal are obtained. In the whole feature process, the construction of general basis function described by some parameters and related filter function is unnecessary, and any prior information about the observed signal is no more required, which felicitates the method for a wide variety of applications. Both computer simulation and rotor set experimental results verify this approach is practicable and effective, improved the precision of feature extraction.
In Chapter five: Starting from de-noising request of nonstationary vibration signals of rotating machine, respectively described four present common filter methods including digital filter, Kalman filter, wavelet de-noise and EMD de-noise, depicted de-noising principle and suit situation of the above-mentioned de-noising methods, explicated the defects of four filter methods for de-noising of nonstationary vibration signals of rotating machine, focusing on the research of mode mixing brought by EMD de-noising method. Appling dyadic scales decomposition characteristics of normal distribution white noise with EMD, an ensembled algorithm of EMD de-noising method was presented. Simulation numerical signal and experimental signal of rotor running state are used to test and compare the performances of the method and EMD based de-noising method and wavelet de-noising method. The results show that the ensembling EMD based noise cancellation method presented in the paper has more effective de-noising performance, not only eliminates random noise, but suppresses intensity noise and extracts vibration intrinsic modes that reflect real physical meaning of signal.
In Chapter six: Physical relationship between instantaneous energy and structural state variation of system was studied therotically, instantaneous energy of mechanical vibration signal changed with variable structural state in the machine running state, different instantaneous energy distribution stand for different fault. By EMD and Hilbert Transformation (HT) methods, the concept of vibration mode instantaneous energy was brought up, a new instantaneous energy distribution characteristics extraction method based on EMD and HT. In terms of depicting signals in time-frequency domain, instantaneous energy distribution and Hilbert margin spectra feature of mechanical vibration signals were extracted. The results of rotor experimental set proved this method is effective, could identify different fault type.
In Chapter seven: The advantages of 2D-HMM method in the aspect of time sequence mode classification for nonstationary vibration signals of rotating machine was discussed, elaborated the essential concept and diagnosis principle of 2D-HMM method. The integration necessity and feasibility of EMD and 2D-HMM for fault diagnosis was analyzed. A diagnosis model based on EMD-2D-HMM was set up. Firstly, decomposed mechanical vibration signal into a number of intrinsic mode function components applying EMD, extracted instantaneous energy distribution and frequency energy spectrum of effective vibration mode, which could be used to set up time-domain and frequency-domain observation sequence; secondly, set up 2D-HMM classifying model by the extracted observation sequence, so constitute 2D-HMM fault diagnosis model database, and judged running state of machine Through calculating the maximal log-likelihood. An experiment system was set up on the basis of rotor experimental table. Experimental results show that EMD-2D-HMM method had higher classification performance and diagnosis availability.
In Chapter eight: Based on the above research of EMD-2D-HMM fault diagnosis method, the concrete demand on designing and developing corresponding fault diagnosis system were analyzed. The overall framework of fault diagnosis system based on EMD-2D-HMM was devised, and the composition and design scheme of data acquisition system and preprocessing unit and fault diagnosis software package were studied in detail. The fault diagnosis software system based on EMD-2D-HMM was designed and developed. System feasibility was tested with the measured data of experimental set.
In Chapter nine: The concolutions are presented and some advanced topics in the proposed methodology that needs further investigation in future are presented and addressed.
本文主要工作包括:
第1章概述了旋转机械振动分析与故障诊断技术的国内外研究现状,分析了现有振动信号处理技术存在的问题,论证了将经验模式分解方法引入到机械振动系统故障诊断的可行性和迫切性,通过对经验模式分解方法在不同领域的国内外研究分析,总结了该方法存在的不足和进一步的研究趋势。最后根据机械系统故障诊断所涉及的信号检测、预处理、特征提取及模式分类等环节,系统地给出了论文的选题背景、研究内容、技术路线和创新点。
第2章从机械系统振动特性的角度研究了EMD方法处理振动信号的物理意义,提出了基于EMD的机械系统振动模式分析方法。论述了振动信号EMD处理的基本原理和算法流程,建立了机械系统振动的理论模型,研究了单自由度和多自由度机械系统的振动响应特性及其EMD分析,研究发现了机械振动模式与固有模式函数(Intrinsic Mode Function,IMF)之间存在高相关性对应关系的现象,并以简支梁横向振动响应为例,结合大量仿真与实验,验证了基于EMD的机械系统振动模式分析方法的有效性,破解了EMD方法在机械系统振动信号处理中存在的物理解释难题,为后续的机械振动模式特征二次提取和故障诊断工作提供指导。
第3章综述了国际国内关于端点效应抑制方法的前沿研究,分析了EMD方法中端点效应产生的机理及其在振动信号分析中引起的数据失真等不良影响与给后续诊断工作带来的困难,针对大型旋转机械振动信号的特点,指出现有抑制端点效应的信号延拓方法存在的不足,提出了一种基于端点优化对称延拓(End Optimization Symmetric Extension,EOSE)的抑制EMD端点效应新方法,该方法通过对信号和其包络线的偏差评价函数的最小化计算,获取最佳的信号端点值,使原始信号的上、下包络线最大化地逼近原始信号两端点,达到从源头上抑制端点效应的目的,使分解得到的振动模式能够较好地反映设备的振动特性。仿真和实验研究验证了该方法的有效性。
第4章主要针对旋转机械振动信号经EMD分解产生高频噪声模式及低频虚假模式的缺陷,重点研究了白噪声在EMD分解中具有的统计特性,在此基础上提出了一种基于白噪声统计特性的机械振动模式有效性检验方法。该方法是对EMD方法的一种发展,可以自适应地消除机械振动信号经EMD分解产生的高频噪声模式及低频虚假模式,得到反映信号实际物理意义的振动模式分量集,整个处理过程不需要构造任何参数表达的基函数及相关滤波函数,也无需有关信号的任何先验知识,因而在实际应用中具有更好的适用性。采用大量实验验证了该方法能够有效识别出反映系统振动特性的振动模式,提高了特征提取的精度。
第5章从机械非平稳振动信号的降噪要求着手,分别描述了数字滤波、Kalman滤波、小波降噪及EMD降噪等四种现有常用降噪方法,给出了各降噪方法的降噪原理和适用情况,明确了这四种降噪方法对于旋转机械非平稳振动信号的降噪存在的不足,重点研究了EMD降噪给非平稳振动信号带来的模式混叠现象,利用正态分布白噪声在经验模式分解中具有的二进尺度分解特性,提出了一种非平稳振动信号的集成EMD降噪方法。通过仿真和转子启动过程试验振动信号对该降噪方法、EMD降噪方法及小波降噪方法的性能进行了比较测试。结果表明,该降噪方法具有更高的信噪比,不仅能够消除高斯噪声,而且能够有效抑制脉冲干扰,较好地降低了噪声对机械振动模式的影响。
第6章对瞬时能量与机械系统结构状态变化的物理联系展开了理论研究,在机械运行过程中,其振动信号的瞬时能量分布会随着结构异常的产生发生变化,不同的瞬时能量分布即代表了不同故障类型。利用EMD和Hilbert变换方法,给出了振动模式瞬时能量的概念,提出了一种基于EMD-HT的瞬时能量分布特征提取方法。从时-频域描述信号的角度出发,提取了机械振动信号的瞬时能量分布和Hilbert边际谱特征,转子实验系统振动信号的分析结果表明,基于瞬时能量分布和Hilbert边际谱的二维特征向量对于识别不同故障类型的有效性。
第7章论述了2D-HMM诊断方法在大型旋转机械非平稳振动信号时序模式分类方面具有的优越性,阐述了2D-HMM的基本概念和诊断原理,分析了EMD和2D-HMM在故障诊断中结合的必要性和可行性,建立了EMD—2D-HMM的诊断模型,提出了一种基于EMD—2D-HMM级联模型的故障诊断方法,该方法利用EMD方法提取的有效振动模式的瞬时能量分布及Hilbert边际谱特征进构造2D-HMM的时频域观测序列,并以此作为输入建立2D-HMM分类器,进而训练出对应各种故障类型的2D-HMM诊断模型库,通过求其最大似然概率值来判断机器的运行状态和故障类型。以转子实验台为基础构建了试验系统,试验研究结果表明,该方法相比HMM和小波包—2D-HMM诊断方法表现出更高的分类性能和诊断适用性。
第8章在基于EMD—2D-HMM的故障诊断方法研究的基础上,分析了设计和开发相应故障诊断系统的具体需求。设计了基于EMD—2D-HMM故障诊断系统总体框架,重点研究了数据采集及预处理单元和故障诊断软件包的结构组成及设计方案。研发了基于EMD—2D-HMM故障诊断软件系统;利用实验台实测数据对系统的可行性进行了测试。
第9章总结了全文的研究成果和创新之处,并对今后的工作提出了展望。
Based on the "Research on method for mechanical vibration source semi-blind source separation and reconstruction" (National Nature Science Fund Project, No: 50675194), and the "Research on the condition monitoring and fault diagnosis techniques and its application system of supercritical and ultra-supercritical steam turbines and pressure generating units" (High Technology Research and Development Program of China, No: 2008AA04Z410), aiming at nonstable charateristics of vibration signals of mechanical system, introduced empirical mode decomposition (EMD) method into vibration analysis and fault diagnosis for mechanical system, research on phsical application basis, end effect and false modes of EMD, presented solution scheme for mechanical vibration mode effective analysis and fault feature extraction method, set up EMD—2D-HMM diagnosis model, and carried out a large number of simulation and experiment. The details were as follows:
In Chapter one: The method of the situation monitoring and fault diagnosis of the rotating machine which uses vibration signals and the techniques were discussed. The problems existed in the techniques of vibration information operation were analyzed. Feasibility and importance of introducing EMD into fault diagnosis of rotating machines were disputed. Through the study and analysis applicaition of EMD in the different fields, concluded the next research development of EMD method. Finally, according to signal detection, pretreatment, feature extraction and mode classification related to meachanical fault diagnosis, described the background to carry out this research and its details, the scheme and the innovation points of this dissertation.
In Chapter two: Researched the phsical meaning of vibration signal analysis with EMD on view of mechanical vibration characteristics, presented an analysis method of vibrating mode of mechanical system based on EMD. The fundamental principle and algorithm procedure of EMD method were discussed in detail. The vibration model of mechanical system was established, studied the vibrating characteristics and its EMD analysis of single-freedom-degree and multi-degree-of-freedom system, the relationship discussion between mechanical vibrating mode and intrinsic mode function (IMF) was introduced. Using transverse vibration response of beam supported of both ends as an example. An important phenomenon that the existence of corresponding relation between system vibrating mode and IMF which obtained by EMD for vibating signal with experimental results, which established substantial theoretical foundation for EMD method in the application of condition monitoring and fault diagnosis for rotating machines, solved phsical difficult problem of EMD for vibration mode analysis for mechanical sysytem.
In Chapter three: The origin of EMD method's end effect and its harmful influence in vibration signal analysis, the front research at home and abroad about restraining end effect methods were summarized. Aiming at vibrating characteristic of rotating machine, drawbacks of the available signal extension methods for restraining end effect were pointed out. A new method of restraining end effect based on end optimization symmetric extension (EOSE) was presented. Firstly, assumed two ends of original signal as unknown value, and extended in a point-symmetrical manner with end-point as its center. Secondly, constituted deviation error evaluation function concerning original signal, and minimized the function, so that obtained the two optimization end-points value. Extended in a point symmetrical manner with new end-point value, the obtained up and down envelops maximally approached original signal end-point, which restrained the envelops divergence in EMD algorithm. Finally, in the process of filtering intrinsic mode function (IMF) discard the extended data, which release end effect to original signal outside and maximally reduced distortion of original signal. Simulation and experiment show that the proposed method could restrain end effect effectively and precisely extract classic fault feature of vibration signal of rotating machine.
In Chapter four: Aiming at the defect of bring high-frequency nosie mode and low-frequency false mode by EMD for mechanical vibration signals, stastistic charactistics of white nosie with EMD method were researched. A method based on the characteristics of white noise is presented to test the validity of mechanical vibrating mode. This method is a developed algorithm of empirical mode decomposition (EMD), which adaptively eliminated high frequency noise components and low frequency false components by applying the characteristics of normalized white noise under EMD, so the intrinsic mode set reflecting actual physical process of vibration signal are obtained. In the whole feature process, the construction of general basis function described by some parameters and related filter function is unnecessary, and any prior information about the observed signal is no more required, which felicitates the method for a wide variety of applications. Both computer simulation and rotor set experimental results verify this approach is practicable and effective, improved the precision of feature extraction.
In Chapter five: Starting from de-noising request of nonstationary vibration signals of rotating machine, respectively described four present common filter methods including digital filter, Kalman filter, wavelet de-noise and EMD de-noise, depicted de-noising principle and suit situation of the above-mentioned de-noising methods, explicated the defects of four filter methods for de-noising of nonstationary vibration signals of rotating machine, focusing on the research of mode mixing brought by EMD de-noising method. Appling dyadic scales decomposition characteristics of normal distribution white noise with EMD, an ensembled algorithm of EMD de-noising method was presented. Simulation numerical signal and experimental signal of rotor running state are used to test and compare the performances of the method and EMD based de-noising method and wavelet de-noising method. The results show that the ensembling EMD based noise cancellation method presented in the paper has more effective de-noising performance, not only eliminates random noise, but suppresses intensity noise and extracts vibration intrinsic modes that reflect real physical meaning of signal.
In Chapter six: Physical relationship between instantaneous energy and structural state variation of system was studied therotically, instantaneous energy of mechanical vibration signal changed with variable structural state in the machine running state, different instantaneous energy distribution stand for different fault. By EMD and Hilbert Transformation (HT) methods, the concept of vibration mode instantaneous energy was brought up, a new instantaneous energy distribution characteristics extraction method based on EMD and HT. In terms of depicting signals in time-frequency domain, instantaneous energy distribution and Hilbert margin spectra feature of mechanical vibration signals were extracted. The results of rotor experimental set proved this method is effective, could identify different fault type.
In Chapter seven: The advantages of 2D-HMM method in the aspect of time sequence mode classification for nonstationary vibration signals of rotating machine was discussed, elaborated the essential concept and diagnosis principle of 2D-HMM method. The integration necessity and feasibility of EMD and 2D-HMM for fault diagnosis was analyzed. A diagnosis model based on EMD-2D-HMM was set up. Firstly, decomposed mechanical vibration signal into a number of intrinsic mode function components applying EMD, extracted instantaneous energy distribution and frequency energy spectrum of effective vibration mode, which could be used to set up time-domain and frequency-domain observation sequence; secondly, set up 2D-HMM classifying model by the extracted observation sequence, so constitute 2D-HMM fault diagnosis model database, and judged running state of machine Through calculating the maximal log-likelihood. An experiment system was set up on the basis of rotor experimental table. Experimental results show that EMD-2D-HMM method had higher classification performance and diagnosis availability.
In Chapter eight: Based on the above research of EMD-2D-HMM fault diagnosis method, the concrete demand on designing and developing corresponding fault diagnosis system were analyzed. The overall framework of fault diagnosis system based on EMD-2D-HMM was devised, and the composition and design scheme of data acquisition system and preprocessing unit and fault diagnosis software package were studied in detail. The fault diagnosis software system based on EMD-2D-HMM was designed and developed. System feasibility was tested with the measured data of experimental set.
In Chapter nine: The concolutions are presented and some advanced topics in the proposed methodology that needs further investigation in future are presented and addressed.
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