Assessing the vulnerability of a platform is crucial in its design.In fact,the results obtained from vulnerability analyses provide valuable information,leading to precise design choices or corrective solutions that e...Assessing the vulnerability of a platform is crucial in its design.In fact,the results obtained from vulnerability analyses provide valuable information,leading to precise design choices or corrective solutions that enhance the platform's chances of surviving different scenarios.Such scenarios can involve various types of threats that can affect the platform's survivability.Among such,blast waves impacting the platform's structure represent critical conditions that have not yet been studied in detail.That is,frameworks for vulnerability assessment that can deal with blast loading have not been presented yet.In this context,this work presents a fast-running engineering tool that can quantify the risk that a structure fails when it is subjected to blast loading from the detonation of high explosive-driven threats detonating at various distances from the structure itself.The tool has been implemented in an in-house software that calculates vulnerability to various impacting objects,and its capabilities have been shown through a simplified,yet realistic,case study.The novelty of this research lies in the development of an integrated computational environment capable of calculating the platform's vulnerability to blast waves,without the need for running expensive finite element simulations.In fact,the proposed tool is fully based on analytical models integrated with a probabilistic approach for vulnerability calculation.展开更多
Reducing the vulnerability of a platform,i.e.,the risk of being affected by hostile objects,is of paramount importance in the design process of vehicles,especially aircraft.A simple and effective way to decrease vulne...Reducing the vulnerability of a platform,i.e.,the risk of being affected by hostile objects,is of paramount importance in the design process of vehicles,especially aircraft.A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats.However,this type of solution can lead to a significant increase in weight,affecting the performance of the aircraft.For this reason,it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight.One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures.Among the many optimization techniques available in the literature for this purpose,multiobjective genetic algorithms stand out as promising tools.In this context,this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms,aiming to simultaneously minimize the weight of protective structures and vulnerability.In addition to the use of the in-house software,which itself represents a novelty in the field of topology optimization of structures,the method incorporates a custom mutation function within the genetic algorithm,specifically developed using a graph-based approach to ensure the continuity of the generated structures.The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects,namely bullets and fragments from detonating objects.The software outputs a set of non-dominated solutions describing different topologies that the user can choose from.展开更多
Laser anti-drone technology is entering the sequence of actual combat,and it is necessary to consider the vulnerability of typical functional parts of UAVs.Since the concept of"vulnerability"was proposed,a v...Laser anti-drone technology is entering the sequence of actual combat,and it is necessary to consider the vulnerability of typical functional parts of UAVs.Since the concept of"vulnerability"was proposed,a variety of analysis programs for battlefield targets to traditional weapons have been developed,but a comprehensive assessment methodology for targets'vulnerability to laser is still missing.Based on the shotline method,this paper proposes a method that equates laser beam to shotline array,an efficient vulnerability analysis program of target to laser is established by this method,and the program includes the circuit board and the wire into the vulnerability analysis category,which improves the precision of the vulnerability analysis.Taking the UAV engine part as the target of vulnerability analysis,combine with the"life-death unit method"to calculate the laser penetration rate of various materials of the UAV,and the influence of laser weapon system parameters and striking orientation on the killing probability is quantified after introducing the penetration rate into the vulnerability analysis program.The quantitative analysis method proposed in this paper has certain general expansibility,which can provide a fresh idea for the vulnerability analysis of other targets to laser.展开更多
The research of groundwater vulnerability is the basic work to protect the groundwater. For utilizing groundwater resource continuably, groundwater vulnerability evaluation is necessary. Useful reference to protect, e...The research of groundwater vulnerability is the basic work to protect the groundwater. For utilizing groundwater resource continuably, groundwater vulnerability evaluation is necessary. Useful reference to protect, exploit and utilize on groundwater resource are provided rationally. According to the real condition of Sanjiang Plain, the indexes system is established based on the traditional DRASTIC model. The new system includes the following seven indexes： Depth of Water, Net Recharge, Aquifer Media, Soil Media, Conductivity of the Aquifer, Land Utilizing Ratio and Populace Density. The related analysis appears that the system is rather reasonable. Because traditional methods, such as analytic hierarchy process and fuzzy mathematics theory, can＇t be avoided human interference in selection of weights, they could lead to an imprecise result. In order to evaluate the groundwater vulnerability reasonably, entropy weight coefficient method is applied for the first time, which provides a new way to groundwater vulnerability evaluation. The method is a model whose weights are insured by the calculation process, so the artificial disturb can be avoided. It has been used to evaluate the groundwater vulnerability in Sanjiang Plain. The satisfied result is acquired. Comparably, the same result is acquired by the other method named projection pursuit evaluation based on real-coded accelerating genetic algorithm. It shows that entropy weight coefficient method is applicable on groundwater vulnerability evaluation. The evaluation result can provide reference on the decision-making departments.展开更多
A potential energy framework for assessment of grid vulnerability was presented.In the framework,the branch potential energy function model was constructed.Two indexes,current vulnerability and forecasting vulnerabili...A potential energy framework for assessment of grid vulnerability was presented.In the framework,the branch potential energy function model was constructed.Two indexes,current vulnerability and forecasting vulnerability,were calculated.The current vulnerability was used to identify the current vulnerable area through calculating the distance between the current transmitted power and initial transmitted power;and the forecast vulnerability under variation of power injection was used to predict the vulnerable area of next step and verify the current vulnerable area.Numerical simulation was performed under variant operating conditions with IEEE-30 bus system,which shows that almost area of 90% overlaps between current vulnerable area and forecasting vulnerable area,the overlapped area is termed as inherent vulnerable area of grid.When considering N-1 contingency,the assessment results of this method proposed agree with those of optimal power flow.When considering N-2 contingency,optimal power flow fails to obtain correct results,while the method based on energy framework gives reliable results.展开更多
Survivability is defined as the capability of a platform to avoid or withstand a man-made hostile environment. Military aircraft in particular, but also other kinds of platforms subjected to external, impacting threat...Survivability is defined as the capability of a platform to avoid or withstand a man-made hostile environment. Military aircraft in particular, but also other kinds of platforms subjected to external, impacting threats, are commonly designed according to increasing survivability requirements. The concept of survivability was first formalized by R. Ball in 1985 in its seminal work on combat aircraft survivability.On the basis of the theory presented in his work, many computer programs have been developed which implement the modelling techniques and computations required by vulnerability assessments. However,a clear and general view of the operative computational procedures is still lacking. Moreover, to date only a limited number of applications to helicopter platforms have been investigated in the survivability field,even though these platforms experience numerous flight conditions exposing the system to different types of threats. In this context, this work aims at establishing a multi-purpose general framework for the vulnerability assessment of different types of platforms subjected to external threats, with a focus on helicopters. The in-house software specifically developed for this application is here described in detail and employed to present a case study on a representative military helicopter.展开更多
Groundwater vulnerability assessment is one of the critical prerequisites to achieve efficient development and management of water resources in Tanghai-Caofeidian area,which has been one of the national key constructi...Groundwater vulnerability assessment is one of the critical prerequisites to achieve efficient development and management of water resources in Tanghai-Caofeidian area,which has been one of the national key constructive districts in North China.According to the influence factors of groundwater vulnerability,this study analyzed the impact of vadose zone that includes the depth to groundwater table,unsaturated zone lithology and permeability with the data achieved from field works in recent years.The evaluation model was established for estimating groundwater vulnerability using three展开更多
China Cardiovascular Disease Report 2017(Summary)pointed out that at present,cardiovascular diseases(CVD)account for the highest number of deaths among urban and rural residents.In the middle or later stages of athero...China Cardiovascular Disease Report 2017(Summary)pointed out that at present,cardiovascular diseases(CVD)account for the highest number of deaths among urban and rural residents.In the middle or later stages of atherosclerosis,the plaques become increasingly unstable with high chance to rupture,which may lead acute death from coronary heart diseases.Medical imaging and image-based computational modeling have been used in recent years to quantify ather-osclerotic plaque morphological and biomechanical characteristics and predict the coronary plaque growth and rupture processes.Analyzing the vulnerability of plaques effectively could lead to better patient screening strategies and enable physicians to adopt timely and necessary intervention or conservative treatment.Earlier investigations of vulnerable plaques were mostly based on histopathological data.With the accumulation of experience in pathology and the gradual enrichment of autopsy materials,the criteria for the diagnosis of vulnerable plaques appeared in 2001,mainly manifested as the necrotic lipid nuclei,fibrous caps that are infiltrated by a large number of macrophages,and fibrous cap thickness less than 65μm.Because of the obvious importance of the thin fibrous cap in the study of plaque vulnerability,it has been a focus of attention by many investigations.Watson,M.G.et al.are concerned about the formation of early fibrous caps in recent years.The presentation of local maximum stress on plaque further confirmed the importance of thin fibrous cap.The development of medical images has greatly promoted the study of coronary atherosclerosis.Compared with autopsy ex vivo,medical image could provide plaque data under in vivo conditions and greatly promote the study of coronary atherosclerosis.Huang XY et al.used ex vivo magnetic resonance imaging(MRI)to study the relationship between plaque wall stress(PWS)and death caused by coronary artery disease.Due to technical limitations and the accessibility of the coronary artery in the body,MRI is not widely used for in vivo coronary studies.Interventional intravascular ultrasound(IVUS),with an image resolution of 150-200μm,has been used in research and clinical practice to identify plaques,quantify plaque morphology,and characterize plaque components.More recently,optical coherence tomography(OCT),with its resolution of 5-10μm,has emerged as an imaging modality which can be used to detect thin fibrous caps and improve diagnostic accuracy.It is commonly believed that mechanical forces play an important role in plaque progression and rupture.Image-based biomechanical plaque models have been developed and used to quantify plaque mechanical conditions and seek their linkage to plaque progression and vulnerability development activities.Based on recent advances in imaging and modeling,this paper attempts to provide a brief review on plaque research,including histological classification,image preparation,biomechanical modeling and analysis methods including medical imaging techniques represented by intravascular ultrasound(IVUS)and optical coherence tomography(OCT),computational modeling and their applications in plaque progression and vulnerability analyses and predictions.The clinical application and future development direction are also briefly described.We focus more on human coronary plaque modeling and mainly included results from our group for illustration purpose.We apologize in advance for our limitations.展开更多
OBJECTIVE Exposure to stressful events can be differently perceived by individuals depending on the level of stress resilience or vulnerability.The neural processes that underlie such clinical y and social y important...OBJECTIVE Exposure to stressful events can be differently perceived by individuals depending on the level of stress resilience or vulnerability.The neural processes that underlie such clinical y and social y important differences are largely unknown.As insula cortex is important in emotional processing,we have examined whether the changes in synaptic plasticity in the insula cortex involved in stress resilience or vulnerability.METHODS Mice were divided into two groups:control and stress group.Stress group was treated by foot electric shock twice daily(0.8 mA,2 s,ten times in 1 min) in continuous two weeks.Then we used fear conditioning test to detect re-experiencing of traumatic experience,open field test to detect avoidance,pre-pulse inhibition experiment to detect hyper arousal.The changes of synaptic plasticity in the insular cortex were recorded by the multiple channels electrophysiology and whole cell patch.RESULTS According to the behavioral scores,it was divided into resilient and vulnerable group.In the fear conditioning test,the vulnerable group showed the significant freezing time decreased than that of the resilient group(P<0.01).In the open field test,the time that enter the center zone of vulnerable group is increased than that resilient group(P<0.01);In the pre-pulse inhibition experiment,there are not significant difference of PPI value in both groups(P=0.4239).And then electrophysiological experiments are performed to detect the synaptic plasticity of the insular cortex.Compared with the resilient group,the LTP level was decreased(P<0.05) and the mEPSC was increased(P<0.01) in vulnerable group.CONCLUSION The impairment of synaptic plasticity in the insular cortex may be one of the neural mechanisms for the vulnerability to chronic stress.展开更多
Groundwater is a finite resource which is being overexploited due to increase in demand over the years leading to decrease in its potentiality.As it is known that ground water is the only major source of drinking wate...Groundwater is a finite resource which is being overexploited due to increase in demand over the years leading to decrease in its potentiality.As it is known that ground water is the only major source of drinking water for both urban and rural India its proper management is very essential for its sustainability. In the present study,DRASTIC model is展开更多
Under the conditions of multiple hits and quadratic effects,the aircraft vulnerability assessment method is proposed by means of kill-tree diagram and state transition matrix.Four instances of the quadratic effects ar...Under the conditions of multiple hits and quadratic effects,the aircraft vulnerability assessment method is proposed by means of kill-tree diagram and state transition matrix.Four instances of the quadratic effects are investigated:non-redundant components to non-redundant components,non-redundant to redundant,redundant to non-redundant and redundant to redundant.The application of the proposed method to the calculation of quadratic effects is also studied.展开更多
文摘Assessing the vulnerability of a platform is crucial in its design.In fact,the results obtained from vulnerability analyses provide valuable information,leading to precise design choices or corrective solutions that enhance the platform's chances of surviving different scenarios.Such scenarios can involve various types of threats that can affect the platform's survivability.Among such,blast waves impacting the platform's structure represent critical conditions that have not yet been studied in detail.That is,frameworks for vulnerability assessment that can deal with blast loading have not been presented yet.In this context,this work presents a fast-running engineering tool that can quantify the risk that a structure fails when it is subjected to blast loading from the detonation of high explosive-driven threats detonating at various distances from the structure itself.The tool has been implemented in an in-house software that calculates vulnerability to various impacting objects,and its capabilities have been shown through a simplified,yet realistic,case study.The novelty of this research lies in the development of an integrated computational environment capable of calculating the platform's vulnerability to blast waves,without the need for running expensive finite element simulations.In fact,the proposed tool is fully based on analytical models integrated with a probabilistic approach for vulnerability calculation.
文摘Reducing the vulnerability of a platform,i.e.,the risk of being affected by hostile objects,is of paramount importance in the design process of vehicles,especially aircraft.A simple and effective way to decrease vulnerability is to introduce protective structures to intercept and possibly stop threats.However,this type of solution can lead to a significant increase in weight,affecting the performance of the aircraft.For this reason,it is crucial to study possible solutions that allow reducing the vulnerability of the aircraft while containing the increase in structural weight.One possible strategy is to optimize the topology of protective solutions to find the optimal balance between vulnerability and the weight of the added structures.Among the many optimization techniques available in the literature for this purpose,multiobjective genetic algorithms stand out as promising tools.In this context,this work proposes the use of a in-house software for vulnerability calculation to guide the process of topology optimization through multi-objective genetic algorithms,aiming to simultaneously minimize the weight of protective structures and vulnerability.In addition to the use of the in-house software,which itself represents a novelty in the field of topology optimization of structures,the method incorporates a custom mutation function within the genetic algorithm,specifically developed using a graph-based approach to ensure the continuity of the generated structures.The tool developed for this work is capable of generating protections with optimized layouts considering two different types of impacting objects,namely bullets and fragments from detonating objects.The software outputs a set of non-dominated solutions describing different topologies that the user can choose from.
基金National Natural Science Foundation of China(Grant Nos.62005276,62175234)the Scientific and Technological Development Program of Jilin,China(Grant No.20230508111RC)to provide fund for this research。
文摘Laser anti-drone technology is entering the sequence of actual combat,and it is necessary to consider the vulnerability of typical functional parts of UAVs.Since the concept of"vulnerability"was proposed,a variety of analysis programs for battlefield targets to traditional weapons have been developed,but a comprehensive assessment methodology for targets'vulnerability to laser is still missing.Based on the shotline method,this paper proposes a method that equates laser beam to shotline array,an efficient vulnerability analysis program of target to laser is established by this method,and the program includes the circuit board and the wire into the vulnerability analysis category,which improves the precision of the vulnerability analysis.Taking the UAV engine part as the target of vulnerability analysis,combine with the"life-death unit method"to calculate the laser penetration rate of various materials of the UAV,and the influence of laser weapon system parameters and striking orientation on the killing probability is quantified after introducing the penetration rate into the vulnerability analysis program.The quantitative analysis method proposed in this paper has certain general expansibility,which can provide a fresh idea for the vulnerability analysis of other targets to laser.
基金Supported by the National Natural Science Foundation of China(30400275)the Tackle Key Problems of Heilongjiang Province(the Hobbledehoy Science Fund of Heilongjiang Province)(QC04C28)
文摘The research of groundwater vulnerability is the basic work to protect the groundwater. For utilizing groundwater resource continuably, groundwater vulnerability evaluation is necessary. Useful reference to protect, exploit and utilize on groundwater resource are provided rationally. According to the real condition of Sanjiang Plain, the indexes system is established based on the traditional DRASTIC model. The new system includes the following seven indexes： Depth of Water, Net Recharge, Aquifer Media, Soil Media, Conductivity of the Aquifer, Land Utilizing Ratio and Populace Density. The related analysis appears that the system is rather reasonable. Because traditional methods, such as analytic hierarchy process and fuzzy mathematics theory, can＇t be avoided human interference in selection of weights, they could lead to an imprecise result. In order to evaluate the groundwater vulnerability reasonably, entropy weight coefficient method is applied for the first time, which provides a new way to groundwater vulnerability evaluation. The method is a model whose weights are insured by the calculation process, so the artificial disturb can be avoided. It has been used to evaluate the groundwater vulnerability in Sanjiang Plain. The satisfied result is acquired. Comparably, the same result is acquired by the other method named projection pursuit evaluation based on real-coded accelerating genetic algorithm. It shows that entropy weight coefficient method is applicable on groundwater vulnerability evaluation. The evaluation result can provide reference on the decision-making departments.
基金Project(51007006) supported by the National Natural Science Foundation of ChinaProject(20090185120023) supported by the Ph.D Programs Foundation for New Teacher of Ministry of Education of China
文摘A potential energy framework for assessment of grid vulnerability was presented.In the framework,the branch potential energy function model was constructed.Two indexes,current vulnerability and forecasting vulnerability,were calculated.The current vulnerability was used to identify the current vulnerable area through calculating the distance between the current transmitted power and initial transmitted power;and the forecast vulnerability under variation of power injection was used to predict the vulnerable area of next step and verify the current vulnerable area.Numerical simulation was performed under variant operating conditions with IEEE-30 bus system,which shows that almost area of 90% overlaps between current vulnerable area and forecasting vulnerable area,the overlapped area is termed as inherent vulnerable area of grid.When considering N-1 contingency,the assessment results of this method proposed agree with those of optimal power flow.When considering N-2 contingency,optimal power flow fails to obtain correct results,while the method based on energy framework gives reliable results.
文摘Survivability is defined as the capability of a platform to avoid or withstand a man-made hostile environment. Military aircraft in particular, but also other kinds of platforms subjected to external, impacting threats, are commonly designed according to increasing survivability requirements. The concept of survivability was first formalized by R. Ball in 1985 in its seminal work on combat aircraft survivability.On the basis of the theory presented in his work, many computer programs have been developed which implement the modelling techniques and computations required by vulnerability assessments. However,a clear and general view of the operative computational procedures is still lacking. Moreover, to date only a limited number of applications to helicopter platforms have been investigated in the survivability field,even though these platforms experience numerous flight conditions exposing the system to different types of threats. In this context, this work aims at establishing a multi-purpose general framework for the vulnerability assessment of different types of platforms subjected to external threats, with a focus on helicopters. The in-house software specifically developed for this application is here described in detail and employed to present a case study on a representative military helicopter.
文摘Groundwater vulnerability assessment is one of the critical prerequisites to achieve efficient development and management of water resources in Tanghai-Caofeidian area,which has been one of the national key constructive districts in North China.According to the influence factors of groundwater vulnerability,this study analyzed the impact of vadose zone that includes the depth to groundwater table,unsaturated zone lithology and permeability with the data achieved from field works in recent years.The evaluation model was established for estimating groundwater vulnerability using three
基金supported in part by NIH grant ( R01 EB004759)Jiangsu Province Science and Technology Agency grant ( BE2016785)
文摘China Cardiovascular Disease Report 2017(Summary)pointed out that at present,cardiovascular diseases(CVD)account for the highest number of deaths among urban and rural residents.In the middle or later stages of atherosclerosis,the plaques become increasingly unstable with high chance to rupture,which may lead acute death from coronary heart diseases.Medical imaging and image-based computational modeling have been used in recent years to quantify ather-osclerotic plaque morphological and biomechanical characteristics and predict the coronary plaque growth and rupture processes.Analyzing the vulnerability of plaques effectively could lead to better patient screening strategies and enable physicians to adopt timely and necessary intervention or conservative treatment.Earlier investigations of vulnerable plaques were mostly based on histopathological data.With the accumulation of experience in pathology and the gradual enrichment of autopsy materials,the criteria for the diagnosis of vulnerable plaques appeared in 2001,mainly manifested as the necrotic lipid nuclei,fibrous caps that are infiltrated by a large number of macrophages,and fibrous cap thickness less than 65μm.Because of the obvious importance of the thin fibrous cap in the study of plaque vulnerability,it has been a focus of attention by many investigations.Watson,M.G.et al.are concerned about the formation of early fibrous caps in recent years.The presentation of local maximum stress on plaque further confirmed the importance of thin fibrous cap.The development of medical images has greatly promoted the study of coronary atherosclerosis.Compared with autopsy ex vivo,medical image could provide plaque data under in vivo conditions and greatly promote the study of coronary atherosclerosis.Huang XY et al.used ex vivo magnetic resonance imaging(MRI)to study the relationship between plaque wall stress(PWS)and death caused by coronary artery disease.Due to technical limitations and the accessibility of the coronary artery in the body,MRI is not widely used for in vivo coronary studies.Interventional intravascular ultrasound(IVUS),with an image resolution of 150-200μm,has been used in research and clinical practice to identify plaques,quantify plaque morphology,and characterize plaque components.More recently,optical coherence tomography(OCT),with its resolution of 5-10μm,has emerged as an imaging modality which can be used to detect thin fibrous caps and improve diagnostic accuracy.It is commonly believed that mechanical forces play an important role in plaque progression and rupture.Image-based biomechanical plaque models have been developed and used to quantify plaque mechanical conditions and seek their linkage to plaque progression and vulnerability development activities.Based on recent advances in imaging and modeling,this paper attempts to provide a brief review on plaque research,including histological classification,image preparation,biomechanical modeling and analysis methods including medical imaging techniques represented by intravascular ultrasound(IVUS)and optical coherence tomography(OCT),computational modeling and their applications in plaque progression and vulnerability analyses and predictions.The clinical application and future development direction are also briefly described.We focus more on human coronary plaque modeling and mainly included results from our group for illustration purpose.We apologize in advance for our limitations.
基金National Natural Science Foundation of China(81402912).
文摘OBJECTIVE Exposure to stressful events can be differently perceived by individuals depending on the level of stress resilience or vulnerability.The neural processes that underlie such clinical y and social y important differences are largely unknown.As insula cortex is important in emotional processing,we have examined whether the changes in synaptic plasticity in the insula cortex involved in stress resilience or vulnerability.METHODS Mice were divided into two groups:control and stress group.Stress group was treated by foot electric shock twice daily(0.8 mA,2 s,ten times in 1 min) in continuous two weeks.Then we used fear conditioning test to detect re-experiencing of traumatic experience,open field test to detect avoidance,pre-pulse inhibition experiment to detect hyper arousal.The changes of synaptic plasticity in the insular cortex were recorded by the multiple channels electrophysiology and whole cell patch.RESULTS According to the behavioral scores,it was divided into resilient and vulnerable group.In the fear conditioning test,the vulnerable group showed the significant freezing time decreased than that of the resilient group(P<0.01).In the open field test,the time that enter the center zone of vulnerable group is increased than that resilient group(P<0.01);In the pre-pulse inhibition experiment,there are not significant difference of PPI value in both groups(P=0.4239).And then electrophysiological experiments are performed to detect the synaptic plasticity of the insular cortex.Compared with the resilient group,the LTP level was decreased(P<0.05) and the mEPSC was increased(P<0.01) in vulnerable group.CONCLUSION The impairment of synaptic plasticity in the insular cortex may be one of the neural mechanisms for the vulnerability to chronic stress.
文摘Groundwater is a finite resource which is being overexploited due to increase in demand over the years leading to decrease in its potentiality.As it is known that ground water is the only major source of drinking water for both urban and rural India its proper management is very essential for its sustainability. In the present study,DRASTIC model is
文摘Under the conditions of multiple hits and quadratic effects,the aircraft vulnerability assessment method is proposed by means of kill-tree diagram and state transition matrix.Four instances of the quadratic effects are investigated:non-redundant components to non-redundant components,non-redundant to redundant,redundant to non-redundant and redundant to redundant.The application of the proposed method to the calculation of quadratic effects is also studied.
