On May 12, 2008, a strong earthquake with a magnitude of 8.0 (Ms) struck Wenchuan town, in the eastern Sichuan area of west China. Following the earthquake on May 18, the Southwest Jiaotong University organized a dama...On May 12, 2008, a strong earthquake with a magnitude of 8.0 (Ms) struck Wenchuan town, in the eastern Sichuan area of west China. Following the earthquake on May 18, the Southwest Jiaotong University organized a damage survey team and dispatched it to the affected area for the investigation into the damage and collection of information and data. This paper outlines the findings of this investigation on the earthquake disaster to mountain tunnels and geotechnical engineering. The systematic investigation, involving geological conditions, design documents, construction and maintenance records of the tunnels, has been conducted and the degree of damage to investigated tunnels has been assessed according to the width and length of cracks, the stability of the slope above the tunnel, and the condition of the groundwater inrush. The results show that the major damage of the mountain tunnels was mainly concentrated in the tunnel portals due to widespread landslides and rockfalls, and the inner part of investigated tunnels suffered moderate damages mainly due to fault displacements. It is hoped that the information shared herein could enhance the outstanding of seismic behavior of mountain tunnels and improve seismic design and construction procedures.展开更多
AIM: To assess the failure and bone-to-implant contact rate of dental implants placed on osteoporotic subjects. METHODS: Extensive examination strategies were created to classify studies for this systematic review. ME...AIM: To assess the failure and bone-to-implant contact rate of dental implants placed on osteoporotic subjects. METHODS: Extensive examination strategies were created to classify studies for this systematic review. MEDLINE(via Pub Med) and EMBASE database were examined for studies in English up to and including May 2014. The examination presented a combination of the MeS H words described as follow: "osteoporosis" or "osteopenia" or "estrogen deficiency" AND "implant" or "dental implant" or "osseointegration". Assessment of clinical and/or histological peri-implant conditions in osteoporosis subjects treated with titanium dental implants. The examination included a combination of the MeS H terms described as follow: "osteoporosis" or "osteopenia" or "estrogen deficiency" AND "implant" or "dental implant" or "osseointegration".RESULTS: Of 943 potentially eligible articles, 12 were included in the study. A total of 133 subjects with osteoporosis, 73 subjects diagnosed with osteopenia and 708 healthy subjects were assessed in this systematic review. In these subjects were installed 367, 205, 2981 dental implants in osteoporotic, osteopenic and healthy subjects, respectively. The failure rate of dental implant was 10.9% in osteoporotic subjects, 8.29% in osteopenic and 11.43% in healthy ones. Bone-to-implant contact obtained from retrieved implants ranged between 49.96% to 47.84%, for osteoporosis and non-osteoporotic subjects. CONCLUSION: Osteoporotic subjects presented higher rates of implant loss, however, there is a lower evidence to strengthen or refute the hypothesis that osteoporosis may have detrimental effects on bone healing. Consequently, final conclusions regarding the effect of osteoporosis in dental implant therapy cannot be made at this time. There are no randomized clinical trial accessible for evaluation and the retrospectivenature of the evaluated studies shall be taken in account when interpreting this study.展开更多
Alternate path(AP) method is the most widely used method for the progressive collapse analysis,and its application in frame structures has been well proved.However,the application of AP method for other structures,esp...Alternate path(AP) method is the most widely used method for the progressive collapse analysis,and its application in frame structures has been well proved.However,the application of AP method for other structures,especially for cable-stayed structures,should be further developed.The four analytical procedures,i.e.,linear static,nonlinear static,linear dynamic,and nonlinear dynamic were firstly improved by taking into account the initial state.Then a cable-stayed structure was studied using the four improved methods.Furthermore,the losses of both one cable and two cables were discussed.The results show that for static and dynamic analyses of the cable-stayed bridges,there is large difference between the results obtained from simulations starting with either a deformed or a nondeformed configuration at the time of cable loss.The static results are conservative in the vicinity of the ruptured cable,but the dynamic effect of the cable loss in the area farther away from the loss-cable cannot be considered.Moreover,the dynamic amplification factor of 2.0 is found to be a good estimate for static analysis procedures,since linear static and linear dynamic procedures yield approximately the same maximum vertical deflection.The results of the comprehensive evaluation of the cable failure show that the tread of the progressive failure of the cable-stayed bridges decreases when the location of the failed cables is closer to the pylon.展开更多
This paper makes a comprehensive survey on power system blackout modeling and analysis based on SOC (self-organized criticality). Firstly,a generalized SOC theory from the viewpoint of cybernetics is introduced. Then ...This paper makes a comprehensive survey on power system blackout modeling and analysis based on SOC (self-organized criticality). Firstly,a generalized SOC theory from the viewpoint of cybernetics is introduced. Then the evolution model of power system and its relative mathematical description,which serves as a concrete example of the proposed generalized SOC,are given. Secondly,five blackout models capturing various critical properties of power systems in different time-scales are listed. Finally,this paper analyzes SOC in power systems,such as,the revelation of criticalities of proposed models in both micro-scale and macro-scale which can be used to assess the security of power system,and cas-cading failures process.展开更多
Critical infrastructures are becoming increasingly interdependent and vulnerable to cascading failures. Existing studies have analyzed the vulnerability of interdependent networks to cascading failures from the static...Critical infrastructures are becoming increasingly interdependent and vulnerable to cascading failures. Existing studies have analyzed the vulnerability of interdependent networks to cascading failures from the static perspective of network topology structure. This paper develops a more realistic cascading failures model that considers the dynamic redistribution of load in power network to explore the vulnerability of interdependent power-water networks. In this model, the critical tolerance threshold is originally proposed to indicate the vulnerability of network to cascading failures. In addition, some key parameters that are important to network vulnerability are identified and quantified through numerical simulation. Results show that cascading failures can be prevented when the values of tolerance parameter are above a critical tolerance threshold. Otherwise interdependent networks collapse after attacking a critical fraction of power nodes. Interdependent networks become more vulnerable with the increase in interdependence strength, which implies the importance of protecting those interconnected nodes to reduce the consequences of cascading failures. Interdependent networks are most vulnerable under high-load attack, which shows the significance of protecting high-load nodes.展开更多
The local-world (LW) evolving network model shows a transition for the degree distribution between the exponential and power-law distributions, depending on the LW size. Cascading failures under intentional attacks in...The local-world (LW) evolving network model shows a transition for the degree distribution between the exponential and power-law distributions, depending on the LW size. Cascading failures under intentional attacks in LW network models with different LW sizes were investigated using the cascading failures load model. We found that the LW size has a significant impact on the network's robustness against deliberate attacks. It is much easier to trigger cascading failures in LW evolving networks with a larger LW size. Therefore, to avoid cascading failures in real networks with local preferential attachment such as the Internet, the World Trade Web and the multi-agent system, the LW size should be as small as possible.展开更多
The problem of robust H-infinity fault-tolerant control against sensor failures for a class of uncertain descriptor systems via dynamical compensators is considered. Based on H-infinity theory in descriptor systems, a...The problem of robust H-infinity fault-tolerant control against sensor failures for a class of uncertain descriptor systems via dynamical compensators is considered. Based on H-infinity theory in descriptor systems, a sufficient condition for the existence of dynamical compensators with H-infinity fault-tolerant function is derived and expressions for the gain matrices in the compensators are presented. The dynamical compensator guarantees that the resultant colsed-loop system is admissible; furthermore, it maintains certain H-infinity norm performance in the normal condition as well as in the event of sensor failures and parameter uncertainties. A numerical example shows the effect of the proposed method.展开更多
The large application of renewable energy generation(REG)has increased the risk of cascading failures in the power system.At the same time REG also provides the possibility of new approaches for the suppression of suc...The large application of renewable energy generation(REG)has increased the risk of cascading failures in the power system.At the same time REG also provides the possibility of new approaches for the suppression of such failures.However,the capacity and position of the synchronous generator(SG)involved in regulation limit the power regu-lation speed(PRS)of REG to the overload line which is the main cause of cascading failures,while the PRS of SG is related to the position and shedding power.REG and SGs have difficulty in achieving effective cooperation under constraints of system power balance.Particularly,the dynamic variation of line flow during power regulation causes new problems for the accurate evaluation of line thermal safety under overload.Therefore,a new strategy for quan-titatively coordinating shedding power and power regulation to block cascading failures in the dynamic security domain is proposed in this paper.The control capability and dynamic security domain of the overload line are mod-eled,and the coordination control method based on power regulation is then proposed to minimize shedding power.The algorithm for the optimal control scheme considers the constraints of load capacity,power source capacity and bus PRS.The correctness of the proposed method is verified using case studies.展开更多
Mg and its alloys evince strong candidature for biodegradable bone implants,cardiovascular stents,and wound closing devices.However,their rapid degradation rate causes premature implant failure,constraining clinical a...Mg and its alloys evince strong candidature for biodegradable bone implants,cardiovascular stents,and wound closing devices.However,their rapid degradation rate causes premature implant failure,constraining clinical applications.Bio-functional surface coatings have emerged as the most competent strategy to fulfill the diverse clinical requirements,besides yielding effective corrosion resistance.This article reviews the progress of biodegradable and advanced surface coatings on Mg alloys investigated in recent years,aiming to build up a comprehensive knowledge framework of coating techniques,processing parameters,performance measures in terms of corrosion resistance,adhesion strength,and biocompatibility.Recently developed conversion and deposition type surface coatings are thoroughly discussed by reporting their essential therapeutic responses like osteogenesis,angiogenesis,cytocompatibility,hemocompatibility,anti-bacterial,and controlled drug release towards in-vitro and in-vivo study models.The challenges associated with metallic,ceramic and polymeric coatings along with merits and demerits of various coatings have been illustrated.The use of multilayered hybrid coating comprising a unique combination of organic and inorganic components has been emphasized with future perspectives to obtain diverse bio-functionalities in a facile single coating system for orthopedic implant applications.展开更多
Anterior cruciate ligament(ACL) reconstruction is one of the most common orthopedic procedures performed worldwide. In this regard, magnetic resonance imaging(MRI) represents a useful pre-operative tool to confirm a d...Anterior cruciate ligament(ACL) reconstruction is one of the most common orthopedic procedures performed worldwide. In this regard, magnetic resonance imaging(MRI) represents a useful pre-operative tool to confirm a disruption of the ACL and to assess for potential associated injuries. However, MRI is also valuable postoperatively, as it is able to identify, in a non-invasive way, a number of aspects and situations that could suggest potential problems to clinicians. Graft signal and integrity, correct tunnel placement, tunnel widening, and problems with fixation devices or the donor site could all compromise the surgical outcomes and potentially predict the failure of the ACL reconstruction. Furthermore, several anatomical features of the knee could be associated to worst outcomes or higher risk of failure. This review provides a practical guide for the clinician to evaluate the post-surgical ACL through MRI, and to analyze all the parameters and features directly or indirectly related to ACL reconstruction, in order to assess for normal or pathologic conditions.展开更多
In this paper,indirect adaptive state feedback control schemes are developed to solve the robust fault-tolerant control （FTC） design problem of actuator fault and perturbation compensations for linear time-invariant...In this paper,indirect adaptive state feedback control schemes are developed to solve the robust fault-tolerant control （FTC） design problem of actuator fault and perturbation compensations for linear time-invariant systems.A more general and practical model of actuator faults is presented.While both eventual faults on actuators and perturbations are unknown,the adaptive schemes are addressed to estimate the lower and upper bounds of actuator-stuck faults and perturbations online,as well as to estimate control effectiveness on actuators.Thus,on the basis of the information from adaptive schemes,an adaptive robust state feed-back controller is designed to compensate the effects of faults and perturbations automatically.According to Lyapunov stability theory,it is shown that the robust adaptive closed-loop systems can be ensured to be asymptotically stable under the influence of actuator faults and bounded perturbations.An example is provided to further illustrate the fault compensation effectiveness.展开更多
The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the i...The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the idea of expectation by conditioning, special Volterra-type integral equations are derived for general types of repairs, considering the length of repair and reduced degradation of the idle object. In addition to minimal repair and failure replacement, partial repairs are also discussed when the repair results in reduction of the number of future failures or decreases the effective age of the object. Numerical integration-based algorithm and simulation study are performed to solve the resulting integral equation. Since the geometry degradation in different dimensions of a rail track and controlling and maintaining defects are of importance, a numerical example using the rail industry data is conducted. Expected number of failures of different failure type modes in rail track is calculated within a two-year interval. Results show that within a two-year period, anticipated occurrences of cross level failures, surface failures, and DPI failures are 2.4, 3.8, and 5.8, respectively.展开更多
基金Supported by the National Science Council of China (Grant No.50878187)
文摘On May 12, 2008, a strong earthquake with a magnitude of 8.0 (Ms) struck Wenchuan town, in the eastern Sichuan area of west China. Following the earthquake on May 18, the Southwest Jiaotong University organized a damage survey team and dispatched it to the affected area for the investigation into the damage and collection of information and data. This paper outlines the findings of this investigation on the earthquake disaster to mountain tunnels and geotechnical engineering. The systematic investigation, involving geological conditions, design documents, construction and maintenance records of the tunnels, has been conducted and the degree of damage to investigated tunnels has been assessed according to the width and length of cracks, the stability of the slope above the tunnel, and the condition of the groundwater inrush. The results show that the major damage of the mountain tunnels was mainly concentrated in the tunnel portals due to widespread landslides and rockfalls, and the inner part of investigated tunnels suffered moderate damages mainly due to fault displacements. It is hoped that the information shared herein could enhance the outstanding of seismic behavior of mountain tunnels and improve seismic design and construction procedures.
基金Supported by Sao Paulo Research Foundation,FAPESP,No.2008/06972-6The National Council for Scientific and Technological Development,CNPq Nos.579157/2008-3,302768/2009-2 and 473282/2007-0+1 种基金Pesq-Doc scholarship to Dr.Shibli from University of GuaruhosScholarship to Dr.Giro from University of Guarulhos
文摘AIM: To assess the failure and bone-to-implant contact rate of dental implants placed on osteoporotic subjects. METHODS: Extensive examination strategies were created to classify studies for this systematic review. MEDLINE(via Pub Med) and EMBASE database were examined for studies in English up to and including May 2014. The examination presented a combination of the MeS H words described as follow: "osteoporosis" or "osteopenia" or "estrogen deficiency" AND "implant" or "dental implant" or "osseointegration". Assessment of clinical and/or histological peri-implant conditions in osteoporosis subjects treated with titanium dental implants. The examination included a combination of the MeS H terms described as follow: "osteoporosis" or "osteopenia" or "estrogen deficiency" AND "implant" or "dental implant" or "osseointegration".RESULTS: Of 943 potentially eligible articles, 12 were included in the study. A total of 133 subjects with osteoporosis, 73 subjects diagnosed with osteopenia and 708 healthy subjects were assessed in this systematic review. In these subjects were installed 367, 205, 2981 dental implants in osteoporotic, osteopenic and healthy subjects, respectively. The failure rate of dental implant was 10.9% in osteoporotic subjects, 8.29% in osteopenic and 11.43% in healthy ones. Bone-to-implant contact obtained from retrieved implants ranged between 49.96% to 47.84%, for osteoporosis and non-osteoporotic subjects. CONCLUSION: Osteoporotic subjects presented higher rates of implant loss, however, there is a lower evidence to strengthen or refute the hypothesis that osteoporosis may have detrimental effects on bone healing. Consequently, final conclusions regarding the effect of osteoporosis in dental implant therapy cannot be made at this time. There are no randomized clinical trial accessible for evaluation and the retrospectivenature of the evaluated studies shall be taken in account when interpreting this study.
基金supported by the National Natural Science Foundation of China(No. 50478075)the Jiangsu "Six Top Talent" Program of China(No. 07-F-008)+1 种基金the Priority Academic Program Development of Jiangsu Higher Education Institutionsthe Scientific Research Foundation of Graduate School of Southeast University (No. YBJJ0817),China
文摘Alternate path(AP) method is the most widely used method for the progressive collapse analysis,and its application in frame structures has been well proved.However,the application of AP method for other structures,especially for cable-stayed structures,should be further developed.The four analytical procedures,i.e.,linear static,nonlinear static,linear dynamic,and nonlinear dynamic were firstly improved by taking into account the initial state.Then a cable-stayed structure was studied using the four improved methods.Furthermore,the losses of both one cable and two cables were discussed.The results show that for static and dynamic analyses of the cable-stayed bridges,there is large difference between the results obtained from simulations starting with either a deformed or a nondeformed configuration at the time of cable loss.The static results are conservative in the vicinity of the ruptured cable,but the dynamic effect of the cable loss in the area farther away from the loss-cable cannot be considered.Moreover,the dynamic amplification factor of 2.0 is found to be a good estimate for static analysis procedures,since linear static and linear dynamic procedures yield approximately the same maximum vertical deflection.The results of the comprehensive evaluation of the cable failure show that the tread of the progressive failure of the cable-stayed bridges decreases when the location of the failed cables is closer to the pylon.
基金National Science Foundation of China (Grant Nos. 50525721, 50595411)Special Fund of the National Basic Research Program of China (Grant No. G2004CB217900)
文摘This paper makes a comprehensive survey on power system blackout modeling and analysis based on SOC (self-organized criticality). Firstly,a generalized SOC theory from the viewpoint of cybernetics is introduced. Then the evolution model of power system and its relative mathematical description,which serves as a concrete example of the proposed generalized SOC,are given. Secondly,five blackout models capturing various critical properties of power systems in different time-scales are listed. Finally,this paper analyzes SOC in power systems,such as,the revelation of criticalities of proposed models in both micro-scale and macro-scale which can be used to assess the security of power system,and cas-cading failures process.
基金Acknowledgments This work is supported by National Natural Science Foundation of China （No. 71501158 71471146） and ＂the Fundamental Research Funds for the Central Universities＂. The authors would like to thank the referees for their efforts to improve the quality of this paper.
文摘Critical infrastructures are becoming increasingly interdependent and vulnerable to cascading failures. Existing studies have analyzed the vulnerability of interdependent networks to cascading failures from the static perspective of network topology structure. This paper develops a more realistic cascading failures model that considers the dynamic redistribution of load in power network to explore the vulnerability of interdependent power-water networks. In this model, the critical tolerance threshold is originally proposed to indicate the vulnerability of network to cascading failures. In addition, some key parameters that are important to network vulnerability are identified and quantified through numerical simulation. Results show that cascading failures can be prevented when the values of tolerance parameter are above a critical tolerance threshold. Otherwise interdependent networks collapse after attacking a critical fraction of power nodes. Interdependent networks become more vulnerable with the increase in interdependence strength, which implies the importance of protecting those interconnected nodes to reduce the consequences of cascading failures. Interdependent networks are most vulnerable under high-load attack, which shows the significance of protecting high-load nodes.
基金the National Basic Research Program (973) of China (No. 2004CB217902)the National Natural Science Foundation of China (Nos. 60421002 and 60804045)the Postdoctoral Science Foundation of China (No. 20070421163)
文摘The local-world (LW) evolving network model shows a transition for the degree distribution between the exponential and power-law distributions, depending on the LW size. Cascading failures under intentional attacks in LW network models with different LW sizes were investigated using the cascading failures load model. We found that the LW size has a significant impact on the network's robustness against deliberate attacks. It is much easier to trigger cascading failures in LW evolving networks with a larger LW size. Therefore, to avoid cascading failures in real networks with local preferential attachment such as the Internet, the World Trade Web and the multi-agent system, the LW size should be as small as possible.
基金This work was supported by the Chinese National Outstanding Youth Science Foundation (No.69925308).
文摘The problem of robust H-infinity fault-tolerant control against sensor failures for a class of uncertain descriptor systems via dynamical compensators is considered. Based on H-infinity theory in descriptor systems, a sufficient condition for the existence of dynamical compensators with H-infinity fault-tolerant function is derived and expressions for the gain matrices in the compensators are presented. The dynamical compensator guarantees that the resultant colsed-loop system is admissible; furthermore, it maintains certain H-infinity norm performance in the normal condition as well as in the event of sensor failures and parameter uncertainties. A numerical example shows the effect of the proposed method.
基金supported in part by the National Natural Science Foundation of China under Grant 51877018in part by the Natural Science Foundation of Chongqing under Grant cstc2019jcyj-msxmX0321in part by the Graduate Research and Innovation Foundation of Chongqing,China under Grant CYB22019.
文摘The large application of renewable energy generation(REG)has increased the risk of cascading failures in the power system.At the same time REG also provides the possibility of new approaches for the suppression of such failures.However,the capacity and position of the synchronous generator(SG)involved in regulation limit the power regu-lation speed(PRS)of REG to the overload line which is the main cause of cascading failures,while the PRS of SG is related to the position and shedding power.REG and SGs have difficulty in achieving effective cooperation under constraints of system power balance.Particularly,the dynamic variation of line flow during power regulation causes new problems for the accurate evaluation of line thermal safety under overload.Therefore,a new strategy for quan-titatively coordinating shedding power and power regulation to block cascading failures in the dynamic security domain is proposed in this paper.The control capability and dynamic security domain of the overload line are mod-eled,and the coordination control method based on power regulation is then proposed to minimize shedding power.The algorithm for the optimal control scheme considers the constraints of load capacity,power source capacity and bus PRS.The correctness of the proposed method is verified using case studies.
文摘Mg and its alloys evince strong candidature for biodegradable bone implants,cardiovascular stents,and wound closing devices.However,their rapid degradation rate causes premature implant failure,constraining clinical applications.Bio-functional surface coatings have emerged as the most competent strategy to fulfill the diverse clinical requirements,besides yielding effective corrosion resistance.This article reviews the progress of biodegradable and advanced surface coatings on Mg alloys investigated in recent years,aiming to build up a comprehensive knowledge framework of coating techniques,processing parameters,performance measures in terms of corrosion resistance,adhesion strength,and biocompatibility.Recently developed conversion and deposition type surface coatings are thoroughly discussed by reporting their essential therapeutic responses like osteogenesis,angiogenesis,cytocompatibility,hemocompatibility,anti-bacterial,and controlled drug release towards in-vitro and in-vivo study models.The challenges associated with metallic,ceramic and polymeric coatings along with merits and demerits of various coatings have been illustrated.The use of multilayered hybrid coating comprising a unique combination of organic and inorganic components has been emphasized with future perspectives to obtain diverse bio-functionalities in a facile single coating system for orthopedic implant applications.
文摘Anterior cruciate ligament(ACL) reconstruction is one of the most common orthopedic procedures performed worldwide. In this regard, magnetic resonance imaging(MRI) represents a useful pre-operative tool to confirm a disruption of the ACL and to assess for potential associated injuries. However, MRI is also valuable postoperatively, as it is able to identify, in a non-invasive way, a number of aspects and situations that could suggest potential problems to clinicians. Graft signal and integrity, correct tunnel placement, tunnel widening, and problems with fixation devices or the donor site could all compromise the surgical outcomes and potentially predict the failure of the ACL reconstruction. Furthermore, several anatomical features of the knee could be associated to worst outcomes or higher risk of failure. This review provides a practical guide for the clinician to evaluate the post-surgical ACL through MRI, and to analyze all the parameters and features directly or indirectly related to ACL reconstruction, in order to assess for normal or pathologic conditions.
基金supported by the Funds for Creative Research Groups of China(No.60821063)National 973 Program of China(No.2009CB320604)+2 种基金the Funds of National Science of China(No.60974043)the 111 Project(No.B08015)the Fundamental Research Funds for the Central Universities(No.N090604001,N090604002)
文摘In this paper,indirect adaptive state feedback control schemes are developed to solve the robust fault-tolerant control （FTC） design problem of actuator fault and perturbation compensations for linear time-invariant systems.A more general and practical model of actuator faults is presented.While both eventual faults on actuators and perturbations are unknown,the adaptive schemes are addressed to estimate the lower and upper bounds of actuator-stuck faults and perturbations online,as well as to estimate control effectiveness on actuators.Thus,on the basis of the information from adaptive schemes,an adaptive robust state feed-back controller is designed to compensate the effects of faults and perturbations automatically.According to Lyapunov stability theory,it is shown that the robust adaptive closed-loop systems can be ensured to be asymptotically stable under the influence of actuator faults and bounded perturbations.An example is provided to further illustrate the fault compensation effectiveness.
文摘The repeated failures of any equipment or systems are modeled as a renewal process. The management needs an assessment of the number of future failures to allocate the resources needed for fast repairs. Based on the idea of expectation by conditioning, special Volterra-type integral equations are derived for general types of repairs, considering the length of repair and reduced degradation of the idle object. In addition to minimal repair and failure replacement, partial repairs are also discussed when the repair results in reduction of the number of future failures or decreases the effective age of the object. Numerical integration-based algorithm and simulation study are performed to solve the resulting integral equation. Since the geometry degradation in different dimensions of a rail track and controlling and maintaining defects are of importance, a numerical example using the rail industry data is conducted. Expected number of failures of different failure type modes in rail track is calculated within a two-year interval. Results show that within a two-year period, anticipated occurrences of cross level failures, surface failures, and DPI failures are 2.4, 3.8, and 5.8, respectively.
