The Galerkin finite element approximation of the fractional cable equation

The cable equation is one of the most fundamental equations for modeling neuronal dynamics. Cable equations with a fractional order temporal derivative have been introduced to model electrotonic properties of spiny neuronal dendrites. In this paper, the fractional cable equation involving two integro-differential operators is considered. The Galerkin finite element approximations of the fractional cable equation are proposed. The main contribution of this work is outlined as follow: • A semi-discrete finite difference approximation in time is proposed. We prove that the scheme is unconditionally stable, and the numerical solution converges to the exact solution with order O(Δt). • A semi-discrete difference scheme for improving the order of convergence for solving the fractional cable equation is proposed, and the numerical solution converges to the exact solution with order O((Δt)2). • Based on the above semi-discrete difference approximations, Galerkin finite element approximations in space for a full discretization are also investigated. • Finally, some numerical results are given to demonstrate the theoretical analysis.

Evaluation of precision time synchronisation methods for substation applications

Many substation applications require accurate time-stamping. The performance of systems such as Network Time Protocol (NTP), IRIG-B and one pulse per second (1-PPS) have been sufficient to date. However, new applications, including IEC 61850-9-2 process bus and phasor measurement, require accuracy of one microsecond or better. Furthermore, process bus applications are taking time synchronisation out into high voltage switchyards where cable lengths may have an impact on timing accuracy. IEEE Std 1588, Precision Time Protocol (PTP), is the means preferred by the smart grid standardisation roadmaps (from both the IEC and US National Institute of Standards and Technology) of achieving this higher level of performance, and integrates well into Ethernet based substation automation systems. Significant benefits of PTP include automatic path length compensation, support for redundant time sources and the cabling efficiency of a shared network. This paper benchmarks the performance of established IRIG-B and 1-PPS synchronisation methods over a range of path lengths representative of a transmission substation. The performance of PTP using the same distribution system is then evaluated and compared to the existing methods to determine if the performance justifies the additional complexity. Experimental results show that a PTP timing system maintains the synchronising performance of 1-PPS and IRIG-B timing systems, when using the same fibre optic cables, and further meets the needs of process buses in large substations.

Compensation for lost services of an employee : pure economic loss and per quod action

Under the common law an employer may take action against a defendant for the loss of an employee’s services due to the act of the defendant (per quod servitium amisit - by reason of which the services were lost). The High Court has recently affirmed the existence of this ancient tort in Barclay v Penberthy [2012] HCA 40.

Underground power cable environment on-line monitoring and analysis

Knowledge of cable parameters has been well established but a better knowledge of the environment in which the cables are buried lags behind. Research in Queensland University of Technology has been aimed at obtaining and analysing actual daily field values of thermal resistivity and diffusivity of the soil around power cables. On-line monitoring systems have been developed and installed with a data logger system and buried spheres that use an improved technique to measure thermal resistivity and diffusivity over a short period. Results based on long term continuous field data are given. A probabilistic approach is developed to establish the correlation between the measured field thermal resistivity values and rainfall data from weather bureau records. This data from field studies can reduce the risk in cable rating decisions and provide a basis for reliable prediction of “hot spot” of an existing cable circuit

Probabilistic cable rating based on cable thermal environment studying

This paper describes a new approach to establish the probabilistic cable rating based on cable thermal environment studies. Knowledge of cable parameters has been well established. However the environment in which the cables are buried is not so well understood. Research in Queensland University of Technology has been aimed at obtaining and analysing actual daily field values of thermal resistivity and diffusivity of the soil around power cables. On-line monitoring systems have been developed and installed with a data logger system and buried spheres that use an improved technique to measure thermal resistivity and diffusivity over a short period. Based on the long-term continuous field data for more than 4 years, a probabilistic approach is developed to establish the correlation between the measured field thermal resistivity values and rainfall data from weather bureau records. Hence, a probabilistic cable rating can be established based on monthly probabilistic distribution of thermal resistivity

PV string per-module maximum power point enabling converters

Many grid connected PV installations consist of a single series string of PV modules and a single DC-AC inverter. This efficiency of this topology can be enhanced with additional low power, low cost per panel converter modules. Most current flows directly in the series string which ensures high efficiency. However parallel Cúk or buck-boost DC-DC converters connected across each adjacent pair of modules now support any desired current difference between series connected PV modules. Each converter “shuffles” the desired difference in PV module currents between two modules and so on up the string. Spice simulations show that even with poor efficiency, these modules can make a significant improvement to the overall power which can be recovered from partially shaded PV strings.

Damage detection in cable structures using vibration characteristics

Cable structures find many applications such as in power transmission, in anchors and especially in bridges. They serve as major load bearing elements in suspension bridges, which are capable of spanning long distances. All bridges, including suspension bridges, are designed to have long service lives. However, during this long life, they become vulnerable to damage due to changes in loadings, deterioration with age and random action such as impacts. The main cables are more vulnerable to corrosion and fatigue, compared to the other bridge components, and consequently reduces the serviceability and ultimate capacity of the bridge. Detecting and locating such damage at the earliest stage is challenging in the current structural health monitoring (SHM) systems of long span suspension bridges. Damage or deterioration of a structure alters its stiffness, mass and damping properties which in turn modify its vibration characteristics. This phenomenon can therefore be used to detect damage in a structure. The modal flexibility, which depends on the vibration characteristics of a structure, has been identified as a successful damage indicator in beam and plate elements, trusses and simple structures in reinforced concrete and steel. Successful application of the modal flexibility phenomenon to detect and locate the damage in suspension bridge main cables has received limited attention in recent research work. This paper, therefore examines the potential of the modal flexibility based Damage Index (DI) for detecting and locating damage in the main cable of a suspension bridge under four different damage scenarios. Towards this end, a numerical model of a suspension bridge cable was developed to extract the modal parameters at both damaged and undamaged states. Damage scenarios considered in this study with varied location and severity were simulated by changing stiffness at particular locations of the cable model. Results confirm that the DI has the potential to successfully detect and locate damage in suspension bridge main cables. This simple method can therefore enable bridge engineers and managers to detect and locate damage in suspension bridges at an early stage, minimize expensive retrofitting and prevent bridge collapse.

Second-order elastic finite element analysis of steel structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included. The accuracy and efficiency of the technique is verified by comparisons with a number of plane and spatial structures, whose structural response has been reported in independent studies.

Second-order elastic finite element analysis of structures using a single element per member

Finite element frame analysis programs targeted for design office application necessitate algorithms which can deliver reliable numerical convergence in a practical timeframe with comparable degrees of accuracy, and a highly desirable attribute is the use of a single element per member to reduce computational storage, as well as data preparation and the interpretation of the results. To this end, a higher-order finite element method including geometric non-linearity is addressed in the paper for the analysis of elastic frames for which a single element is used to model each member. The geometric non-linearity in the structure is handled using an updated Lagrangian formulation, which takes the effects of the large translations and rotations that occur at the joints into consideration by accumulating their nodal coordinates. Rigid body movements are eliminated from the local member load-displacement relationship for which the total secant stiffness is formulated for evaluating the large member deformations of an element. The influences of the axial force on the member stiffness and the changes in the member chord length are taken into account using a modified bowing function which is formulated in the total secant stiffness relationship, for which the coupling of the axial strain and flexural bowing is included.

Planes, trains, automobiles and the action per quod servitium amisit

The action per quod servitium amisit compensates an employer for the loss of an employee’s services, where such loss is caused due to the commission of a tort by a third party which injures the employee. Although not commonly pleaded, such actions often arise when employees are harmed due to transportation accidents. For example, where allowed, physical injury caused by the negligent driving of automobiles, and the psychiatric injury suffered by an engine driver upon averting a collision with a motorcyclist crossing before an oncoming train...

Eclectic blend somehow makes sense at Cable Beach Resort in Broome

A travel article about Cable Beach, Broome. A DAY of flights, confined spaces and queues comes to an end. I'm more tired than when my kids were infants. I've lost all sensation in my knees. And I'm thinking that perhaps I should have taken my wallet out my back pocket. In the course of a day's sitting, it seems to have indented a deep square into my right buttock...

Structural damage alarming and localization of cable-supported bridges using multi-novelty indices: A feasibility study

This paper presents a feasibility study on structural damage alarming and localization of long-span cable-supported bridges using multi-novelty indices formulated by monitoring-derived modal parameters. The proposed method which requires neither structural model nor damage model is applicable to structures of arbitrary complexity. With the intention to enhance the tolerance to measurement noise/uncertainty and the sensitivity to structural damage, an improved novelty index is formulated in terms of auto-associative neural networks (ANNs) where the output vector is designated to differ from the input vector while the training of the ANNs needs only the measured modal properties of the intact structure under in-service conditions. After validating the enhanced capability of the improved novelty index for structural damage alarming over the commonly configured novelty index, the performance of the improved novelty index for damage occurrence detection of large-scale bridges is examined through numerical simulation studies of the suspension Tsing Ma Bridge (TMB) and the cable-stayed Ting Kau Bridge (TKB) incurred with different types of structural damage. Then the improved novelty index is extended to formulate multi-novelty indices in terms of the measured modal frequencies and incomplete modeshape components for damage region identification. The capability of the formulated multi-novelty indices for damage region identification is also examined through numerical simulations of the TMB and TKB.

Statistical, electrical and mathematical analysis of water treed cross-linked polyethylene cable insulation

This work examined a new method of detecting small water filled cracks in underground insulation ('water trees') using data from commecially available non-destructive testing equipment. A testing facility was constructed and a computer simulation of the insulation designed in order to test the proposed ageing factor - the degree of non-linearity. This was a large industry-backed project involving an ARC linkage grant, Ergon Energy and the University of Queensland, as well as the Queensland University of Technology.

Use of modal flexibility method to detect damage in suspended cables and the effects of cable parameters

Modal flexibility is a widely accepted technique to detect structural damage using vibration characteristics. Its application to detect damage in long span large diameter cables such as those used in suspension bridge main cables has not received much attention. This paper uses the modal flexibility method incorporating two damage indices (DIs) based on lateral and vertical modes to localize damage in such cables. The competency of those DIs in damage detection is tested by the numerically obtained vibration characteristics of a suspended cable in both intact and damaged states. Three single damage cases and one multiple damage case are considered. The impact of random measurement noise in the modal data on the damage localization capability of these two DIs is next examined. Long span large diameter cables are characterized by the two critical cable parameters named bending stiffness and sag-extensibility. The influence of these parameters in the damage localization capability of the two DIs is evaluated by a parametric study with two single damage cases. Results confirm that the damage index based on lateral vibration modes has the ability to successfully detect and locate damage in suspended cables with 5% noise in modal data for a range of cable parameters. This simple approach therefore can be extended for timely damage detection in cables of suspension bridges and thereby enhance their service during their life spans.