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While steady-state analysis is useful, it does not consider the inherent transient characteristics of repairable systems' behavior, especially in systems that have relatively short life spans, or when their transient behavior is of special concern such as the motivating example used in this paper, military systems. Therefore, a maintenance policy that considers both transient and steady-state availability and aims to achieve the best trade-off between high steady-state availability and rapid stabilization is essential.

This paper studies the transient behavior of system availability under the Kijima Type II virtual age model. While such systems achieve steady-state availability, and it has been proved that deploying preventive maintenance (PM) can significantly improve its steady-state availability, this improvement often comes at the price of longer and increased fluctuating transient behavior, which affects overall system performance. The authors present a methodology that identifies the optimal PM policy that achieves the best trade-off between high steady-state availability and rapid stabilization based on cost-availability analysis.

When the proposed simulation-based optimization and cost analysis methodology is applied to the motivating example, it produces an optimal PM policy that achieves an availability–variability balance between transient and steady-state system behaviors. The optimal PM policy produces a notably lower availability coefficient of variation (by 11.5%), while at the same time suffering a negligible limiting availability loss of only 0.3%. The new optimal PM policy also provides cost savings of about 5% in total maintenance cost. The performed sensitivity analysis shows that the system's optimal maintenance cost is sensitive to the repair time, the shape parameter of the Weibull distribution and the downtime cost, but is robust with respect to changes in the remaining parameters.

Most of the current maintenance models emphasize the steady-state behavior of availability and neglect its transient behavior. For some systems, using steady-state availability as the sole metric for performance is not adequate, especially in systems that have relatively short life spans or when their transient behavior affects the overall performance. However, little work has been done on the transient analysis of such systems. In this paper, the authors aim to fill this gap by emphasizing such systems and applications where transient behavior is of critical importance to efficiently optimize system performance. The authors use military systems as a motivating example.

The purpose of this paper is to apply asymptotic waveform evaluation (AWE) to the transient analysis of a two‐layered counter‐flow microchannel heat sink.

A two‐layered counter‐flow microchannel heat sink in both steady state and transient conditions is analysed. Finite element analysis is used in the steady state analysis whereas AWE is used in the transient analysis.

A two‐layered microchannel produces different temperature distribution compared to that obtained for a single‐layered microchannel. The maximum temperature occurs at the middle of the bottom wall whereas the maximum temperature of a single‐layered microchannel is at the outlet of the bottom wall. The time taken to reach steady state is also investigated for different coolant flow rate and heat flux boundary conditions. It is observed that when fluid velocity increases, the time taken to reach steady state decreases, however, when the heat flux increases, the time taken to reach steady state does not change.

The fluid is incompressible and does not undergo phase change. The use of AWE provides an alternative method in solving heat transfer problem.

New and additional data will be useful in the design of a microchannel heat sink for the purpose of cooling of electronic components.

AWE is widely used in analyses of signal delays in electronic circuits, and rarely applied to mechanical systems. The present study applies AWE to heat transfer problems, and reveals that it reduces the computational time considerably. The results obtained are compared with conventional methods available in the literature, and they show good agreement. Hence the computational time is reduced, and the accuracy of results is verified.

We extend the Jones (1971) analysis of the effects of distortions in 2×2 trade models to the case of a two-sector dynamic general equilibrium model of a small open economy with capital accumulation. We do a comparative steady state analysis for the effect of policy changes on factor prices and the capital stock, and examine the dynamics of the system in the neighborhood of the steady state. We also show that the system will have multiple equilibria when value and physical factor intensity rankings of the sectors do not agree.

The purpose of this paper is to present the Galerkin method for analysis of steady-state processes in periodically time-varying circuits.

A converter circuit working on a time-varying load is often controlled by different signals. In the case of incommensurable frequencies, one can find a steady-state process only via calculation of a transient process. As the obtained results will not be periodical, one must repeat this procedure to calculate the steady-state process on a different time interval. The proposed methodology is based on the expansion of ordinary differential equations with one time variable into a domain of two independent variables of time. In this case, the steady-state process will be periodical. This process is calculated by the use of the Galerkin method with bases and weight functions in the form of the double Fourier series.

Expansion of differential equations and use of the Galerkin method enable discovery of the steady-state processes in converter circuits. Steady-state processes in the circuits of buck and boost converters are calculated and results are compared with numerical and generalized state-space averaging methods.

The Galerkin method is used to find a steady-state process in a converter circuit with a time-varying load. Processes in such a load depend on two incommensurable signals. The state-space averaging method is generalized for extended differential equations. A balance of active power for extended equations is shown.

The purpose of this paper is to propose a new method for mathematical modeling of the buck dc‐dc converter in discontinuous conduction mode (DCM). By using the presented modeling method, the analysis of the transient and the steady states of the buck dc‐dc converter can be performed.

The proposed method is based on the two Laplace and Z transforms. In the proposed method, at first, the equations of the inductor current and the capacitor voltage are obtained as the power switch is on and off. Then by using the Laplace and Z transforms, the obtained equations are solved and the relations of the inductor current and the output voltage are obtained. In the proposed method, the Laplace transform is used for determining of the general relations of the inductor current and the output voltage. Also the Z‐transform is used as a tool for determining the initial values of the inductor current and the output voltage.

The transient and the steady state response of the dc‐dc converter is analyzed by the proposed method. By using the Z‐transform, the transient response of the converter and the effect of the elements of the converter on the time constant of the transient response are investigated. In addition, the effect of the elements of the converter and the load resistance on the electrical parameters of the converter such as the output voltage ripple and the inductor current ripple are investigated.

The proposed method in this paper is a suitable method for mathematical modeling of dc‐dc converters. The acernote of this method is that it can be used in both transient and steady state response, analysis of the dc‐dc converters. By using the final value theorem of the Z‐transform, the steady state response of the converter is investigated. Also by using this transform, the time constants of the transient response of the converter are determined. Finally, the results of the theoretical analysis are compared with the results of simulation in PSCAD/EMTDC and also the experimental results to prove the validity of the presented subjects.

The purpose of this paper is to investigate the steady‐state stability and features of the brushless cascaded doubly fed machine (BCDFM), which is made up of two wound‐rotor induction machines: the power machine (PM) and the control one, with their rotors mechanically and electrically coupled.

The machine modelling is first treated considering a Park reference frame linked to the rotating field of the PM. Then, a state representation related to small perturbations is established following the linearisation of the BCDFM model around a steady‐state operating point. This allows the investigation of BCDFM steady‐state stability, power flow and the torque‐speed characteristics.

It has been found that the electrical variables of the control machine greatly affect the BCDFM steady‐state stability and characteristics.

The work should be extended considering a validation of the established results through experimental tests.

The steady‐state small perturbation of the BCDFM model has been introduced for the first time, which is the key of the machine steady‐stability analysis and features investigation.

The purpose of this paper is to propose a novel hybrid approach called as Markov System Dynamics (MSD) approach which combines the Markov approach with system dynamics (SD) simulation approach for availability modeling and to study the dynamic behavior of repairable systems.

In the proposed approach the identification of the single unit repairable system all possible states has been performed by using the Markov approach. The remaining stages of traditional Markov analysis are highly mathematically intensive. The present work proposes a hybrid approach called as MSD approach which combines the Markov approach with SD simulation approach to overcome some of the limitations of Markov process in a simple and efficient way for availability modeling and to study the dynamic behavior of this system.

The proposed framework is illustrated for a single unit repairable system. The worked out example shows the steady state point and also it gives the point, interval and steady state availabilities and also the dynamic behavior of the system. However this methodology can be extended easily for more complex multi-state maintainable systems. The results of the simulation when compared with that obtained by traditional Markov analysis clearly validate the proposed approach as an alternative approach for availability modeling of repairable systems.

In many practical situations we require to find the time at which our system reaches steady state conditions for planning maintenance activities. The proposed MSD method in this paper is capable of finding this steady state point very easily.

The proposed approach clearly indicates the time at which the system reaches its steady state and calculates the point, interval availabilities for planning maintenance activities. The different parties, i.e., engineers and machine operators, can jointly work with this model in order to understand the dynamic behavior of repairable systems.

The purpose of this study is to identify a novel methodology for direct calculation of steady-state periodic solutions for electrical circuits described by nonlinear differential equations, in the time domain.

An iterative algorithm was created to determine periodic steady-state solutions for circuits with nonlinear elements in a chosen set of time instants.

This study found a novel differential operator for periodic functions and its application in the steady-state analysis.

This approach can be extended to the determination of two- or multi-periodic solutions of nonlinear dynamic systems.

The complexity of the steady-state analysis can be reduced in comparison with the frequency-domain approach.

This study identified novel difference equations for direct steady-state analysis of nonlinear electrical circuits.

The paper seeks to investigate the effect of the rotor‐phase sequence connection on the steady‐state stability of the brushless cascaded doubly‐fed machine (BCDFM). The stability analysis is carried out considering the eigenvalue method.

The BCDFM includes a two wound‐rotor induction machines: a power machine cascaded to a control one. The BCDFM modeling is firstly treated considering a Park reference frame linked to the rotating field of the power machine, and for both rotor‐phase sequence connections. Then, a state representation related to small perturbations is established following the linearisation of the BCDFM model around a steady‐state operating point. This allows the investigation of the BCDFM steady‐state stability and efficiency.

It has been found that the electrical variables of the control machine power supply greatly affect the BCDFM steady‐state stability and efficiency.

The work should be extended considering a validation of the established results through experimental tests.

The small perturbation model of the BCDFM has been introduced for the first time which is the key of the machine steady‐state stability analysis and efficiency investigation.

This paper aims to omit the difficulties of directly finding the periodic steady-state solutions for electromagnetic devices described by circuit models.

Determine the discrete integral operator of periodic functions and develop an iterative algorithm determining steady-state solutions by a multiplication of matrices only.

An alternative method to creating finite-difference relations directly determining steady-state solutions in the time domain.

Reduction of software and hardware requirements for determining steady-states of electromagnetic.

A unified approach for directly finding steady-state solutions for ordinary nonlinear differential equations presented in the normal form.

Eliminate the necessity of solving high-order finite-difference equations for steady-state analysis of electromagnetic devices described by circuit models.