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The purpose of this paper is to evaluate the worst-case behavior of a given electronic circuit by varying the values of the components in a meaningful way in order not to exceed pre-defined currents or voltages limits during a transient operation.

An analytic formulation is used to identify the time-dependent solution of voltages or currents using proper state equations in closed form. Circuits with linear elements can be described by a system of differential equations, while circuits composing nonlinear elements are described by piecewise-linear models. A sequential quadratic program (SQP) is used to find the worst-case scenario.

It is found that the worst-case scenario can be obtained with as few solutions to the forward problem as possible by applying an SQP method.

The SQP method in combination with the analytic forward solver approach shows that the worst-case limit converges in a few steps even if the worst-case limit is not on the boundary of the parameters.

Integrated modular avionics (IMA) aims to provide highly flexible, reliable and integrated solutions for future aircraft systems which can readily exploit new advances in processor and networking technologies. In this paper, we discuss the problems involved in the provision of appropriate scheduling and timing analysis techniques for IMA systems and suggest a potential solution.

The collapse of a structure resulting from the instability of steel frames due to fire is the worst failure mode to consider in fire-structural engineering, and should be avoided. The purpose of this paper is to propose a new method for estimating the minimum possible duration of a fire event that could result in the instability of an unbraced steel frame.

The proposed method is in the form of a constrained minimization problem that determines the worst case fire scenario that can cause instability of a structure, and is solved using nonlinear constrained mathematical programming algorithms. The formulation is demonstrated via a numerical example.

For frames subjected to fire events modelled with monotonically increasing fire curves, the worst case fire causing instability of a frame is always one where all of the compartments catch fire at the same time. For frames subjected to fire events where fire curves decay, the minimization problem must be solved rigorously. The results are significantly affected by the fire curves and amount of insulation applied to each member.

The proposed method is an extension of a method previously established by Xu et al. (2018) to assess the stability of unbraced steel frames subjected to elevated member temperatures. The previous method does not consider fire duration and heat transfer mechanics, which are included in the proposed method. The proposed method is potentially useful for designers in conducting fire scenario analysis in the performance-based design of structures.

Maximum Loss was one of the risk measures proposed as alternatives to Value at Risk following criticism that Value at Risk is not coherent. Although the power of Maximum Loss is recognised for non‐linear portfolios, there are arguments that for linear portfolios Maximum Loss does not convey more information than Value at Risk. This paper argues for the usefulness of Maximum Loss for both linear and non‐linear portfolios.

This is a synthesis of existing theorems. Results are established by means of counterexamples. The worst case based risk‐return management strategy is presented as a case study.

For linear portfolios under elliptic distributions Maximum Loss is proportional to Value at Risk, and to Expected Shortfall, with the proportionality constant not depending on the portfolio composition. The paper gives a new example of Value at Risk violating subadditivity, using a portfolio of simple European options. For non‐linear portfolios, Maximum Loss need not even approximately be explained by the sum of Maximum Loss contributions of the individual risk factors. Finally, is proposed a strategy of risk‐return management with Maximum Loss.

The paper is restricted to elliptically distributed risk factors. Although Maximum Loss can be defined for more general continuous and even discrete distributions of risk factor changes, the paper does not address this matter.

The paper proposes an intuitive, computationally easy way how to improve average returns of linear portfolios while reducing worst case losses.

One is a synthesis of existing theorems. The counterexample establishing result is the first example of a portfolio of plain vanilla options violating Value at Risk subadditivity, an effect hitherto only known for portfolios of exotic options. Furthermore, the strategy of risk‐return management with Maximum Loss is original.

Manufacturing processes, such as laminations, may introduce uncertainties in the magnetic properties of materials used in electrical machines. This issue, together with magnetization errors, can cause serious deterioration in the performance of the machines. Hence, stochastic material models are required for the study of the influences of the material uncertainties. The purpose of this paper is to present a methodology to study the impact of magnetization pattern uncertainties in permanent magnet electric machines.

The impacts of material uncertainties on the performances of an interior permanent magnet (IPM) machine were analyzed using two different robustness metrics (worst-case analysis and statistical study). In addition, two different robust design formulations were applied to robust multi-objective machine design problems.

The computational analyses show that material uncertainties may result in deviations of the machine performances and cause nominal solutions to become non-robust.

In this paper, the authors present stochastic models for the quantification of uncertainties in both ferromagnetic and permanent magnet materials. A robust multi-objective evolutionary algorithm is demonstrated and successfully applied to the robust design optimization of an IPM machine considering manufacturing errors and operational condition changes.

Robust design is very important for manufacturers to ensure the quality of the finished product. Therefore, a robustness measure is needed for the topological design of electromagnetic problems which may be sensitive to parameter variations. The purpose of this paper is to propose a robust objective function for topological design problems.

In this paper, a robust objective function for topology optimization is defined on an uncertainty set using the worst case analysis. The robustness of a topological design is defined as the worst response due to the variations of the location of the topology change. The approach is based on the definition of a topological gradient.

The robust topology optimization (RTO) was applied to eddy current crack reconstruction problems. The numerical applications showed that this method can provide more reliable results for the reconstruction in the presence of significant noise in the measured signal.

The RTO may be applied to some more complicated design problems; however large computational costs may result.

This paper has defined a robustness metric for topology design and a robust design model is proposed for topology optimization problems.

The purpose of this study is to analyze direct current (DC) drive stability, including parameter uncertainty and perturbation in the feedback loop, by computing disk margins.

Although the closed-loop stability analysis of a DC drive has been presented well in the referenced papers, the effect of parameter uncertainty and perturbation in the feedback loop has not yet been discussed well. In this study, the conventional and disk-based stability margins were measured and compared for the nominal parameters of the DC drive. Subsequently, the smallest disk-based margins that destabilize the feedback loop for a given perturbation are computed and compared with normal disk margins.

The disk-based margin offered by the DC drive controlled by the JAYA-PID controller is disk gain margins (DGM) = 8.41 dB and disk phase margin (DPM) = 48.410 and the smallest disk-based margin offered is DGM = 1.51 dB and DPM = 9.950. In addition, the effect of the modeled uncertainty on the disk stability margins was analyzed, and it was observed that the maximum allowable parameter uncertainty with the JAYA controller was 73% of its nominal parameters. The simulation results were validated using an experimental testbed.

This research work is not published anywhere else.

To study the effect of Knightian uncertainty – as opposed to statistical estimation error – in the evaluation of value‐at‐risk (VaR) of financial investments. To develop methods for augmenting existing VaR estimates to account for Knightian uncertainty.

The value at risk of a financial investment is assessed as the quantile of an estimated probability distribution of the returns. Estimating a VaR from historical data entails two distinct sorts of uncertainty: probabilistic uncertainty in the estimation of a probability density function (PDF) from historical data, and non‐probabilistic Knightian info‐gaps in the future size and shape of the lower tail of the PDF. A PDF is estimated from historical data, while a VaR is used to predict future risk. Knightian uncertainty arises from the structural changes, surprises, etc., which occur in the future and therefore are not manifested in historical data. This paper concentrates entirely on Knightian uncertainty and does not consider the statistical problem of estimating a PDF. Info‐gap decision theory is used to study the robustness of a VaR to Knightian uncertainty in the distribution.

It is shown that VaRs, based on estimated PDFs, have no robustness to Knightian errors in the PDF. An info‐gap safety factor is derived that multiplies the estimated VaR in order to obtain a revised VaR with specified robustness to Knightian error in the PDF. A robustness premium is defined as a supplement to the incremental VaR for comparing portfolios.

The revised VaR and incremental VaR augment existing tools for evaluating financial risk.

Info‐gap theory, which underlies this paper, is a non‐probabilistic quantification of uncertainty that is very suitable for representing Knightian uncertainty. This enables one to assess the robustness to future surprises, as distinct from existing statistical techniques for assessing estimation error resulting from randomness of historical data.

The purpose of this paper is to present a methodology for the automated design of a fixturing system for a rapid machining process.

The method proposed is the use of sacrificial fixturing, similar to the support structures in existing rapid prototyping (RP) processes. During the machining process, sacrificial supports emerge incrementally and, at the end of the process, are the only entities connecting the part to the remaining stock material.

The support design methods have been shown to be extremely flexible in securing a variety of complex parts with relatively tight part tolerances using a rapid machining process.

The automated design of support structures is currently relegated to use in a CNC rapid prototyping process that uses a fourth axis for rotary setups.

The methods used here make rapid machining feasible, as it solves the daunting problem of automated fixturing.

The paper proposes an innovative solution for an automatic fixturing system in subtractive RP.

This study aims to form a new concept of power-to-gas-based virtual power plant (GVPP) and propose a low-carbon economic scheduling optimization model for GVPP considering carbon emission trading.

In view of the strong uncertainty of wind power and photovoltaic power generation in GVPP, the information gap decision theory (IGDT) is used to measure the uncertainty tolerance threshold under different expected target deviations of the decision-makers. To verify the feasibility and effectiveness of the proposed model, nine-node energy hub was selected as the simulation system.

GVPP can coordinate and optimize the output of electricity-to-gas and gas turbines according to the difference in gas and electricity prices in the electricity market and the natural gas market at different times. The IGDT method can be used to describe the impact of wind and solar uncertainty in GVPP. Carbon emission rights trading can increase the operating space of power to gas (P2G) and reduce the operating cost of GVPP.

This study considers the electrical conversion and spatio-temporal calming characteristics of P2G, integrates it with VPP into GVPP and uses the IGDT method to describe the impact of wind and solar uncertainty and then proposes a GVPP near-zero carbon random scheduling optimization model based on IGDT.

This study designed a novel structure of the GVPP integrating P2G, gas storage device into the VPP and proposed a basic near-zero carbon scheduling optimization model for GVPP under the optimization goal of minimizing operating costs. At last, this study constructed a stochastic scheduling optimization model for GVPP.