A Bayesian approach based on the vulnerability distribution is proposed to estimate the confidence limits of the state probability and the threat level of multistate electronic systems interfered by intentional electromagnetic interference (IEMI). The vulnerability distribution is used to describe the state probability function of the multi-state system (MSS) for a given IEMI threat level. When a small number of test samples are under a specific threat level and prior MSS information is known, the posterior estimation of the state probability function can be obtained based on Bayesian theory. Furthermore, to effectively apply the state probability function to assess the vulnerability of the MSS, the uncertainty of the state probability function is discussed. Considering state probabilities under the same threat level as random variables, all these state probabilities also follow the Dirichlet distribution. Thus, the confidence limits of the posteriori state probability and the threat level can be inferred by the marginal distribution of the state probability, which is induced by combining the Dirichlet and vulnerability distributions. Finally, a case study is given to demonstrate the details of the calculation process of the vulnerability distribution, the state probability function, and the confidence limits under a lognormal distribution.

This paper presents a compensated algorithm for accurate evaluation of a polynomial in Legendre basis. Since the coefficients of the evaluated polynomial are fractions, we propose to store these coefficients in two floating point numbers, such as double-double format, to reduce the effect of the coefficients’ perturbation. The proposed algorithm is obtained by applying error-free transformation to improve the Clenshaw algorithm. It can yield a full working precision accuracy for the ill-conditioned polynomial evaluation. Forward error analysis and numerical experiments illustrate the accuracy and efficiency of the algorithm.

The health of aero-engines is pivotal to the safe operation of aircraft. With increasing service time, the internal components of the engine will be damaged by threats from different sources, so it is necessary to regularly detect the damage inside the engine. At present, most of the detection methods of major airlines rely on the internal images of the engine obtained by manual use of a borescope to detect damage or traditional machine learning methods, which consume high levels of human and computational resources but have low efficiency. Artificial intelligence in various fields can achieve better performance than traditional methods, but to achieve the industrialization standard of Green AI, we need further research. Accordingly, we introduce a multi-layer contrastive learning method to a lightweight target detection model design, which is applied to real aero-engine borescope images of complex components to accomplish real-time damage detection. We intensively conduct comparative experiments to evaluate the effectiveness of our method. The verification results demonstrate that the method can help our model perform excellently compared with other available baseline models.

The Horner and Goertzel algorithms are frequently used in polynomial evaluation. Each of them can be less expensive than the other in special cases. In this paper, we present a new compensated algorithm to improve the accuracy of the Goertzel algorithm by using error-free transformations. We derive the forward round-off error bound for our algorithm, which implies that our algorithm yields a full precision accuracy for polynomials that are not too ill-conditioned. A dynamic error estimate in our algorithm is also presented by running round-off error analysis. Moreover, we show the cases in which our algorithms are less expensive than the compensated Horner algorithm for evaluating polynomials. Numerical experiments indicate that our algorithms run faster than the compensated Horner algorithm in those cases while producing the same accurate results, and our algorithm is absolutely stable when the condition number is smaller than ${10}^{16}$. An application is given to illustrate that our algorithm is more accurate than MATLAB’s $\mathtt{fft}$ function. The results show that the relative error of our algorithm is from ${10}^{15}$ to ${10}^{17}$, and that of the $\mathtt{fft}$ was from ${10}^{12}$ to ${10}^{15}$.