Search Results (10)

Time-dependent reliability analysis (TRA) is essential for the life-cycle risk assessment of engineering systems. However, existing TRA methods often require extensive statistical data or computationally expensive surrogate models, which limit their applicability under sparse sampling conditions. This paper presents a novel TRA framework that integrates probability-weighted moments (PWMs), a maximum entropy-based quantile function, and a fourth-order moment saddle-point approximation (FMSPA). The PWM method provides asymptotically unbiased moment estimates for small samples, while the maximum entropy-based quantile function directly computes the first four central moments of random variables. Subsequently, the FMSPA method is extended for use in TRA to efficiently evaluate the cumulative failure probability at each time point. The effectiveness of the proposed method is demonstrated through three engineering examples. The results indicate that the method delivers accurate and efficient TRA under sparse sampling conditions. Full article

The negative multinomial distribution appears in many areas of applications such as polarimetric image processing and the analysis of longitudinal count data. In previous studies, general formulas for the falling factorial moments and cumulants of the negative multinomial distribution were obtained. However, despite the availability of the moment generating function, no comprehensive formulas for the moments have been calculated thus far. This paper addresses this gap by presenting general formulas for both central and non-central moments of the negative multinomial distribution. These formulas are expressed in terms of binomial coefficients and Stirling numbers of the second kind. Utilizing these formulas, we provide explicit expressions for all central moments up to the fourth order and all non-central moments up to the eighth order. Full article

Moment-based methods can measure the safety degrees of mechanical systems affected by unavoidable uncertainties, utilizing only the statistical moments of random variables for reliability analysis. For the conventional derivation of the first four statistical moments based on the second-order Taylor expansion series evaluated at the most likelihood point (MLP), skewness and kurtosis involve the higher fourth raw moments of random variables and thus are unfavorable for engineering applications. This paper develops new computing formulae for the first four statistical moments which require only the first four central moments of random variables, and the probability distribution of the performance function is approximated using cubic normal transformation. Several numerical examples are given to demonstrate the accuracy of the proposed methods. Comparisons of the two proposed approaches and the maximum entropy method (ME) are also made regarding reliability assessment. Full article

In this paper, we define a new Kantorovich-type $\left(p,q\right)$-generalization of the Balázs–Szabados operators. We derive a recurrence formula, and with the help of this formula, we give explicit formulas for the first and second-order moments, which follow a symmetric pattern. We estimate the second and fourth-order central moments. We examine the local approximation properties in terms of modulus of continuity, we give a Voronovskaja type theorem, and we give the weighted approximation properties of the operators. Full article

In the last few years, induction motor fault detection has provoked great interest among researchers because it is a fundamental element of the electric-power industry, manufacturing enterprise, and services. Hence, considerable efforts have been carried out on developing reliable, low-cost procedures for fault diagnosis in induction motors (IM) since the early detection of any failure may prevent the machine from suffering a catastrophic damage. Therefore, many methodologies based on the IM startup transient current analysis have been proposed whose major disadvantages are the high mathematical complexity and demanding computational cost for their development. In this study, a straightforward procedure was introduced for identifying and classifying faults in IM. The proposed approach is based on the analysis of the startup transient current signal through the current signal homogeneity and the fourth central moment (kurtosis) analysis. These features are used for training a feed-forward, backpropagation artificial neural network used as a classifier. From experimentally obtained results, it was demonstrated that the brought-in scheme attained high certainty in recognizing and discriminating among five induction motor conditions, i.e., a motor in good physical condition (HLT), a motor with one broken rotor bar (1BRB), a motor with two broken rotor bars (2BRB), a motor with damage on the bearing outer race (BRN), and a motor with an unbalanced mechanical load (UNB). Full article

This paper focuses on the development of an explicit finite difference numerical method for approximating the solution of the inhomogeneous fourth-order Euler–Bernoulli beam bending equation with velocity-dependent damping and second moment of area, mass and elastic modulus distribution varying with distance along the beam. We verify the method by comparing its predictions with an exact analytical solution of the homogeneous equation, we use the generalised Richardson extrapolation to show that the method is grid convergent and we extend the application of the Lax–Richtmyer stability criteria to higher-order schemes to ensure that it is numerically stable. Finally, we present three sets of computational experiments. The first set simulates the behaviour of the un-loaded beam and is validated against the analytic solution. The second set simulates the time-dependent dynamic behaviour of a damped beam of varying stiffness and mass distributions under arbitrary externally applied loading in an aeroelastic analysis setting by approximating the inhomogeneous equation using the finite difference method derived here. We compare the third set of simulations of the steady-state deflection with the results of static beam bending experiments conducted at Cranfield University. Overall, we developed an accurate, stable and convergent numerical framework for solving the inhomogeneous Euler–Bernoulli equation over a wide range of boundary conditions. Aircraft manufacturers are starting to consider configurations with increased wing aspect ratios and reduced structural weight which lead to more slender and flexible designs. Aeroelastic analysis now plays a central role in the design process. Efficient computational tools for the prediction of the deformation of wings under external loads are in demand and this has motivated the work carried out in this paper. Full article

To evaluate the metatarsal head that was associated with the highest plantar pressure after metatarsal head resection (MHR) and the relations with reulceration at one year, a prospective was conducted with a total of sixty-five patients with diabetes who suffered from the first MHR and with an inactive ulcer at the moment of inclusion. Peak plantar pressure and pressure time integral were recorded at five specific locations in the forefoot: first, second, third, fourth, and fifth metatarsal heads. The highest value of the four remaining metatarsals was selected. After resection of the first metatarsal head, there is a displacement of the pressure beneath the second metatarsal head (p < 0.001). Following the resection of the minor metatarsal bones, there was a medial displacement of the plantar pressure. In this way, plantar pressure was displaced under the first metatarsal head following resection of the second or third head (p = 0.001) and under the central heads after resection of the fourth or fifth metatarsal head (p < 0.009 and p < 0.001 respectively). During the one-year follow-up, patients who underwent a metatarsal head resection in the first and second metatarsal heads suffered transfer lesion in the location with the highest pressure. Patients who underwent a minor metatarsal head resection (second–fifth metatarsal heads) showed a medial transference of pressure. Additionally, following the resection of the first metatarsal head there was a transference of pressure beneath the second metatarsal head. Increase of pressure was found to be a predictor of reulceration in cases of resection of the first and second metatarsal heads. Full article

We introduce two families of continuous distribution functions with not-necessarily symmetric densities, which contain a parent distribution as a special case. The two families proposed depend on two parameters and are presented as an alternative to the skew normal distribution and other proposals in the statistical literature. The density functions of these new families are given by a closed expression which allows us to easily compute probabilities, moments and related quantities. The second family can exhibit bimodality and its standardized fourth central moment (kurtosis) can be lower than that of the Azzalini skew normal distribution. Since the second proposed family can be bimodal we fit two well-known data set with this feature as applications. We concentrate attention on the case in which the normal distribution is the parent distribution but some consideration is given to other parent distributions, such as the logistic distribution. Full article

We present the development of the approach to thermodynamics based on measurement. First of all, we recall that considering classical thermodynamics as a theory of measurement of extensive variables one gets the description of thermodynamic states as Legendrian or Lagrangian manifolds representing the average of measurable quantities and extremal measures. Secondly, the variance of random vectors induces the Riemannian structures on the corresponding manifolds. Computing higher order central moments, one drives to the corresponding higher order structures, namely the cubic and the fourth order forms. The cubic form is responsible for the skewness of the extremal distribution. The condition for it to be zero gives us so-called symmetric processes. The positivity of the fourth order structure gives us an additional requirement to thermodynamic state. Full article

Ground-penetrating radar (GPR) is an effective tool for subsurface detection. Due to the influence of the environment and equipment, the echoes of GPR contain significant noise. In order to suppress noise for GPR data, a method based on singular value decomposition (SVD) of a window-length-optimized Hankel matrix is proposed in this paper. First, SVD is applied to decompose the Hankel matrix of the original data, and the fourth root of the fourth central moment of singular values is used to optimize the window length of the Hankel matrix. Then, the difference spectrum of singular values is used to construct a threshold, which is used to distinguish between components of effective signals and components of noise. Finally, the Hankel matrix is reconstructed with singular values corresponding to effective signals to suppress noise, and the denoised data are recovered from the reconstructed Hankel matrix. The effectiveness of the proposed method is verified with both synthetic and field measurements. The experimental results show that the proposed method can effectively improve noise removal performance under different detection scenarios. Full article