Quadratic-exponential functionals of Gaussian quantum processes

This paper is concerned with exponential moments of integral-of-quadratic functions of quantum processes with canonical commutation relations of position-momentum type. Such quadratic-exponential functionals (QEFs) arise as robust performance criteria in control problems for open quantum harmonic oscillators (OQHOs) driven by bosonic fields. We develop a randomised representation for the QEF using a Karhunen–Loeve expansion of the quantum process on a bounded time interval over the eigenbasis of its two-point commutator kernel, with noncommuting position-momentum pairs as coefficients. This representation holds regardless of a particular quantum state and employs averaging over an auxiliary classical Gaussian random process whose covariance operator is specified by the commutator kernel. This allows the QEF to be related to the moment-generating functional of the quantum process and computed for multipoint Gaussian states. For stationary Gaussian quantum processes, we establish a frequency-domain formula for the QEF rate in terms of the Fourier transform of the quantum covariance kernel in composition with trigonometric functions. A differential equation is obtained for the QEF rate with respect to the risk sensitivity parameter for its approximation and numerical computation. The QEF is also applied to large deviations and worst-case mean square cost bounds for OQHOs in the presence of statistical uncertainty with a quantum relative entropy description.

Numerical study of the vertical vibration of a vehicle model with variable speed

The paper deals with the numerical analysis of the general model of vehicle oscillations considering the non-stationarity of random excitation. The model parameters of the applied railway vehicle are deterministic functions. The non-stationary random function will be modelled by the variable speed of the vehicle and the vertical unevenness of the track. The so-called evolutionary Gaussian random process will be considering. The proposed comparative study of the dynamics of the vertical motion of the analysed railway vehicle will be realized using Monte Carlo simulation and a numerical procedure based on the theory of Markov processes. The originality of the article can be found in the implementation and algorithmization of the principles of solving non-stationary oscillation problems of machines. A universal methodology applicable in the dynamics of machines of various purposes is presented.

Efficient Propagation of Epistemic Uncertainty for Probabilistic Seismic Hazard Analyses (PSHAs) Including Partial Correlation of Magnitude–Distance Scaling

ABSTRACT Probabilistic seismic hazard analysis (PSHA) is moving from ergodic ground-motion models (GMMs) to nonergodic GMMs that account for site-source-specific source, path, and site effects and which require a much larger number of GMM branches on the logic tree to capture the full epistemic uncertainty. An efficient method for computing PSHA with a large number of GMM branches was developed by Lacour and Abrahamson (2019) using polynomial chaos (PC) expansion with the key assumption that the epistemic uncertainty in the median ground motion is fully correlated. In the current study, we remove the assumption of full correlation using a multivariate PC expansion. The correlation structure of the available median GMMs across scenarios is computed empirically. The median ground motion is modeled as a Gaussian random process with the correlation structure of the GMMs across the range of relevant earthquake scenarios. This Gaussian random process is discretized using the Karhunen–Loeve expansion, which leads to multivariate PC expansions of uncertain hazard curves. The hazard fractiles can be reconstructed during an efficient postprocessing phase that includes the effects of partial correlation between the GMMs. Multivariate PC expansions require significantly more terms than for the fully correlated case, which increases the calculation time by about a factor of 5, but it is still much more efficient than direct sampling of the branches of the GMM logic for a large number of branches. An example hazard calculation shows that the effect of using partial correlation in place of full correlation of the GMMs is small for the Next Generation Attenuation-West2 (NGA-West2) set of GMMs, indicating that the fully correlated assumption may be adequate for many applications. The multivariate PC method can be used to evaluate the effects of the partial correlation of the GMMs for sets of GMMs that are different from the NGA-West2 GMMs.

Serviceability Assessment of Footbridges via Improved Interval Analysis

This paper studies the propagation of uncertainties on serviceability assessment of footbridges in unrestricted traffic condition based on a non-deterministic approach. Multi-pedestrian loading is modeled as a stationary Gaussian random process through the Equivalent Spectral Model [1] which yields analytical expressions of the spectral moments of the footbridge dynamic response. The uncertain pedestrian-induced loading parameters and structural dynamic properties are modeled as interval variables. An approximate analytical procedure, based on the Improved Interval Analysis [2], is introduced as an efficient alternative to classical optimization in order to propagate interval uncertainties. The presented procedure allows us to derive closed-form expressions of the bounds of the spectral moments of the response, as well as of the expected value and cumulative distribution function of the maximum footbridge acceleration. Two strategies are proposed to assess footbridges' serviceability. The first one leads to the definition of a range of comfort classes. The second strategy enables us to estimate an interval of probability of reaching at least a suitable comfort level.

Quantitative Representation of Aleatoric Uncertainties in Network-like Topological Structural Systems

The complex topological characteristics of network-like structural systems, such as lattice structures, cellular metamaterials, and mass transport networks, pose a great challenge for uncertainty quantification (UQ). Existing UQ approaches are only applicable to parametric uncertainties or high dimensional random quantities distributed in a simply connected space (e.g., line section, rectangular area, etc.). Those methods do not consider the topological characteristics of the spatial domain. To resolve this issue, a network distance-based Gaussian random process UQ approach is proposed. By representing the topological input space as a node-edge network, the network distance is employed to replace the Euclidean distance in characterizing the spatial correlations. Furthermore, a conditional simulation-based sampling approach is proposed for generating realizations from the UQ model. Network node values are modeled by a multivariate Gaussian distribution, and the network edge values are simulated conditionally on the node values and the known network edge values. The effectiveness of the proposed approach is demonstrated on two engineering case studies: thermal conduction analysis of 3D lattice structures with stochastic properties, and characterization of the distortion patterns of additively manufactured cellular structures.

Dynamic loadings of moving vehicles on curved concrete segmental single box girder bridges

<p>This paper presents the dynamic behaviors of curved concrete segmental bridges. The bridges are modeled as thin-wall structures and analyzed using the thin-wall finite element method. The effects of bridge torsion and distortion are considered in the analysis. A vehicle is simulated as a three- dimensional nonlinear model. The road profile is modeled as a stationary Gaussian random process that is described by a power spectral density (PSD) function. The effects of vehicle speeds, bridge radii, bridge span lengths on the bridge dynamic loadings are analyzed. Through an extensive numerical analysis on 20 typical curved bridges, an approximate method for determining the concrete segmental bridges is proposed. The research results are applicable to the design of concrete segmental bridges.</p>

Detección óptica en 3D de un objeto flotante en una superficie marina agitada

In this paper we realize a comparison between two detectors: Matched Subspace Detector (MSD) and Modify Matched Subspace Detector (MMSD) when there is a images secuence (3D detection), where the parameters of sea surface and the parameters of floating object are priori unknown in computer simulation, with help of computer software MATLAB. Both detectors (MSD and MMSD) are based in the General Likelihood Ratio Test (GLRT); this method helps solve detection problems when the sea surface and floating object parameters are unknown. The sea surface is simulated as a Gaussian random process, and the floating object is simulated as a priori unknown deterministic process. The paper considers the dependence of the probability of detection with a fixed probability of false alarm on the difference between the average values of reflections from the sea surface and from a floating object with different ratios of the power of fluctuations of reflections from the object and from the sea Surface.

Quantification of Uncertainties Distributed in Network-Like Systems

Network-like engineering systems, such as transport networks and lattice metamaterials, are featured by high dimensional, complex topological characteristics, which pose a great challenge for uncertainty quantification (UQ). Existing UQ approaches are only applicable to parametric uncertainties, or high dimensional random quantities distributed in a simply connected space (e.g., line section, rectangular area, etc.). The topological characteristics of the input space cannot be captured by existing UQ models. To resolve this issue, a network-based Gaussian random process UQ approach is proposed in this work. By representing the topological input space as a node-edge network, network distance is employed to replace the Euclidean distance in characterizing the spatial correlations. Furthermore, a conditional simulation-based approach is proposed for sampling. Realizations of random quantities on each edge of the network is sampled conditionally on the node values, which are modeled by a multivariable Gaussian distribution. The effectiveness of the proposed approach is demonstrated with two engineering case studies: stochastic thermal conduction analysis of a 3D lattice structure, and characterization of the distortion pattern of an additively manufactured cellular structure.

Multi-wavelet level comparison on compressive sensing for MRI image reconstruction

In this study, we proposed compressive sampling for MRI reconstruction based on sparse representation using multi-wavelet transformation. Comparing the performance of wavelet decomposition level, which are Level 1, Level 2, Level 3, and Level 4. We used gaussian random process to generate measurement matrix. The algorithm used to reconstruct the image is . The experimental results showed that the use of wavelet multi-level can generate higher compression ratio but requires a longer processing time. MRI reconstruction results based on the parameters of the peak signal to noise ratio (PSNR) and structural similarity index measure (SSIM) show that the higher the level of decomposition in wavelets, the value of both decreases.