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In the field of operational modal analysis (OMA), obtained modal information is frequently used to assess the current state of aerospace, mechanical, offshore and civil structures. However, the stochasticity of operational systems and the lack of forcing information can lead to inconsistent results. Quantifying the uncertainty of the recovered modal parameters through OMA is therefore of significant value. In this article, a new perspective on Bayesian OMA is proposed: a Bayesian stochastic subspace identification (SSI) algorithm. Distinct from existing approaches to Bayesian OMA, a hierarchical probabilistic model is embedded at the core of covariance-driven SSI. Through substitution of canonical correlation analysis with a Bayesian equivalent, posterior distributions over the modal properties are obtained. Two inference schemes are presented for the proposed Bayesian formulation: Markov Chain Monte Carlo and variational Bayes. Two case studies are then explored. The first is benchmark study using data from a simulated, multi degree-of-freedom, linear system. Following application of Bayesian SSI, it is shown that the same posterior is targeted and recovered by both inference schemes, with good agreement between the posterior mean and the conventional SSI result. The second study applies the variational form to data obtained from an in-service structure: The Z24 bridge. The results of this study are presented at single model orders, and then using a stabilisation diagram. The recovered posterior uncertainty is presented and compared to the classic SSI result. It is observed that the posterior distributions with mean values coinciding with the natural frequencies exhibit lower variance than values situated away from the natural frequencies.

Model parsimony is an important \emph{cognitive bias} in data-driven modelling that aids interpretability and helps to prevent over-fitting. Sparse identification of nonlinear dynamics (SINDy) methods are able to learn sparse representations of complex dynamics directly from data, given a basis of library functions. In this work, a novel Bayesian treatment of dictionary learning system identification, as an alternative to SINDy, is envisaged. The proposed method -- Bayesian identification of nonlinear dynamics (BINDy) -- is distinct from previous approaches in that it targets the full joint posterior distribution over both the terms in the library and their parameterisation in the model. This formulation confers the advantage that an arbitrary prior may be placed over the model structure to produce models that are sparse in the model space rather than in parameter space. Because this posterior is defined over parameter vectors that can change in dimension, the inference cannot be performed by standard techniques. Instead, a Gibbs sampler based on reversible-jump Markov-chain Monte-Carlo is proposed. BINDy is shown to compare favourably to ensemble SINDy in three benchmark case-studies. In particular, it is seen that the proposed method is better able to assign high probability to correct model terms.

The use of measured vibration data from structures has a long history of enabling the development of methods for inference and monitoring. In particular, applications based on system identification and structural health monitoring have risen to prominence over recent decades and promise significant benefits when implemented in practice. However, significant challenges remain in the development of these methods. The introduction of realistic, full-scale datasets will be an important contribution to overcoming these challenges. This paper presents a new benchmark dataset capturing the dynamic response of a decommissioned BAE Systems Hawk T1A. The dataset reflects the behaviour of a complex structure with a history of service that can still be tested in controlled laboratory conditions, using a variety of known loading and damage simulation conditions. As such, it provides a key stepping stone between simple laboratory test structures and in-service structures. In this paper, the Hawk structure is described in detail, alongside a comprehensive summary of the experimental work undertaken. Following this, key descriptive highlights of the dataset are presented, before a discussion of the research challenges that the data present. Using the dataset, non-linearity in the structure is demonstrated, as well as the sensitivity of the structure to damage of different types. The dataset is highly applicable to many academic enquiries and additional analysis techniques which will enable further advancement of vibration-based engineering techniques.

Nonlinear system identification remains an important open challenge across research and academia. Large numbers of novel approaches are seen published each year, each presenting improvements or extensions to existing methods. It is natural, therefore, to consider how one might choose between these competing models. Benchmark datasets provide one clear way to approach this question. However, to make meaningful inference based on benchmark performance it is important to understand how well a new method performs comparatively to results available with well-established methods. This paper presents a set of ten baseline techniques and their relative performances on five popular benchmarks. The aim of this contribution is to stimulate thought and discussion regarding objective comparison of identification methodologies.

In engineering, accurately modeling nonlinear dynamic systems from data contaminated by noise is both essential and complex. Established Sequential Monte Carlo (SMC) methods, used for the Bayesian identification of these systems, facilitate the quantification of uncertainty in the parameter identification process. A significant challenge in this context is the numerical integration of continuous-time ordinary differential equations (ODEs), crucial for aligning theoretical models with discretely sampled data. This integration introduces additional numerical uncertainty, a factor that is often over looked. To address this issue, the field of probabilistic numerics combines numerical methods, such as numerical integration, with probabilistic modeling to offer a more comprehensive analysis of total uncertainty. By retaining the accuracy of classical deterministic methods, these probabilistic approaches offer a deeper understanding of the uncertainty inherent in the inference process. This paper demonstrates the application of a probabilistic numerical method for solving ODEs in the joint parameter-state identification of nonlinear dynamic systems. The presented approach efficiently identifies latent states and system parameters from noisy measurements. Simultaneously incorporating probabilistic solutions to the ODE in the identification challenge. The methodology's primary advantage lies in its capability to produce posterior distributions over system parameters, thereby representing the inherent uncertainties in both the data and the identification process.

A stochastic optimal control problem for incompressible Newtonian channel flow past a circular cylinder is used as a prototype optimal control problem for the stochastic Navier-Stokes equations. The inlet flow and the rotation speed of the cylinder are allowed to have stochastic perturbations. The control acts on the cylinder via adjustment of the rotation speed. Possible objectives of the control include, among others, tracking a desired (given) velocity field or minimizing the kinetic energy, enstrophy, or the drag of the flow over a given body. Owing to the high computational requirements, the direct application of the classical Monte Carlo methods for our problem is limited. To overcome the difficulty, we use a multi-fidelity data-driven compressive sensing based polynomial chaos expansions (MDCS-PCE). An effective gradient-based optimization for the discrete optimality systems resulted from the MDCS-PCE discretization is developed. The strategy can be applied broadly to many stochastic flow control problems. Numerical tests are performed to validate our methodology.

Research developments for structural dynamics in the fields of design, system identification and structural health monitoring (SHM) have dramatically expanded the bounds of what can be learned from measured vibration data. However, significant challenges remain in the tasks of identification, prediction and evaluation of full-scale structures. A significant aid in the roadmap to the application of cutting-edge methods to the demands of in-service engineering structures, is the development of comprehensive benchmark datasets. With the aim of developing a useful and worthwhile benchmark dataset for structural dynamics, an extensive testing campaign is presented here. This recent campaign was performed on a decommissioned BAE system Hawk T1A aircraft at the Laboratory for Verification and Validation (LVV) in Sheffield. The aim of this paper is to present the dataset, providing details on the structure, experimental design, and data acquired. The collected data is made freely and openly available with the intention that it serve as a benchmark dataset for challenges in full-scale structural dynamics. Here, the details pertaining to two test phases (frequency and time domain) are presented. So as to ensure that the presented dataset is able to function as a benchmark, some baseline-level results are additionally presented for the tasks of identification and prediction, using standard approaches. It is envisaged that advanced methodologies will demonstrate superiority by favourable comparison with the results presented here. Finally, some dataset-specific challenges are described, with a view to form a hierarchy of tasks and frame discussion over their relative difficulty.

A great deal of research has been conducted in the consideration of meta-heuristic optimisation methods that are able to find global optima in settings that gradient based optimisers have traditionally struggled. Of these, so-called particle swarm optimisation (PSO) approaches have proven to be highly effective in a number of application areas. Given the maturity of the PSO field, it is likely that novel variants of the PSO algorithm stand to offer only marginal gains in terms of performance -- there is, after all, no free lunch. Instead of only chasing performance on suites of benchmark optimisation functions, it is argued herein that research effort is better placed in the pursuit of algorithms that also have other useful properties. In this work, a highly-general, interpretable variant of the PSO algorithm -- particle attractor algorithm (PAO) -- is proposed. Furthermore, the algorithm is designed such that the transition densities (describing the motions of the particles from one generation to the next) can be computed exactly in closed form for each step. Access to closed-form transition densities has important ramifications for the closely-related field of Sequential Monte Carlo (SMC). In order to demonstrate that the useful properties do not come at the cost of performance, PAO is compared to several other state-of-the art heuristic optimisation algorithms in a benchmark comparison study., Comment: Preprint

In the context of Gaussian process regression with functional inputs, it is common to treat the input as a vector. The parameter space becomes prohibitively complex as the number of functional points increases, effectively becoming a hindrance for automatic relevance determination in high-dimensional problems. Generalizing a framework for time-varying inputs, we introduce the asymmetric Laplace functional weight (ALF): a flexible, parametric function that drives predictive relevance over the index space. Automatic dynamic relevance determination (ADRD) is achieved with three unknowns per input variable and enforces smoothness over the index space. Additionally, we discuss a screening technique to assess under complete absence of prior and model information whether ADRD is reasonably consistent with the data. Such tool may serve for exploratory analyses and model diagnostics. ADRD is applied to remote sensing data and predictions are generated in response to atmospheric functional inputs. Fully Bayesian estimation is carried out to identify relevant regions of the functional input space. Validation is performed to benchmark against traditional vector-input model specifications. We find that ADRD outperforms models with input dimension reduction via functional principal component analysis. Furthermore, the predictive power is comparable to high-dimensional models, in terms of both mean prediction and uncertainty, with 10 times fewer tuning parameters. Enforcing smoothness on the predictive relevance profile rules out erratic patterns associated with vector-input models., Comment: Submitted to Technometrics. 34 pages, 5 figures, 2 tables

For quantum computations without error correction, the dynamics of a simulation can strongly influence the overall fidelity decay rate as well as the relative impact of different noise processes on the fidelity. Theoretical models of Markovian noise that include incoherent Lindblad noise, gate-based errors, and stochastic Hamiltonian noise qualitatively agree that greater diffusion and entanglement throughout Hilbert space typically increase the fidelity decay rate. Simulations of the gate-efficient quantum sawtooth map support these predictions, and experiments performed on three qubits on the IBM-Q quantum hardware platform at fixed gate count qualitatively confirm the predictions. A pure depolarizing noise model, often used within randomized benchmarking (RB) theory, cannot explain the observed effect, but gate-based Lindblad models can provide an explanation. They can also estimate the effective Lindblad coherence times during gates, and find a consistent $2\text{-}3\times$ shorter effective $T_2$ dephasing time than reported for idle qubits. Additionally, the observed error per CNOT gate exceeds IBM-Q's reported value from RB by $3.0\times$ during localized dynamics and $4.5\times$ during diffusive dynamics. This demonstrates the magnitude by which RB understates error in a complex quantum simulation due to dynamics and crosstalk., Comment: 29 pages, 9 figures

Understanding the chirality of molecular reaction pathways is essential for a broad range of fundamental and applied sciences. However, the current ability to probe chirality on the time scale of chemical reactions remains very limited. Here, we demonstrate time-resolved photoelectron circular dichroism (TRPECD) with ultrashort circularly polarized vacuum-ultraviolet (VUV) pulses from a table-top source. We demonstrate the capabilities of VUV-TRPECD by resolving the chirality changes in time during the photodissociation of atomic iodine from two chiral molecules. We identify several general key features of TRPECD, which include the ability to probe dynamical chirality along the complete photochemical reaction path, the sensitivity to the local chirality of the evolving scattering potential, and the influence of electron scattering off dissociating photofragments. Our results are interpreted by comparison with novel high-level ab-initio calculations of transient PECDs from molecular photoionization calculations. Our experimental and theoretical techniques define a general approach to femtochirality., Comment: 17 pages, 6 figures, 57 references, Accepted in Science Advances

Although high-performance computing (HPC) systems have been scaled to meet the exponentially-growing demand for scientific computing, HPC performance variability remains a major challenge and has become a critical research topic in computer science. Statistically, performance variability can be characterized by a distribution. Predicting performance variability is a critical step in HPC performance variability management and is nontrivial because one needs to predict a distribution function based on system factors. In this paper, we propose a new framework to predict performance distributions. The proposed model is a modified Gaussian process that can predict the distribution function of the input/output (I/O) throughput under a specific HPC system configuration. We also impose a monotonic constraint so that the predicted function is nondecreasing, which is a property of the cumulative distribution function. Additionally, the proposed model can incorporate both quantitative and qualitative input variables. We evaluate the performance of the proposed method by using the IOzone variability data based on various prediction tasks. Results show that the proposed method can generate accurate predictions, and outperform existing methods. We also show how the predicted functional output can be used to generate predictions for a scalar summary of the performance distribution, such as the mean, standard deviation, and quantiles. Our methods can be further used as a surrogate model for HPC system variability monitoring and optimization., Comment: 31 pages, 10 figures

In certain regimes, the fidelity of quantum states will decay at a rate set by the classical Lyapunov exponent. This serves both as one of the most important examples of the quantum-classical correspondence principle and as an accurate test for the presence of chaos. While detecting this phenomenon is one of the first useful calculations that noisy quantum computers without error correction can perform [G. Benenti et al., Phys. Rev. E 65, 066205 (2001)], a thorough study of the quantum sawtooth map reveals that observing the Lyapunov regime is just beyond the reach of present-day devices. We prove that there are three bounds on the ability of any device to observe the Lyapunov regime and give the first quantitatively accurate description of these bounds: (1) the Fermi golden rule decay rate must be larger than the Lyapunov rate, (2) the quantum dynamics must be diffusive rather than localized, and (3) the initial decay rate must be slow enough for Lyapunov decay to be observable. This last bound, which has not been recognized previously, places a limit on the maximum amount of noise that can be tolerated. The theory implies that an absolute minimum of 6 qubits is required. Recent experiments on IBM-Q and IonQ imply that some combination of a noise reduction by up to 100$\times$ per gate and large increases in connectivity and gate parallelization are also necessary. Finally, scaling arguments are given that quantify the ability of future devices to observe the Lyapunov regime based on trade-offs between hardware architecture and performance., Comment: 22 pages, 7 figures

Researchers at the Ames Laboratory-USDOE and the Federal Bureau of Investigation (FBI) conducted a study to assess the performance of forensic examiners in firearm investigations. The study involved three different types of firearms and 173 volunteers who compared both bullets and cartridge cases. The total number of comparisons reported is 20,130, allocated to assess accuracy (8,640), repeatability (5,700), and reproducibility (5,790) of the evaluations made by participating examiners. The overall false positive error rate was estimated as 0.656% and 0.933% for bullets and cartridge cases, respectively, while the rate of false negatives was estimated as 2.87% and 1.87% for bullets and cartridge cases, respectively. Because chi-square tests of independence strongly suggest that error probabilities are not the same for each examiner, these are maximum likelihood estimates based on the beta-binomial probability model and do not depend on an assumption of equal examiner-specific error rates. Corresponding 95% confidence intervals are (0.305%,1.42%) and (0.548%,1.57%) for false positives for bullets and cartridge cases, respectively, and (1.89%,4.26%) and (1.16%,2.99%) for false negatives for bullets and cartridge cases, respectively. These results are based on data representing all controlled conditions considered, including different firearm manufacturers, sequence of manufacture, and firing separation between unknown and known comparison specimens. The results are consistent with those of prior studies, despite its more robust design and challenging specimens.