Stochastic Frequency Research Articles

Operational modal characterisation for long-term monitoring in offshore structures

In the effort to increase sustainability and help drive the energy sector to support oil and gas decarbonisation, the importance of identifying and characterising the current state of assets is becoming ever more crucial for operators, especially with regards to life extension and repurposing. Structural Health Monitoring (SHM) offers a promising and forward-thinking methodology for tracking asset integrity. In particular, Operational Modal Analysis (OMA) presents a proven, output only method for structure characterisation and modal tracking. However, Environmental and Operational Variations (EOV) can influence the modal properties of the structure making modal parameter estimation and tracking less reliable in the short- and long-term. This study employs an Automated Operational Modal Analysis (AOMA) methodology based on the combination of stochastic subspace identification and natural frequency histogram bin analysis for robust parameter extraction. The methodology is implemented in a complex of three bridge linked offshore platforms. Structural complexity, operational loading and significant modal couplings require sophisticated analysis. The preliminary results show discontinuity of the operational modes over a 6-month long monitoring period. The findings demonstrate the need of further analysis to understand the time-variant parameters which determine structural response across the asset lifetime.

Versatile, fast, and accurate frequency excursions with a semiconductor laser

Achieving accurate arbitrary frequency excursions with a laser can be quite a technical challenge, especially when steep slopes (GHz/µs) are required, due to both deterministic and stochastic frequency fluctuations. In this work we present a multistage correction combining four techniques: pre-distorsion of the laser modulation, iterative correction, opto-electronic feedback loop, and feed-forward correction. This combination allows us not only to compensate for the non-instantaneous response of the laser to an input modulation but also to correct in real time the stochastic frequency fluctuations. We implement this multistage architecture on a commercial DBR laser and verify its efficiency, first, with monochromatic operation, and second, with highly demanding frequency excursions. We demonstrate that our multistage correction not only enables a strong reduction of the laser linewidth but also allows steep frequency excursions with a relative RMS frequency error well below 1% and a laser spectral purity consistently better than 100 kHz, even in the midst of gigahertz-scale frequency excursions.

A quantitative genetic model of background selection in humans.

Across the human genome, there are large-scale fluctuations in genetic diversity caused by the indirect effects of selection. This "linked selection signal" reflects the impact of selection according to the physical placement of functional regions and recombination rates along chromosomes. Previous work has shown that purifying selection acting against the steady influx of new deleterious mutations at functional portions of the genome shapes patterns of genomic variation. To date, statistical efforts to estimate purifying selection parameters from linked selection models have relied on classic Background Selection theory, which is only applicable when new mutations are so deleterious that they cannot fix in the population. Here, we develop a statistical method based on a quantitative genetics view of linked selection, that models how polygenic additive fitness variance distributed along the genome increases the rate of stochastic allele frequency change. By jointly predicting the equilibrium fitness variance and substitution rate due to both strong and weakly deleterious mutations, we estimate the distribution of fitness effects (DFE) and mutation rate across three geographically distinct human samples. While our model can accommodate weaker selection, we find evidence of strong selection operating similarly across all human samples. Although our quantitative genetic model of linked selection fits better than previous models, substitution rates of the most constrained sites disagree with observed divergence levels. We find that a model incorporating selective interference better predicts observed divergence in conserved regions, but overall our results suggest uncertainty remains about the processes generating fitness variation in humans.

Broadband Ground-Motion Synthesis via Generative Adversarial Neural Operators: Development and Validation

ABSTRACT We present a data-driven framework for ground-motion synthesis that generates three-component acceleration time histories conditioned on moment magnitude (M), rupture distance (Rrup), time-average shear-wave velocity at the top 30 m (VS30), and style of faulting. We use a Generative Adversarial Neural Operator (GANO)—a resolution invariant architecture that guarantees model training independent of the data sampling frequency. We first present the conditional ground-motion synthesis algorithm (cGM-GANO) and discuss its advantages compared to the previous work. We next train cGM-GANO on simulated ground motions generated by the Southern California Earthquake Center Broadband Platform (BBP) and on recorded the Kiban–Kyoshin network (KiK-net) data, and show that the model can learn the overall magnitude, distance, and VS30 scaling of effective amplitude spectra (EAS) ordinates and pseudospectral accelerations (PSA). Results specifically show that cGM-GANO produces consistent median scaling with the training data for the corresponding tectonic environments over a wide range of frequencies for scenarios with sufficient data coverage. For the BBP dataset, cGM-GANO cannot learn the ground-motion scaling of the stochastic frequency components (f > 1 Hz); for the KiK-net dataset, the largest misfit is observed at short distances (Rrup<50 km) and for soft-soil conditions (VS30<200 m/s) due to the scarcity of such data. Except for these conditions, the aleatory variability of EAS and PSA are captured reasonably well. Finally, cGM-GANO produces similar median scaling to traditional ground-motion models (GMMs) for frequencies greater than 1 Hz for both PSA and EAS but underestimates the aleatory variability of EAS. Discrepancies in the comparisons between the synthetic ground motions and GMMs are attributed to inconsistencies between the training dataset and the datasets used in GMM development. Our pilot study demonstrates GANO’s potential for efficient synthesis of broadband ground motions.

Average decayed dynamics of one-step transformation process with randomly varying return transition rate

The problem of stochastic averaging of the decayed dynamics of the output state population of a one-step transformation process with constant deterministic forward transition rate and randomly varying return transition rate is solved in approximation where random variation is modeled as a dichotomous stochastic process. The form of the obtained solution represented as a product between bimodal sigmoid rise of average population and its unimodal exponential decay is shown to largely be dependent on the stochastic frequency and amplitude parameters. For example, at high stochastic frequency, the behavior of population is reduced to that of a decayed one-step deterministic system. However, for resonance stochastic amplitude at low stochastic frequency, such behavior coincides with that of three-exponential rise-decay kinetics typical rather of a three-step deterministic slowly decaying process. Thus, there is an equivalence between using a more complex deterministic kinetic model and a less complex stochastic kinetic model for describing the decayed dynamics of different irreversible systems.

Hierarchical Stochastic Frequency Constrained Micro-Market Model for Isolated Microgrids

With the developments of isolated microgrids (IMGs) and prosumers in remote areas, energy trading has emerged as a critical aspect of IMGs. However, the lack of an upstream network and the low inertia of the system may threaten the secure operation of these networks. This paper proposes a Micro-Market (lM) model for IMGs that includes a precise hierarchical control structure. To address the IMGs low inertia and high intermittency of renewable energy sources (RES), the proposed lM manages the active-reactive power and schedules primary and secondary active reserves to maintain the frequency within in a predefined range. Additionally, a bidirectional linearized AC power flow is established to schedule the reactive reserve and the proposed model is formulated as a two-stage stochastic mixed-integer linear problem (MILP) to maximize social welfare (SW) over the next 24 hours. To validate the effectiveness of the proposed model, the lM is tested on an IMG based on a CIGRE medium-voltage benchmark system, and different operational cases are simulated. The results demonstrate that the proposed model, which takes into account hierarchical control levels and technical issues of the IMG, is a cost-effective way to maximize social welfare while ensuring the secure operation of the IMG.

Stochastic competitive release and adaptive chemotherapy.

We develop a finite-cell model of tumor natural selection dynamics to investigate the stochastic fluctuations associated with multiple rounds of adaptive chemotherapy. The adaptive cycles are designed to avoid chemoresistance in the tumor by managing the ecological mechanism of competitive release of a resistant subpopulation. Our model is based on a three-component evolutionary game played among healthy (H), sensitive (S), and resistant (R) populations of N cells, with a chemotherapy control parameter, C(t), which we use to dynamically impose selection pressure on the sensitive subpopulation to slow tumor growth and manage competitive release of the resistant population. The adaptive chemoschedule is designed based on the deterministic (N→∞) adjusted replicator dynamical system, then implemented using the finite-cell stochastic frequency dependent Moran process model (N=10K-50K) to ascertain the cumulative effect of the stochastic fluctuations on the efficacy of the adaptive schedules over multiple rounds. We quantify the stochastic fixation probability regions of the R and S populations in the HSR trilinear phase plane as a function of the control parameter C∈[0,1], showing that the size of the R region increases with increasing C. We then implement an adaptive time-dependent schedule C(t) for the stochastic model and quantify the variances (using principal component coordinates) associated with the evolutionary cycles over multiple rounds of adaptive therapy. The variances increase subquadratically through several rounds before the evolutionary cycle begins to break down. Despite this, we show the stochastic adaptive schedules are more effective at delaying resistance than standard maximum tolerated dose and low-dose metronomic schedules. The simplified low-dimensional model provides some insights on how well multiple rounds of adaptive therapies are likely to perform over a range of tumor sizes (i.e., different values of N) if the goal is to maintain a sustained balance among competing subpopulations of cells to avoid chemoresistance via competitive release in a stochastic environment.

Development of a software platform for bridge modal and damage identification based on ambient excitation

Modal and damage identification based on ambient excitation can greatly improve the efficiency of high-speed railway bridge vibration detection. This paper first describes the basic principles of stochastic subspace identification, peak-picking, and frequency domain decomposition method in modal analysis based on ambient excitation, and the effectiveness of these three methods is verified through finite element calculation and numerical simulation. Then the damage element is added to the finite element model to simulate the crack, and the curvature mode difference and the curvature mode area difference square ratio are calculated by using the stochastic subspace identification results to verify their ability of damage identification and location. Finally, the above modal and damage identification techniques are integrated to develop a bridge modal and damage identification software platform. The final results show that all three modal identification methods can accurately identify the vibration frequency and mode shape, both damage identification methods can accurately identify and locate the damage, and the developed software platform is simple and efficient.

Noise-induced dynamics and photon statistics in bimodal quantum-dot micropillar lasers

Emission characteristics of quantum-dot micropillar lasers (QDMLs) are located at the intersection of nanophotonics and nonlinear dynamics, which provides an ideal platform for studying the optical interface between classical and quantum systems. In this work, a noise-induced bimodal QDML with orthogonal dual-mode outputs is modeled, and nonlinear dynamics, stochastic mode jumping and quantum statistics with the variation of stochastic noise intensity are investigated. Noise-induced effects lead to the emergence of two intensity bifurcation points for the strong and the weak mode, and the maximum output power of the strong mode becomes larger as the noise intensity increases. The anti-correlation of the two modes reaches the maximum at the second intensity bifurcation point. The dual-mode stochastic jumping frequency and effective bandwidth can exceed 100 GHz and 30 GHz under the noise-induced effect. Moreover, the noise-induced photon correlations of both modes simultaneously exhibit super-thermal bunching effects () in the low injection current region. The -value of the strong mode can reach over 6 in the high injection current region. Photon bunching () of both modes is observed over a wide range of noise intensities and injection currents. In the presence of the noise-induced effect, the photon number distribution of the strong or the weak mode is a mixture of Bose–Einstein and Poisson distributions. As the noise intensity increases, the photon number distribution of the strong mode is dominated by the Bose–Einstein distribution, and the proportion of the Poisson distribution is increased in the high injection current region, while that of the weak mode is reduced. Our results contribute to the development preparation of super-bunching quantum integrated light sources for improving the spatiotemporal resolution of quantum sensing measurements and enhancing the security of optical communication.

Voltage fluctuations and probe frequency jitter in electric force microscopy of a conductor.

Electric force microscopy probes the statistics of electric field fluctuations from a sample surface, both through measurement of the noncontact friction exerted on the oscillating charged probe and by determination of the power spectrum of stochastic probe frequency fluctuations, referred to as "jitter." Here we calculate the frequency jitter power spectrum determined over a conducting sample of finite thickness, whose response is characterized by a dielectric function that is wavevector-dependent. These calculations complement previous predictions of the coefficient of noncontact friction in an electric force microscopy measurement for the same model, and also previous predictions of the jitter power spectrum for a dielectric continuum. The inclusion both of a finite sample thickness and a wavevector-dependent dielectric response can significantly enhance the magnitude of the predicted jitter spectrum for a conductor, relative to a simpler model of an infinitely thick dielectric continuum. These calculations provide a baseline prediction of the jitter power spectrum generated by the dynamics of conduction electrons in a metal sample.

Fault Detection for Unmanned Marine Vehicles Under Replay Attack

This paper investigates the fault detection problem of unmanned marine vehicles (UMV) under the influence caused by replay attacks. Firstly, the dynamics of UMV are modeled by a T-S fuzzy system with an unknown membership function, which includes the nonlinear coupling of the internal state of the system, the environmental multi-source disturbance as well as the potential thruster failure on UMV. Then, the possible replay attack from the sensor to the shore-based center is considered, and a switching-type attack tolerant fault detection filter is designed. Sufficient conditions are given to ensure that the filtering augmented system is stable and with stochastic finite frequency <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{\infty }$</tex-math></inline-formula> and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$H_{-}$</tex-math></inline-formula> performances, which reflect the robustness to the disturbance and sensitivity to the fault. On this basis, through a series of mathematical processing, the linear solvable conditions for the design of fault detection filters are obtained. Finally, the effectiveness of the proposed algorithm is verified by simulations.

On the stochastic natural frequency of graphene reinforced functionally graded porous panels with unconventional boundary conditions

The present study explores the stochastic natural frequency of graphene reinforced functionally graded porous panels with unconventional boundary conditions. The material uncertainty is considered in the parameters associated with constituents that is, metal and graphene nanoplatelets (GPLs) individually and simultaneously. The metal matrix is reinforced with ultra-lightweight and high stiffness carbonaceous nanofiller, that is, GPLs. Halpin-Tsai micromechanics model is adopted to estimate effective Young’s modulus of the metal-GPLs composite whereas effective mass density and Poisson’s ratio are calculated using the Voigt model. The micro-structural gradation by creating pores is accomplished along the thickness direction of the panel employing certain continuous functions. These functions describe symmetric and asymmetric porosity distributions and associated patterns of GPLs. The equation of motion is developed using Euler-Lagrange’s equation which is based on C 0-continuous structural kinematics with 7 degrees of freedom. Finite element modeling in conjunction with the first-order perturbation technique has been applied to quantify the stochastic natural frequency in terms of the mean and standard deviation of the natural frequency. Various results have been examined to highlight the influence of parameters especially related to porosity, and graphene nanoplatelets on the stochastic natural frequency of FG-GPLs porous panel constrained with conventional and unconventional boundary conditions.

Probabilistic analysis of long-term loss incorporating maximum entropy method and analytical higher-order moments

Quantifying economic losses of civil infrastructures subjected to various hazards under a life-cycle context is of vital importance for risk assessment and management. In previous studies, the expected long-term loss has been widely applied as a standard decision criterion during the life-cycle analysis. However, the expectation may not be informative enough to illustrate uncertainties associated with the long-term loss. Therefore, the higher-order moments and the probability distribution should be investigated. In this paper, a probabilistic analysis framework is proposed to construct the probability density function and cumulative distribution function of long-term loss by assessing the analytical statistical moments. The stochastic renewal process is utilized to assess the long-term loss by considering uncertainties associated with stochastic occurrence and frequency of the hazards. Based on the maximum entropy method, the proposed approach shows superior efficiency to assess the probability distribution of long-term loss than crude Monte Carlo simulation. The probability distribution can be essential information for decision-making process of risk management. An illustrative example is investigated to show the probability density function of long-term loss of civil infrastructure subjected to hurricane hazards. A good agreement of results obtained by the proposed approach and Monte Carlo simulation has verified the accuracy and effectiveness of the proposed method.

Decentralized Stochastic Disturbance Observer-Based Optimal Frequency Control Method for Interconnected Power Systems With High Renewable Shares

This article proposes a novel, disturbance observer-based decentralized frequency control method for interconnected power systems. The method employs extended Kalman filter (EKF) as an observer to estimate inaccessible dynamic states of the system, including the total disturbance as one of the state variables. An optimal decentralized disturbance observer based controller is suggested for multiarea power systems that compensates the estimated disturbance and further based on minimizing the joint error energies of state estimation error and state tracking error provides its value to the controller for regulating the frequency variation. The proposed method is mathematically designed to be robust against parametric and nonparametric uncertainties. The efficacy and accuracy of the proposed control method is verified considering different types of practical operation scenarios. The results confirm the brilliant and superiority of the proposed method in controlling the frequency in power systems with high renewable shares.

Dynamic bidding strategy for a demand response aggregator in the frequency regulation market

As a low-cost flexible resource, dynamic controllable load on the demand side offers potential for great application prospects in power system frequency regulation. To overcome the risks of various uncertain factors in electricity markets and realize the economic benefits of demand response, this study proposed a dynamic bidding strategy for demand-side resources to participate in the frequency regulation market by a demand response (DR) aggregator. A correlative uncertainty model of the market price and frequency regulation demand was constructed employing the copula function, while the corresponding copula conditional value-at-risk model was used as a market risk measurement index to quantify the DR aggregator’s decision risk. Consequently, an objective function that maximises the profit of the DR aggregator was established. Simultaneously, based on the analysis of the response potential of demand-side resources, a time-varying compensation method for the DR was proposed, and the bidding decision of the DR aggregator was dynamically optimised considering load deviation. Finally, case studies demonstrated that the accuracy and rationality of the uncertainty modelling are improved. The proposed dynamic optimisation method resulted in an increase of 16 % in operating profits. In addition, the revenue of users increased by 12 %. The impact of different risk preferences and the correlation between the stochastic electricity price and frequency regulation demand on the optimal decision result was analysed, based on which the manager of the DR aggregator can make decisions under different situations.

Design Techniques for a 6.4–32-Gb/s 0.96-pJ/b Continuous-Rate CDR With Stochastic Frequency–Phase Detector

This article presents design techniques for a continuous-rate reference-free clock and data recovery (CDR) circuit employing a stochastic frequency–phase detector (SFPD). By taking a histogram-based design methodology, optimal weights for both frequency and phase detection are obtained by utilizing the same information as the Alexander phase detector. The design methodology is inductive and stochastic, distinguished from the conventional, deductive, and procedural methods. To verify a robust operation, the effects of varied data patterns, noise, and channel loss are examined, together with the avoidance of harmonic locking. In addition, a consideration of a sample window is analyzed by fast Fourier transform (FFT) simulation. Fabricated in 40-nm low-power (LP) CMOS technology, the proposed CDR circuit achieves a capture range from 6.4 to 32 Gb/s and a lock time of less than <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$11 \mu \text{s}$ </tex-math></inline-formula> . The measured frequency acquisition behavior shows that harmonic locking is avoided with a seamless transition to the fundamental mode. The CDR circuit tested over a 10-dB loss channel achieves a bit error rate (BER) less than 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">−12</sup> and energy efficiency of 0.96 pJ/b.

Why did theWolbachiatransinfection cross the road? drift, deterministic dynamics, and disease control.

Maternally inherited Wolbachia transinfections are being introduced into natural mosquito populations to reduce the transmission of dengue, Zika, and other arboviruses. Wolbachia-induced cytoplasmic incompatibility provides a frequency-dependent reproductive advantage to infected females that can spread transinfections within and among populations. However, because transinfections generally reduce host fitness, they tend to spread within populations only after their frequency exceeds a critical threshold. This produces bistability with stable equilibrium frequencies at both 0 and 1, analogous to the bistability produced by underdominance between alleles or karyotypes and by population dynamics under Allee effects. Here, we analyze how stochastic frequency variation produced by finite population size can facilitate the local spread of variants with bistable dynamics into areas where invasion is unexpected from deterministic models. Our exemplar is the establishment of wMel Wolbachia in the Aedes aegypti population of Pyramid Estates (PE), a small community in far north Queensland, Australia. In 2011, wMel was stably introduced into Gordonvale, separated from PE by barriers to A. aegypti dispersal. After nearly 6 years during which wMel was observed only at low frequencies in PE, corresponding to an apparent equilibrium between immigration and selection, wMel rose to fixation by 2018. Using analytic approximations and statistical analyses, we demonstrate that the observed fixation of wMel at PE is consistent with both stochastic transition past an unstable threshold frequency and deterministic transformation produced by steady immigration at a rate just above the threshold required for deterministic invasion. The indeterminacy results from a delicate balance of parameters needed to produce the delayed transition observed. Our analyses suggest that once Wolbachia transinfections are established locally through systematic introductions, stochastic "threshold crossing" is likely to only minimally enhance spatial spread, providing a local ratchet that slightly-but systematically-aids area-wide transformation of disease-vector populations in heterogeneous landscapes.

Vibration and Uncertainty Analysis of Functionally Graded Sandwich Plate Using Layerwise Theory

In the present study, free vibration analyses of porous functionally graded material (FGM) sandwich plates are carried out in thermal environment. Two types of sandwich plates such as sandwich with FGM face sheets and homogeneous core and sandwich with homogeneous face sheets and FGM core are considered for free vibration analysis with nonlinear temperature variation over the thickness direction. The metal and ceramic components are assumed to be temperature dependent. The higher-order layerwise theory is adopted with an eight-noded rectangular element to build a finite element model for free vibration analysis. A radial basis function network (RBFN) based surrogate model is developed to investigate the stochastic frequency response due to the uncertain material properties. The accuracy and the efficiency of the RBFN model are established by comparing the results with that of Monte Carlo simulation. Further, the developed surrogate model is implemented to perform various parametric studies and sensitivity analyses. The influence of the volume fraction index, types of porosity, and thermal gradient on the stochastic frequency response are analyzed. Though the influence of different stochastic input parameters is strongly dependent on the volume fraction index, the mass density of metal is found to be the most sensitive parameter for the sandwich plate with FGM face sheets and homogeneous core.

Cosmic Coincidences of Primordial-Black-Hole Dark Matter.

If primordial black holes (PBHs) contribute more than 10% of the dark matter (DM) density, their energy density today is of the same order as that of the baryons. Such a cosmic coincidence might hint at a mutual origin for the formation scenario of PBHs and the baryon asymmetry of the Universe. Baryogenesis can be triggered by a sharp transition of the rolling rate of inflaton from slow-roll to (nearly) ultraslow-roll phases that produce large curvature perturbations for PBH formation in single-field inflationary models. We show that the baryogenesis requirement drives the PBH contribution to DM, along with the inferred PBH mass range, the resulting stochastic gravitational wave background frequency window, and the associated cosmic microwave background tensor-to-scalar ratio amplitude, into potentially observable regimes.

A Criterion and Stochastic Unit Commitment Towards Frequency Resilience of Power Systems

High-capacity long-distance transmission lines, such as high-voltage direct-current (HVDC) lines, are vulnerable to extreme weather. Their failures may cause significant power loss and frequency drop in the receiving-end power systems, which should be considered in the power system scheduling. In this paper, the failure rates of transmission lines subject to extreme weather conditions are firstly modeled to obtain the probability of failure events. Then, a novel criterion defined by the integration of abnormal frequency during the primary and secondary frequency regulation process is proposed to measure frequency security. This criterion is capable to reflect the cumulative frequency deviation effect and distinguish the contributions of different frequency regulation reserve providers, e.g., generators and flexible loads. Moreover, the linearity of the criterion makes it easy to be incorporated into optimization problems. Finally, a two-stage stochastic frequency constrained unit commitment (FCUC) model is developed to optimally schedule generators and flexible loads while satisfying the frequency security constraints under transmission line failure events. The proposed FCUC model is efficiently solved by a regularized L-shape algorithm. The proposed model and techniques are validated based on the modified IEEE 118 and 300 bus systems with realistic meteorological data.