Magnitude Of Stochasticity Research Articles

Maximum likelihood estimation of probabilistically described loads in beam structures

In recent years, focus has been shifted towards predictive maintenance in an effort to improve the reliability of operating structures. Processing structural response data obtained from in-situ sensors during operation can provide added value towards this direction. Structural Health Monitoring (SHM) methods are uniquely suited for this task; however, accounting for the effect of stochastic structural loads is critical for their robustness. In this work, a framework based on Maximum Likelihood Estimation (MLE) is presented, whose goal is to obtain inferences on typically unobservable quantities that describe stochastic structural loading. A structural beam is employed as a demonstrative case study, that is subjected to point loads with stochastic magnitude and application points. The hyperparameters that govern their underlying probability distribution functions (pdf) are the quantities of inferential interest. The inverse (load) identification process is performed using a marginalized MLE objective, where stochastic Monte Carlo (MC) integration is employed to perform the marginalization and Genetic Algorithms (GAs) are used as the optimizer. The Cramer–Rao (CR) lower bound is used to produce 95 % Confidence Intervals (CIs) to quantify estimation uncertainty.

Deterministic and stochastic components of atmospheric CO[formula omitted] inside forest canopies and consequences for predicting carbon and water exchange

Atmospheric CO2 concentrations strongly influence the exchange of energy, water and carbon between the atmosphere and the terrestrial biosphere. The CO2 available to plants can be highly variable given the stochastic nature of the phenomena involved in its dynamics. However, most terrestrial ecosystem models consider CO2 concentration as a quasi-deterministic variable or use measurements taken from heights above the canopy where CO2 is usually well mixed. Therefore, in this study, we aimed to evaluate if a stochastic treatment of CO2 concentrations leads to different predictions of carbon assimilation (An) and transpiration (T) compared to a strictly deterministic approach, as well as the use of CO2 measurements from different heights. To address this goal, we used a set of observations taken in forests from the ICOS network and the ATTO research site. We applied the exponential smoothing method to decompose the time series into their trend, seasonal and stochastic (residual) components. We found that the residual component of CO2 (rCO2) follows a Laplace probability density function and its stochastic magnitude is inversely proportional to the height above the ground. To quantify the degree to which predictions of An and T would be affected by stochastic effects, we ran simulations considering the different components of the time series and Farquhar’s and Penman–Monteith’s models. We found significant differences in the predictions of An and T for diverse heights, with larger An (T) fluxes closer (farther) to the ground. Still, this effect is mainly due to the deterministic component that increases with decreasing height. The stochastic component tends to reduce (increase) An (T) compared to the deterministic approach. However, the difference between approaches is not large enough to compensate for the deterministic effect, suggesting that there is no merit for the consideration of rCO2 in future simulations as long as measurements taken inside the canopy are used.

Reconstructing ecological networks with noisy dynamics.

Ecosystems functioning is based on an intricate web of interactions among living entities. Most of these interactions are difficult to observe, especially when the diversity of interacting entities is large and they are of small size and abundance. To sidestep this limitation, it has become common to infer the network structure of ecosystems from time series of species abundance, but it is not clear how well can networks be reconstructed, especially in the presence of stochasticity that propagates through ecological networks. We evaluate the effects of intrinsic noise and network topology on the performance of different methods of inferring network structure from time-series data. Analysis of seven different four-species motifs using a stochastic model demonstrates that star-shaped motifs are differentially detected by these methods while rings are differentially constructed. The ability to reconstruct the network is unaffected by the magnitude of stochasticity in the population dynamics. Instead, interaction between the stochastic and deterministic parts of the system determines the path that the whole system takes to equilibrium and shapes the species covariance. We highlight the effects of long transients on the path to equilibrium and suggest a path forward for developing more ecologically sound statistical techniques.

Estimating 3D Movements from 2D Observations Using a Continuous Model of Helical Swimming

Helical swimming is among the most common movement behaviors in a wide range of microorganisms, and these movements have direct impacts on distributions, aggregations, encounter rates with prey, and many other fundamental ecological processes. Microscopy and video technology enable the automated acquisition of large amounts of tracking data; however, these data are typically two-dimensional. The difficulty of quantifying the third movement component complicates understanding of the biomechanical causes and ecological consequences of helical swimming. We present a versatile continuous stochastic model-the correlated velocity helical movement (CVHM) model-that characterizes helical swimming with intrinsic randomness and autocorrelation. The model separates an organism's instantaneous velocity into a slowly varying advective component and a perpendicularly oriented rotation, with velocities, magnitude of stochasticity, and autocorrelation scales defined for both components. All but one of the parameters of the 3D model can be estimated directly from a two-dimensional projection of helical movement with no numerical fitting, making it computationally very efficient. As a case study, we estimate swimming parameters from videotaped trajectories of a toxic unicellular alga, Heterosigma akashiwo (Raphidophyceae). The algae were reared from five strains originally collected from locations in the Atlantic and Pacific Oceans, where they have caused Harmful Algal Blooms (HABs). We use the CVHM model to quantify cell-level and strain-level differences in all movement parameters, demonstrating the utility of the model for identifying strains that are difficult to distinguish by other means.

THRESHOLD HARVESTING FOR SUSTAINABILITY OF FLUCTUATING RESOURCES

Commercially important species often are overexploited, and many endan- gered mammals and birds are threatened by hunting and international trade. To sustain biological resources requires harvesting strategies that maximize yield while accounting for stochastic dynamics, uncertainty, and risk of resource collapse or extinction. For a large class of population dynamics, the optimal strategy is to harvest all individuals above a threshold population size, with no harvest below the threshold. Maximizing the expected cumulative harvest before extinction puts the optimal threshold at carrying capacity, re- gardless of the form of expected dynamics or the magnitude of stochasticity. Maximizing the mean annual yield lowers the optimal threshold, which then depends on the form of expected dynamics and the magnitude of stochasticity. Uncertainty in estimated population sizes increases the threshold, and with large uncertainty, the optimal strategy is proportional threshold harvesting, involving harvest of only a fraction of the excess in estimated pop- ulation above the threshold. The theoretical justification for the common strategy of a constant harvest rate is extremely weak in comparison to that for optimal threshold strat- egies. Thresholds are a necessary feature of any harvesting strategy with the objective of minimizing risks of resource depletion or extinction, while optimizing yields.