Knowledge Of Instants Research Articles

Influence of uncertain identification of triggering rainfall on the assessment of landslide early warning thresholds

Abstract. Uncertainty in rainfall datasets and landslide inventories is known to have negative impacts on the assessment of landslide-triggering thresholds. In this paper, we perform a quantitative analysis of the impacts of uncertain knowledge of landslide initiation instants on the assessment of rainfall intensity–duration landslide early warning thresholds. The analysis is based on a synthetic database of rainfall and landslide information, generated by coupling a stochastic rainfall generator and a physically based hydrological and slope stability model, and is therefore error-free in terms of knowledge of triggering instants. This dataset is then perturbed according to hypothetical reporting scenarios that allow simulation of possible errors in landslide-triggering instants as retrieved from historical archives. The impact of these errors is analysed jointly using different criteria to single out rainfall events from a continuous series and two typical temporal aggregations of rainfall (hourly and daily). The analysis shows that the impacts of the above uncertainty sources can be significant, especially when errors exceed 1 day or the actual instants follow the erroneous ones. Errors generally lead to underestimated thresholds, i.e. lower than those that would be obtained from an error-free dataset. Potentially, the amount of the underestimation can be enough to induce an excessive number of false positives, hence limiting possible landslide mitigation benefits. Moreover, the uncertain knowledge of triggering rainfall limits the possibility to set up links between thresholds and physio-geographical factors.

Itô–Volterra Optimal State Estimation With Continuous, Multirate, Randomly Sampled, and Delayed Measurements

The optimal filter for continuous, linear, stochastic, time-varying systems described by the Itocirc-Volterra equations with discontinuous measure is derived. With an appropriately selected measure, the result is applicable to a wide range of observation processes, including the hybrid case of observations formed by an arbitrary combination of continuous and discrete measurements, which may be sampled with a priori unknown, changing, and, possibly, random rates and delays. The simultaneous presence of continuous and sampled measurements causes impulsive discontinuity in the inputs of the optimal filter equations, which leads to a discontinuous change in state estimates every time a sampled measurement becomes available. Using the theory of vibrosolutions, the explicit and unique expressions for the jumps in state estimates and estimation error covariance are derived. Several examples illustrate the procedure of modeling hybrid measurement systems by selecting an appropriate discontinuous measure. We further show that the Itocirc-Volterra model and the main result of the paper can be specialized to several important cases, including state space systems, for which we recover several known state estimation results, and derive a novel optimal filter for continuous LTV systems with an arbitrary combination of continuous and delayed sampled measurements. This optimal filter updates the state estimates for incoming measurements as soon as they become available and does not require prior knowledge of sampling instants and delays, which makes it applicable when deterministic and random changes in sampling and delays are present. Several computational examples demonstrate the implementation of the developed filter and compare its performance to the traditional alternatives using Monte-Carlo simulations

Adaptive Lexicographic Optimization in Multi-Class M/GI/1 Queues

We consider a multi-class M/GI/1 system, in which an average response time objective is associated with each class. The performance of each class is measured by the ratio of the average response time over the corresponding value of the objective. To achieve fairness in service allocation it is required to find a policy that lexicographically minimizes the vector of performance ratios arranged in nonincreasing order. We provide such a policy that is adaptive, uses only knowledge of arrival and departure instants, and is thus easy to implement. We also consider a variant of this policy which adapts faster to changes in the statistical parameters of the model. Both policies are analyzed via associated stochastic recursions using techniques of stochastic approximation.