Jérôme Morio

The French Aerospace Lab ONERA | ONERA · Information Processing and System Branch - TIS

Moment-independent importance measures are increasingly used by practitioners to understand how output uncertainty may be shared between a set of stochastic inputs. Computing Borgonovo's sensitivity indices for a large group of inputs is still a challenging problem due to the curse of dimensionality and it is addressed in this article. An estimatio...

Reliability assessment in presence of epistemic uncertainty leads to consider the failure probability as a quantity depending on the state of knowledge about uncertain input parameters. The input joint distribution is often learnt from a small-sized dataset provided by operating experience. The computed failure probability depends on the estimated...

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. In...

Airspace design is subject to a multitude of constraints, which are mainly driven by the concern to keep the risk of mid-air collision below a target level of safety. For that purpose, Monte Carlo simulation methods can be applied to estimate aircraft conflict probability but require the accurate generation of artificial trajectories. Generative mo...

Some classical uncertainty quantification problems require the estimation of multiple expectations. Estimating all of them accurately is crucial and can have a major impact on the analysis to perform, and standard existing Monte Carlo methods can be costly to do so. We propose here a new procedure based on importance sampling and control variates f...

Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine whi...

This paper proposes hybrid methods using physics-informed (PI) lightweight Temporal Convolution Neural Network (PITCN) for bearings’ remaining useful life (RUL) prediction under stiffness degradation. It includes three PI hybrid models: a) PI Feature model (PIFM) — constructing physics-informed health indicator (PIHI) to augment the feature space,...

Reliability-oriented sensitivity analysis aims at combining both reliability and sensitivity analyses by quantifying the influence of each input variable of a numerical model on a quantity of interest related to its failure. In particular, target sensitivity analysis focuses on the occurrence of the failure, and more precisely aims to determine whi...

Citation: Morio, J.; Junqua, I.; Bertuol, S.; Parmantier, J.-P. Optimisation of segregation distances between electric cable-bundles bundles embedded in a structure. Appl. Sci. 2021, 1, 0. https://doi.org/ Received: Accepted: Published: Publisher's Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional aff...

Aircraft trajectory generation is a high stakes problem with a wide scope of applications, including collision risk estimation, capacity management and airspace design. Most generation methods focus on optimizing a criterion under constraints to find an optimal path, or on predicting aircraft trajectories. Nevertheless, little in the way of contrib...

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we propose a new cross-entropy-based importance sampling algorithm to improve rare event probability estimation in...

In this paper we propose a dimension-reduction strategy in order to improve the performance of importance sampling in high dimension. The idea is to estimate variance terms in a small number of suitably chosen directions. We first prove that the optimal directions, i.e., the ones that minimize the Kullback--Leibler divergence with the optimal auxil...

This chapter considers a probabilistic framework for the input uncertainty modeling assuming sufficient information is available to construct a relevant input probabilistic model. It focuses on a specific class of reliability‐oriented sensitivity analysis (ROSA) methods and its extension to reliability problems involving two uncertainty levels in i...

This paper addresses the estimation of accurate extreme ground impact footprints and probabilistic maps due to a total loss of control of fixed-wing Unmanned Aerial Vehicles after a main engine failure. In this paper, we focus on the ground impact footprints that contains 95%, 99% and 99.9% of the drone impacts. These regions are defined here with...

Considérer le contexte incertain en ingénierie mécanique dans le but d’améliorer les performances des futurs produits ou systèmes apparaît désormais comme un avantage compétitif, voire une nécessité pour garantir une exigence de sûreté de plus en plus élevée. Ingénierie mécanique en contexte incertain traite de la modélisation, de la quantification...

Rare event probability estimation is an important topic in reliability analysis. Stochastic methods, such as importance sampling, have been developed to estimate such probabilities but they often fail in high dimension. In this paper, we propose a simple cross-entropy-based importance sampling algorithm to improve rare event estimation in high dime...

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive, requiring advanced simulation methods to reduce the overall numerical cost. Gaussian process based active learning methods for reliability analysis have emerged as a promising way for reducing this computational cost. The...

In rare event analysis, the estimation of the failure probability is a crucial objective. However , focusing only on the occurrence of the failure event may be insufficient to entirely characterize the reliability of the considered system. This paper provides a common estimation scheme of two complementary moment independent sensitivity measures, a...

Due to the large amount of electrical equipment aboard modern aircraft, several EMC problems appear which can be tackled by filtering disturbances at the equipment inputs and shielding cable links (braiding, covering, over-braiding). Among the others, the segregation between interfering cables or bundles of cables becomes crucial to ensure that cou...

Spotlighting the field of Multidisciplinary Design Optimization (MDO), this book illustrates and implements state-of-the-art methodologies within the complex process of aerospace system design under uncertainties. The book provides approaches to integrating a multitude of components and constraints with the ultimate goal of reducing design cycles....

Due to the large amount of electrical equipment aboard modern aircraft, several EMC problems appear which can be tackled by filtering disturbances at the equipment inputs and shielding cable links (braiding, covering, over-braiding). Among the others, the segregation between interfering cables or bundles of cables becomes crucial to ensure that cou...

Modern aircraft hosts a large number of electric systems. Due to the transition to a More Electrical Aircraft, future platforms will use even more electric systems. This increases the complexity of the EWIS design from an EMC point of view. When possible, segregation between potentially interfering cables or bundles is a convenient solution to avoi...

Segregation rules are one of the three solutions to overcome EMC problems together with filtering of disturbances at the equipment inputs and shielding of cable links (braiding, covering, over-braiding, etc.). These rules enable mass reduction in the selection of cables and optimal route definition in which compatible cables (having similar levels...

Assessing the reliability of a complex system with uncertainty propagation consists in estimating its probability of failure. Common sampling strategies for such tasks are notably based on Monte Carlo sampling. This kind of methods is well suited to characterize events of which associated probabilities are not too low with respect to the simulation...

The design process of complex systems such as aerospace vehicles involves physics-based and mathematical models. A model is a representation of the reality through a set of simulations and/or experimentations under appropriate assumptions. Due to simplification hypotheses, lack of knowledge, and inherent stochastic quantities, models represent real...

The uncertainty propagation consists in determining the impact of the input uncertainties of a simulation code on the outputs of this model. In the MDO context, the simulation code represents, for instance, a set of coupled disciplines and the uncertainty propagation consists in characterizing the multidisciplinary system outputs considering a give...

Optimization under uncertainty is a key problem in order to solve complex system design problem while taking into account inherent physical stochastic phenomena, lack of knowledge, modeling simplifications, etc. Different reviews of optimization techniques in the presence of uncertainty can be found in the literature. The choice of the algorithm is...

Running a reliability analysis on engineering problems involving complex numerical models can be computationally very expensive. Hence, advanced methods are required to reduce the number of calls to the expensive computer codes. Adaptive sampling based reliability analysis methods are one promising way to reduce computational costs. Reduced order m...

In reliability-based design, the estimation of the failure probability is a crucial objective. However, focusing only on the occurrence of the failure event may be insufficient to entirely characterize the reliability of the considered system. This paper provides a common estimation scheme of two complementary moment independent sensitivity measure...

The reliability analysis of complex systems often requires dealing with a computationally expensive simulation code. To estimate the failure probability, a frequently used method aims at propagating the input uncertainties through the black-box model. In this paper, as marginal distributions are assumed provided, the lack of knowledge about the joi...

Space launcher complexity arises, on the one hand, from the coupling between several subsystems such as stages or boosters and other embedded systems, and on the other hand, from the physical phenomena endured during the flight. Optimal trajectory assessment is a key discipline since it is one of the cornerstones of the mission success. However, du...

We present a new approach to separate air traffic trajectories in an area constrained by operational procedures. This technique is applied on a set of real trajectories in Toulouse terminal manoeuvring area (TMA). The resulting clusters foster good understanding of the structure of traffic and of how controllers schedule landings at Toulouse–Blagna...

In measurement-based probabilistic timing analysis, the execution conditions imposed to tasks as measurement scenarios, have a strong impact to the worst-case execution time estimates. The scenarios and their effects on the task execution behavior have to be deeply investigated. The aim has to be to identify and to guarantee the scenarios that lead...

Analytical and Monte Carlo DCNU prediction methods are compared. The difference is studied according to the different assumptions used for the calculations. The analysis is performed as a function of the incident proton fluence. The convergence of the DCNU toward a Gaussian distribution predicted by the central limit theorem is also investigated.

This paper aims at presenting sensitivity estimators of a rare event probability in the context of uncertain distribution parameters (which are often not known precisely or poorly estimated due to limited data). Since the distribution parameters are also affected by uncertainties, a possible solution consists in considering a second probabilistic u...

The moment-independent sensitivity analysis technique introduced by E. Borgonovo has gained increasing attention to characterize the uncertainties of complex systems and optimize their reliability. The estimation of the corresponding indices is a challenging task. In this paper, a new estimation scheme involving the copula estimation via maximum en...

Moment independent importance measures have been proposed by E. Borgonovo in order to alleviate some of the drawbacks of variance-based sensibility indices. They have gained increasing attention over the last years but their estimation remains a challenging issue. An effective estimation scheme in the case of correlated inputs, referred to as singl...

More than 90% of the space objects orbiting around the earth are space debris. Since the orbits of these debris often overlap the trajec-tories of spacecraft, they create a potential collision risk. The problem of removing the most dangerous space debris can be modeled as a biob-jective time dependent traveling salesman problem (BiTDTSP). In this p...

This paper describes a framework to automatically identify air traffic flows from a set of trajectories by using a clustering algorithm. The framework offers two methods to cluster trajectories, each one using a different distance/similarity measure between trajectories. Results and performance characteristics of both methods are compared by applyi...

Several methods of DCNU prediction (Monte Carlo and simplified methods based on the central limit theorem) are presented and compared with experimental data. Their domain of validity is explored on a large range of fluences.

This paper aims at comparing two different approaches to perform a reliability analysis in a context of uncertainties affecting probability distribution parameters. The first approach called “nested reliability approach” (NRA) is a classical double-loop-approach involving a sampling phase of the parameters and then a reliability analysis for each s...

The Measurement-Based Probabilistic Timing Analysis (MBPTA) infers probabilistic Worst-Case Execution Time (pWCET) estimates from measurements of tasks execution times; the Extreme Value Theory (EVT) is the statistical tool that MBPTA applies for inferring worst-cases from observations/measurements of the actual task behavior. MBPTA and EVT capabil...

Collision between satellites and space debris seldom happens, but the loss of a satellite by collision may have catastrophic consequences both for the satellite mission and for the space environment. To support the decision to trigger off a collision avoidance manoeuver, an adapted tool is the determination of the collision probability between debr...

The interacting particle system (IPS) for rare event algorithm has been well mathematically formulated, with a wide variety of results on the estimation accuracy of the probability of rare event. Despite this theoretical point of view, the practical side of this algorithm has not been handled completely. Indeed, a tuning parameter has a significant...

Maintaining some specific security zones between aircraft to avoid collisions is mandatory in air traffic management. In this paper, we improve the accuracy of conflict probability estimation with an interacting particle system (IPS) algorithm. More precisely, a set of intermediate conflict zones is automatically created during IPS procedure to red...

Task execution is heavily affected by the different elements composing real-time systems. Modeling and analyzing such effects would allow reducing the pessimism lying behind the worst-cases. A measurement-based probabilistic approach is developed in order to characterize cache behavior with prob-abilistic average and worst-case profiles. The approa...

Estimating rare event probability with accuracy is of great interest for safety and reliability applications. In this paper, we focus on rare events which can be modeled by a threshold exceedance of a deterministic input–output function with random inputs. Some parameters of this function or density parameters of input random variables may be fixed...

The estimation of launch vehicle fall back safety zone is a crucial problem in space application since the consequence of a mistake may be dramatic for the population. It consists in estimating the probability that the distance between the launcher stage fall-back position calculated, with a trajectory simulation code, and the predicted one is lowe...

The accurate estimation of rare event probabilities is a crucial problem in engi- neering to characterize the reliability of complex systems. Several methods such as Impor- tance Sampling or Importance Splitting have been proposed to perform the estimation of such events more accurately (i.e. with a lower variance) than crude Monte Carlo method. Ho...

Probabilistic Worst-Case Execution Time estimates, through Measurement-Based Probabilistic Timing Analyses and statistical inference, desperately need for formal definition and reliability. The automatic DIAGnostic tool for applying the eXTReMe value theory within the Probabilistic Timing Analysis framework we are proposing defines a complete set o...

In this chapter, we discuss several categories for the different efficient algorithms to estimate a rare event probability in the case of input–output functions. We also describe the toy cases that will be used to present and analyze the different rare event probability estimation methods.

Rare event probability (10 −4 and less) estimation has become a large area of research in the reliability engineering and system safety domains. A significant number of methods have been proposed to reduce the computation burden for the estimation of rare events from advanced sampling approaches to extreme value theory. However, it is often difficu...

In this chapter, we propose a synthesis of the different available rare event probability estimation methods for time-dependent systems. Doing so enables us to distinguish the most efficient algorithms from our experience using the Markov process modeling.

From our experience, most industrial systems can be categorized in two classes: input–output systems for which the system is seen as a black-box function and time-variant systems in which temporal evolution is taken into account. The characteristics of these systems are different, and, thus, rare event probability estimation methods often differ fr...

Conflict probability between aircraft in uncontrolled airspace can be estimated in simulation. In that case, a possible approach is to model aircraft trajectories with stochastic Markov processes. This use case consists in estimating the probability that the distance between two aircraft trajectories is lower than a given threshold during a time in...

In this chapter, we propose a synthesis for the different available rare event probability estimation methods. The object is to help the user to choose algorithms that are the best adapted to a specific case.

The estimation of a launch vehicle fallback safety zone is a very important problem in space application because the consequence of a mistake in the estimation can be dramatic for the populations. This test case consists in estimating the probability that the distance between the estimated launcher stage fallback position and the predicted one is g...

Collision between satellites and space debris seldom happens, but the loss of a satellite by collision can have catastrophic consequences both for the mission and the space environment. To support the decision to trigger a collision avoidance maneuver, an adapted measure is the estimation of the collision probability of debris and a satellite. We a...

Because of its take-off, an aircraft generates a wake essentially made of a pair of counter-rotating vortices notably characterized by their total circulation. In this test case, we analyze the evolution of wake vortex total circulation with the extreme value theory. It consists in estimating the probability that a wake vortex circulation exceeds a...

Complex simulation codes such as the ones used in aerospace industry are often computationally expensive and involve a large number of variables. These features significantly hamper the estimation of rare event probabilities. To reduce the computational burden, an analysis of the most important variables of the problem can be performed before apply...

Statistical techniques enable to derive a probability estimate and associated confidence interval with a fixed set of samples . The main statistical approaches, extreme value theory and large deviation theory, model the behavior of the pdf tails. This chapter reviews the theoretical features of these techniques

In this chapter, we analyze the different methods for estimating the probability of a rare event in dynamical systems modeled by Markov chains. These algorithms are relatively similar in principle to the ones defined for static input–output systems. Some special developments must nevertheless be considered for an efficient applicability.

Crude Monte Carlo methods are well suited to characterize events of which associated probabilities are not too low with respect to a given simulation budget. For very seldom observed events, such as the collision probability between two aircraft in airspace, Monte Carlo based approaches do not lead to accurate results. Indeed, the number of availab...

Simulation techniques consist in sampling the input and characterizing the uncertainty of the corresponding output. This is notably the case of the crude Monte Carlo method that is well suited to characterize events whose associated probabilities are not too low with respect to the simulation budget. However, for very seldom observed events, this a...

It is necessary to have a minimal knowledge of some fundamental definitions and theorems of probability and statistics to understand the principles of the different rare event probability estimation methods. The main goal of this chapter is thus to review the elementary notions on this subject, which will be continuously used in the remainder of th...