Http:// Monte-Carlo based Expertise A powerful Tool for System Evaluation & Optimization Introduction Features System Performance

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Monte-Carlo based ExpertiseMonte-Carlo based ExpertiseA powerful Tool for System Evaluation & OptimizationA powerful Tool for System Evaluation & Optimization

IntroductionIntroduction FeaturesFeatures System Performance EvaluationSystem Performance Evaluation Optimal Control DesignOptimal Control Design


IntroductionIntroduction In order to validate a system in a robust sense, it is not enough to In order to validate a system in a robust sense, it is not enough to

rely on the results of a nominal System Simulation, only optimal rely on the results of a nominal System Simulation, only optimal for a single specific environment.for a single specific environment.

Robust design consists of searching for a product design that Robust design consists of searching for a product design that guarantees low variations in the performance level of the system guarantees low variations in the performance level of the system due to uncontrolled environmental variations. due to uncontrolled environmental variations.

This approach leads to what is known as a system parameter This approach leads to what is known as a system parameter optimization that tend to minimize the risk of getting poor optimization that tend to minimize the risk of getting poor performance when the environment changes.performance when the environment changes.

This risk is evaluated by simulating the system over a range of This risk is evaluated by simulating the system over a range of environmental scenarios.environmental scenarios.


Introduction Introduction (ctd.)(ctd.)

““Monte Carlo” (MC) is a method of calculation based on Monte Carlo” (MC) is a method of calculation based on combining the operation of an automaton with the intentional combining the operation of an automaton with the intentional injection of random datainjection of random data

The Monte Carlo method is, in certain practical cases, more The Monte Carlo method is, in certain practical cases, more efficient in arriving at correct answers than purely efficient in arriving at correct answers than purely deterministic methods - since the random data represent real-deterministic methods - since the random data represent real-life variables uncertaintieslife variables uncertainties


Introduction Introduction (ctd.)(ctd.)

The Monte-Carlo (MC) Simulation Mode is a batch of System The Monte-Carlo (MC) Simulation Mode is a batch of System Simulation runsSimulation runs

Each run uses a different set of parameters and variables Each run uses a different set of parameters and variables which reflect its uncertaintieswhich reflect its uncertainties

Each MC run starts by selecting the constant parameters Each MC run starts by selecting the constant parameters randomly from their distribution functions, whereas the time randomly from their distribution functions, whereas the time dependent processes are selected randomly during the rundependent processes are selected randomly during the run

The MC Mode purpose is to verify the design of a System and The MC Mode purpose is to verify the design of a System and determine its performance in a statistical way to reach the goal determine its performance in a statistical way to reach the goal of “Robust System”of “Robust System”


FeaturesFeatures Generic method: any type of application can use this methodGeneric method: any type of application can use this method

Repeatability of parameter perturbations between the same run in all the Repeatability of parameter perturbations between the same run in all the applications using this methodapplications using this method

Capability of reconstructing a particular discrete run without running the Capability of reconstructing a particular discrete run without running the whole batchwhole batch

can solve a family of problems, not just a single nominal case.can solve a family of problems, not just a single nominal case.

The Monte-Carlo method is a complete procedure that include intrinsically The Monte-Carlo method is a complete procedure that include intrinsically a number of other major applications, like optimization, parametric a number of other major applications, like optimization, parametric studies, sensitivity analyses, what-if analyses, etc.studies, sensitivity analyses, what-if analyses, etc.

It provides a natural link to experimentation and tests reconstruction.It provides a natural link to experimentation and tests reconstruction.

That method is a technology that treat multi-disciplinary problems just as That method is a technology that treat multi-disciplinary problems just as easily as simple problems. easily as simple problems.


System Performance evaluationSystem Performance evaluation CEP and SEP calculationsCEP and SEP calculations

Sleeves of selected parametersSleeves of selected parameters

Safety Zones analysisSafety Zones analysis

Statistical analysisStatistical analysis


System Performance evaluationSystem Performance evaluation

Example: Typical UAV automatic landing scenario analyzed by Monte-Carlo


ImplementationImplementationMonte-Carlo based Optimal Control DesignMonte-Carlo based Optimal Control Design

finding the set of decision parameters that minimizes a performance index (i.e. finding the set of decision parameters that minimizes a performance index (i.e. cost function) of a static or dynamic system for a given application.cost function) of a static or dynamic system for a given application.

Monte-Carlo method enables to evaluate the spectrum of parameters of Monte-Carlo method enables to evaluate the spectrum of parameters of interest of a system, as determined by the incertitude /variation range of the interest of a system, as determined by the incertitude /variation range of the system's physical parameters as well as sensor measurements, for a given set of system's physical parameters as well as sensor measurements, for a given set of decision parameters.decision parameters.

By connecting the Monte-Carlo process to an Optimization master module, By connecting the Monte-Carlo process to an Optimization master module, one can find the optimal set of decision/control parameters over all the possible one can find the optimal set of decision/control parameters over all the possible behaviors of any stochastic system, depending on the physical parameters behaviors of any stochastic system, depending on the physical parameters fluctuation model (For example, an optimal automatic landing and take-off fluctuation model (For example, an optimal automatic landing and take-off system will provide the minimum standard deviation of the touch down point. system will provide the minimum standard deviation of the touch down point. In the passengers transport domain, a train/bus/shuttle schedule management In the passengers transport domain, a train/bus/shuttle schedule management can be optimized to achieve the maximum passengers flow per time).can be optimized to achieve the maximum passengers flow per time).


ImplementationImplementationMonte-Carlo based Optimal Control DesignMonte-Carlo based Optimal Control Design

This optimal control tool is based on a Conjugate Gradient This optimal control tool is based on a Conjugate Gradient Method algorithm that computes an updated decision vector at Method algorithm that computes an updated decision vector at each iteration until the nearest local minimum of the performance each iteration until the nearest local minimum of the performance index is reached. The algorithm handles equality and inequality index is reached. The algorithm handles equality and inequality constraints in the parameters of decision, by adding penalty constraints in the parameters of decision, by adding penalty functions to the desired performance index. The problem of functions to the desired performance index. The problem of finding local minimum versus absolute minimum is solved by finding local minimum versus absolute minimum is solved by trying different initial guess for each decision parameters.trying different initial guess for each decision parameters.

The whole optimization process is illustrated in the following The whole optimization process is illustrated in the following figure:figure:


Monte Carlo based Optimal ControlMonte Carlo based Optimal Control

OPTIMIZATION

Module

MONTE-CARLO

Processor

Decision / Control System

Platform /system Physical Model

Post-Run Analysis

Updated control parameters

Random variables

SYSTEM SIMULATION

Initial Guess

Constraints

Performance index

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Http:// Monte-Carlo based Expertise A powerful Tool for System Evaluation & Optimization Introduction Features System Performance