Stéphane Segonds

Optimization Based Algorithms for Uncertainty Propagation Through Functions With Multidimensional Output Within Evidence Theory

Evidence theory is one of the approaches designed specifically for dealing with epistemic uncertainty. This type of uncertainty modeling is often useful at preliminary design stages where the uncertainty related to lack of knowledge is the highest. While multiple approaches for propagating epistemic uncertainty through one-dimensional functions have been proposed, propagation through functions having a multidimensional output that need to be considered at once received less attention. Such propagation is particularly important when the multiple function outputs are not independent, which frequently occurs in real world problems. The present paper proposes an approach for calculating belief and plausibility measures by uncertainty propagation through functions with multidimensional, nonindependent output by formulating the problem as one-dimensional optimization problems in spite of the multidimensionality of the output. A general formulation is first presented followed by two special cases where the multidimensional function is convex and where it is linear over each focal element. An analytical example first illustrates the importance of considering all the function outputs at once when these are not independent. Then, an application example to preliminary design of a propeller aircraft then illustrates the proposed algorithm for a convex function. An approximate solution found to be almost identical to the exact solution is also obtained for this problem by linearizing the previous convex function over each focal element.

Compensation for machining defects due to spindle dilatation

Defects are a common occurrence in industry when it comes to prolonged machining tasks (machining moulds, series of work-pieces, etc.). The relatively long machining time is generally what gives significant value added to the work-piece. We therefore need to avoid having to produce test work-pieces as much as possible [NC Machines, Hermes Paris (1997)]. This article considers dispersions introduced by dilatation of the spindle during machining on NC machine tools. Such dispersions are obviously prejudicial to obtaining accurate dimensions along the Z-axis of the machine. Firstly, we introduce the context of the study and the problem we had to confront. Secondly, the experimental study enabled us to highlight those parameters having an influence and quantify defects. By expressing dilatation and relaxation in the form of an equation, we were then able to calculate defects at a given instant. This enabled us to generate an algorithm for processing of the N.C. program so we could correct errors by compensating for defects during machining. We completed the study by machining a series of work-pieces using the programme integrating compensation for dilatation so as to validate the approach.

Using the global optimisation methods to minimise the machining path length of the free-form surfaces in three-axis milling

During the machining of free-form surfaces using three-axis numerically controlled machine (NC), several parameters are chosen arbitrary and one of the most important is the feed motion direction. The main objective of this study is to minimise the machining time of complex surfaces while respecting a scallop height criteria. The analytical expression of the machining time is not known and by hypothesis, it is assumed to be proportional to the path length crossed by the cutting tool. This path length depends on the feed direction. To have an optimal feed direction at any point, the surface is divided into zones with low variation of the steepest slope direction. The optimization problem was formulated aiming at minimizing the global path length. Furthermore, a penalty reflecting the time loss due to the movement of the tool from one zone to another one is taken into account. Several heuristics are used to resolve this problem: Clarke and Wrights, Greedy randomized adaptive search procedure, Tabu search and Nearest neighbour search. An example illustrates our work by applying the different heuristics on a test surface. After simulations, the results obtained present a significant saving of paths length of 24% compared to the machining in one zone.

Method for rapid characterisation of cutting forces in end milling considering runout

Pocket machining is currently performed by moulds and dies manufacturers as well as in the aeronautical industry. The good prediction of cutting forces during end milling is so required in order to determine the behaviour of the tool and the workpiece that are the cause of a large number of defects and breakages, or to effectively size the clamping system. Cutting forces depend on a large number of factors, because of cutting parameters and runouts. This study proposes a new method for rapid characterisation of the cutting forces during end milling for a given tool/material couple, from a unique reference test using a single-tooth milling cutter. The variations in forces due to changes in cutting conditions, as in the corners of pockets, as well as axial and radial runouts of the teeth, are integrated in order to effectively predict the instantaneous cutting forces. The comparison between predicted and measured forces is presented. This approach is validated through a milling operation.

Determination of angular fields outside low and high collisions to mill free-form surfaces on 5-axis CNC Machines

The present article addresses positioning of a flat end milling cutter to ensure avoidance of local and global interference. The activity concerned is end milling of parts modelled by free-form surfaces on 5-axis numerical control machines. The tool positioning defined here uses two corrective angles and thus takes full advantage of all the possibilities for 5-axis machine movement. Local interference is cancelled out from a set of points defining the domain of the surface in collision with the cutter and an angular solution domain is proposed to orient the cutter. Global interference is resolved using a set of points; here too, a collision-free angular domain is defined. To obtain a collision-free tool, the two previously mentioned angular domains are superimposed. An additional corrective method is defined if no solution is found using the previous method. Finally, positioning free from local and global interference is obtained. The method was coded and positioning simulations were used to validate the approachs effectiveness.

Tool flank wear influence on workpiece heating in dry machining

Following a lathe turning operation modification in order to work in dry machining condition, it appears that new tools and cutting condition modifications where insufficient to recover surface quality previously obtained with cutting fluid. Indeed, workpiece temperature evolutions produced with a single tool insert have conducted preventive replacements but no law where found for this substitution. Some responses have been found in literature review, especially on cutting zone temperature estimation in orthogonal and dry cutting with a new tool. But no solutions are provided to avoid production drop due to the important temperature raise in the cutting zone. The aim of this paper is to study tool flank wear influence on workpiece temperature distribution during dry cutting operations. The first part stands up a new analytical model, which takes account of tool wear and elastic deformation of the workpiece in heat generation in the cutting zone. The second part shows by an experimental procedure that temperature growth in cutting zone during machining process is dependant on the tool flank wear evolution.

Methodology Based on Multiagent for Solving Multidisciplinary Optimization Problem Under Uncertainty

T HERE are a large number ofmethodologies available inmultidisciplinary design optimization (MDO) for deterministic environments [1–3]. However, to design systems that are both robust and reliable, uncertainties regarding models and parameters have to be catered for to ensure success of the project in terms of timeliness, cost, and performance. This is crucial, especially during the preliminary design phasewhere there are still many uncertainties and decisions have to be compatible with the more detailed analysis of future development phases. To cope with this problem, reliability-based and robust design methods [4] have been developed to assist designers in the decision-making process. A number of relatively time-consuming techniques to solve optimization problems under uncertainty have been devised [5–8]. The main drawback with these methods is the computational burden associated with evaluation of robustness and reliability during design. A powerful methodology stemming from artificial intelligence, the autoadaptive multiagent system (AMAS), has recently been developed to solve complexmultidisciplinary optimization problems, especially in the aeronautical field [9–11]. Due to both its local and parallel approach, the AMAS method allows complex deterministic optimization problems to be solved rapidly, even in multidisciplinary contexts such as aircraft design where thermal engineering, structural, and fluid mechanics issues all interact. However, the said AMASmethodwas developed to respond to a deterministic environment only. The aim of the present Note is to extend theAMASmethodwith its multiagent framework to copewithMDO under conditions of uncertainty, providing a new methodology so it can be effectively used in an uncertain environment. To do so, a strategy to integrate and propagate uncertainties in themultiagent framework is first developed. Then, to optimize computing time,multiagent propagation is combined with a sequential optimization process coupled with the use of AMAS. This Note is organized as follows. Section II gives the approach used to solve a deterministic multidisciplinary optimization problem with a multiagent system. For didactic purposes, this approach is presented through an extremely simple mathematical application. Section III then goes on to describe the proposedmethodology to solveMDOproblems in an uncertain environment. This section is broken down into two subsections. The first describes the integration and propagation of uncertainties in the multiagent framework, whereas the second looks at the interactions between uncertainty propagation, the sequential optimization process, and the AMAS method. More precisely, at each step of the sequential optimization process, the AMAS method is effectively used to solve a deterministic optimization problem. From the given AMAS deterministic optimum, a reliability analysis is than conducted. Violated constraints are shiftedwith the introduction of adaptive safety coefficients as computed from multiagent uncertainty propagation. These coefficients are applied to define a new deterministic optimization problem to be solved by the AMAS over the following cycle. Iterations stop once the safety coefficients have been brought down to a low enough level. Finally, in Sec. IV, this newmethodology is applied to a preliminary aircraft design test case. Results show substantial improvements in terms of robustness and efficiency comparedwith the standard double-loop optimization process used to solve classicalMDOproblems. Conclusions and perspectives are presented in Sec. V.

Milling plan optimization with an emergent problem solving approach

To minimize the machining time of the free-form surfaces.Using the Adaptive Multi-Agent System approach to resolve this problem.A visualization program for zoning surface is developed.Optimal cutting is presented on an industrial example. With elaboration of products having the more complex design and good quality, minimize machining time becomes very important. The machining time is assumed, by hypothesis, to be proportional to the paths length crossed by the tool on the surface. The path length depends on the feed direction and the surface topology. To get an optimal feed direction at all points of surface, this study concerns machining with zones of the free-form surfaces on a 3-axis machine tool. In each zone, the variation of the steepest slope direction is lower, total path length is minimized and the feed direction is near the optimal feed direction. To resolve this problem, the Adaptive Multi-Agent System approach is used. Furthermore, a penalty reflecting the displacement of the tool from a zone to another one is taken into account. After several simulations and comparisons with the machining in one zone (what is being done at present), the results obtained present a significant saving about 22%.

Belief and plausibility approximation methods for multidimensional functions

Evidence theory is one of the approaches designed s pecifically for dealing with epistemic uncertainty. While multiple approaches for propagating epistemic uncertainty through onedimensional functions have been proposed, propagation through multidimensional functions received less attention. Such propagation is partic ularly important when the multiple function outputs are not independent. The present paper proposes various algorithms for calculating belief and plausibility measures by unc ertainty propagation through multidimensional functions. A general approach is f irst presented followed by approaches in cases where the function is convex or linear over e ach focal element. An analytical example illustrates the importance of considering the funct ion output together when they are not independent. An application example to preliminary design of a propeller aircraft then illustrates the proposed algorithms for the convex and the linear cases. While the linear case is only an approximate method in this example it st ill found the exact results here.

One Engine Out Takeoff Trajectory Optimization

Aircraft Maximum TOW (Takeo Weight) is calculated on the SID (Standard Instrument Departure) in the case of a engine failure, so as to respect regulatory constraints. In case of mountainous landscape, a alternative trajectory can be design to reduce obstacle clearance constraints. This trajectory, called EOSID (Engine Out Standard Instrument Departure) is only used in the case of engine failure. Nowadays, EOSID are designed manually by engineers. The aim of this study is to develop a software able to optimize EOSID lateral path so as to maximize the regulatory TOW. In case of mountainous landscape, a alternative takeo trajectory, called EOSID (Engine Out Standard Instrument Departure), can be design to reduce obstacle clearance constraints. The aim of this study is to develop a software able to optimize EOSID lateral path so as to maximize the TOW. In case of mountainous landscape and one engine failure during takeo, an alternative trajectory called EOSID (Engine Out Standard Instrument Departure) that reduces obstacle clearance constraints is flown. This study aims at developing a software that optimizes EOSID lateral path so as to maximize the TOW.