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DOE OSTI2016

Evaluation of Robustness to Setup and Range Uncertainties for Head and Neck Patients Treated With Pencil Beam Scanning Proton Therapy

Purpose: To evaluate the robustness of head and neck plans for treatment with intensity modulated proton therapy to range and setup errors, and to establish robustness parameters for the planning of future head and neck treatments. Methods and Materials: Ten patients previously treated were evaluated in terms of robustness to range and setup errors. Error bar dose distributions were generated for each plan, from which several metrics were extracted and used to define a robustness database of acceptable parameters over all analyzed plans. The patients were treated in sequentially delivered series, and plans were evaluated for both the first series and for the combined error over the whole treatment. To demonstrate the application of such a database in the head and neck, for 1 patient, an alternative treatment plan was generated using a simultaneous integrated boost (SIB) approach and plans of differing numbers of fields. Results: The robustness database for the treatment of head and neck patients is presented. In an example case, comparison of single and multiple field plans against the database show clear improvements in robustness by using multiple fields. A comparison of sequentially delivered series and an SIB approach for this patient show both to be of comparable robustness, although the SIB approach shows a slightly greater sensitivity to uncertainties. Conclusions: A robustness database was created for the treatment of head and neck patients with intensity modulated proton therapy based on previous clinical experience. This will allow the identification of future plans that may benefit from alternative planning approaches to improve robustness.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2013

Effectiveness of robust optimization in intensity-modulated proton therapy planning for head and neck cancers

Purpose: Intensity-modulated proton therapy (IMPT) is highly sensitive to uncertainties in beam range and patient setup. Conventionally, these uncertainties are dealt using geometrically expanded planning target volume (PTV). In this paper, the authors evaluated a robust optimization method that deals with the uncertainties directly during the spot weight optimization to ensure clinical target volume (CTV) coverage without using PTV. The authors compared the two methods for a population of head and neck (H and N) cancer patients. Methods: Two sets of IMPT plans were generated for 14 H and N cases, one being PTV-based conventionally optimized and the other CTV-based robustly optimized. For the PTV-based conventionally optimized plans, the uncertainties are accounted for by expanding CTV to PTV via margins and delivering the prescribed dose to PTV. For the CTV-based robustly optimized plans, spot weight optimization was guided to reduce the discrepancy in doses under extreme setup and range uncertainties directly, while delivering the prescribed dose to CTV rather than PTV. For each of these plans, the authors calculated dose distributions under various uncertainty settings. The root-mean-square dose (RMSD) for each voxel was computed and the area under the RMSD-volume histogram curves (AUC) was used to relatively compare plan robustness. Data derived from the dose volume histogram in the worst-case and nominal doses were used to evaluate the plan optimality. Then the plan evaluation metrics were averaged over the 14 cases and were compared with two-sided paired t tests. Results: CTV-based robust optimization led to more robust (i.e., smaller AUCs) plans for both targets and organs. Under the worst-case scenario and the nominal scenario, CTV-based robustly optimized plans showed better target coverage (i.e., greater D{sub 95%}), improved dose homogeneity (i.e., smaller D{sub 5%}- D{sub 95%}), and lower or equivalent dose to organs at risk. Conclusions: CTV-based robust optimization provided significantly more robust dose distributions to targets and organs than PTV-based conventional optimization in H and N using IMPT. Eliminating the use of PTV and planning directly based on CTV provided better or equivalent normal tissue sparing.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

SU-E-J-137: Incorporating Tumor Regression Into Robust Plan Optimization for Head and Neck Radiotherapy

Purpose: To develop a robust planning paradigm which incorporates a tumor regression model into the optimization process to ensure tumor coverage in head and neck radiotherapy. Methods: Simulation and weekly MR images were acquired for a group of head and neck patients to characterize tumor regression during radiotherapy. For each patient, the tumor and parotid glands were segmented on the MR images and the weekly changes were formulated with an affine transformation, where morphological shrinkage and positional changes are modeled by a scaling factor, and centroid shifts, respectively. The tumor and parotid contours were also transferred to the planning CT via rigid registration. To perform the robust planning, weekly predicted PTV and parotid structures were created by transforming the corresponding simulation structures according to the weekly affine transformation matrix averaged over patients other than him/herself. Next, robust PTV and parotid structures were generated as the union of the simulation and weekly prediction contours. In the subsequent robust optimization process, attainment of the clinical dose objectives was required for the robust PTV and parotids, as well as other organs at risk (OAR). The resulting robust plans were evaluated by looking at the weekly and total accumulated dose to the actual weekly PTV and parotid structures. The robust plan was compared with the original plan based on the planning CT to determine its potential clinical benefit. Results: For four patients, the average weekly change to tumor volume and position was −4% and 1.2 mm laterally-posteriorly. Due to these temporal changes, the robust plans resulted in an accumulated PTV D95 that was, on average, 2.7 Gy higher than the plan created from the planning CT. OAR doses were similar. Conclusion: Integration of a tumor regression model into target delineation and plan robust optimization is feasible and may yield improved tumor coverage. Part of this research is supported by Varian Medical System.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

TH-C-BRD-11: Robustness of Pencil Beam Scanning Proton Therapy for Pelvic Cancer Under Anatomical Changes

Purpose: Pencil beam scanning (PBS) proton therapy provides excellent dosimetric benefits in pelvic cancer treatment, yet day-to-day anatomical variations in pelvic region tend to cause range uncertainties. This study evaluates the dosimetric robustness under anatomical changes for three PBS intensity-modulated proton therapy (IMPT), IMPT using worstcase robust optimization (thereafter ‘Robust IMPT’), and single-field uniform dose (SFUD), in cervical cancer treatment. Methods: IMPT, Robust IMPT, and SFUD plans using the same beam directions and the same prescription (Rx) were generated on computed tomography (CT) images acquired on the simulation day. The dose from each plan was then recomputed on CT images acquired in subsequent two to five weeks using the same protocol. The weekly CTs were registered to the planning CT based on bony anatomy. Target coverage was considered adequate on each weekly CT if dose to 99% of the internal target volume (D-ITV99%) reached at least 95% of the Rx dose. Statistical analysis was then performed on the 21 weekly CT images available for the 7 enrolled patients. Results: Statistically, IMPT was unable to maintain target coverage (mean D-ITV99% = 90.5% Rx, p = 0.004), and SFUD was able to maintain target coverage (mean D-ITV99% = 98.0% Rx, p = 0.0064), in the weeks following simulation. Robust IMPT was able to improve the robustness of IMPT significantly (p < 0.0001), though its maintenance of target coverage was not statistically significant by the 95% Rx criteria (mean D-ITV99% = 96.0%, p = 0.1677). Conclusion: During the multi-week treatment course with anatomical variations, SFUD is robust in terms of maintaining target coverage while IMPT is not. The worst-case optimized Robust IMPT, assuming ±3.5% range uncertainties, improves the robustness of IMPT under anatomical changes significantly, even though it was not designed to account for anatomical changes by mechanism.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2014

TH-C-BRD-12: Robust Intensity Modulated Proton Therapy Plan Can Eliminate Junction Shifts for Craniospinal Irradiation

Purpose: The passive scattering proton therapy (PSPT) technique is the commonly used radiotherapy technique for craniospinal irradiation (CSI). However, PSPT involves many numbers of junction shifts applied over the course of treatment to reduce the cold and hot regions caused by field mismatching. In this work, we introduced a robust planning approach to develop an optimal and clinical efficient techniques for CSI using intensity modulated proton therapy (IMPT) so that junction shifts can essentially be eliminated. Methods: The intra-fractional uncertainty, in which two overlapping fields shift in the opposite directions along the craniospinal axis, are incorporated into the robust optimization algorithm. Treatment plans with junction sizes 3,5,10,15,20,25 cm were designed and compared with the plan designed using the non-robust optimization. Robustness of the plans were evaluated based on dose profiles along the craniospinal axis for the plans applying 3 mm intra-fractional shift. The dose intra-fraction variations (DIV) at the junction are used to evaluate the robustness of the plans. Results: The DIVs are 7.9%, 6.3%, 5.0%, 3.8%, 2.8% and 2.2%, for the robustly optimized plans with junction sizes 3,5,10,15,20,25 cm. The DIV are 10% for the non-robustly optimized plans with junction size 25 cm. The dose profiles along the craniospinal axis exhibit gradual and tapered dose distribution. Using DIVs less than 5% as maximum acceptable intrafractional variation, the overlapping region can be reduced to 10 cm, leading to potential reduced number of the fields. The DIVs are less than 5% for 5 mm intra-fractional shifts with junction size 25 cm, leading to potential no-junction-shift for CSI using IMPT. Conclusion: This work is the first report of the robust optimization on CSI based on IMPT. We demonstrate that robust optimization can lead to much efficient carniospinal irradiation by eliminating the junction shifts.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

TH-CD-209-05: Impact of Spot Size and Spacing On the Quality of Robustly-Optimized Intensity-Modulated Proton Therapy Plans for Lung Cancer

Purpose: To investigate how spot size and spacing affect plan quality, especially, plan robustness and the impact of interplay effect, of robustly-optimized intensity-modulated proton therapy (IMPT) plans for lung cancer. Methods: Two robustly-optimized IMPT plans were created for 10 lung cancer patients: (1) one for a proton beam with in-air energy dependent large spot size at isocenter (σ: 5–15 mm) and spacing (1.53σ); (2) the other for a proton beam with small spot size (σ: 2–6 mm) and spacing (5 mm). Both plans were generated on the average CTs with internal-gross-tumor-volume density overridden to irradiate internal target volume (ITV). The root-mean-square-dose volume histograms (RVH) measured the sensitivity of the dose to uncertainties, and the areas under RVH curves were used to evaluate plan robustness. Dose evaluation software was developed to model time-dependent spot delivery to incorporate interplay effect with randomized starting phases of each field per fraction. Patient anatomy voxels were mapped from phase to phase via deformable image registration to score doses. Dose-volume-histogram indices including ITV coverage, homogeneity, and organs-at-risk (OAR) sparing were compared using Student-t test. Results: Compared to large spots, small spots resulted in significantly better OAR sparing with comparable ITV coverage and homogeneity in the nominal plan. Plan robustness was comparable for ITV and most OARs. With interplay effect considered, significantly better OAR sparing with comparable ITV coverage and homogeneity is observed using smaller spots. Conclusion: Robust optimization with smaller spots significantly improves OAR sparing with comparable plan robustness and similar impact of interplay effect compare to larger spots. Small spot size requires the use of larger number of spots, which gives optimizer more freedom to render a plan more robust. The ratio between spot size and spacing was found to be more relevant to determine plan robustness and the impact of interplay effect than spot size alone. This research was supported by the National Cancer Institute Career Developmental Award K25CA168984, by the Fraternal Order of Eagles Cancer Research Fund Career Development Award, by The Lawrence W. and Marilyn W. Matteson Fund for Cancer Research, by Mayo Arizona State University Seed Grant, and by The Kemper Marley Foundation.

60 APPLIED LIFE SCIENCES↗

NASA NTRS2005

Robust Control Design for Systems With Probabilistic Uncertainty

This paper presents a reliability- and robustness-based formulation for robust control synthesis for systems with probabilistic uncertainty. In a reliability-based formulation, the probability of violating design requirements prescribed by inequality constraints is minimized. In a robustness-based formulation, a metric which measures the tendency of a random variable/process to cluster close to a target scalar/function is minimized. A multi-objective optimization procedure, which combines stability and performance requirements in time and frequency domains, is used to search for robustly optimal compensators. Some of the fundamental differences between the proposed strategy and conventional robust control methods are: (i) unnecessary conservatism is eliminated since there is not need for convex supports, (ii) the most likely plants are favored during synthesis allowing for probabilistic robust optimality, (iii) the tradeoff between robust stability and robust performance can be explored numerically, (iv) the uncertainty set is closely related to parameters with clear physical meaning, and (v) compensators with improved robust characteristics for a given control structure can be synthesized.

Crespo, Luis G.↗

DOE OSTI2016

Limited Impact of Setup and Range Uncertainties, Breathing Motion, and Interplay Effects in Robustly Optimized Intensity Modulated Proton Therapy for Stage III Non-small Cell Lung Cancer

Purpose: To investigate the impact of setup and range uncertainties, breathing motion, and interplay effects using scanning pencil beams in robustly optimized intensity modulated proton therapy (IMPT) for stage III non-small cell lung cancer (NSCLC). Methods and Materials: Three-field IMPT plans were created using a minimax robust optimization technique for 10 NSCLC patients. The plans accounted for 5- or 7-mm setup errors with ±3% range uncertainties. The robustness of the IMPT nominal plans was evaluated considering (1) isotropic 5-mm setup errors with ±3% range uncertainties; (2) breathing motion; (3) interplay effects; and (4) a combination of items 1 and 2. The plans were calculated using 4-dimensional and average intensity projection computed tomography images. The target coverage (TC, volume receiving 95% of prescribed dose) and homogeneity index (D{sub 2} − D{sub 98}, where D{sub 2} and D{sub 98} are the least doses received by 2% and 98% of the volume) for the internal clinical target volume, and dose indexes for lung, esophagus, heart and spinal cord were compared with that of clinical volumetric modulated arc therapy plans. Results: The TC and homogeneity index for all plans were within clinical limits when considering the breathing motion and interplay effects independently. The setup and range uncertainties had a larger effect when considering their combined effect. The TC decreased to <98% (clinical threshold) in 3 of 10 patients for robust 5-mm evaluations. However, the TC remained >98% for robust 7-mm evaluations for all patients. The organ at risk dose parameters did not significantly vary between the respective robust 5-mm and robust 7-mm evaluations for the 4 error types. Compared with the volumetric modulated arc therapy plans, the IMPT plans showed better target homogeneity and mean lung and heart dose parameters reduced by about 40% and 60%, respectively. Conclusions: In robustly optimized IMPT for stage III NSCLC, the setup and range uncertainties, breathing motion, and interplay effects have limited impact on target coverage, dose homogeneity, and organ-at-risk dose parameters.

62 RADIOLOGY AND NUCLEAR MEDICINE↗

DOE OSTI2018

Designing Phononic Crystals with Wide and Robust Band Gaps

Here, phononic crystals (PnCs) engineered to manipulate and control the propagation of mechanical waves have enabled the design of a range of novel devices, such as waveguides, frequency modulators, and acoustic cloaks, for which wide and robust phononic band gaps are highly preferable. While numerous PnCs have been designed in recent decades, to the best of our knowledge, PnCs that possess simultaneous wide and robust band gaps (to randomness and deformations) have not yet been reported. Here, we demonstrate that by combining the band-gap formation mechanisms of Bragg scattering and local resonances (the latter one is dominating), PnCs with wide and robust phononic band gaps can be established. The robustness of the phononic band gaps are then discussed from two aspects: robustness to geometric randomness (manufacture defects) and robustness to deformations (mechanical stimuli). Analytical formulations further predict the optimal design parameters, and an uncertainty analysis quantifies the randomness effect of each designing parameter. Moreover, we show that the deformation robustness originates from a local resonance-dominant mechanism together with the suppression of structural instability. Importantly, the proposed PnCs require only a small number of layers of elements (three unit cells) to obtain broad, robust, and strong attenuation bands, which offer great potential in designing flexible and deformable phononic devices.

36 MATERIALS SCIENCE↗

DOE OSTI2014

SU-E-T-266: Proton PBS Plan Design and Robustness Evaluation for Head and Neck Cancers

Purpose: To describe a newly designed proton pencil beam scanning (PBS) planning technique for radiotherapy of patients with bilateral oropharyngeal cancer, and to assess plan robustness. Methods: We treated 10 patients with proton PBS plans using 2 posterior oblique field (2F PBS) comprised of 80% single-field uniform dose (SFUD) and 20% intensity-modulated proton therapy (IMPT). All patients underwent weekly CT scans for verification. Using dosimetric indicators for both targets and organs at risk (OARs), we quantitatively compared initial plans and verification plans using student t-tests. We created a second proton PBS plan for each patient using 2 posterior oblique plus 1 anterior field comprised of 100% SFUD (3F PBS). We assessed plan robustness for both proton plan groups, as well as a photon volumetric modulated arc therapy (VMAT) plan group by comparing initial and verification plans. Results: The 2F PBS plans were not robust in target coverage. D98% for clinical target volume (CTV) degraded from 100% to 96% on average, with maximum change Δ D98% of −24%. Two patients were moved to photon VMAT treatment due to insufficient CTV coverage on verification plans. Plan robustness was especially weak in the low-anterior neck. The 3F PBS plans, however, demonstrated robust target coverage, which was comparable to the VMAT photon plan group. Doses to oral cavity were lower in the Proton PBS plans compared to photon VMAT plans due to no lower exit dose to the oral cavity. Conclusion: Proton PBS plans using 2 posterior oblique fields were not robust for CTV coverage, due to variable positioning of redundant soft tissue in the posterior neck. We designed 3-field proton PBS plans using an anterior field to avoid long heterogeneous paths in the low neck. These 3-field proton PBS plans had significantly improved plan robustness, and the robustness is comparable to VMAT photon plans.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Feasibility and robustness of dose painting by numbers in proton therapy with contour-driven plan optimization

Purpose: To prove the ability of protons to reproduce a dose gradient that matches a dose painting by numbers (DPBN) prescription in the presence of setup and range errors, by using contours and structure-based optimization in a commercial treatment planning system. Methods: For two patients with head and neck cancer, voxel-by-voxel prescription to the target volume (GTV{sub PET}) was calculated from {sup 18}FDG-PET images and approximated with several discrete prescription subcontours. Treatments were planned with proton pencil beam scanning. In order to determine the optimal plan parameters to approach the DPBN prescription, the effects of the scanning pattern, number of fields, number of subcontours, and use of range shifter were separately tested on each patient. Different constant scanning grids (i.e., spot spacing = Δx = Δy = 3.5, 4, and 5 mm) and uniform energy layer separation [4 and 5 mm WED (water equivalent distance)] were analyzed versus a dynamic and automatic selection of the spots grid. The number of subcontours was increased from 3 to 11 while the number of beams was set to 3, 5, or 7. Conventional PTV-based and robust clinical target volumes (CTV)-based optimization strategies were considered and their robustness against range and setup errors assessed. Because of the nonuniform prescription, ensuring robustness for coverage of GTV{sub PET} inevitably leads to overdosing, which was compared for both optimization schemes. Results: The optimal number of subcontours ranged from 5 to 7 for both patients. All considered scanning grids achieved accurate dose painting (1% average difference between the prescribed and planned doses). PTV-based plans led to nonrobust target coverage while robust-optimized plans improved it considerably (differences between worst-case CTV dose and the clinical constraint was up to 3 Gy for PTV-based plans and did not exceed 1 Gy for robust CTV-based plans). Also, only 15% of the points in the GTV{sub PET} (worst case) were above 5% of DPBN prescription for robust-optimized plans, while they were more than 50% for PTV plans. Low dose to organs at risk (OARs) could be achieved for both PTV and robust-optimized plans. Conclusions: DPBN in proton therapy is feasible with the use of a sufficient number subcontours, automatically generated scanning patterns, and no more than three beams are needed. Robust optimization ensured the required target coverage and minimal overdosing, while PTV-approach led to nonrobust plans with excessive overdose. Low dose to OARs can be achieved even in the presence of a high-dose escalation as in DPBN.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2015

Comparison of organ-at-risk sparing and plan robustness for spot-scanning proton therapy and volumetric modulated arc photon therapy in head-and-neck cancer

Purpose: Proton radiotherapy for head-and-neck cancer (HNC) aims to improve organ-at-risk (OAR) sparing over photon radiotherapy. However, it may be less robust for setup and range uncertainties. The authors investigated OAR sparing and plan robustness for spot-scanning proton planning techniques and compared these with volumetric modulated arc therapy (VMAT) photon plans. Methods: Ten HNC patients were replanned using two arc VMAT (RapidArc) and spot-scanning proton techniques. OARs to be spared included the contra- and ipsilateral parotid and submandibular glands and individual swallowing muscles. Proton plans were made using Multifield Optimization (MFO, using three, five, and seven fields) and Single-field Optimization (SFO, using three fields). OAR sparing was evaluated using mean dose to composite salivary glands (Comp{sub Sal}) and composite swallowing muscles (Comp{sub Swal}). Plan robustness was determined for setup and range uncertainties (±3 mm for setup, ±3% HU) evaluating V95% and V107% for clinical target volumes. Results: Averaged over all patients Comp{sub Sal}/Comp{sub Swal} mean doses were lower for the three-field MFO plans (14.6/16.4 Gy) compared to the three-field SFO plans (20.0/23.7 Gy) and VMAT plans (23.0/25.3 Gy). Using more than three fields resulted in differences in OAR sparing of less than 1.5 Gy between plans. SFO plans were significantly more robust than MFO plans. VMAT plans were the most robust. Conclusions: MFO plans had improved OAR sparing but were less robust than SFO and VMAT plans, while SFO plans were more robust than MFO plans but resulted in less OAR sparing. Robustness of the MFO plans did not increase with more fields.

60 APPLIED LIFE SCIENCES↗

DOE OSTI2016

SU-F-T-187: Quantifying Normal Tissue Sparing with 4D Robust Optimization of Intensity Modulated Proton Therapy

Purpose: To report an approach to quantify the normal tissue sparing for 4D robustly-optimized versus PTV-optimized IMPT plans. Methods: We generated two sets of 90 DVHs from a patient’s 10-phase 4D CT set; one by conventional PTV-based optimization done in the Eclipse treatment planning system, and the other by an in-house robust optimization algorithm. The 90 DVHs were created for the following scenarios in each of the ten phases of the 4DCT: ± 5mm shift along x, y, z; ± 3.5% range uncertainty and a nominal scenario. A Matlab function written by Gay and Niemierko was modified to calculate EUD for each DVH for the following structures: esophagus, heart, ipsilateral lung and spinal cord. An F-test determined whether or not the variances of each structure’s DVHs were statistically different. Then a t-test determined if the average EUDs for each optimization algorithm were statistically significantly different. Results: T-test results showed each structure had a statistically significant difference in average EUD when comparing robust optimization versus PTV-based optimization. Under robust optimization all structures except the spinal cord received lower EUDs than PTV-based optimization. Using robust optimization the average EUDs decreased 1.45% for the esophagus, 1.54% for the heart and 5.45% for the ipsilateral lung. The average EUD to the spinal cord increased 24.86% but was still well below tolerance. Conclusion: This work has helped quantify a qualitative relationship noted earlier in our work: that robust optimization leads to plans with greater normal tissue sparing compared to PTV-based optimization. Except in the case of the spinal cord all structures received a lower EUD under robust optimization and these results are statistically significant. While the average EUD to the spinal cord increased to 25.06 Gy under robust optimization it is still well under the TD50 value of 66.5 Gy from Emami et al. Supported in part by the NCI U19 CA021239.

60 APPLIED LIFE SCIENCES↗

NASA NTRS1989

Application of stochastic robustness to aircraft control systems

Stochastic robustness, a simple numerical procedure for estimating the stability robustness of linear, time-invariant systems, is applied to a forward-swept-wing aircraft control system. Based on Monte Carlo evaluation of the system's closed-loop eignevalues, this analysis approach introduces the probability of instability as a scalar stability robustness measure. The related stochastic root locus provides insight into robustness characteristics of the closed-loop system. Three Linear Quadratic controllers of decreasing robustness are chosen to demonstrate the use of stochastic robustness to analyze and compare control designs. Examples are presented illustrating the use of stochastic robustness analysis to address the effects of actuator dynamics and unmodeled dynamics on the stability robustness of the forward-swept-wing aircraft.

Stengel, Robert F.↗

NASA NTRS1993

A comparative study of multivariable robustness analysis methods as applied to integrated flight and propulsion control

Three multivariable robustness analysis methods are compared and contrasted. The focus of the analysis is on system stability and performance robustness to uncertainty in the coupling dynamics between two interacting subsystems. Of particular interest is interacting airframe and engine subsystems, and an example airframe/engine vehicle configuration is utilized in the demonstration of these approaches. The singular value (SV) and structured singular value (SSV) analysis methods are compared to a method especially well suited for analysis of robustness to uncertainties in subsystem interactions. This approach is referred to here as the interacting subsystem (IS) analysis method. This method has been used previously to analyze airframe/engine systems, emphasizing the study of stability robustness. However, performance robustness is also investigated here, and a new measure of allowable uncertainty for acceptable performance robustness is introduced. The IS methodology does not require plant uncertainty models to measure the robustness of the system, and is shown to yield valuable information regarding the effects of subsystem interactions. In contrast, the SV and SSV methods allow for the evaluation of the robustness of the system to particular models of uncertainty, and do not directly indicate how the airframe (engine) subsystem interacts with the engine (airframe) subsystem.

Schierman, John D.↗

NASA NTRS2006

Towards Robust Designs Via Multiple-Objective Optimization Methods

Fabricating and operating complex systems involves dealing with uncertainty in the relevant variables. In the case of aircraft, flow conditions are subject to change during operation. Efficiency and engine noise may be different from the expected values because of manufacturing tolerances and normal wear and tear. Engine components may have a shorter life than expected because of manufacturing tolerances. In spite of the important effect of operating- and manufacturing-uncertainty on the performance and expected life of the component or system, traditional aerodynamic shape optimization has focused on obtaining the best design given a set of deterministic flow conditions. Clearly it is important to both maintain near-optimal performance levels at off-design operating conditions, and, ensure that performance does not degrade appreciably when the component shape differs from the optimal shape due to manufacturing tolerances and normal wear and tear. These requirements naturally lead to the idea of robust optimal design wherein the concept of robustness to various perturbations is built into the design optimization procedure. The basic ideas involved in robust optimal design will be included in this lecture. The imposition of the additional requirement of robustness results in a multiple-objective optimization problem requiring appropriate solution procedures. Typically the costs associated with multiple-objective optimization are substantial. Therefore efficient multiple-objective optimization procedures are crucial to the rapid deployment of the principles of robust design in industry. Hence the companion set of lecture notes (Single- and Multiple-Objective Optimization with Differential Evolution and Neural Networks ) deals with methodology for solving multiple-objective Optimization problems efficiently, reliably and with little user intervention. Applications of the methodologies presented in the companion lecture to robust design will be included here. The evolutionary method (DE) is first used to solve a relatively difficult problem in extended surface heat transfer wherein optimal fin geometries are obtained for different safe operating base temperatures. The objective of maximizing the safe operating base temperature range is in direct conflict with the objective of maximizing fin heat transfer. This problem is a good example of achieving robustness in the context of changing operating conditions. The evolutionary method is then used to design a turbine airfoil; the two objectives being reduced sensitivity of the pressure distribution to small changes in the airfoil shape and the maximization of the trailing edge wedge angle with the consequent increase in airfoil thickness and strength. This is a relevant example of achieving robustness to manufacturing tolerances and wear and tear in the presence of other objectives.

Man Mohan, Rai↗

DOE OSTI2013

Stretching the limits of forming processes by robust optimization: A demonstrator

Robust design of forming processes using numerical simulations is gaining attention throughout the industry. In this work, it is demonstrated how robust optimization can assist in further stretching the limits of metal forming processes. A deterministic and a robust optimization study are performed, considering a stretch-drawing process of a hemispherical cup product. For the robust optimization study, both the effect of material and process scatter are taken into account. For quantifying the material scatter, samples of 41 coils of a drawing quality forming steel have been collected. The stochastic material behavior is obtained by a hybrid approach, combining mechanical testing and texture analysis, and efficiently implemented in a metamodel based optimization strategy. The deterministic and robust optimization results are subsequently presented and compared, demonstrating an increased process robustness and decreased number of product rejects by application of the robust optimization approach.

36 MATERIALS SCIENCE↗

DOE OSTI2014

TH-C-BRD-10: An Evaluation of Three Robust Optimization Approaches in IMPT Treatment Planning

Purpose: Various robust optimization approaches have been proposed to ensure the robustness of intensity modulated proton therapy (IMPT) in the face of uncertainty. In this study, we aim to investigate the performance of three classes of robust optimization approaches regarding plan optimality and robustness. Methods: Three robust optimization models were implemented in our in-house IMPT treatment planning system: 1) L2 optimization based on worst-case dose; 2) L2 optimization based on minmax objective; and 3) L1 optimization with constraints on all uncertain doses. The first model was solved by a L-BFGS algorithm; the second was solved by a gradient projection algorithm; and the third was solved by an interior point method. One nominal scenario and eight maximum uncertainty scenarios (proton range over and under 3.5%, and setup error of 5 mm for x, y, z directions) were considered in optimization. Dosimetric measurements of optimized plans from the three approaches were compared for four prostate cancer patients retrospectively selected at our institution. Results: For the nominal scenario, all three optimization approaches yielded the same coverage to the clinical treatment volume (CTV) and the L2 worst-case approach demonstrated better rectum and bladder sparing than others. For the uncertainty scenarios, the L1 approach resulted in the most robust CTV coverage against uncertainties, while the plans from L2 worst-case were less robust than others. In addition, we observed that the number of scanning spots with positive MUs from the L2 approaches was approximately twice as many as that from the L1 approach. This indicates that L1 optimization may lead to more efficient IMPT delivery. Conclusion: Our study indicated that the L1 approach best conserved the target coverage in the face of uncertainty but its resulting OAR sparing was slightly inferior to other two approaches.

60 APPLIED LIFE SCIENCES↗