Different policies constrained agricultural non-point pollutants emission trading management for water system under interval, fuzzy, and stochastic information.

Formulating suitable policies is essential for resources and environmental management. In this study, an agricultural pollutants emission trading management model driven by water resources and pollutants control is developed to search reasonable policies for agricultural water resources allocation under multiple uncertainties. Random-fuzzy and interval information in water resources system that have directly impact on the effectiveness of management schemes is reflected through interval two-stage stochastic fuzzy-probability programming. The model was root from regional agricultural water resources system in Jining City, China under considering the relationship among effective precipitation, crop water demand, and pollutants emission. Two types policies (water consumption-control and pollutants emission-control) are designed for searching the related interaction on water resources management and water quality improvement. The results indicated that water resources policies would be of water and environmental double benefits, and a large rainfall would reduce irrigation amount from water sources and lead to a larger pollutants emission trading. The results will help for defining scientific and effective water resources protection and management policies and analyzing the related interacted effects on water consumption, pollutants control and system benefit.

Technical variability of cornea parameters derived from anterior segment OCT fitted with Fringe Zernike polynomials.

BACKGROUND: This study uses bootstrapping to evaluate the technical variability (in terms of model parameter variation) of Zernike corneal surface fit parameters based on Casia2 biometric data. METHODS: Using a dataset containing N = 6953 Casia2 biometric measurements from a cataractous population, a Fringe Zernike polynomial surface of radial degree 10 (36 components) was fitted to the height data. The fit error (height - reconstruction) was bootstrapped 100 times after normalisation. After reversal of normalisation, the bootstrapped fit errors were added to the reconstructed height, and characteristic surface parameters (flat/steep axis, radii, and asphericities in both axes) extracted. The median parameters refer to a robust surface representation for later estimates of elevation, whereas the SD of the 100 bootstraps refers to the variability of the surface fit. RESULTS: Bootstrapping gave median radius and asphericity values of 7.74/7.68 mm and -0.20/-0.24 for the corneal front surface in the flat/steep meridian and 6.52/6.37 mm and -0.22/-0.31 for the corneal back surface. The respective SD values for the 100 bootstraps were 0.0032/0.0028 mm and 0.0093/0.0082 for the front and 0.0126/0.0115 mm and 0.0366/0.0312 for the back surface. The uncertainties for the back surface are systematically larger as compared to the uncertainties of the front surface. CONCLUSION: As measured with the Casia2 tomographer, the fit parameters for the corneal back surface exhibit a larger degree of variability compared with those for the front surface. Further studies are needed to show whether these uncertainties are representative for the situation where actual repeat measurements are possible.

Mixed uncertainty analysis on pumping by peristaltic hearts using Dempster-Shafer theory.

In this paper, we introduce the numerical strategy for mixed uncertainty propagation based on probability and Dempster-Shafer theories, and apply it to the computational model of peristalsis in a heart-pumping system. Specifically, the stochastic uncertainty in the system is represented with random variables while epistemic uncertainty is represented using non-probabilistic uncertain variables with belief functions. The mixed uncertainty is propagated through the system, resulting in the uncertainty in the chosen quantities of interest (QoI, such as flow volume, cost of transport and work). With the introduced numerical method, the uncertainty in the statistics of QoIs will be represented using belief functions. With three representative probability distributions consistent with the belief structure, global sensitivity analysis has also been implemented to identify important uncertain factors and the results have been compared between different peristalsis models. To reduce the computational cost, physics constrained generalized polynomial chaos method is adopted to construct cheaper surrogates as approximations for the full simulation.

Prediction of refraction error after toric lens implantation with biometric input data uncertainties and power labelling tolerances.

BACKGROUND: The purpose of this study was to simulate the impact of biometric measure uncertainties, lens equivalent and toric power labelling tolerances and axis alignment errors on the refractive outcome after cataract surgery with toric lens implantation. METHODS: In this retrospective non-randomised cross sectional Monte-Carlo simulation study we evaluated a dataset containing 7458 LenStar 900 preoperative biometric measurements. The biometric uncertainties from literature, lens power labelling according to ISO 11979, and axis alignment tolerances of a modern toric lens (Hoya Vivinex) were taken to be normally distributed and used in a Monte-Carlo simulation with 100 000 samples per eye. The target variable was the defocus equivalent (DEQ) derived using the Castrop (DEQC) and the Haigis (DEQH) formulae. RESULTS: Mean/median / 90% quantile DEQC was 0.22/0.21/0.36 D and DEQH was 0.20/0.19/0.32 D. Ignoring the variation in lens power labelling and toric axis alignment the respective DEQC was 0.20/0.19/0.32 D and DEQH was 0.18/0.17/0.29 D. DEQC and DEQH increased with shorter eyes, steeper corneas, equivalent lens power and highly with toric lens power. CONCLUSIONS: According to our simulation results, uncertainties in biometric measures, lens power labelling tolerances, and axis alignment errors are responsible for a significant part of the refraction prediction error after cataract surgery with toric lens implantation. Additional labelling of the exact equivalent and toric power on the lens package could be a step to improve postoperative results.

Frequency- and Temperature-Dependent Uncertainties in Hysteresis Measurements of a 3D-Printed FeSi wt6.5% Material.

Additive manufacturing of soft magnetic materials is a promising technology for creating topologically optimized electrical machines. High-performance electrical machines can be made from high-silicon-content FeSi alloys. Fe-6.5wt%Si material has exceptional magnetic properties; however, manufacturing this steel with the classical cold rolling methodology is not possible due to the brittleness of this material. Laser powder bed fusion technology (L-PBF) offers a solution to this problem. Finding the optimal printing parameters is a challenging task. Nevertheless, it is crucial to resolve the brittleness of the created materials so they can be used in commercial applications. The temperature dependence of magnetic hysteresis properties of Fe-6.5wt%Si materials is presented in this paper. The magnetic hysteresis properties were examined from 20 °C to 120 °C. The hysteresis measurements were made by a precision current generator-based hysteresis measurement tool, which uses fast Fourier transformation-based filtering techniques to increase the accuracy of the measurements. The details of the applied scalar hysteresis sensor and the measurement uncertainties were discussed first in the paper; then, three characteristic points of the static hysteresis curve of the ten L-PBF-manufactured identical toroidal cores were investigated and compared at different temperatures. These measurements show that, despite the volumetric ratio of the porosities being below 0.5%, the mean crack length in the samples is not significant for the examined samples. These small defects can cause a significant 5% decrement in some characteristic values of the examined hysteresis curve.

Uncertainty Evaluation of a Gas Turbine Model Based on a Nonlinear Autoregressive Exogenous Model and Monte Carlo Dropout.

Gas turbines are thermoelectric plants with various applications, such as large-scale electricity production, petrochemical industry, and steam generation. In order to optimize the operation of a gas turbine, it is necessary to develop system identification models that allow for the development of studies and analyses to increase the system's reliability. Current strategies for modeling complex and non-linear systems can be based on artificial intelligence techniques, using autoregressive neural networks of the NARX and LSTM type. In this context, this work aims to develop a model of a gas turbine capable of estimating the rotation speed of the turbine and simultaneously estimating the uncertainty associated with the estimation. These methodologies are based on artificial neural networks and the Monte Carlo dropout simulation method. The results were obtained from experimental data from a 215 MW gas turbine, getting the best model with a MAPE of 0.02% and an uncertainty associated with the turbine rotation speed of 2.2 RPM.

A Joint State and Fault Estimation Scheme for State-Saturated System with Energy Harvesting Sensors.

In this article, the issue of joint state and fault estimation is ironed out for delayed state-saturated systems subject to energy harvesting sensors. Under the effect of energy harvesting, the sensors can harvest energy from the external environment and consume an amount of energy when transmitting measurements to the estimator. The occurrence probability of measurement loss is computed at each instant according to the probability distribution of the energy harvesting mechanism. The main objective of the addressed problem is to construct a joint state and fault estimator where the estimation error covariance is ensured in some certain sense and the estimator gain is determined to accommodate energy harvesting sensors, state saturation, as well as time delays. By virtue of a set of matrix difference equations, the derived upper bound is minimized by parameterizing the estimator gain. In addition, the performance evaluation of the designed joint estimator is conducted by analyzing the boundedness of the estimation error in the mean-squared sense. Finally, two experimental examples are employed to illustrate the feasibility of the proposed estimation scheme.

Sensor Fault Reconstruction Using Robustly Adaptive Unknown-Input Observers.

Sensors are a key component in industrial automation systems. A fault or malfunction in sensors may degrade control system performance. An engineering system model is usually disturbed by input uncertainties, which brings a challenge for monitoring, diagnosis, and control. In this study, a novel estimation technique, called adaptive unknown-input observer, is proposed to simultaneously reconstruct sensor faults as well as system states. Specifically, the unknown input observer is used to decouple partial disturbances, the un-decoupled disturbances are attenuated by the optimization using linear matrix inequalities, and the adaptive technique is explored to track sensor faults. As a result, a robust reconstruction of the sensor fault as well as system states is then achieved. Furthermore, the proposed robustly adaptive fault reconstruction technique is extended to Lipschitz nonlinear systems subjected to sensor faults and unknown input uncertainties. Finally, the effectiveness of the algorithms is demonstrated using an aircraft system model and robotic arm and comparison studies.

Tolerance Considerations for MHMIC Manufacturing Process at Millimeter-Wave Band.

This paper investigates the manufacturing uncertainties at a 60 GHz millimeter-wave band for the monolithic hybrid microwave integrated circuits (MHMIC) fabrication process. It specifically deals with the implementation tolerances of thin-film gold microstrip transmission lines, titanium oxide thin-layer resistors, microstrip quarter-wavelength radial stubs, and active device implementation using the gold-bonding ribbons. The impacts of these manufacturing tolerances are assessed and experimentally quantified through prototyped MHMIC circuits. This allows us, on one hand, to identify the acceptable amount of dimensional variation enabling reasonable performances. On the other hand, it aims to establish a relationship between the manufacturing tolerances and the circuit parameters to provide more flexibility for the tolerance compensation and accuracy enhancement of the MHMIC fabrication processes.

Metrology for Indoor Radon Measurements and Requirements for Different Types of Devices.

Indoor radon measurements have been conducted in many countries worldwide for several decades. However, to date, there is a lack of a globally harmonized measurement standard. Furthermore, measurement protocols in the US (short-term tests for 2-7 days) and European Union countries (long-term tests for at least 2 months) differ significantly, and their metrological support is underdeveloped, as clear mathematical algorithms (criteria) and QA/QC procedures considering fundamental ISO/IEC concepts such as "measurement uncertainty" and "conformity assessment" are still absent. In this context, for many years, the authors have been advancing and refining the theory of metrological support for standardizing indoor radon measurements based on a rational criterion for conformity assessment within the ISO/IEC concepts. The rational criterion takes into account the main uncertainties arising from temporal variations in indoor radon and instrumental errors, enabling the utilization of both short- and long-term measurements while ensuring specified reliability in decision making (typically no less than 95%). The paper presents improved mathematical algorithms for determining both temporal and instrumental uncertainties. Additionally, within the framework of the rational criterion, unified metrological requirements are formulated for various methods and devices employed in indoor radon measurements.

Regional bioethanol supply chain optimization with the integration of GIS-MCDM method and quantile-based scenario analysis.

This study presents a novel decision-support framework for the bioethanol supply chain network planning and management under uncertainties. Under the holistic framework, the most suitable sites for biorefineries are first screened out by adopting a GIS-based multi-criteria decision-making approach. Then, a mixed-integer linear programming model combined with quantile-based scenario analysis is developed to determine the strategic planning (i.e. locations and size of biorefineries) and tactical management (i.e. biomass purchasing, feedstock transportation, bioethanol production, and product delivery) under uncertainties. The model can effectively search for reliable solutions under uncertainties and achieve tradeoff solutions with the consideration of decision makers' risk tolerance. The proposed framework is demonstrated through a case study in China. It is suggested to build seven biorefineries with a capacity of 100 million liters in Zhumadian city. Utilizing 41% of local agricultural residues could satisfy the bioethanol requirement in the transportation sector under the E20 policy. However, the estimated production cost of bioethanol in Zhumadian is very high, about 1.11 $/L, which makes it lose cost advantage in the fuel market. Thus, currently, effective subsidies, mandatory energy substitution policies, along other environmental regulatory measures are desired to promote the bioethanol industry development.

Optimum investment strategy for hydrogen-based steelmaking project coupled with multiple uncertainties.

The large-scale application of hydrogen steelmaking technology is expected to substantially accelerate the decarbonization process of the iron and steel industry. However, hydrogen steelmaking projects are still in the experimental or demonstration stage, and scientific investment decision-making methods are urgently needed to support the large-scale development of the technology. When assessing the investment value, existing studies usually only consider the intrinsic project value under a specific pathway, while ignoring the option value under realistic multiple uncertainties in terms of technology, market, and policy, leading to an underestimation of the investment value. To address this issue, this study constructs a real options model to explore the optimal investment timing and revenue of the hydrogen steelmaking project, by taking into account multi-dimensional uncertainties stemming from price fluctuations in the steel market, the development of the carbon market, and technological advances. Additionally, the impacts of various subsidy policies on the investment strategy are also investigated. Least Squares Monte Carlo method is applied to overcome computational challenges posed by dynamic programming under multi-dimensional uncertainties. The results show that: (i) Investment is not recommended based on current crude steel price and hydrogen price. (ii) When the annual reduction rate of hydrogen price reaches 5%, the optimal investment timing would advance to 2036. (iii) On this basis, with the introduction of a 20% green hydrogen subsidy policy, the optimal investment timing would be further brought forward to 2033. The implementation of tax incentives would significantly increase the investment value. The investment value would surge from 170 million CNY to 262 million CNY as the tax rate decreases from 20% to zero. The findings could provide reasonable suggestions for investment decisions under realistic volatile environments, as well as scientific references for policy design, thus facilitating the large-scale and high-level development of hydrogen-based steelmaking technology.

Regional policy options for carbon peaking in the Yangtze River Delta under uncertainty.

The Yangtze River Delta (YRD) region plays a crucial role in achieving China's carbon peaking goal. However, due to uncertainties surrounding future economic growth, energy consumption, energy structure, and population, the attainment of carbon peaking in this region remains uncertain. To address this issue, this study utilized the generalized Divisia index method to analyze the driving factors of carbon emissions, including economy, energy, investment, and population. Subsequently, Monte Carlo simulations were combined with scenario analysis to dynamically explore the peak path of regional heterogeneity in the YRD from 2022 to 2035 under uncertain conditions. The findings highlighted that economic uncertainty has the most significant impact on carbon emissions. Furthermore, reducing energy intensity and promoting the transformation of the energy consumption structure contribute to carbon reduction. The study also revealed that the carbon peak in the YRD exhibits regional heterogeneity. According to the baseline scenario, carbon emissions in the YRD will not peak before 2035. However, under the low-carbon development scenario, the carbon emissions of Zhejiang and Shanghai will peak before 2030. Moreover, under the enhanced emission reduction (EE) scenario, carbon emissions in Jiangsu, Zhejiang, and Shanghai will peak before 2025, while Anhui will reach its peak before 2030. Collectively, the entire YRD region is forecasted to attain a carbon emissions peak of 2.29 billion tons by 2025 under the EE scenario. This study provides valuable insights into the carbon emission trajectories of the YRD region under uncertain conditions. The findings can be instrumental in formulating carbon peaking policies that account for regional heterogeneity.

Reliability-Based Design Optimization for Polymer Electrolyte Membrane Fuel Cells: Tackling Dimensional Uncertainties in Manufacturing and Their Effects on Costs of Cathode Gas Diffusion Layer and Bipolar Plates.

Polymer Electrolyte Membrane Fuel Cells (PEMFCs) have emerged as a pivotal technology in the automotive industry, significantly contributing to the reduction of greenhouse gas emissions. However, the high material costs of the gas diffusion layer (GDL) and bipolar plate (BP) create a barrier for large scale commercial application. This study aims to address this challenge by optimizing the material and design of the cathode, GDL and BP. While deterministic design optimization (DDO) methods have been extensively studied, they often fall short when manufacturing uncertainties are introduced. This issue is addressed by introducing reliability-based design optimization (RBDO) to optimize four key PEMFC design variables, i.e., gas diffusion layer thickness, channel depth, channel width and land width. The objective is to maximize cell voltage considering the material cost of the cathode gas diffusion layer and cathode bipolar plate as reliability constraints. The results of the DDO show an increment in cell voltage of 31 mV, with a reliability of around 50% in material cost for both the cathode GDL and cathode BP. In contrast, the RBDO method provides a reliability of 95% for both components. Additionally, under a high level of uncertainty, the RBDO approach reduces the material cost of the cathode GDL by up to 12.25 $/stack, while the material cost for the cathode BP increases by up to 11.18 $/stack Under lower levels of manufacturing uncertainties, the RBDO method predicts a reduction in the material cost of the cathode GDL by up to 4.09 $/stack, with an increase in the material cost for the cathode BP by up to 6.71 $/stack, while maintaining a reliability of 95% for both components. These results demonstrate the effectiveness of the RBDO approach in achieving a reliable design under varying levels of manufacturing uncertainties.

Hybrid modelling of biological systems using fuzzy continuous Petri nets.

Integrated modelling of biological systems is challenged by composing components with sufficient kinetic data and components with insufficient kinetic data or components built only using experts' experience and knowledge. Fuzzy continuous Petri nets (FCPNs) combine continuous Petri nets with fuzzy inference systems, and thus offer an hybrid uncertain/certain approach to integrated modelling of such biological systems with uncertainties. In this paper, we give a formal definition and a corresponding simulation algorithm of FCPNs, and briefly introduce the FCPN tool that we have developed for implementing FCPNs. We then present a methodology and workflow utilizing FCPNs to achieve hybrid (uncertain/certain) modelling of biological systems illustrated with a case study of the Mercaptopurine metabolic pathway. We hope this research will promote the wider application of FCPNs and address the uncertain/certain integrated modelling challenge in the systems biology area.

Validation of an isotope dilution mass spectrometry (IDMS) measurement procedure for the reliable quantification of steroid hormones in waters.

Reliable data are compulsory to efficiently monitor pollutants in aquatic environments, particularly steroid hormones that can exert harmful effects at challenging analytical levels below the ng L-1. An isotope dilution two-step solid-phase extraction followed by an ultra-performance liquid chromatography separation coupled to tandem mass spectrometry (UPLC-MS/MS) detection method was validated for the quantification of 21 steroid hormones (androgens, estrogens, glucocorticoids, and progestogens) in whole waters. To achieve a realistic and robust assessment of the performances of this method, the validation procedure was conducted using several water samples representative of its intended application. These samples were characterized in terms of concentration of ionic constituents, suspended particulate matter (SPM), and dissolved organic carbon contents (DOC). For estrogens that are part of the European Water Framework Directive Watchlist (17beta-estradiol and estrone), the performances met the European requirements (decision 2015/495/EU) in terms of limit of quantification (LQ) and measurement uncertainty. For 17alpha-ethinylestradiol, the challenging LQ of 0.035 ng L-1 was reached. More generally, for 15 compounds out of 21, the accuracy, evaluated in intermediate precision conditions at concentrations ranging between 0.1 and 10 ng L-1, was found to be within a 35% tolerance. The evaluation of the measurement uncertainty was realized following the Guide to the expression of Uncertainty in Measurement. Finally, a water monitoring survey demonstrated the suitability of the method and pointed out the contamination of Belgium rivers by five estrogens (17alpha-ethinylestradiol, estriol, 17alpha-estradiol, 17beta-estradiol, and estrone) and three glucocorticoids (betamethasone, cortisol, and cortisone) which have been up to now poorly documented in European rivers.

Parametric delineation uncertainties contouring (PDUC) modeling on CT scans of prostate cancer patients.

PURPOSE: Variability in contouring contributes to large variations in radiation therapy planning and treatment outcomes. The development and testing of tools to automatically detect contouring errors require a source of contours that includes well-understood and realistic errors. The purpose of this work was to develop a simulation algorithm that intentionally injects errors of varying magnitudes into clinically accepted contours and produces realistic contours with different levels of variability. METHODS: We used a dataset of CT scans from 14 prostate cancer patients with clinician-drawn contours of the regions of interest (ROI) of the prostate, bladder, and rectum. Using our newly developed Parametric Delineation Uncertainties Contouring (PDUC) model, we automatically generated alternative, realistic contours. The PDUC model consists of the contrast-based DU generator and a 3D smoothing layer. The DU generator transforms contours (deformation, contraction, and/or expansion) as a function of image contrast. The generated contours undergo 3D smoothing to obtain a realistic look. After model building, the first batch of auto-generated contours was reviewed. Editing feedback from the reviews was then used in a filtering model for the auto-selection of clinically acceptable (minor-editing) DU contours. RESULTS: Overall, C values of 5 and 50 consistently produced high proportions of minor-editing contours across all ROI compared to the other C values (0.936 ± $ \pm \;$ 0.111 and 0.552 ± $ \pm \;$ 0.228, respectively). The model performed best on the bladder, which had the highest proportion of minor-editing contours (0.606) of the three ROI. In addition, the classification AUC for the filtering model across all three ROI is 0.724 ± $ \pm \;$ 0.109. DISCUSSION: The proposed methodology and subsequent results are promising and could have a great impact on treatment planning by generating mathematically simulated alternative structures that are clinically relevant and realistic enough (i.e., similar to clinician-drawn contours) to be used in quality control of radiation therapy.

Quantifying uncertainties associated with reference dosimetry in an MR-Linac.

BACKGROUND: Magnetic resonance (MR)-guided radiation therapy provides capabilities to utilize high-resolution and real-time MR imaging before and during treatment, which is critical for adaptive radiotherapy. This emerging modality has been promptly adopted in the clinic settings in advance of adaptations to reference dosimetry formalism that are needed to account for the presence of strong magnetic fields. In particular, the influence of magnetic field on the uncertainty of parameters in the reference dosimetry equation needs to be determined in order to fully characterize the uncertainty budget for reference dosimetry in MR-guided radiation therapy systems. PURPOSE: To identify and quantify key sources of uncertainty in the reference dosimetry of external high energy radiotherapy beams in the presence of a strong magnetic field. METHODS: In the absence of a formalized Task Group report for reference dosimetry in MR-integrated linacs, the currently suggested formalism follows the TG-51 protocol with the addition of a quality conversion factor kBQ accounting for the effects of the magnetic field on ionization chamber response. In this work, we quantify various sources of uncertainty that impact each of the parameters in the formalism, and evaluate their overall contribution to the final dose. Measurements are done in a 1.5 T MR-Linac (Unity, Elekta AB, Stockholm, Sweden) which integrates a 1.5 T Philips MR scanner and a 7 MVFFF linac. The responses of several reference-class small volume ionization chambers (Exradin:A1SL, IBA:CC13, PTW:Semiflex-3D) and Farmer type ionization chambers (Exradin:A19, IBA:FC65-G) were evaluated throughout this process. Long-term reproducibility and stability of beam quality, TPR 10 20 ${\mathrm{TPR}}_{10}^{20}$ , was also measured with an in-house built phantom. RESULTS: Relative to the conventional external high energy linacs, the uncertainty on overall reference dose in MR-linac is more significantly affected by the chamber setup: A translational displacement along y-axis of ± 3 mm results in dose variation of < |0.20| ± 0.02% (k = 1), while rotation of ± 5° in horizontal and vertical parallel planes relative to relative to the direction of magnetic field, did not exceed variation of < |0.44| ± 0.02% for all 5 ionization chambers. We measured a larger dose variation for xy-plane (horizontal) rotations (< |0.44| ± 0.02% (k = 1)) than for yz-plane (vertical) rotations (< ||0.28| ± 0.02% (k = 1)), which we associate with the gradient of kB,Q as a function of chamber orientation with respect to direction of the B0 -field. Uncertainty in Pion (for two depths), Ppol (with various sub-studies including effects of cable length, cable looping in the MRgRT bore, connector type in magnetic environment), and Prp were determined. Combined conversion factor kQ × kB,Q was provided for two reference depths at four cardinal angle orientations. Over a two-year period, beam quality was quite stable with TPR 10 20 ${\mathrm{TPR}}_{10}^{20}$ being 0.669 ± 0.01%. The actual magnitude of TPR 10 20 ${\mathrm{TPR}}_{10}^{20}$ was measured using identical equipment and compared between two different Elekta Unity MR-Linacs with results agreeing to within 0.21%. CONCLUSION: In this work, the uncertainty of a number of parameters influencing reference dosimetry was quantified. The results of this work can be used to identify best practice guidelines for reference dosimetry in the presence of magnetic fields, and to evaluate an uncertainty budget for future reference dosimetry protocols for MR-linac.

Viability of the virtual cone technique using a fixed small multi-leaf collimator field for stereotactic radiosurgery of trigeminal neuralgia.

Dosimetric uncertainties in very small (≤1.5 × 1.5 cm2 ) photon fields are remarkably higher, which undermines the validity of the virtual cone (VC) technique with a diminutive and variable MLC fields. We evaluate the accuracy and reproducibility of the VC method with a very small, fixed MLC field setting, called a fixed virtual cone (fVC), for small target radiosurgery such as trigeminal neuralgia (TGN). The fVC is characterized by 0.5 cm x 0.5 cm high-definition (HD) MLC field of 10MV FFF beam defined at 100 cm SAD, while backup jaws are positioned at 1.5 cm x 1.5 cm. A spherical dose distribution equivalent to 5 mm (diameter) physical cone was generated using 10-14 non-coplanar, partial arcs. Dosimetric accuracy was validated using SRS diode (PTW 60018), SRS MapCHECK (SNC) measurements. As a quality assurance measure, 10 treatment plans (SRS) for TGN, consisting of various arc ranges at different collimator angles were analyzed using 6 MV FFF and 10 MV FFF beams, including a field-by-field study (n = 130 fields). Dose outputs were compared between the Eclipse TPS and measurements (SRS MapCHECK). Moreover, dosimetric changes in the field defining fVC, prompted by a minute (± 0.5-1.0 mm) leaf shift, was examined among TPS, diode measurements, and Monte Carlo (MC) simulations. The beam model for fVC was validated (≤3% difference) using SRS MapCHECK based absolute dose measurements. The equivalent diameters of the 50% isodose distribution were found comparable to that of a 5 mm cone. Additionally, the comparison of field output factors, dose per MU between the TPS and SRS diode measurements using the fVC field, including ± 1 mm leaf shift, yielded average discrepancies within 5.5% and 3.5% for 6 MV FFF and 10 MV FFF beams, respectively. Overall, the fVC method is a credible alternative to the physical cone (5 mm) that can be applied in routine radiosurgical treatment of TGN.

Optimal Control Algorithm for Stochastic Systems with Parameter Drift.

A novel optimal control problem is considered for multiple input multiple output (MIMO) stochastic systems with mixed parameter drift, external disturbance and observation noise. The proposed controller can not only track and identify the drift parameters in finite time but, furthermore, drive the system to move towards the desired trajectory. However, there is a conflict between control and estimation, which makes the analytic solution unattainable in most situations. A dual control algorithm based on weight factor and innovation is, therefore, proposed. First, the innovation is added to the control goal by the appropriate weight and the Kalman filter is introduced to estimate and track the transformed drift parameters. The weight factor is used to adjust the degree of drift parameter estimation in order to achieve a balance between control and estimation. Then, the optimal control is derived by solving the modified optimization problem. In this strategy, the analytic solution of the control law can be obtained. The control law obtained in this paper is optimal because the estimation of drift parameters is integrated into the objective function rather than the suboptimal control law, which includes two parts of control and estimation in other studies. The proposed algorithm can achieve the best compromise between optimization and estatimation. Finally, the effectiveness of the algorithm is verified by numerical experiments in two different cases.