Search results for: compatibility requirement
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1359

Search results for: compatibility requirement

9 Sensorless Machine Parameter-Free Control of Doubly Fed Reluctance Wind Turbine Generator

Authors: Mohammad R. Aghakashkooli, Milutin G. Jovanovic

Abstract:

The brushless doubly-fed reluctance generator (BDFRG) is an emerging, medium-speed alternative to a conventional wound rotor slip-ring doubly-fed induction generator (DFIG) in wind energy conversion systems (WECS). It can provide competitive overall performance and similar low failure rates of a typically 30% rated back-to-back power electronics converter in 2:1 speed ranges but with the following important reliability and cost advantages over DFIG: the maintenance-free operation afforded by its brushless structure, 50% synchronous speed with the same number of rotor poles (allowing the use of a more compact, and more efficient two-stage gearbox instead of a vulnerable three-stage one), and superior grid integration properties including simpler protection for the low voltage ride through compliance of the fractional converter due to the comparatively higher leakage inductances and lower fault currents. Vector controlled pulse-width-modulated converters generally feature a much lower total harmonic distortion relative to hysteresis counterparts with variable switching rates and as such have been a predominant choice for BDFRG (and DFIG) wind turbines. Eliminating a shaft position sensor, which is often required for control implementation in this case, would be desirable to address the associated reliability issues. This fact has largely motivated the recent growing research of sensorless methods and developments of various rotor position and/or speed estimation techniques for this purpose. The main limitation of all the observer-based control approaches for grid-connected wind power applications of the BDFRG reported in the open literature is the requirement for pre-commissioning procedures and prior knowledge of the machine inductances, which are usually difficult to accurately identify by off-line testing. A model reference adaptive system (MRAS) based sensor-less vector control scheme to be presented will overcome this shortcoming. The true machine parameter independence of the proposed field-oriented algorithm, offering robust, inherently decoupled real and reactive power control of the grid-connected winding, is achieved by on-line estimation of the inductance ratio, the underlying rotor angular velocity and position MRAS observer being reliant upon. Such an observer configuration will be more practical to implement and clearly preferable to the existing machine parameter dependent solutions, and especially bearing in mind that with very little modifications it can be adapted for commercial DFIGs with immediately obvious further industrial benefits and prospects of this work. The excellent encoder-less controller performance with maximum power point tracking in the base speed region will be demonstrated by realistic simulation studies using large-scale BDFRG design data and verified by experimental results on a small laboratory prototype of the WECS emulation facility.

Keywords: brushless doubly fed reluctance generator, model reference adaptive system, sensorless vector control, wind energy conversion

Procedia PDF Downloads 51
8 A Modular Solution for Large-Scale Critical Industrial Scheduling Problems with Coupling of Other Optimization Problems

Authors: Ajit Rai, Hamza Deroui, Blandine Vacher, Khwansiri Ninpan, Arthur Aumont, Francesco Vitillo, Robert Plana

Abstract:

Large-scale critical industrial scheduling problems are based on Resource-Constrained Project Scheduling Problems (RCPSP), that necessitate integration with other optimization problems (e.g., vehicle routing, supply chain, or unique industrial ones), thus requiring practical solutions (i.e., modular, computationally efficient with feasible solutions). To the best of our knowledge, the current industrial state of the art is not addressing this holistic problem. We propose an original modular solution that answers the issues exhibited by the delivery of complex projects. With three interlinked entities (project, task, resources) having their constraints, it uses a greedy heuristic with a dynamic cost function for each task with a situational assessment at each time step. It handles large-scale data and can be easily integrated with other optimization problems, already existing industrial tools and unique constraints as required by the use case. The solution has been tested and validated by domain experts on three use cases: outage management in Nuclear Power Plants (NPPs), planning of future NPP maintenance operation, and application in the defense industry on supply chain and factory relocation. In the first use case, the solution, in addition to the resources’ availability and tasks’ logical relationships, also integrates several project-specific constraints for outage management, like, handling of resource incompatibility, updating of tasks priorities, pausing tasks in a specific circumstance, and adjusting dynamic unit of resources. With more than 20,000 tasks and multiple constraints, the solution provides a feasible schedule within 10-15 minutes on a standard computer device. This time-effective simulation corresponds with the nature of the problem and requirements of several scenarios (30-40 simulations) before finalizing the schedules. The second use case is a factory relocation project where production lines must be moved to a new site while ensuring the continuity of their production. This generates the challenge of merging job shop scheduling and the RCPSP with location constraints. Our solution allows the automation of the production tasks while considering the rate expectation. The simulation algorithm manages the use and movement of resources and products to respect a given relocation scenario. The last use case establishes a future maintenance operation in an NPP. The project contains complex and hard constraints, like on Finish-Start precedence relationship (i.e., successor tasks have to start immediately after predecessors while respecting all constraints), shareable coactivity for managing workspaces, and requirements of a specific state of "cyclic" resources (they can have multiple states possible with only one at a time) to perform tasks (can require unique combinations of several cyclic resources). Our solution satisfies the requirement of minimization of the state changes of cyclic resources coupled with the makespan minimization. It offers a solution of 80 cyclic resources with 50 incompatibilities between levels in less than a minute. Conclusively, we propose a fast and feasible modular approach to various industrial scheduling problems that were validated by domain experts and compatible with existing industrial tools. This approach can be further enhanced by the use of machine learning techniques on historically repeated tasks to gain further insights for delay risk mitigation measures.

Keywords: deterministic scheduling, optimization coupling, modular scheduling, RCPSP

Procedia PDF Downloads 183
7 Xen45 Gel Implant in Open Angle Glaucoma: Efficacy, Safety and Predictors of Outcome

Authors: Fossarello Maurizio, Mattana Giorgio, Tatti Filippo.

Abstract:

The most widely performed surgical procedure in Open-Angle Glaucoma (OAG) is trabeculectomy. Although this filtering procedure is extremely effective, surgical failure and postoperative complications are reported. Due to the its invasive nature and possible complications, trabeculectomy is usually reserved, in practice, for patients who are refractory to medical and laser therapy. Recently, a number of micro-invasive surgical techniques (MIGS: Micro-Invasive Glaucoma Surgery), have been introduced in clinical practice. They meet the criteria of micro-incisional approach, minimal tissue damage, short surgical time, reliable IOP reduction, extremely high safety profile and rapid post-operative recovery. Xen45 Gel Implant (Allergan, Dublin, Ireland) is one of the MIGS alternatives, and consists in a porcine gelatin tube designed to create an aqueous flow from the anterior chamber to the subconjunctival space, bypassing the resistance of the trabecular meshwork. In this study we report the results of this technique as a favorable option in the treatment of OAG for its benefits in term of efficacy and safety, either alone or in combination with cataract surgery. This is a retrospective, single-center study conducted in consecutive OAG patients, who underwent Xen45 Gel Stent implantation alone or in combination with phacoemulsification, from October 2018 to June 2019. The primary endpoint of the study was to evaluate the reduction of both IOP and number of antiglaucoma medications at 12 months. The secondary endpoint was to correlate filtering bleb morphology evaluated by means of anterior segment OCT with efficacy in IOP lowering and eventual further procedures requirement. Data were recorded on Microsoft Excel and study analysis was performed using Microsoft Excel and SPSS (IBM). Mean values with standard deviations were calculated for IOPs and number of antiglaucoma medications at all points. Kolmogorov-Smirnov test showed that IOP followed a normal distribution at all time, therefore the paired Student’s T test was used to compare baseline and postoperative mean IOP. Correlation between postoperative Day 1 IOP and Month 12 IOP was evaluated using Pearson coefficient. Thirty-six eyes of 36 patients were evaluated. As compared to baseline, mean IOP and the mean number of antiglaucoma medications significantly decreased from 27,33 ± 7,67 mmHg to 16,3 ± 2,89 mmHg (38,8% reduction) and from 2,64 ± 1,39 to 0,42 ± 0,8 (84% reduction), respectively, at 12 months after surgery (both p < 0,001). According to bleb morphology, eyes were divided in uniform group (n=8, 22,2%), subconjunctival separation group (n=5, 13,9%), microcystic multiform group (n=9, 25%) and multiple internal layer group (n=14, 38,9%). Comparing to baseline, there was no significative difference in IOP between the 4 groups at month 12 follow-up visit. Adverse events included bleb function decrease (n=14, 38,9%), hypotony (n=8, 22,2%) and choroidal detachment (n=2, 5,6%). All eyes presenting bleb flattening underwent needling and MMC injection. The higher percentage of patients that required secondary needling was in the uniform group (75%), with a significant difference between the groups (p=0,03). Xen45 gel stent, either alone or in combination with phacoemulsification, provided a significant lowering in both IOP and medical antiglaucoma treatment and an elevated safety profile.

Keywords: anterior segment OCT, bleb morphology, micro-invasive glaucoma surgery, open angle glaucoma, Xen45 gel implant

Procedia PDF Downloads 133
6 Governance Challenges for the Management of Water Resources in Agriculture: The Italian Way

Authors: Silvia Baralla, Raffaella Zucaro, Romina Lorenzetti

Abstract:

Water management needs to cope with economic, societal, and environmental changes. This could be guaranteed through 'shifting from government to governance'. In the last decades, it was applied in Europe through and within important legislative pillars (Water Framework Directive and Common Agricultural Policy) and their measures focused on resilience and adaptation to climate change, with particular attention to the creation of synergies among policies and all the actors involved at different levels. Within the climate change context, the agricultural sector can play, through sustainable water management, a leading role for climate-resilient growth and environmental integrity. A recent analysis on the water management governance of different countries identified some common gaps dealing with administrative, policy, information, capacity building, funding, objective, and accountability. The ability of a country to fill these gaps is an essential requirement to make some of the changes requested by Europe, in particular the improvement of the agro-ecosystem resilience to the effect of climatic change, supporting green and digital transitions, and sustainable water use. This research aims to contribute in sharing examples of water governances and related advantages useful to fill the highlighted gaps. Italy has developed a strong and exhaustive model of water governance in order to react with strategic and synergic actions since it is one of the European countries most threatened by climate change and its extreme events (drought, floods). In particular, the Italian water governance model was able to overcome several gaps, specifically as concerns the water use in agriculture, adopting strategies as a systemic/integrated approach, the stakeholder engagement, capacity building, the improvement of planning and monitoring ability, and an adaptive/resilient strategy for funding activities. They were carried out, putting in place regulatory, structural, and management actions. Regulatory actions include both the institution of technical committees grouping together water decision-makers and the elaboration of operative manuals and guidelines by means of a participative and cross-cutting approach. Structural actions deal with the funding of interventions within European and national funds according to the principles of coherence and complementarity. Finally, management actions regard the introduction of operational tools to support decision-makers in order to improve planning and monitoring ability. In particular, two cross-functional and interoperable web databases were introduced: SIGRIAN (National Information System for Water Resources Management in Agriculture) and DANIA (National Database of Investments for Irrigation and the Environment). Their interconnection allows to support sustainable investments, taking into account the compliance about irrigation volumes quantified in SIGRIAN, ensuring a high level of attention on water saving, and monitoring the efficiency of funding. Main positive results from the Italian water governance model deal with a synergic and coordinated work at the national, regional, and local level among institutions, the transparency on water use in agriculture, a deeper understanding from the stakeholder side of the importance of their roles and of their own potential benefits and the capacity to guarantee continuity to this model, through a sensitization process and the combined use of management operational tools.

Keywords: agricultural sustainability, governance model, water management, water policies

Procedia PDF Downloads 108
5 Evaluating Viability of Using South African Forestry Process Biomass Waste Mixtures as an Alternative Pyrolysis Feedstock in the Production of Bio Oil

Authors: Thembelihle Portia Lubisi, Malusi Ntandoyenkosi Mkhize, Jonas Kalebe Johakimu

Abstract:

Fertilizers play an important role in maintaining the productivity and quality of plants. Inorganic fertilizers (containing nitrogen, phosphorus, and potassium) are largely used in South Africa as they are considered inexpensive and highly productive. When applied, a portion of the excess fertilizer will be retained in the soil, a portion enters water streams due to surface runoff or the irrigation system adopted. Excess nutrient from the fertilizers entering the water stream eventually results harmful algal blooms (HABs) in freshwater systems, which not only disrupt wildlife but can also produce toxins harmful to humans. Use of agro-chemicals such as pesticides and herbicides has been associated with increased antimicrobial resistance (AMR) in humans as the plants are consumed by humans. This resistance of bacterial poses a threat as it prevents the Health sector from being able to treat infectious disease. Archaeological studies have found that pyrolysis liquids were already used in the time of the Neanderthal as a biocide and plant protection product. Pyrolysis is thermal degradation process of plant biomass or organic material under anaerobic conditions leading to production of char, bio-oils and syn gases. Bio-oil constituents can be categorized as water soluble (wood vinegar) and water insoluble fractions (tar and light oils). Wood vinegar (pyro-ligneous acid) is said to contain contains highly oxygenated compounds including acids, alcohols, aldehydes, ketones, phenols, esters, furans, and other multifunctional compounds with various molecular weights and compositions depending on the biomass material derived from and pyrolysis operating conditions. Various researchers have found the wood vinegar to be efficient in the eradication of termites, effective in plant protection and plant growth, has antibacterial characteristics and was found effective in inhibiting the micro-organisms such as candida yeast, E-coli, etc. This study investigated characterisation of South African forestry product processing waste with intention of evaluating the potential of using the respective biomass waste as feedstock for boil oil production via pyrolysis process. Ability to use biomass waste materials in production of wood-vinegar has advantages that it does not only allows for reduction of environmental pollution and landfill requirement, but it also does not negatively affect food security. The biomass wastes investigated were from the popular tree types in KZN, which are, pine saw dust (PSD), pine bark (PB), eucalyptus saw dust (ESD) and eucalyptus bark (EB). Furthermore, the research investigates the possibility of mixing the different wastes with an aim to lessen the cost of raw material separation prior to feeding into pyrolysis process and mixing also increases the amount of biomass material available for beneficiation. A 50/50 mixture of PSD and ESD (EPSD) and mixture containing pine saw dust; eucalyptus saw dust, pine bark and eucalyptus bark (EPSDB). Characterisation of the biomass waste will look at analysis such as proximate (volatiles, ash, fixed carbon), ultimate (carbon, hydrogen, nitrogen, oxygen, sulphur), high heating value, structural (cellulose, hemicellulose and lignin) and thermogravimetric analysis.

Keywords: characterisation, biomass waste, saw dust, wood waste

Procedia PDF Downloads 54
4 Design, Control and Implementation of 3.5 kW Bi-Directional Energy Harvester for Intelligent Green Energy Management System

Authors: P. Ramesh, Aby Joseph, Arya G. Lal, U. S. Aji

Abstract:

Integration of distributed green renewable energy sources in addition with battery energy storage is an inevitable requirement in a smart grid environment. To achieve this, an Intelligent Green Energy Management System (i-GEMS) needs to be incorporated to ensure coordinated operation between supply and load demand based on the hierarchy of Renewable Energy Sources (RES), battery energy storage and distribution grid. A bi-directional energy harvester is an integral component facilitating Intelligent Green Energy Management System (i-GEMS) and it is required to meet the technical challenges mentioned as follows: (1) capability for bi-directional mode of operation (buck/boost) (2) reduction of circuit parasitic to suppress voltage spikes (3) converter startup problem (4) high frequency magnetics (5) higher power density (6) mode transition issues during battery charging and discharging. This paper is focused to address the above mentioned issues and targeted to design, develop and implement a bi-directional energy harvester with galvanic isolation. In this work, the hardware architecture for bi-directional energy harvester rated 3.5 kW is developed with Isolated Full Bridge Boost Converter (IFBBC) as well as Dual Active Bridge (DAB) Converter configuration using modular power electronics hardware which is identical for both solar PV array and battery energy storage. In IFBBC converter, the current fed full bridge circuit is enabled and voltage fed full bridge circuit is disabled through Pulse Width Modulation (PWM) pulses for boost mode of operation and vice-versa for buck mode of operation. In DAB converter, all the switches are in active state so as to adjust the phase shift angle between primary full bridge and secondary full bridge which in turn decides the power flow directions depending on modes (boost/buck) of operation. Here, the control algorithm is developed to ensure the regulation of the common DC link voltage and maximum power extraction from the renewable energy sources depending on the selected mode (buck/boost) of operation. The circuit analysis and simulation study are conducted using PSIM 9.0 in three scenarios which are - 1.IFBBC with passive clamp, 2. IFBBC with active clamp, 3. DAB converter. In this work, a common hardware prototype for bi-directional energy harvester with 3.5 kW rating is built for IFBBC and DAB converter configurations. The power circuit is equipped with right choice of MOSFETs, gate drivers with galvanic isolation, high frequency transformer, filter capacitors, and filter boost inductor. The experiment was conducted for IFBBC converter with passive clamp under boost mode and the prototype confirmed the simulation results showing the measured efficiency as 88% at 2.5 kW output power. The digital controller hardware platform is developed using floating point microcontroller TMS320F2806x from Texas Instruments. The firmware governing the operation of the bi-directional energy harvester is written in C language and developed using code composer studio. The comprehensive analyses of the power circuit design, control strategy for battery charging/discharging under buck/boost modes and comparative performance evaluation using simulation and experimental results will be presented.

Keywords: bi-directional energy harvester, dual active bridge, isolated full bridge boost converter, intelligent green energy management system, maximum power point tracking, renewable energy sources

Procedia PDF Downloads 122
3 [Keynote Speech]: Evidence-Based Outcome Effectiveness Longitudinal Study on Three Approaches to Reduce Proactive and Reactive Aggression in Schoolchildren: Group CBT, Moral Education, Bioneurological Intervention

Authors: Annis Lai Chu Fung

Abstract:

While aggression had high stability throughout developmental stages and across generations, it should be the top priority of researchers and frontline helping professionals to develop prevention and intervention programme for aggressive children and children at risk of developing aggressive behaviours. Although there is a substantial amount of anti-bullying programmes, they gave disappointingly small effect sizes. The neglectful practical significance could be attributed to the overly simplistic categorisation of individuals involved as bullies or victims. In the past three decades, the distinction between reactive and proactive aggression has been well-proved. As children displaying reactively aggressive behaviours have distinct social-information processing pattern with those showing proactively aggressive behaviours, it is critical to identify the unique needs of the two subtypes accordingly when designing an intervention. The onset of reactive aggression and proactive aggression was observed at earliest in 4.4 and 6.8 years old respectively. Such findings called for a differential early intervention targeting these high-risk children. However, to the best of the author’s knowledge, the author was the first to establish an evidence-based intervention programme against reactive and proactive aggression. With the largest samples in the world, the author, in the past 10 years, explored three different approaches and their effectiveness against aggression quantitatively and qualitatively with longitudinal design. The three approaches presented are (a) cognitive-behavioral approach, (b) moral education, with Chinese marital arts and ethics as the medium, and (c) bioneurological measures (omega-3 supplementation). The studies adopted a multi-informant approach with repeated measures before and after the intervention, and follow-up assessment. Participants were recruited from primary and secondary schools in Hong Kong. In the cognitive-behavioral approach, 66 reactive aggressors and 63 proactive aggressors, aged from 11 to 17, were identified from 10,096 secondary-school children with questionnaire and subsequent structured interview. Participants underwent 10 group sessions specifically designed for each subtype of aggressor. Results revealed significant declines in aggression levels from the baseline to the follow-up assessment after 1 year. In moral education through the Chinese martial arts, 315 high-risk aggressive children, aged 6 to 12 years, were selected from 3,511 primary-school children and randomly assigned into four types of 10-session intervention group, namely martial-skills-only, martial-ethics-only, both martial-skills-and-ethics, and physical fitness (placebo). Results showed only the martial-skills-and-ethics group had a significant reduction in aggression after treatment and 6 months after treatment comparing with the placebo group. In the bioneurological approach, 218 children, aged from 8 to 17, were randomly assigned to the omega-3 supplement group and the placebo group. Results revealed that compared with the placebo group, the omega-3 supplement group had significant declines in aggression levels at the 6-month follow-up assessment. All three approaches were effective in reducing proactive and reactive aggression. Traditionally, intervention programmes against aggressive behaviour often adapted the cognitive and/or behavioural approach. However, cognitive-behavioural approach for children was recently challenged by its demanding requirement of cognitive ability. Traditional cognitive interventions may not be as beneficial to an older population as in young children. The present study offered an insightful perspective in aggression reduction measures.

Keywords: intervention, outcome effectiveness, proactive aggression, reactive aggression

Procedia PDF Downloads 213
2 Biodegradation of Chlorophenol Derivatives Using Macroporous Material

Authors: Dmitriy Berillo, Areej K. A. Al-Jwaid, Jonathan L. Caplin, Andrew Cundy, Irina Savina

Abstract:

Chlorophenols (CPs) are used as a precursor in the production of higher CPs and dyestuffs, and as a preservative. Contamination by CPs of the ground water is located in the range from 0.15-100mg/L. The EU has set maximum concentration limits for pesticides and their degradation products of 0.1μg/L and 0.5μg/L, respectively. People working in industries which produce textiles, leather products, domestic preservatives, and petrochemicals are most heavily exposed to CPs. The International Agency for Research on Cancers categorized CPs as potential human carcinogens. Existing multistep water purification processes for CPs such as hydrogenation, ion exchange, liquid-liquid extraction, adsorption by activated carbon, forward and inverse osmosis, electrolysis, sonochemistry, UV irradiation, and chemical oxidation are not always cost effective and can cause the formation of even more toxic or mutagenic derivatives. Bioremediation of CPs derivatives utilizing microorganisms results in 60 to 100% decontamination efficiency and the process is more environmentally-friendly compared with existing physico-chemical methods. Microorganisms immobilized onto a substrate show many advantages over free bacteria systems, such as higher biomass density, higher metabolic activity, and resistance to toxic chemicals. They also enable continuous operation, avoiding the requirement for biomass-liquid separation. The immobilized bacteria can be reused several times, which opens the opportunity for developing cost-effective processes for wastewater treatment. In this study, we develop a bioremediation system for CPs based on macroporous materials, which can be efficiently used for wastewater treatment. Conditions for the preparation of the macroporous material from specific bacterial strains (Pseudomonas mendocina and Rhodococus koreensis) were optimized. The concentration of bacterial cells was kept constant; the difference was only the type of cross-linking agents used e.g. glutaraldehyde, novel polymers, which were utilized at concentrations of 0.5 to 1.5%. SEM images and rheology analysis of the material indicated a monolithic macroporous structure. Phenol was chosen as a model system to optimize the function of the cryogel material and to estimate its enzymatic activity, since it is relatively less toxic and harmful compared to CPs. Several types of macroporous systems comprising live bacteria were prepared. The viability of the cross-linked bacteria was checked using Live/Dead BacLight kit and Laser Scanning Confocal Microscopy, which revealed the presence of viable bacteria with the novel cross-linkers, whereas the control material cross-linked with glutaraldehyde(GA), contained mostly dead cells. The bioreactors based on bacteria were used for phenol degradation in batch mode at an initial concentration of 50mg/L, pH 7.5 and a temperature of 30°C. Bacterial strains cross-linked with GA showed insignificant ability to degrade phenol and for one week only, but a combination of cross-linking agents illustrated higher stability, viability and the possibility to be reused for at least five weeks. Furthermore, conditions for CPs degradation will be optimized, and the chlorophenol degradation rates will be compared to those for phenol. This is a cutting-edge bioremediation approach, which allows the purification of waste water from sustainable compounds without a separation step to remove free planktonic bacteria. Acknowledgments: Dr. Berillo D. A. is very grateful to Individual Fellowship Marie Curie Program for funding of the research.

Keywords: bioremediation, cross-linking agents, cross-linked microbial cell, chlorophenol degradation

Procedia PDF Downloads 205
1 Ensemble Sampler For Infinite-Dimensional Inverse Problems

Authors: Jeremie Coullon, Robert J. Webber

Abstract:

We introduce a Markov chain Monte Carlo (MCMC) sam-pler for infinite-dimensional inverse problems. Our sam-pler is based on the affine invariant ensemble sampler, which uses interacting walkers to adapt to the covariance structure of the target distribution. We extend this ensem-ble sampler for the first time to infinite-dimensional func-tion spaces, yielding a highly efficient gradient-free MCMC algorithm. Because our ensemble sampler does not require gradients or posterior covariance estimates, it is simple to implement and broadly applicable. In many Bayes-ian inverse problems, Markov chain Monte Carlo (MCMC) meth-ods are needed to approximate distributions on infinite-dimensional function spaces, for example, in groundwater flow, medical imaging, and traffic flow. Yet designing efficient MCMC methods for function spaces has proved challenging. Recent gradi-ent-based MCMC methods preconditioned MCMC methods, and SMC methods have improved the computational efficiency of functional random walk. However, these samplers require gradi-ents or posterior covariance estimates that may be challenging to obtain. Calculating gradients is difficult or impossible in many high-dimensional inverse problems involving a numerical integra-tor with a black-box code base. Additionally, accurately estimating posterior covariances can require a lengthy pilot run or adaptation period. These concerns raise the question: is there a functional sampler that outperforms functional random walk without requir-ing gradients or posterior covariance estimates? To address this question, we consider a gradient-free sampler that avoids explicit covariance estimation yet adapts naturally to the covariance struc-ture of the sampled distribution. This sampler works by consider-ing an ensemble of walkers and interpolating and extrapolating between walkers to make a proposal. This is called the affine in-variant ensemble sampler (AIES), which is easy to tune, easy to parallelize, and efficient at sampling spaces of moderate dimen-sionality (less than 20). The main contribution of this work is to propose a functional ensemble sampler (FES) that combines func-tional random walk and AIES. To apply this sampler, we first cal-culate the Karhunen–Loeve (KL) expansion for the Bayesian prior distribution, assumed to be Gaussian and trace-class. Then, we use AIES to sample the posterior distribution on the low-wavenumber KL components and use the functional random walk to sample the posterior distribution on the high-wavenumber KL components. Alternating between AIES and functional random walk updates, we obtain our functional ensemble sampler that is efficient and easy to use without requiring detailed knowledge of the target dis-tribution. In past work, several authors have proposed splitting the Bayesian posterior into low-wavenumber and high-wavenumber components and then applying enhanced sampling to the low-wavenumber components. Yet compared to these other samplers, FES is unique in its simplicity and broad applicability. FES does not require any derivatives, and the need for derivative-free sam-plers has previously been emphasized. FES also eliminates the requirement for posterior covariance estimates. Lastly, FES is more efficient than other gradient-free samplers in our tests. In two nu-merical examples, we apply FES to challenging inverse problems that involve estimating a functional parameter and one or more scalar parameters. We compare the performance of functional random walk, FES, and an alternative derivative-free sampler that explicitly estimates the posterior covariance matrix. We conclude that FES is the fastest available gradient-free sampler for these challenging and multimodal test problems.

Keywords: Bayesian inverse problems, Markov chain Monte Carlo, infinite-dimensional inverse problems, dimensionality reduction

Procedia PDF Downloads 148