Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Cost optimization”

Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 883 records · Page 49

Optimizing an Integrated Renewable-Electrolysis System

Hydrogen is a versatile energy carrier that is used in a wide variety of chemical and industrial processes. Producing hydrogen using electrolysis can enable integration of multiple sectors including electricity, heating, and industrial sectors; however, the cost of producing hydrogen from electrolysis remains a challenge for encouraging greater adoption. With growing amounts of renewable generation on the California grid, there is downward pressure on wholesale electricity prices, particularly during the afternoon from photovoltaics (PV). These lower, or even potentially negative prices, challenge the business cases for new and existing PV plants. In addition, as the grid transitions to less flexible generation, there is greater need for system flexibility. To help improve the economics for both solar PV and hydrogen production using electrolyzers, we explore the benefit of combining PV and electrolysis systems. The optimal breakeven hydrogen production cost for six unique market participation configurations is calculated at six candidate locations where PV is already installed. The six market configurations include islanded, separated, retail, net energy metering (NEM), hybrid retail/wholesale and wholesale. Using the Revenue Operation and Device Optimization Model (RODeO) model, the optimal breakeven hydrogen price over the lifetime of the equipment is calculated. The cost includes production, storage, and compression in preparation for gaseous delivery trucks. Revenue streams include the sale of hydrogen, low carbon fuel standard (LCFS) credits, renewable electricity sold to the grid, and Renewable Energy Credits (REC). The costs included are the electricity costs, capital and fixed operation and maintenance cost (FOM) for the electrolyzer, PV, and storage and compression systems as well as taxes and financing costs. In addition, cost reductions are achieved through retail and wholesale rate optimization, by which electricity is purchased at the lowest price and sold, if possible, at the highest price. For all locations, the breakeven hydrogen production cost results show that, in the order of decreasing cost, the system configurations are islanded (highest), separated, NEM, retail, hybrid retail/wholesale, and wholesale (lowest). The resulting system design balances between the capital and maintenance cost components, the operation costs (i.e., electricity costs) and the additional market revenues. The integration of solar PV and electrolysis is shown to provide a mutually beneficial relationship. For PV, integration with electrolysis offers the potential to hedge against wholesale market price volatility, and integration with electrolysis may offer the potential to defer or avoid transmission investment to deliver power to the point-of-use and instead use it on-site. When compared with SMR without considering any renewable hydrogen premiums, this study finds that PV + Electrolysis systems with current costs are likely not competitive; however, with cost reductions for electrolysis equipment consistent with DOE projections, it was found that systems with wholesale market access would be competitive, largely on account of both low capital costs and low-cost electricity. The electrolysis units can provide greater flexibility than is required based on retail rate optimization, so there is an opportunity for a utility or CAISO to increase system flexibility with PV + Electrolysis systems in return for commensurate compensation. In this way, there are potentially several solutions that fall between the hybrid configuration and the wholesale configuration that could provide sufficient compensation for a PV + Electrolysis unit to compete with SMR while also providing greater flexibility to the grid.

24 POWER TRANSMISSION AND DISTRIBUTION↗

Analytics-at-scale of Sensor Data for Digital Monitoring in Nuclear Plants (3 rd Annual Report)

Nuclear power plants collect and store large volumes of heterogeneous data from various components and systems. With recent advances in machine learning (ML) techniques, these data can be leveraged to develop diagnostic and short-term forecasting models to better predict future equipment condition. Maintenance operations can then be planned in advance whenever degraded performance is predicted, thus resulting in fewer unplanned outages and the optimization of maintenance activities. This enables lower maintenance costs and improves the overall economics of nuclear power. This report primarily focuses on developing a short-term forecasting process that leverages a feature selection process to distill large volumes of heterogeneous data and predict specific equipment parameters. A variety of feature selection methods, including Shapley Additive Explanations (SHAP) and variance inflation factor (VIF), were used to select the optimal features as inputs for three ML methods: long short-term memory (LSTM) networks, support vector regression (SVR), and random forest (RF). Each combination of model and input features was used to predict a pump bearing temperature both 1 and 24 hours in advance, based on actual plant system data. The optimal inputs for the LSTM and SVR were selected using the SHAP values, while the optimal input for the RF consisted solely of the response variable itself. Each model produced similar 1-hour-ahead predictions, with root mean square errors (RMSEs) of roughly 0.006. For the 24-hour-ahead predictions, differences could be seen between LSTM, SVR, and RF, as reflected by model performances of 0.036 ± 0.014, 0.0026 ± 0, and 0.063 ± 0.004 RMSE, respectively. As big data and continuous online monitoring become more widely available, the proposed feature selection process can be used for many applications beyond the prediction of process parameters within nuclear infrastructure. This report summarizes the Fiscal Year 2021 research progress encompassing the (1) data cleaning and feature selection necessary for ML applications; (2) development of short-term forecasting models to predict future plant process parameters for both single and multiple time steps ahead; and (3) validation of the feature selection methods and short-term forecasting models given new data from different systems.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

Environmental and Economic Implications of Emerging Plastic Recycling Technologies

Recycling will play a crucial role in mitigating plastic pollution and promoting a circular economy for polymers. Quantitative analysis can help guide the optimization and implementation of these plastic management strategies, enabling increased circularity while minimizing costs, energy use, greenhouse gas emissions, and other environmental impacts. This talk will outline the Bio-Optimized Technologies to keep Thermoplastics out of Landfills and the Environment (BOTTLE) Consortium's approach to analysis-guided plastic recycling research. Stringent process modelling, life cycle assessment, and techno-economic analysis are used to benchmark the technical feasibility, environmental impacts, and costs of chemical and biological recycling technologies in comparison to conventional fossil fuel-based plastic manufacturing. Across emerging recycling strategies, several key challenges become apparent - including plastic feedstock pretreatment requirements, high energy or chemical use, and recycled plastic yields and quality - highlighting opportunities for future innovation. Through this consistent and in-depth analysis approach, BOTTLE aims to provide the plastics community with key metrics and insights to drive plastic recycling innovation towards a more sustainable and circular economy.

circular economy↗

A Trapping-Micro-LC-FAIMS/dCV-MS Strategy for Ultrasensitive and Robust Targeted Quantification of Protein Drugs and Biomarkers

The sensitivity of LC-MS in quantifying target proteins in plasma/tissues is significantly hindered by co-eluted matrix interferences. While antibody-based immuno-enrichment effectively reduces interferences, developing and optimizing antibodies are often time-consuming and costly. Here, in this study, by leveraging the orthogonal separation capability of Field Asymmetric Ion Mobility Spectrometry (FAIMS), we developed a FAIMS/differential-compensation-voltage (FAIMS/dCV) method for antibody-free, robust, and ultra-sensitive quantification of target proteins directly from plasma/tissue digests. By comparing the intensity-CV profiles of the target vs. co-eluted endogenous interferences, the FAIMS/dCV approach identifies the optimal CV for quantification of each target protein, thus maximizing the signal-to-noise ratio (S/N). Compared to quantification without FAIMS, this technique dramatically reduces endogenous interferences, showing a median improvement of the S/N by 14.8-fold for the quantification of 17 representative protein drugs and biomarkers in plasma or tissues and a 5.2-fold median increase in S/N over conventional FAIMS approach, which uses the peak CV of each target. We also discovered that the established CV parameters remain consistent over months and are matrix-independent, affirming the robustness of the developed FAIMS/dCV method and the transferability of the method across matrices. The developed method was successfully demonstrated in three applications: the quantification of monoclonal antibodies with sub-ng/mL LOQ in plasma, an investigation of the time courses of evolocumab and its target PCSK9 in a preclinical setting, and a clinical investigation of low abundance obesity-related biomarkers. This innovative and easy-to-use method has extensive potential in clinical and pharmaceutical research, particularly where sensitive and high-throughput quantification of protein drugs and biomarkers is required.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Data-driven simultaneous process optimization and adsorbent selection for vacuum pressure swing adsorption

Technologies for post-combustion carbon capture are essential for the reduction of greenhouse gas emissions to the atmosphere. However, they are still associated with high costs and energy consumption. Intensified processes for carbon capture have the potential to overcome these challenges due to their higher efficiency, lower capital cost, and increased operational flexibility. Here, this work investigates simultaneous optimization of process conditions and adsorbent selection for a modular Vacuum Pressure-Swing Adsorption system designed for CO 2 capture. Both surrogate-based Nonlinear Programming and Mixed-Integer Nonlinear Programming approaches are applied and compared in terms of computational efficiency and solution accuracy. Moreover, process performance results are examined by applying several data analytics techniques to gain insights into the material-process correlations. Data-driven classifiers and neural networks can accurately predict whether a material is likely to satisfy purity, recovery, and energy constraints when operated at optimal process conditions.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

Transmission-distribution long-term volt-var planning considering reactive power support capability of distributed PV

High penetration of grid-edge, inverter-based photovoltaic (PV) can cause significant voltage fluctuations not only at the distribution but also at the sub-transmission levels due to PV output intermittency. Traditional reactive power planning approaches do not consider intermittency, nor the possibility of coordinating the control of existing and future volt-ampere reactive resources. This paper proposes a reactive power planning tool for sub-transmission systems to mitigate voltage violations and fluctuations caused by high PV penetration and intermittency with a minimum investment cost. The planning tool coordinates with an optimization-based volt-var operational tool for: a) modeling the coordination of all existing var assets in both sub-transmission and distribution systems to reduce the need of new equipment, and b)selecting a set of scenarios with voltage violations, derived from PV intermittency c) testing the final investment decision. The tool obtains an investment need for each intermittency scenario with a proposed optimal power-flow framework with efficient techniques to handle a high number of discrete variables. Two options are provided for final planning decision: i) a conservative direct combination of investment need solutions and ii) a machine learning-based selection of representative investment needs at most time steps. The final investment decision options are verified using a realistic large-scale sub-transmission system and 5-minute PV and load data. The results show a significant voltage performance improvement with a lower investment cost for additional var equipment compared to conventional approaches.

14 SOLAR ENERGY↗

Impact of model predictive control-enabled home energy management on large-scale distribution systems with photovoltaics

Residential customers use more than one-quarter of the electricity in the world. Optimally managing home energy consumption is an effective way of easing the operational challenges facing the electric grid with increasing solar photovoltaics (PV). This paper studies the impact of the future proliferation of home energy management systems (HEMS) in the presence of PV on large-scale distribution systems. First, we present a stochastic HEMS model that minimizes residential customers' thermal discomfort and energy costs under uncertainty. The HEMS model schedules the optimal operations of residential appliances in the presence of PV within a mixed-integer linear programming-based model predictive control framework that links the proposed HEMS to a quasi-steady-state time-series simulation tool. Additionally, extensive simulations are conducted for a stand-alone residential home using two tariff structures and for 1977 homes on an 8,500-node distribution feeder. Simulation results quantify the impact of the future proliferation of HEMS on the large-scale distribution system with PV.

14 SOLAR ENERGY↗

Optimizing resource allocation in Miscanthus breeding via sparse testing designs for genomic prediction

Phenotyping high-biomass perennial crops is laborious and the rate of genetic gain in conventional perennial crop breeding programs is typically low. So, it is especially important to identify methods that produce efficiency gains in the breeding process. Miscanthus is a C4 perennial grass with favorable characteristics for producing biomass as a feedstock for biofuels and diverse bio-based products. Increasing biomass yield will increase profitability and environmental benefits, so it is a key target for Miscanthus breeding. In addition, the identification of well-adapted genotypes across a wide range of environmental conditions requires the establishment of multi-environment trials (METs). Sparse testing is a genomic prediction-based strategy that reduces the phenotyping costs in METs by selecting a subset of genotypes to evaluate in a subset of environments and then predicts the performance of the unobserved genotype-environment combinations. A Miscanthus sacchariflorus (MSA) population comprising 336 genotypes observed across three environments was analyzed implementing sparse testing designs. Three prediction models considering main effects (environments, genotypes, genomic) and interaction effects (genotype-by-environment; G×E interaction) were implemented for forecasting dry biomass yield (YDY), total culm (TCM), average internode length (AIL), and culm node number (CNN). Multiple calibration sets based on different compositions and sizes were considered to evaluate performance in terms of the predictive ability (PA) and the mean square error (MSE) for a fixed testing set size. The training set size ranged from 52 to 112 to predict a fixed set of 224 unobserved genotypes across all three environments. The results showed that the model accounting for G×E interaction consistently presented the highest PA and the lowest MSE: for CNN (PA: ~0.77, MSE: ~0.5) and YDY (PA: ~0.70, MSE: ~1.3) while for TCM and AIL these ranged from ~0.28 to 0.41 and ~1.3 to 4.3, respectively. Overall, varying training sets and allocation strategies did not affect PA and MSE, with 52 non-overlapping and 0 overlapping genotypes per environment as the optimal cost-effective allocation framework. This suggests that implementing sparse testing designs could significantly reduce phenotyping costs by fivefold, without compromising PA in breeding programs for perennial crops such as Miscanthus.

Miscanthus sacchariflorus (MSA)↗

Impact of heating and cooling loads on battery energy storage system sizing in extreme cold climates

Efficient operation of battery energy storage systems requires that battery temperature remains within a specific range. Current techno-economic models neglect the parasitic loads heating and cooling operations have on these devices, assuming they operate at constant temperature. In this work, these effects are investigated considering the optimal sizing of battery energy storage systems when deployed in cold environments. Here, a peak shaving application is presented as a linear programming problem which is then formulated in the PYOMO optimization programming language. The building energy simulation software EnergyPlus is used to model the heating, ventilation, and air conditioning load of the battery energy storage system enclosure. Case studies are conducted for eight locations in the United States considering a nickel manganese cobalt oxide lithium ion battery type and whether the power conversion system is inside or outside the enclosure. The results show an increase of 42% to 300% in energy capacity size, 43% to 217% in power rating, and 43% to 296% increase in capital cost dependent on location. This analysis shows that the heating, ventilation, and air conditioning load can have a large impact on the optimal sizes and cost of a battery energy storage system and merit consideration in techno-economic studies.

25 ENERGY STORAGE↗

DCFC + Hydrogen Station Design Optimization [Slides]

Both direct current fast charging (DCFC) and Hydrogen stations are working to create successful long-term business models; however, analyses for DCFC and hydrogen fueling infrastructure are almost always performed separately. This work provides a detailed exploration of the benefit of integrating DCFC and hydrogen stations to lower the total system cost from load balancing and equipment cost sharing. To achieve this we have adapted the REopt optimization framework to simultaneously optimize the design and operation of integrated DCFC and H2 fueling station. Results indicate that 1) combining hydrogen fueling and DCFC stations can significantly reduce lifetime costs compared to separated stations. 2) Co-location with additional site load reduces DCFC costs, however, integration of DCFC with hydrogen provides an even greater cost reduction. 3) Adding PV to combined stations further reduces the lifetime station cost. 4) Capital investments in station combination today can help reduce the cost of operating DCFC tomorrow and 5) product diversification acts as a hedge against variability and enables a more dynamic response to market changes.

08 HYDROGEN↗

CASTELO: clustered atom subtypes aided lead optimization—a combined machine learning and molecular modeling method

Background: Drug discovery is a multi-stage process that comprises two costly major steps: pre-clinical research and clinical trials. Among its stages, lead optimization easily consumes more than half of the pre-clinical budget. We propose a combined machine learning and molecular modeling approach that partially automates lead optimization workflow in silico, providing suggestions for modification hot spots. Results: The initial data collection is achieved with physics-based molecular dynamics simulation. Contact matrices are calculated as the preliminary features extracted from the simulations. To take advantage of the temporal information from the simulations, we enhanced contact matrices data with temporal dynamism representation, which are then modeled with unsupervised convolutional variational autoencoder (CVAE). Finally, conventional and CVAE-based clustering methods are compared with metrics to rank the submolecular structures and propose potential candidates for lead optimization. Conclusion: With no need for extensive structure-activity data, our method provides new hints for drug modification hotspots which can be used to improve drug potency and reduce the lead optimization time. It can potentially become a valuable tool for medicinal chemists.

59 BASIC BIOLOGICAL SCIENCES↗

Towards cost-competitive middle distillate fuels from ethanol within a market-flexible C2 platform-based biorefinery concept

Ethanol to middle distillates (ETMD) is a promising pathway to produce sustainable liquid fuels to decarbonize the hard-to-electrify transportation sectors due to (1) the abundant sugar/starch and lignocellulosic biomass, (2) the existing deployment scale of fuel ethanol production (similar to 29 billion gallons per year globally), and (3) emerging opportunities in C2+ alcohol synthesis from CO2. Here we report a conceptual market-responsive biorefinery centered around a new ETMD pathway based on one-step ethanol to butene-rich olefins (ETO) over a Cu-Zn-Y/Beta catalyst. Specifically, this ethanol conversion pathway comprises one-step ETO, oligomerization, and hydrotreating. This ETO is distinct from that in the conventional ethanol-to-jet process which is based on two-step ethanol to ethylene and ethylene oligomerization to butenes. Butene-rich olefins can be shifted to butadiene-rich products by simply changing the reaction atmosphere from hydrogen to inert gas over the same ETO catalyst. Leveraging the experimental results, baseline techno-economic analysis (TEA) and sensitivity analysis indicate that the ethanol conversion cost is $0.60 per gallon gasoline equivalent (GGE), with opportunities for further cost reduction via improving the liquid hydrocarbon yield and space velocities, and process optimization on balancing dewatering of ethanol feed prior to the ETO step. The minimum fuel selling price (MFSP) of liquid hydrocarbons derived from corn starch ethanol with butadiene as coproduct is $1.64 per GGE, in the range that is cost competitive with petroleum kerosene-type jet fuel. Projected MFSP for cellulosic ethanol (corn stover) derived hydrocarbons is below $3.00 per GGE and co-production of butadiene further reduces the MFSP to $1.70 per GGE. The Well-to-Wake life-cycle analysis indicates that 85% greenhouse gas emission reduction can be achieved when using corn stover compared to petroleum reference and the associated carbon credits will provide significant economic incentives to favor the cellulosic ethanol-derived hydrocarbon fuels. This study demonstrates a low-cost pathway to middle distillate fuels leveraging existing ethanol infrastructure, where catalysis innovation drives the reduction of process complexity and flexible coproduction of a value-added chemical product.

Zhang, Junyan↗

Parametric analysis on optimized design of hybrid solar power plants

There is increasing interest in utility-scale solar power plants with storage which can flexibly dispatch renewable energy to the grid. However, plant design possesses many degrees of freedom and non-obvious trade-offs in performance. Software tools can estimate or optimize the performance of a specific plant configuration under market and weather conditions of interest; the associated cost parameters and operating assumptions strongly influence estimates of plant performance and decisions regarding optimal sizing. We employ the National Renewable Energy Laboratory's Hybrid Optimization and Performance Platform, which incorporates optimal dispatch when evaluating plant performance, and investigate the sensitivity to weather and market conditions, operating limitations, and the presence of a capacity-based incentive. We demonstrate changes in plant performance and optimal sizing with respect to these inputs and discuss implications. Here results show that PV-with-battery designs are more profitable under our assumptions, but that designs including a concentrated solar power (CSP) system produce significantly greater annual energy; and that CSP-with-thermal energy storage designs maximizing the benefit-to-cost ratio have an input-dependent linear relationship between the CSP field solar multiple and the hours of storage as the project budget varies.

14 SOLAR ENERGY↗

An analytical method for identifying synergies between behind-the-meter battery and thermal energy storage

Electric utilities build generation capacity to meet the highest demand period, and they often pass on the costs associated with these peaking generators to building owners through demand charges. Building owners can minimize these demand charges by shifting energy use away from peak periods with behind-the-meter storage. This storage can include batteries, which can directly shift the metered load, or thermal energy storage, which can shift thermal-driven electric loads like air conditioning. However, there is a lack of research on how best to combine battery and thermal energy storage. In this study, we develop an analytical sizing method to calculate the potential demand reduction and annualized cost savings for different combinations of thermal and battery energy storage sizes. We show that adding batteries to a thermal energy storage system can increase the total system's load shaving potential. This is particularly true when the building has onsite photovoltaic generation or electric vehicle charging, which add significant variability to the load shape. We also show that for a given total storage size, selecting a higher fraction of thermal energy storage can significantly lower the cycling of the battery, and therefore extend the battery life. This, combined with the expected lower first cost of thermal energy storage materials compared to batteries, shows that hybrid energy storage systems can outperform a standalone battery or standalone thermal storage system. Assuming the thermal storage has a capital cost 6x lower than the battery, our analysis shows that the optimal system is 71% thermal energy storage and 29% battery energy storage for a scenario with electric vehicle charging. The annualized cost savings for this system are $48.6 k/yr, whereas an equivalently sized standalone thermal energy storage system would provide annualized cost savings of $28.5 k/yr and a standalone battery would lead to savings of $8.72 k/yr. The hybrid system also reduces battery cycling by 52% compared to a standalone battery, extending battery lifetime.

25 ENERGY STORAGE↗

Structural design and optimization of a series of 13.2 MW downwind rotors

The quest for reduced LCOE has driven significant growth in wind turbine size. A key question to enable larger rotor designs is how to configure and optimize structural designs to constrain blade mass and cost while satisfying a growing set of challenging structural design requirements. In this paper, we investigate the performance of a series of three two-bladed downwind rotors with different blade lengths (104.3-m, 122.9-m, and 143.4-m) all rated at 13.2 MW. The primary goals are to achieve 25% rotor mass and 25% LCOE reduction. A comparative analysis of the structural performance and economics of this family rotors is presented. To further explore optimization opportunities for large rotors, we present new results in a root and spar cap design optimization. In summary, we present structural design solutions that achieve 25% rotor mass reduction in a SUMR13i design (104.3-m) and 25% LCOE reduction in a SUMR13C design (143.4-m).

Yao, Shulong↗

High-Efficiency, Low-Cost III-V Solar Cells by Dynamic Hydride Vapor Phase Epitaxy Coupled with Rapid, Polishing-Free Wafer Reuse through Orientation-Optimized (110) Spalling

We demonstrated (110) GaAs solar cells grown by D-HVPE with equivalent performance and material quality relative to (100) devices. Also, we developed a procedure for repeatable wafer-scale spalling of (110) GaAs. Spalled surfaces were free of the facets founds in (100) GaAs spalling, the large arrest lines found in (100) Ge spalling, and surface features greater than 3 µm in peak-to-valley height, which can otherwise degrade the efficiency of regrown III-V devices. A sub-µm step-terrace morphology was discovered on the post-spall wafer surface, resulting from the restricted cleavage system of GaAs, but we developed understanding of the factors that determine the resulting morphology, enabling ample opportunity for optimization of morphologies suitable for device growth and spall depth waste minimization on (110) GaAs. Lastly, we demonstrated a device grown on a previously spalled surface with only 8% relative efficiency difference to a cell grown on a new unspalled wafer. Significant optimization of the substrate regrowth conditions are required to enable higher efficiency, but these results highlight the promise of (110)-oriented devices coupled with substrate reuse by spalling as a pathway for low-cost III-V photovoltaics.

14 SOLAR ENERGY↗

Techno-economic Analysis of Novel PV Plant Designs for Extreme Cost Reductions

A techno-economic analysis is underway examining the cost and performance of future large-scale photovoltaic (PV) plant components, including bifacial modules, tandem modules, increased plant voltage architectures, and module-level power electronics. Integration of these components into PV plant designs is compared with current PV technologies based on levelized cost of electricity (LCOE). Baseline models are developed and validated against recorded PV plant performance data. Expected cost and performance data of future PV technologies are incorporated into the baseline models. An evolutionary algorithm is utilized to optimize PV plant configuration, technology combination, and LCOE. Furthermore, this paper focuses on the bifacial module analysis.

14 SOLAR ENERGY↗

LOGOS

LOGOS is a software package which contains a set of discrete optimization models that can be employed for capital budgeting optimization problems. More specifically, provided a set of items (characterized by cost and reward values) and constraints, these models select the best combination of items which maximizes overall reward and satisfies the provided constraints. The developed models are based on different versions of the knapsack optimization algorithms. Two main classes of optimization models have been initially developed: deterministic and stochastic. Stochastic optimization models evolve deterministic models by explicitly considering data uncertainties (associated to constraints or item cost and reward). These models can be employed as stand-alone models or interfaced with the INL developed RAVEN code to propagate data uncertainties and analyze the generated data (i.e., sensitivity analysis).

Wang, Congjian↗