Phenomena Identification Research Articles

Fatigue Life Prediction of a SAE Keyhole Specimen as a Subcase of Certification by Analysis.

To advance the technology of Certification by Analysis (CbA), as called for by the aerospace industry, the fatigue problems of SAE keyhole specimens are analyzed to demonstrate a subcase of CbA. First, phenomena identification and ranking table (PIRT) analysis is performed. Second, modeling of the key phenomena is conducted, and finally, verification and validation with the experimental results are achieved. In particular, the elastic/elastoplastic stress distributions in the keyhole specimens are obtained using the finite element method (FEM). Plasticity correction for stress/strain at the notch root is made using the modified Neuber's rule along with the Ramberg-Osgood equation. The low cycle fatigue (LCF) crack nucleation life is analytically predicted using the modified Tanaka-Mura model, a.k.a. the TMW model, given the material's elastic modulus, Poisson's ratio, Burgers vector, and surface energy, without the need for coupon fatigue data regression. The Tomkins equation is used to simulate plastic crack growth within the notch plastic zone. The above analytical life predictions are validated against the SAE keyhole specimen tests, becoming the first successful case of fatigue CbA at a sub-element level.

Knowledge representation to support EMDAP implementation in advanced reactor licensing applications

The Data, Information, Knowledge, and Wisdom (DIKW) pyramid depicts the general principle of a decision-making process. Various levels of abstraction are required to formalize the available data/information/knowledge with respect to the decision being supported. The Evaluation Model Development and Assessment Process (EMDAP) was developed by the United States Nuclear Regulatory Commission (US NRC) to guide the development and assessment of Evaluation Models (EMs) for transient and accident analysis of nuclear power plants under design basis accidents. It concerns the decision of adequacy of an EM with respect to the purpose of analysis (NPP application). However, lack of data, scaling issues, modeling limitations, computation, and experimental overhead are some of the key factors that challenge the EM adequacy decision in EMDAP. Phenomena Identification and Ranking Table (PIRT) which is used for complexity resolution can also introduce noise due to bias and variance in expert opinion and judgment. The uncertainty in the decision due to these issues and challenges can be minimized by enhancing the EMDAP from the DIKW perspective. In this work, we formulate a systematic scheme for knowledge representation, and classification and characterization of evidence to enhance clarity and transparency in the EMDAP implementation. The proposed scheme is governed by the concept of the value of information, where we contextualize, classify, characterize, and evaluate the evidence (relevant data/knowledge/information related to EM development, verification, validation, and uncertainty quantification) with respect to the relevant decision attributes or elements of EMDAP. We make use of the Predictive Capability Maturity Model (PCMM), Argumentation technique, and process quality assurance for knowledge representation to support EMDAP implementation in advanced reactor licensing applications. The main objective of the proposed scheme is to support decision-making by making it more transparent, traceable, and accountable. The illustration of the proposed scheme is provided using a system simulation code (SAS4A/SASSYS-1) as the primary EM and a generic sodium fast reactor under loss of flow accident as the target reactor application.EMDAP involves different elements that require expert input and insights. However, the process of expert elicitation may require significant resources and time. To address these issues, we identify generative artificial intelligence models as potential tool which (after systematic testing and capabilities analysis) can be used for domain specific expert elicitation and information extraction for efficient implementation of EMDAP.

Development of a phenomena identification and ranking table (PIRT) for intermediate break loss-of-coolant accident in PWRs

Recent safety issues such as cladding oxidation and fuel fragmentation, relocation and dispersal (FFRD) make the loss-of-coolant accident (LOCA) acceptance criteria more difficult to be satisfied. To obtain the adequate safety margin and more economical use of the nuclear power plant, re-classification of LOCAs for Korean operating PWRs is now under consideration to exclude the large break LOCA (LBLOCA) from the design basis accidents (DBAs). Therefore, the intermediate break LOCA (IBLOCA) might become the limiting break size of concern in the LOCA analysis. To accomplish this reform of LOCA classification, an extensive understanding of IBLOCA is crucial, and the applicability of safety analysis code should be confirmed. For this purpose, IBLOCA PIRT was developed. The PIRT panel was organized and the general process of the PIRT development established by Wilson and Boyack (1998) was adopted to develop the IBLOCA PIRT. Based on IBLOCA analyses using the safety and performance analyzing code (SPACE), the PIRT panel defined the temporal phases, systems, components and possible phenomena during an IBLOCA. For all possible phenomena, the relative importance and the knowledge level were determined for each component and each phase via discussions among PIRT panel members. For phenomena having relatively high importance, a code validation matrix was also developed. The results of the IBLOCA PIRT will be used to improve the SPACE code for IBLOCA application and resolve future regulatory issues.

Lead Fast Reactor Thermal-Hydraulic Testing Facilities in Support of the UK Advanced Modular Reactor Program

The Westinghouse lead-cooled fast reactor (LFR) is a next-generation nuclear power plant whose primary mission is to reduce front-end capital costs and generate flexible and cost-competitive electricity for global markets, while offering mission versatility and satisfying the highest safety and sustainability standards. The LFR is an economical choice for carbon-free power generation to meet the ambitious goals of reducing carbon emissions. The plant utilizes passive safety systems for high reliability and public safety. The LFR testing program aims to fill the technology gaps in the key materials, components, and systems of the LFR plant. It provides demonstrations of LFR engineering that reduce the uncertainty of the LFR design and experimental data for the verification and validation of the modeling and simulation computer codes. With the support of the LFR phenomena identification and ranking table, the phenomena important to plant safety with insufficient states of knowledge have been identified and a Westinghouse testing plan developed to address them. The United Kingdom Advanced Modular Reactor Program Phase 2 was purposed to advance the level of design maturity toward eventual regulatory approval and deployment. Westinghouse and its partners have developed eight state-of-the-art test facilities within the program. Among them, the Passive Heat Removal Facility, Versatile Lead Facility, Lead Water Interaction Facility, and the Lead Freezing Facility are thermal-hydraulic testing facilities, with the other four facilities dedicated to testing lead corrosion and material mechanical behavior in lead. The design, development, and testing of the four thermal-hydraulic facilities are presented in this paper. A variety of computer codes ranging from system-level analysis, component-level analysis, and high-resolution computational fluid dynamics analysis, are utilized to support the development of the facilities. The analyses provide operational and accidental conditions in the LFR to identify major testing conditions and inform the facility design and testing matrix. With a significant amount of experimental data being generated with these highly instrumented test facilities, the computer codes and models will be benchmarked against the experimental results to improve their validation and verification status.

Time-Series Forecasting of a Typical PWR Undergoing Large Break LOCA

In this work, a machine learning (ML) metamodel is developed for the time-series forecasting of a typical nuclear power plant response undergoing a loss of coolant accident (LOCA). The plant model of choice is based on the APR1400 nuclear reactor. The key systems and components of APR1400 relevant to the investigated scenario are modelled using the thermal-hydraulic code, RELAP5/MOD3.4, following the description published in the design control document. The model is tested under a spectrum of initial and boundary conditions via propagation of key uncertain parameters (UPs) which are derived from the phenomena identification and ranking table (PIRT). This is achieved by loosely coupling RELAP5/MOD3.4 with the statistical tool, Dakota. The most probable nuclear power plant (NPP) response was calculated using the best estimate plus uncertainty (BEPU) approach. Next, the database generated from the NPP system response was used as an input for the ML model. The NPP system response was represented by peak cladding temperature (PCT), safety injection system (SIT), mass flow rate, reactor power, and primary system pressure. In this research, two regression models were tested with reasonably good performance, namely, the gated recurrent unit (GRU) and the long short-term memory (LSTM).

Phenomena Identification and Ranking Table for Thermal-Hydraulic Safety of China Fusion Engineering Test Reactor

The China Fusion Engineering Test Reactor (CFETR) is presently in the engineering design phase, and it is crucial to establish a thermal-hydraulic safety analysis method. First of all, the identification of phenomena in selected accident scenarios affecting reactor safety performance metrics should be focused on with the phenomenon identification and ranking table (PIRT), in which phenomena related to the thermal-hydraulic safety of the vacuum vessel and related systems are screened, including both design-basis accidents and beyond-design-basis accidents. The development of this PIRT exercise for CFETR thermal-hydraulic safety is addressed in this study; specifically, the importance ranking and stage of knowledge (SoK) of phenomena in the selected accidents are evaluated by the PIRT panel. The results of the PIRT analysis revealed that there exist certain safety-critical phenomena for which SoK is relatively low despite their perceived significance in safety performance metrics, which include the phase change of coolant, the migration of the multicomponent gas mixture, the migration of radionuclides within confinement, and the dispersion of gaseous radionuclides in the atmosphere. Ongoing research works and follow-up plans to improve the SoK of phenomena are presented.

A graph neural network-based framework to identify flow phenomena on unstructured meshes

Driven by the abundant data generated from computational fluid dynamics (CFD) simulations, machine learning (ML) methods surpass the deterministic criteria on flow phenomena identification in the way that they are independent of a case-by-case threshold by combining the flow field properties and the topological distribution of the phenomena. The current most popular and successful ML models based on convolutional neural networks are limited to structured meshes and unable to directly digest the data generated from unstructured meshes, which are more widely used in real industrial CFD simulations. We proposed a framework based on graph neural networks with the proposed fast Gaussian mixture model as the convolution kernel and U-Net architecture to detect flow phenomena based on a graph hierarchy generated by the algebraic multigrid method embedded in the open-source CFD solver, code_saturne. We demonstrate the superiority of the proposed kernel and U-Net architecture, along with the generality of the framework to unstructured mesh and unseen case, on detecting the vortices once trained on a single backward-facing step case. Our proposed framework can be trivially extended to detect more flow phenomena in three dimensional cases, which is ongoing work.

Phenomena identification Ranking Table (PIRT) study for suppression containment of small modular reactor using new methodology

The Phenomena Identification and Ranking Table (PIRT) is a significant method for analyzing the safety of nuclear reactors. It helps researchers identify important phenomena within the reactor, enabling a focused and appropriate simplification of accident scenarios during the study. However, traditional PIRT methods often rely on experts' subjective opinions to rank phenomena’ importance and knowledge level, potentially distorting the PIRT results. This paper proposes a new PIRT method inspired by literature evaluation techniques used in the medical and healthcare field, which can be more objective. This new method utilizes a literature evaluation framework instead of relying solely on expert judgments, resulting in a more objective assessment of the phenomena’ importance and knowledge level. This study applies the new method to a simplified small modular reactor with a suppression containment system. Following a Loss of Coolant Accident (LOCA), the suppression containment can effectively suppress temperature and pressure increases, ensuring containment integrity. Relevant PIRT tables and a knowledge-level structure are obtained using the new method.

A review of artificial intelligence in marine science

Utilization and exploitation of marine resources by humans have contributed to the growth of marine research. As technology progresses, artificial intelligence (AI) approaches are progressively being applied to maritime research, complementing traditional marine forecasting models and observation techniques to some degree. This article takes the artificial intelligence algorithmic model as its starting point, references several application trials, and methodically elaborates on the emerging research trend of mixing machine learning and physical modeling concepts. This article discusses the evolution of methodologies for the building of ocean observations, the application of artificial intelligence to remote sensing satellites, smart sensors, and intelligent underwater robots, and the construction of ocean big data. We also cover the method of identifying internal waves (IW), heatwaves, El Niño-Southern Oscillation (ENSO), and sea ice using artificial intelligence algorithms. In addition, we analyze the applications of artificial intelligence models in the prediction of ocean components, including physics-driven numerical models, model-driven statistical models, traditional machine learning models, data-driven deep learning models, and physical models combined with artificial intelligence models. This review shows the growth routes of the application of artificial intelligence in ocean observation, ocean phenomena identification, and ocean elements forecasting, with examples and forecasts of their future development trends from several angles and points of view, by categorizing the various uses of artificial intelligence in the ocean sector.

CSNI status report “3D capabilities of thermalhydraulic system codes”: Lessons learned

In September 2015, an activity was endorsed by the OECD/CSNI/WGAMA to prepare a state of the art report presenting the 3D features of current thermal–hydraulic system codes. This activity was coordinated by IRSN and started in April 2016. This document is a synthesis of the full OECD report which is expected by 2023.Multi-dimensional phenomena that may have an important impact on the current thermalhydraulic models occur in the course of asymmetric scenarios such as feed water line break, main steam line break and loss of coolant accident. Most physical models were first established and validated in 1D geometry. The growing role of 3D modelling of reactor core and pressure vessel requires additional experimental data for a proper validation. Elements on available experimental support are proposed. However, the need of additional experimental support for validation has been identified in several directions such as the friction pressure losses, the diffusion–dispersion of momentum and energy dependency with space averaging, passive systems and the dispersion of void in core and downcomer. There are also several axes for progress, namely the development of phenomena identification and their ranking, the terms in the field equations and the mesh size dependence and the time step strategy.

Chemistry E-Module Based on Socio Scientific Issues (SSI) for Reaction Rate Material to Increase Senior High School Students' Chemical Literacy

Learning chemistry contributes to chemical literacy in specific and science literacy in general. Chemical literacy relates to the ability to think scientifically by using chemical knowledge and natural phenomena identification. Chemical literacy is defined as the ability to understand and implement chemistry knowledge in everyday life by comprehending three aspects comprising: knowledge, awareness and chemistry implementation in everyday life accurately and effectively. Based on the result of the questionnaire which has been distributed to chemistry teachers in Jember regency through chemistry MGMP, it shows that 71,8% of chemistry teachers stated that students’ chemical literacy skill in learning did not meet the target. Chemical literacy has significant relation to the Socio-Scientific Issues (SSI) drown as social problem by using scientific context. This problem considered as scientific issue developed in society. Then, this problem is analyzed further in rate reaction materials. This research used quasi-pretest-posttest experiment without using control class. To analyze the data, this research used both quantitative and qualitative methodologies. The sample in this research consisted of 36 senior high school students in Senior High School of Ambulu grade XI MIPA 6. The result of this research based on both pretest and posttest using open ended questions showed that there was significant improvement on students’ chemical literacy. Therefore, it was in high category 0,71

International case survey and literature review of maintenance strategy for decommissioning nuclear power plant during transition period

The Chinshan nuclear power plant in Taiwan has currently shutdown when the operating license expired in 2018. However, because the operation license of the independent spent nuclear fuel dry storage facility has not been approved yet, and the fuel storage racks of Spent Fuel Pool (SFP) has almost saturated, there is not enough space to accommodate all irradiated fuels from the reactor core during the transition period. Therefore, part of the mechanical systems, plant structures and electrical equipment of the plant still have to meet the functional requirements for maintaining the safety under the pre-decommissioning activities.In this article, we introduce the international cases of permanent shutdown but the fuel still in the reactor core, and also describe the actions of the Taiwan Power Company in response to this situation. For the providing regulatory advice, we have also proposed a framework of the maintenance strategy associated with important issues for the transition period since 2018, including a revised Aging Management Program (AMP) for keeping the safety of spent nuclear fuel. From the knowledge level and important issues related to the topic, the Phenomena Identification and Ranking Table (PIRT) is quoted to complete the understanding level of requirements during the transition period.

Aerosol pool scrubbing phenomena during the containment depressurization venting. Part I: Scaling analysis

For the Chinese Advanced Passive Pressurized Water Reactor, one of the possible containment depressurization measures is to discharge to the Spent Fuel Pool (SFP) during severe accidents. During containment depressurization venting process, carrier gas with aerosol is injected into the SFP from the containment through a discharge sparger. To obtain the aerosol retention effect during this process, a scaled-down test facility have been designed and built. In this paper, the Phenomena Identification and Ranking Tables (PIRT) in the discharge pipe and the SFP is developed. Then, based on the Hierarchical Two-tiered Scaling analysis (H2TS) method, the scaling analysis of SFP scrubbing phenomena is completed. A jet flow model and a particle retention model are developed to analyze these important phenomenon, and a series of similarity criteria are obtained. Based on these similarity criteria, the CASSI test facility is designed, and the scaling rationality is evaluated.

Using Machine Learning to Predict the Fuel Peak Cladding Temperature for a Large Break Loss of Coolant Accident

In this paper the use of machine learning (ML) is explored as an efficient tool for uncertainty quantification. A machine learning algorithm is developed to predict the peak cladding temperature (PCT) under the conditions of a large break loss of coolant accident given the various underlying uncertainties. The best estimate approach is used to simulate the thermal-hydraulic system of APR1400 large break loss of coolant accident (LBLOCA) scenario using the multidimensional reactor safety analysis code (MARS-KS) lumped parameter system code developed by Korea Atomic Energy Research Institute (KAERI). To generate the database necessary to train the ML model, a set of uncertainty parameters derived from the phenomena identification and ranking table (PIRT) is propagated through the thermal hydraulic model using the Dakota-MARS uncertainty quantification framework. The developed ML model uses the database created by the uncertainty quantification framework along with Keras library and Talos optimization to construct the artificial neural network (ANN). After learning and validation, the ML model can predict the peak cladding temperature (PCT) reasonably well with a mean squared error (MSE) of ∼0.002 and R2 of ∼0.9 with 9 to 11 key uncertain parameters. As a bounding accident scenario analysis of the LBLOCA case paves the way to using machine learning as a decision making tool for design extension conditions as well as severe accidents.

Phenomenon Identification and Ranking Table Development for Future Application Figure-of-Merit Studies on Thermal Energy Storage Integrations with Light Water Reactors

There are no standard prioritization criteria for evaluating thermal energy storage (TES) options for use in integrated energy systems. A framework for proposing, analyzing, and presenting energy storage integration with power producers and users is presented along with a specific figure-of-merit (FOM) study based in this framework. This basis for evaluating storage technologies can provide a structure for the energy industry to analyze and prioritize energy storage in different applications and environments. The phenomena identification and ranking table (PIRT) presents a series of design questions specific to energy storage applications. The FOM study, built in this PIRT framework based on a nuclear-renewable hybrid energy system using TES to produce power and provide process energy for a secondary user, successfully identified specific technologies to use based on the project requirements. Expanding the library of projects using this framework will expand the deployable options for energy storage and increase its potential for energy security.

Harmonic Resonance Identification and Mitigation in Power System Using Modal Analysis

Due to a rising share of power electronic devices in power networks and the consequent rise in harmonic distortion, impedance resonances are an important issue. Nowadays, the frequency scan method is used for resonance phenomena identification and analysis. The main disadvantage of the method is its inability to decouple different resonance phenomena. This means that the method is also unable to provide sufficient information about the effects that the parameters of network elements have on different resonance phenomena. Furthermore, it was also noted that despite the fact that the harmonic resonance mode analysis is well described in the literature, there is a lack of systematic approach to the analysis procedure. Thus the main objective of this paper is to address this disadvantage and to propose a systematic approach to harmonic resonance analysis and mitigation, utilizing modal analysis. In the first part of the paper, dominant network nodes in terms of resonance amplification of harmonics are determined. This is done by analysis of the eigenvalues of the network admittance matrix. Using the eigenvalue analysis results, key parameters of network elements involved in a specific resonance are determined next. This is performed by calculating the critical mode (i.e., the mode that experiences resonance) sensitivity coefficients with respect to network parameters. In the second part of the paper, the procedure for modal resonance frequency shift is presented. The shift is performed by changing the value of a selected parameter so that the modal resonance frequency matches the desired resonance frequency value. The parameter value is calculated with the Newton–Rhapson method. Presented analysis considers both parallel and series resonances. The effectiveness of the proposed method is demonstrated on an actual industrial-network model.

Liquid spray modeling under sodium fire accidents

The Sodium-Cooled Fast Reactor (SFR) system, which features a fast-spectrum, sodium-cooled reactor and a closed fuel cycle for efficient management of actinides and conversion of fertile uranium, is rather prominent in the nuclear reactor design in Generation IV (Gen IV), and likely to be widespreadly used and well-constructed all over the world. However, molten sodium may be sprayed into the ambient or secondary side of steam generator, induced by the pressure drop, in case of an inevitable break in the primary system. This kind of leakage can result in sodium spray fire accident, as a result of the chemical activity of sodium, significantly damaging the equipment and working staffs nearby. Sodium spray fire, which occurs not only in the nuclear industry, but also in solar industry, is a complex process consisting of several specific phenomena, such as the spray dynamics (e.g. droplet particle size/velocity distribution, particle collision and agglomeration), droplets evaporation, sodium aerosol diffusion, thus being drawn many experts’ attention. Based on International Atomic Energy Agency (IAEA)’s effort on phenomena identification and ranking table (PIRT) for sodium spray fire, prediction of droplet size distribution and the mean diameter in particular, are supposed to be in the very first place at level 2, due to the lack of available experimental data for both of model development and validation, and code inadequacy, as well. In this paper, sodium droplet size distribution model is theoretically derived, regarding both of mass and momentum equations as constraints, based on the maximum entropy principle, which can quantitatively describe the effects of two main influencing factors, including initial injection velocity and thermophysical properties of molten sodium. This analytical model is implemented in three typical conditions, including two sodium droplets size distribution experiments and one water droplet experiment. Validations against both of the available test data and predictions by an empirical model, named of Nukiyama-Tanasawa correlation, are conducted with the relative error of median diameter ranging from 17.3% to 18.2%, which ensures the reliability and feasibility of the new model. Moreover, sensitivity analyses are carried out, in terms of typical test conditions of sodium spray fire, which demonstrates that the median diameter of droplets’ size decreases with both of the increase of initial injection velocity and sodium temperature, thus probable triggering positive effect on the propagation of the accident, due to rapid interaction of violent chemical reaction and sodium spray. Besides, the present work can provide a reliable analytical model for the development of safety analysis codes for SFRs.

Challenges and opportunities in verification and validation of low temperature plasma simulations and experiments

This paper describes the verification and validation (V&V) framework developed for the stochastic Particle-in-Cell, Direct Simulation Monte Carlo code Aleph. An ideal framework for V&V from the viewpoint of the authors is described where a physics problem is defined, and relevant physics models and parameters to the defined problem are assessed and captured in a Phenomena Identification and Ranking Table (PIRT). Numerous V&V examples guided by the PIRT for a simple gas discharge are shown to demonstrate the V&V process applied to a real-world simulation tool with the overall goal to demonstrably increase the confidence in the results for the simulation tool and its predictive capability. Although many examples are provided here to demonstrate elements of the framework, the primary goal of this work is to introduce this framework and not to provide a fully complete implementation, which would be a much longer document. Comparisons and contrasts are made to more usual approaches to V&V, and techniques new to the low-temperature plasma community are introduced. Specific challenges relating to the sufficiency of available data (e.g., cross sections), the limits of ad hoc validation approaches, the additional difficulty of utilizing a stochastic simulation tool, and the extreme cost of formal validation are discussed.

Phenomena identification and ranking table of station blackout accidents for China sodium cooled fast reactor

In order to satisfy analysis of safety requirements for China pool type sodium-cooled fast reactor, a phenomena identification and ranking table (PIRT) is developed for station blackout (SBO) accidents by 15 experts. The SBO accidents could be divided into two phases, i.e. phase 1: force circulation and phase 2: natural circulation, and the most important phenomena but maximum disagreements among experts are the gap conductance model between fuel and clad, the inter wrapper flow, the heat transfer between coolant and inter wrapper. Those phenomena should be carefully assessed and done more theorical and experiment analysis to develop more accurate and realistic model, to reduce uncertainty of safety analysis. The PIRT could be also used for developing verification and validation matrix for thermal hydraulic safety code, guiding researchers and designers to conduct experiments to close technological gap and giving related researcher and designer a comprehensive understanding for pool-type sodium-cooled fast reactor.

Assessment of the Predictive Capability of VERA—CS for CASL Challenge Problems

Abstract This paper describes the process for assessing the predictive capability of the Consortium for the advanced simulation of light-water reactors (CASL) virtual environment for reactor applications code suite (VERA—CS) for different challenge problems. The assessment process is guided by the two qualitative frameworks, i.e., phenomena identification and ranking table (PIRT) and predictive capability maturity model (PCMM). The capability and credibility of VERA codes (individual and coupled simulation codes) are evaluated. Capability refers to evidence of required functionality for capturing phenomena of interest while credibility refers to the evidence that provides confidence in the calculated results. For this assessment, each challenge problem defines a set of phenomenological requirements (based on PIRT) against which the VERA software is evaluated. This approach, in turn, enables the focused assessment of only those capabilities that are relevant to the challenge problem. The credibility assessment using PCMM is based on different decision attributes that encompass verification, validation, and uncertainty quantification (VVUQ) of the CASL codes. For each attribute, a maturity score from zero to three is assigned to ascertain the acquired maturity level of the VERA codes with respect to the challenge problem. Credibility in the assessment is established by mapping relevant evidence obtained from VVUQ of codes to the corresponding PCMM attribute. The illustration of the proposed approach is presented using one of the CASL challenge problems called chalk river unidentified deposit (CRUD) induced power shift (CIPS). The assessment framework described in this paper can be considered applicable to other M & S code development efforts.