On-line Temperature Measurements Research Articles

Experimental study on surface temperature and emissivity of rotating turbine blades of a micro turbojet engine

The temperature of the rotating turbine blades of a turbojet engine must be known to assess the combustion state and improve turbine blade quality. Obtaining online temperature measurements of high-speed rotating turbine blades in high-temperature gas flow remains challenging. A multispectral radiation thermometry method without emissivity assumption is proposed to measure the temperature of high-speed rotating turbine blades of a micro turbojet engine. The relative radiative intensity is calculated by accounting for smooth changes in the wavelength using the moving narrowband method to determine the influence of emissivity on multispectral radiation thermometry results. The method’s performance in measuring the surface temperature of high-speed rotating objects is tested. The wavelength range of 970 nm to 1700 nm is selected because the radiation from gases is weaker in comparison to the radiation emitted by solid surfaces within this band. The spectral radiation of the turbine blade surface is measured at three rotational speeds: 38,000 r/min, 48,000 r/min, and 58,000 r/min. The results show that, unlike thermocouples that measure the temperature of the hot gas flow near the blade, multispectral radiation thermometry provides the average surface temperature with high consistency (with a deviation smaller than 50 K). Multispectral radiation thermometry can be applied to measure the surface temperature and emissivity of high-speed rotating objects, such as the blades of turbojet engines.

Manufacturing thick laminates using a layer by layer curing approach

The work presented in this paper puts forward a manufacturing strategy for the processing of thermosetting composites based on Layer by Layer (LbL) curing. The process operates additively with sublaminates placed in a heated press, partially cured while consolidating, followed by loading of the next sublaminate and repeating the cycle until part completion. Coupled consolidation-cure simulation was utilised to design the process and establish its capabilities showing that halving the cure time is possible for thick parts. Mechanical testing showed that for pre-cure of placed layers below the gelation degree of cure, interlaminar properties are equivalent to those of conventionally manufactured material. A trial was carried out demonstrating successfully the LbL process. On-line measurements of temperature and compaction matched the predictions of the simulation, whilst the quality of the material produced is equivalent to that of conventionally produced composites.

A data-driven method for estimating sewer inflow and infiltration based on temperature and conductivity monitoring

Quantitation of sewer inflow and infiltration (I/I) is important for maintaining efficient wastewater transport and treatment. I/I flows can be quantified based on flow rate and water quality measurements. Flow rate-based methods require continuous monitoring of flow rates using flow meters that are costly and prone to fouling. In comparison, conductivity and temperature, as simple water quality parameters, are more easily measurable with more cost-effective and reliable sensors. In this study, a data-driven methodology is developed for estimating I/I flows based on online conductivity and temperature measurements. A Prophet-model-based analytic algorithm is first developed to reconstruct the temperature and conductivity profiles of the base wastewater flow (BWF) from the measured temperature and conductivity time series. The algorithm is shown to be able to reconstruct the BWF temperature and conductivity profiles in two monitored catchments. The reconstructed BWF data are then incorporated into mass/energy balance equations for estimating I/I flows from the measured temperature and conductivity data. The overall I/I quantification method is finally demonstrated using simulation studies of a real-life sewer network and validated against the known I/I flows. This work provides a reliable method for I/I quantification based on simple measurements.

Real-time FPGA-based laser absorption spectroscopy using on-chip machine learning for 10 kHz intra-cycle emissions sensing towards adaptive reciprocating engines

Fast emissions sensing is needed to enable rapid optimization on-the-fly for increasingly adaptive engine architectures to improve performance over a wide range of loads and to offer fuel flexibility towards a low-carbon energy future. In this work, a real-time laser absorption spectroscopy technique is developed for 10 kHz on-line measurements of engine exhaust gas temperature and carbon monoxide. Latency due to data reduction is significantly shortened through a machine learning approach to spectral analysis and minimization of post-processing complexity for implementation on a high-bandwidth field-programmable gate array (FPGA). The data reduction method is tested on cycle-resolved laser-absorption thermochemistry measurements in reciprocating piston engine exhaust. The sensor employs a quantum cascade laser to spectrally-resolve two fundamental rovibrational absorption lines of carbon monoxide near 4.9 μm at a rate of 10 kHz. The recorded signals are passed to an FPGA to infer CO concentration and gas temperature through either a pre-trained ridge regression or artificial neural network model. Models are constructed to limit complexity with the aim of minimizing resource utilization and latency on the FPGA. Experimental data are used to evaluate the prediction accuracy of the models, with the neural network achieving RMS errors in CO mole fraction and gas temperature of 0.0390% and 15.0 K, respectively, compared to spectral fitting of the absorption lineshapes. The data reduction latencies are measured through hardware-in-the-loop demonstration, achieving a 10 kHz throughput and 25 μs latency. Computational time of the end-to-end data reduction process on the FPGA is measured at 300 ns and 600 ns for the ridge regression and neural network, respectively. The data reduction methods presented in this work expand the utility of laser absorption spectroscopy for low-latency sensors that match the timescales of combustion and increase the potential for real-time sensing and control to minimize engine exhaust emissions and maximize performance.

Cutting Parameter Optimization based on Online Temperature Measurements

The deformation of metallic materials during the machining operation requires a significant amount of energy. During the chip formation process and due to the plastic deformation of the metal and the friction along the tool-part interface, the thermal loads generated are strongly impacted by the cutting factors. Thus, the choice of optimized cutting conditions is essential to control the quality of the work required. The aim of the present experimental study is to optimize the cutting parameters using temperature measurements. The average temperature of the cutting tool is studied using a FLIR A325sc type infrared camera. Optimal cutting parameters for each performance metric were obtained using the Taguchi techniques.

Effect of start and stop cycles on hydropower plants: modelling the deterioration of the equipment to evaluate the cycling cost

With the high energy demand, renewable energies emerged and the deregulation of the energy market appeared in the late ’90. These types of energies are intermittent and can produce high fluctuations in the power grid because they are connected only in certain weather conditions (for example: solar energy can be produced only by day and wind energy only when it is windy). Hydropower energy is recognized for its flexibility in responding to the demands of the network in order to maintain a constant level of energy and to guarantee the security of the electrical network. Nowadays, the hydropower plants are the main provider of energy adjustments thanks to a high number of start and stop cycles (which can sometimes be around 6 per day), the fast variations in load and the use of PSH (pumped-storage hydropower). But these rapid changes in the production conditions of hydroelectric power plants lead to high stresses on the components and consequently to faster degradation (mechanical, electrical, thermal, hydraulic, etc.). This work focuses on the design of a methodology that relies on auditable methods to estimate the cost of start and stop cycles and presents three complementary, representative (by equipment), reproductible (can be applied by different operators) methods based on explicit assumptions and validated by experts and in function of the available data in order to estimate the degradation of the main components of the hydropower plant (shut-off valve, runner, generator, transformer and circuit-breaker). These methods are based on the main degradation phenomena. The first method uses on-site measurements to study the fatigue on runners, the second method uses a reliability law to estimate the lifetime of generators and a predictive model using online temperature measurements and the last method uses expert judgement due to the lack of measurements on the equipment.

Fast Simultaneous CO2 Gas Temperature and Concentration Measurements by Quantum Cascade Laser Absorption Spectroscopy

A quantum cascade laser-based sensing technique is presented which allows for in situ high-precision temperature and/or CO2 concentration measurements of gases in the room temperature regime with sampling rates up to about 40 kHz. The method is based on Boltzmann-like thermally populated fundamental and hot-band rovibrational transitions of CO2 with opposite temperature dependence. Single absorption spectra at about 2350 to 2352 cm−1 are recorded by a nanosecond frequency down chirped IR pulse of a pulsed distributed feedback quantum cascade laser (intrapulse mode). The statistical uncertainty (1σ) in the temperature measurement within one laser pulse is about 1 K and can be further reduced down to about 0.1 K by time averaging over 100 ms. Online temperature and CO2 concentration measurements on a breath simulator controlled gas flow were performed to demonstrate response-time and sensitivity for an application-driven test system.

Experimental and Theoretical Investigations on Cold Metal Transfer Welds Using Neural Networks: A Computational Model of Weld Geometry

Cold metal transfer (CMT) welding is a sophisticated version of fusion welding process available with advanced features incorporated in it. During the process of joining metallic parts with CMT, the bead shape and size have significant effects on the weld quality. Typically, bead geometry is characterized by the three important parameters namely weld width, weld depth and reinforcement height. For rapid and intelligent welding, it is imperative to monitor the bead shape and size during the process. However, the measurement system of three parameters is often time consuming and complex. In this paper, an attempt is made to reduce the computational time of artificial intelligence models that are used for intelligent welding processes. Bead coefficient is modelled as an alternative for bead geometry properties. Computationally efficient artificial neural network models are developed for examining the feasibility of bead coefficient over bead geometry properties with and without online-temperature measurements. The predicted results of both forward and reverse neural network models are in good coherence with the experimental values. The outcome of this study is expected to provide a detailed understanding of effects of process parameters on bead geometry and bead coefficient, which facilitates online monitoring of welding processes.

Control of a natural gas liquid recovery plant in a GSP unit under feed and composition disturbances

Abstract Recent technological improvements have driven the rapid increase in natural gas production from unconventional reservoirs. The heaviest hydrocarbon fraction of this fossil fuel, the so-called natural gas liquids (NGL), have greater economic interest justifying the attention on its separation process from the raw gas. Various process schemes have been developed and studied for the NGL recovery, including the conventional, cold residue recycle (CRR), and the gas subcooled process (GSP). This study aims to assess different control strategies for a GSP unit and determine the most appropriate and effective process control scheme. For this, the dynamic responses for each control scheme are evaluated by changing feed flow rate and composition. The main targets are the achievement of 84% ethane recovery and low levels of methane impurity at the bottom of the demethanizer column. Due to the high cost of composition analyzers and the high delays introduced by composition controllers under the presence of flow disturbances, the control goals are reached by the knowledge of on-line temperature measurements. This is done by considering different temperature control structures such as the direct temperature control and cascade control, plus a pressure compensator. The results are compared, in presence of composition disturbances, with the action of a hybrid cascade control that uses in-line delayed concentration measurements to update the controller reference at each sampling period. Here, the hybrid and the simple cascade controls show the best control performance.

Temperature sensing during Raman spectroscopy of lead white films in different purity grades and boundary conditions

In the field of laser-based diagnostics and treatment techniques for artwork conservation it is known that lead white, wide use as art pigment in the past, shows low photothermal stability upon laser irradiation. Thermal alterations of lead white paint films are often observed during Raman spectroscopy, although the origin of heating has not yet been exhaustively explained. Here, we approach the interpretation of this phenomenon through the preparation of high- (analytes) and low-grade (art pigment) lead white films, thorough compositional and structural characterizations, measurement of the optical parameters, and online temperature measurements during Raman spectroscopy excited at 1064 nm. Spectra and associated temperature profiles were achieved using a system equipped with an online thermal sensor. The data collected show the crucial importance of the degree of purity in heat generation upon laser exposure. Due to their higher content of Fe2O3 inclusions, low-grade films (150−250 ppm against 50 ppm of high-grade) showed absorption coefficients five times higher than high-grades films, and temperature rises up to 80−100 °C upon 207 W/cm2 irradiation and 25 s exposure. Optical absorption and heating of low-grade films determined weaker signals and higher backgrounds in the Raman spectra, whose origin was ascribed to luminescence of Fe2O3 inclusions. Moreover, the spectral and thermal influence of the substrate was also investigated thus achieving a complete picture of the photothermal behavior of lead-white art pigments during Raman spectroscopy.

Investigation of the Effect of Process Parameters on Bone Grinding Performance Based on On-Line Measurement of Temperature and Force Sensors.

This study investigates the effect of process parameters on neurosurgical bone grinding performance using a miniature surgical diamond wheel. Bone grinding is an important procedure in the expanded endonasal approach for removing the cranial bone and access to the skull base tumor via nasal corridor. Heat and force are generated during the grinding process, which may cause thermal and mechanical damage to the adjacent tissues. This study investigates the effect of grinding process parameters (including the depth of cut, feed rate, and spindle speed) on the bone grinding performance using temperature and force measurement sensors in order to optimize the grinding process. An orthogonal experimental design with a standard orthogonal array, L9 (33), is selected with each parameter in three levels. The experimental results have been statistically analyzed using the range and variance analysis methods in order to determine the importance order of the process parameters. The results indicate that the effect of the cutting depth on the grinding temperature and normal force is the largest, while the effect of the spindle speed on the tangential force is the largest. A high spindle speed would make the temperature rise to a certain extent; however, it significantly reduces the grinding force. At a certain spindle speed, a lower depth of cut and feed rate help to reduce the grinding temperature and force.

A High Precision On-Line Detection Method for IGBT Junction Temperature Based on Stepwise Regression Algorithm

The insulated gate bipolar transistor (IGBT), one of the most vulnerable component, is one of the most precious central component in the converter interior. High junction temperature will lead to device failure, which is the main reason of failure of power electronic system. Therefore, on-line high precision measurement of IGBT module junction temperature is the basis of life prediction and reliability evaluation of high-power power conversion equipment. In this paper, the principle of IGBT junction temperature extraction and the latest development of related technologies are summarized. In particular, the working principle and shortcomings of temperature sensitive electrical parameter (TSEP) method are summarized. The change of junction temperature will affect the inter-electrode capacitance in the internal structure of IGBT, which will cause the change of temperature sensitive electrical parameters. The single temperature sensitive electrical parameter method is easily affected by IGBT structure and inter-electrode capacitance. This paper presents an algorithm for high precision on-line detection of IGBT junction temperature. The parameter types are optimized by stepwise regression and the model is established accordingly. In this paper, IGBT: FF50R12RT4 is used as the experimental equipment. By comparing the junction temperature model established based on multiple linear stepwise regression algorithm with the junction temperature model based on traditional temperature sensitive electrical parameters, it is proved that the algorithm has better fitting degree and precision, and the algorithm can be used for high precision online extraction of junction temperature.

Experimental study: comparison of conventional and low-frequency vibration-assisted drilling (LF-VAD) of CFRP/aluminium stacks

The increasing substitution of metallic structural components by carbon fibre reinforced polymers (CFRP) in aerospace applications results in a growing need for drilling metal and CFRP in one operation, the so-called stack machining. The different material properties of the stack components in combination with high geometrical tolerance requirements result in large challenges for the drilling tool and the process strategy. Focussing on the process strategy, this paper deals with an extensive comparison of conventional and low-frequency vibration-assisted drilling (LF-VAD) of CFRP/aluminium stacks. The influence of the cutting speed, the feed rate and the amplitude of the superimposed oscillation in LF-VAD on the resulting bore quality is analysed. For the bore quality, three separate aspects are considered, namely, damages at the CFRP entrance, burr formation at the aluminium exit and deviations from the nominal diameter in both materials. Online temperature and force measurements enable interpretation of the influence on the bore quality. Based on experimental data, a clear dependency of the bore quality and the chip transport on both, the process parameters and the drilling strategy are identified. Based on high-speed recordings, the dynamic loading situation due to the superimposed oscillation in LF-VAD is found to be crucial for the formation of peel-up delaminations.

Development of direct temperature measurements of ISAC and ARIEL targets at TRIUMF

To improve the thermal modelling of high power isotope separation on-line (ISOL) targets at TRIUMF, an optical technique is being developed that allows for direct off-line and on-line temperature measurements of targets for radioactive isotope production. In this setup the light coming from a hot target through the ionizer opening is collected via a set of optics and coupled into a spectrometer. Thus, from the emission spectrum and Planck’s law, the target temperature can be deduced. Tantalum targets were heated to high temperatures and preliminary temperature measurements confirm the correlation between the spectrum of the radiation emitted from the target and the currents used to resistively heat the targets. The final goal is to apply this technique to on-line targets and correlate the isotope releases with the target temperatures for a better understanding of the diffusion and effusion processes happening in the target and for optimizing the delivery of short-lived species.

Online measurement of temperature and relative humidity as marker tools for quality changes in onion bulbs during storage.

A long shelf life of onions (Allium cepa L.) is of high importance in the onion industry. Onions are dried and stored in large wooden boxes that are difficult to access. Monitoring temperature and relative humidity during these processes is challenging. Moreover, quality may change in storage without being noticed. Therefore, there is a need to find alternative methods for monitoring and controlling the drying and storage processes of onions and to identify early changes in quality during storage. The potential use of online measurements of temperature and relative humidity (RH) in the vicinity of onions was evaluated during drying and long-term storage of six onion batches (four cultivars and three selections of one of the cultivars) in commercial storage. The batches varied in bulb weight, dry matter content, firmness and disease incidence. The dry matter content and firmness decreased during storage, while the respiration rate and incidences of individual and total disease increased. Two of the batches had low storability with high disease incidences and high average temperatures and variations in the RH. The results showed that tracking the temperature and RH in the vicinity of the onions is a promising tool for improving the drying and storage processes in commercial storage and for identifying onion batches with reduced storability early in storage.

Thermal Dissipation Effect on Temperature-controlled Friction Stir Welding

Abstract During Friction Stir Welding (FSW) of complex geometries, the thermal dissipation, induced by geometric features or the surrounding environment, may strongly affect the final weld quality. In order to guarantee a consistent weld quality for different conditions, in-process welding parameter adaptation is needed. This paper studies the effect of thermal dissipation, induced by the backing bar thermal conductivity, on the weld temperature and the temperature controller response to it. A new temperature sensor solution, the Tool-Workpiece Thermocouple (TWT) method, was applied to acquire online temperature measurements during welding. An FSW-robot equipped with temperature control, achieved by rotation speed adaptation, was used. AA7075-T6 lap joints were performed with and without temperature control. The cooling rate during welding was register plus macrographs and tensile tests were assessed. The controller demonstrated a fast response promoting the heat input necessary to maintain the set welding temperature. The results demonstrated that temperature control using the TWT method is suitable to achieve higher joint performance and provides a fast setup of optimal parameters for different environments.

Accelerated thermal profiling of gas turbine components using luminescent thermal history paints

Abstract Environmental requirements to reduce CO2 emissions and the drive towards higher efficiencies have resulted in increased operating temperatures in gas turbines. Subsequently, Original Equipment Manufacturer (OEMs) require improved component design and material selection to withstand the harsher conditions. This demands rapid evaluation of new components and their surface temperature to accelerate their market entry. Accurate temperature information proves key in the design of more efficient, longer-lasting machinery and in monitoring thermal damage. A number of traditional temperature measurement techniques are available, but can incur a number of limitations. Online temperature measurements, such as pyrometry or phosphor thermography, often require optical access to the component during operation and are therefore not suitable for inaccessible components. Other options including thermocouples can only provide point measurements and cannot deliver profiles across the surface. Offline techniques store temperature information that can be measured and analysed following operation. Several of these, however, are of destructive nature, can affect local thermal gradients and only provide point measurements. This article discusses an innovative offline measurement technique: luminescent Thermal History Paints (THPs). THPs are comprised of ceramic pigments in a binder matrix that can be applied to any hot component as a thin coating. These pigments are doped with optically active ions, which will phosphoresce when excited with a light source. The coating material experiences irreversible structural changes depending on the temperature it is exposed to. Changes in the material structure are reflected in its phosphorescent properties, which are measured with standard optical instrumentation at any surface location. Since the changes are permanent, the temperature information is stored in the coating and can be extracted after operation. Following calibration, it is therefore possible to relate phosphorescent behaviour to the past maximum temperature experienced at each location. This is done with Sensor Coating Systems Ltd. (SCS)’s portable instrumentation, which can provide rapid, automated and objective measurements across a component surface. Unlike the more traditional thermal paints, THPs are non-toxic, and provide a continuous measurement capability across the range 150°C–900°C with significantly improved durability. This article describes the underlying principles behind this novel technology and the advantages it provides over existing state-of-the-art methods. The benefits will be demonstrated through measurements on nozzle guide vanes (NGVs), with the view to compare and validate them against thermocouple measurements. The results show that the THP extends the limited information from thermocouples to provide a more complete view of the thermal processes on the component.

Sustainable energy saving: A junction temperature numerical calculation method for power insulated gate bipolar transistor module

Abstract This study is significant to ensure its safe and reliable operation for promoting the sustainable energy saving. The insulated gate bipolar transistor module was widely applied as the core electronic component in energy-saving and new energy industries. A junction temperature numerical calculation method was proposed to calculate the module operating junction temperature that has closed connection with the reliability and lifetime of module accurately in real time. Various parameters were obtained through tests and surfaces that have connected with the degree of the parameters. Junction temperature polynomial fitting equations under each power cycle were established on the above basis. The corresponding polynomial fitting equation was selected according to the aging degree of the module, and the value of junction temperature was obtained by taking the collector current and the saturation voltage. The polynomial fitting algorithm was compared with the junction temperature prediction algorithm based on particle swarm optimization-support vector machine. This study showed that the absolute error of the junction temperature obtained by polynomial fitting equations is mainly concentrated in the temperature and the maximum absolute error is no more than ±5 Celsius degree, and the average relative error of the junction temperature is about 2%. Therefore, polynomial fitting algorithm is more explicit and accurate to calculate the junction temperature of the module. Because the polynomial fitting method simplifies the method of selecting the junction temperature value with the saturation voltage drop as the temperature calibration criterion, and the process of building database between parameters in the whole aging process is omitted, it realizes the on-line measurement of the junction temperature of the module in the aging process, which has remarkable practical value.

Pyrolysis behavior of thermally thick wood particles: Time-resolved characterization with laser based in-situ diagnostics

Infrared laser absorption spectroscopy (IRLAS) and laser-induced fluorescence spectroscopy (LIF) are applied in the present study for online in-situ characterization of volatiles products in the close vicinity of a single pyrolysing wood sphere. These advanced analytical techniques are combined with online measurements of temperature and mass evolutions in order to gain further insight into the complex processes occurring during slow pyrolysis of thermally thick wood particles. Three different heating rates (5, 10, 20°C/min) and two wood types (beech, pine) were used. Time-resolved absolute concentrations of the main permanent gases CO2, CO, CH4 and H2O were measured applying IRLAS. From the LIF measurements the qualitative temporal release of polycyclic aromatic hydrocarbons (PAHs) could be deduced. Different behaviors regarding the release of volatiles, temperature evolution and conversion rates were observed for both wood species, which could not be ascribed only to the different content of cellulose, hemicellulose and lignin. According to the measured volatiles evolution an enhancement of heterogeneous catalytic tar cracking seemed to be present with higher heating rates for both wood types. However, the evolution of exothermicity and PAH release differed for both wood types indicating different reaction pathways. An analysis of possible reaction pathways including secondary reactions is performed taking into account all experimental findings about the in-situ composition of the volatiles and the evolution of the PAHs as well as the exothermicity. The differences in the pyrolytic behavior of both species can be related to both the chemical and physical properties of the raw materials.

High-efficiency on-line measurement of junction temperature based on bipolar transistors in accelerated experiment

Junction temperature is an important factor affecting the reliabilities of semiconductor devices. Usually, the method of measuring the junction temperature is not tested on-line. However, due to the fact that neither contact thermal resistance nor thermal resistance varying with temperature is taken into account, there exists an error in the off-line measurement. A way to solve the problem of off-line measurement is to measure the junction temperature on-line. In this paper, we propose an electrical method of measuring the temperature rise of high-power bipolar transistor in the working condition. The measurement method is based on a good linear relationship between base-emitter voltage (Vbe) and temperature during the steady-state. Taking the model 2N3055 of bipolar high power transistor for example, in this paper we study the relationship between base-emitter voltage (Vbe) and temperature under the conditions of constant collector-emitter voltage (Vce) and collector-current (Ice). During the experiment, the device is placed in a thermostat. A voltage is applied to the device collector, a current is applied to the base, and the emitter is earthed. Before the device is measured, we set different temperatures and make sure that the equipment is in a steady state. In order to avoid the effect of self-heating, the pulse current is used in the experiment. The pulse width and the period are 500 μups and 1 ms, respectively.The research result shows that the base-emitter voltage (Vbe) decreases linearly with temperature increasing and the base-emitter current is changed below 4% when the temperature is in a range of 40 ℃-140 ℃. In this paper we also deduce the mathematical expressions for base-emitter voltage (Vbe) and temperature under a steady state. It is proved that the Vbe-temperatrue curve is linear and temperature error is less than 0.5 ℃ when the changes of base current value does not exceed 4%. Therefore, in this paper we deduce a new method of testing the junction temperature in the speeding up measurement experiment. By measuring any of the reference points on the calibration curve under certain experimental conditions, the junction temperature can be calculated quickly according to the proposed formula.Finally, the phase 11 is used to verify the proposed method. We measure the thermal resistance upper the case for the junction of model 2N3055 and the thermal resistance under the case for the junction of model 2SD1047. The measurement results of phase11are compared with the junction temperature calculated using the test formula. The results show that the error of junction temperature between the two methods is less than 0.7%, which is corresponding with the needs of practical application. It proves the correctness and feasibility of the method.