Single Transfer Function Research Articles

Forecasting the Export Unit Value Index in Indonesia Using the Single Input Transfer Function

Export is one of the factors that increase the economic growth of a country. One measure of export activity that can describe economic growth in Indonesia is The Export Unit Value Index, which is an index that measures changes in the price of export commodities sold by residents of one country to residents of other countries. The purpose of this study is to predict the unit value index of exports in Indonesia using a single input transfer function model and to see the influence of the value of oil and gas and non-oil and gas exports on the unit value index of exports in Indonesia. The single input transfer function model is a model that describes the future forecast of a series (output series) obtained based on the past values of the output series and other time series (input series) that affect the output series. The results of this study obtained a transfer function model with the order (0,0,1) with a noise series following ARIMA (1,0,1). Based on this model, the export unit value index at time t is influenced by the unit value export index in the previous month and is influenced by the oil and gas and non-oil and gas export value in the same month. As indicated by its MAPE value of 4.89%, the forecast value does not diverge much from the actual value, which suggests that the transfer function model can be used to predict the export unit value index in Indonesia.
 Keywords: forecasting, export unit value index, single input, transfer function

A Simple State-Space Model of Human Driver Applicable to Windy Conditions

The paper is concerned with the design, verification and evaluation of a car-driving test scenario for human driver assessment. The scenario implemented in Unreal Engine adds four different wind characteristics which disturb the motion of a simulated vehicle. Besides, the driver is instructed to change the driving lane at defined intervals. These forcing functions enable the identification of the human-machine loop using state-space models. The parameters characterising the human dynamics are extracted from the model of the whole loop. As opposed to rather obsolete McRuer models, this approach follows the recent trends in the modelling of human-machine systems as multiloop systems or quadratically optimal controllers. Our results suggest that the model relying on a single transfer function with 4 parameters loses prediction capabilities during more realistic scenarios, in which random disturbances, such as wind gusts, affect the vehicle. In such cases, the multiloop model with the same number of parameters is able to capture human behaviour more accurately than McRuer model.

Sufficient and Necessary Graphical Conditions for MISO Identification in Networks With Observational Data

This article addresses the problem of consistently identifying a single transfer function in a network of dynamic systems using only observational data. It is assumed that the topology is partially known, the forcing inputs are not measured, and that only a subset of the nodes outputs is accessible. The developed technique is applicable to scenarios encompassing confounding variables and feedback loops, which are complicating factors potentially introducing bias in the estimate of the transfer function. The results are based on the prediction of the output node using the input node along with a set of additional auxiliary variables which are selected only from the observed nodes. Similar prediction error methods provide only sufficient conditions for the appropriate choice of auxiliary variables and assume <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> information about the location of strictly causal operators in the network. In this article, such an <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">a priori</i> knowledge is not required. A most remarkable feature of our approach is that the conditions for the selection of the auxiliary variables are purely graphical. Furthermore, within single-output prediction methods, such conditions are proven to be necessary and sufficient to consistently identify all networks with a given topology. A fundamental consequence of this characterization is to enable the search of a set of auxiliary variables minimizing a suitable cost function for single-output prediction error identification. In the article, we suggest possible approaches to tackle such optimal identification problems.

Optimal Selection of Observations for Identification of Multiple Modules in Dynamic Networks

This article presents a systematic algorithm to select a set of auxiliary measurements in order to consistently identify certain transfer functions in a dynamic network from observational data. The selection of the auxiliary measurements is obtained by minimizing an appropriate cost function. It is assumed that the topology of the network is known, the forcing inputs are not measured, and the observations have positive additive costs. It is shown that sufficient and necessary conditions for consistent identification of a single transfer function based on a multi-input single-output prediction error method, are equivalent to the notion of minimum cut in an augmented graph resulted from systematically manipulating the graphical representation of the network. Then, the optimal set of auxiliary measurements minimizing the cost could be found using different approaches such as algorithms from graph theory (i.e., Ford-Fulkerson), distributed algorithms (i.e., push-relabel algorithm), or purely optimization based procedures (i.e., linear programming). The results are also extended to the more challenging scenario, where the objective is simultaneously identifying multiple transfer functions.

ULF geomagnetic anomaly associated with the Sumatra-Pagai Islands earthquake swarm during 2020

Observations of earthquake precursors via geomagnetic anomalies from ultra-low frequency (ULF) could provide an expectation for short-term earthquake prediction. However, there are still several obstacles in determining this precursor, one of which is the presence of a precursor bias if the earthquake occurs at a close time and location. To cope with this problem, we analysed six earthquakes with a magnitude &gt;5 on Pagai Island, Mentawai, Sumatra, during 2020. These earthquakes have epicentres close to each other and occur within a short time (one month). This study used geomagnetic data recorded by the Magnetic Data Acquisition System (MAGDAS) magnetometer network at Sicincin station (SCN), West Sumatra, and Kepahiyang station (KPY), Bengkulu, with a span of one month before the earthquake. The anomaly of ULF emission was analysed using the power spectral density method at a frequency of 0.012 Hz for the H and Z components of the geomagnetic data. The onset time of the ULF emission anomaly was determined by the standard deviation value (pz + σ, pz – σ) of the SZ/SH power ratio polarization. The disturbance storm time index (Dst) was used to ensure that the anomaly occurred was not caused by geomagnetic storm. Also, the single station transfer function was used to calculate the azimuth, and the empirical formula between the anomaly amplitude and the magnitude was used to calculate the earthquake magnitude as the validation of the anomaly source. Several ULF anomalies as earthquake precursors were observed, especially at the KPY station. The estimated azimuth shows a good accuracy compared to the earthquake's azimuth, with an average value of 97.8%. Furthermore, the earthquake magnitude calculated from the ULF anomaly shows a good agreement with the actual earthquake magnitude, with an average accuracy of 98.13%.

On the Capacity of MIMO-MAC in Rician channel

The information theoretic limits for the single user MIMO (Nt×Nr) communication channel are well established in literature for different scenarios of channel types and channel state information (CSI) availability. However, all obtained results are based on the linear system model in which the channel transfer function is defined as a single entity in which all environmental effects are captured. The capacity gain in MIMO over SISO systems is acquired by exploring the diversity in the channel transfer function. We show that, exploring the geographical location of the MIMO system nodes independently is of great influence to the overall system capacity. This is done by decomposing the channel transfer function into its equivalent transfer function in which we separate the effect of the signal bearing information (Angle of Arrival (AoA)) from the original channel. We show that, by exploring the geographical location of the system nodes, the capacity of the single user MIMO channel scales linearly with min {Nr2, Nt2} as opposed to min {Nr, Nt} if the channel is considered as a single transfer function. We show that these results holds for both deterministic, Rayleigh and Rician fading channels

Estimating Central Blood Pressure From a Single Peripheral Pressure Measurement

Abstract This paper presents a set of criteria used to identify the parameters describing a tube-load model of the arterial system to estimate central blood pressure (BP). The criteria are generalizable to accommodate for inter- and intra-subject variability encountered in the ICU. The proposed single measurement transfer function (SMTF) requires only a single peripheral pressure measurement, commonly available in the ICU, for central pressure estimation, removing the need for an additional measurement of pulse transit time, common to other central BP estimation models. The method was tested using data from six (6) porcine experiments where septic shock was induced and subsequent treatment was performed. Systolic pressure (SP), pulse pressure (PP) and root-mean-squared (RMSE) errors relative to invasive measurements of aortic pressure were used to assess accuracy. The SMTF method produced mean errors ≤5mmHg across all metrics with 84.4, 88.7 and 63.2% of SP, PP, and RMSE, respectively, within this bound of measured central pressure. Peripheral BP accuracy was also assessed as it is commonly used as a surrogate for central BP in clinical settings. Finally, two alternate methods utilizing the same model equations with additional inputs, one using the measured pulse transit time and the other minimizing the RMSE with measured aortic pressure, were implemented to compare the SMTF accuracy to best case outputs given the model equations.

A constant-frequency feedback loop for non-contact frequency-modulated atomic force microscopy via root locus: Implemented on a single-board field-programmable gate array device.

Non-contact, frequency modulated atomic force microscopy is often operated in the constant-frequency mode to obtain a height map of the sample's surface. Once linearized, the dynamics of the constant-frequency closed-loop system are reduced to a single transfer function. By modifying the bandwidth of this transfer function, a tradeoff is achieved between image noise and imaging speed. In this article, a new constant-frequency feedback loop is developed, utilizing the self-excitation technique for resonating the cantilever. Along with the proposed controller, it will be shown with the root locus that one needs to vary a single parameter, the loop gain, to modify the closed-loop bandwidth. The result is a robust, low-order, real-poled, feedback loop that is very easy to tune. The methodology is validated experimentally on a single-board field-programmable gate array device.

Impedance Circuit Model of Grid-Forming Inverter: Visualizing Control Algorithms as Circuit Elements

The impedance model is widely used for analyzing power converters. However, the output impedance is an external representation of a converter system, i.e., it compresses the entire dynamics into a single transfer function with internal details of the interaction between states hidden. As a result, there are no programmatic routines to link each control parameter to the system dynamic modes and to show the interactions among them, which makes the designers rely on their experience and heuristic to interpret the impedance model and its implications. To overcome these obstacles, this article proposes a new modeling tool named as impedance circuit model, visualizing the closed-loop power converter as an impedance circuit with discrete circuit elements rather than an all-in-one impedance transfer function. It can reveal the virtual impedance essence of all control parameters at different impedance locations and/or within different frequency bandwidths, and show their interactions and coupling effects. A grid-forming voltage source inverter is investigated as an example, with considering its voltage controller, current controller, control delay, voltage/current dq-frame cross-decoupling terms, output-voltage/current feedforward control, droop controllers, and three typical virtual impedances. The proposed modeling tool is validated by frequency-domain spectrum measurement and time-domain step response in simulations and experiments.

Forecasting the farmers’ terms of trade in Yogyakarta using transfer function model

The transfer function model is one of the forecasting models that predicts future values from a time series based on its past values and the other variables. In this paper, the transfer function model is utilized to forecast the farmers’ terms of trade in Yogyakarta province. The farmers’ term of trade (FTT) is one indicator of farmers’ welfare. The variables included in the model inputs are the inflation and exchange rate in Yogyakarta. The procedure for transfer function modeling is through two stages, those are building a single input transfer function model for each input based on the autoregressive integrated moving average model, and then building the transfer functions simultaneously for all variables. The result demonstrates that the transfer function can predict farmers’ terms of trade accurately with the mean absolute percentage error value of 0.841%.

Modeling active optical networks

The recently introduced complex active optical network (LANER) generalizes the concept of laser system to a collection of links, building a bridge with random-laser physics and quantum-graphs theory. So far, LANERs have been studied with a linear approach. Here, we develop a nonlinear formalism in the perspective of describing realistic experimental devices. The propagation along active links is treated via suitable rate equations, which require the inclusion of an auxiliary variable: the population inversion. Altogether, the resulting mathematical model can be viewed as an abstract network, its nodes corresponding to the fields along the physical links. The dynamical equations differ from standard network models in that, they are a mixture of differential delay (for the active links) and algebraic equations (for the passive links). The stationary states of a generic setup with a single active medium are thoroughly discussed, showing that the role of the passive components can be combined into a single transfer function that takes into account the corresponding resonances.

Unified Power-Based Vehicle Fuel Consumption Model Covering a Range of Conditions

&lt;div class="section abstract"&gt;&lt;div class="htmlview paragraph"&gt;Previously fuel consumption on a drive cycle has been shown to be proportional to traction work, with an offset for powertrain losses. This model had different transfer functions for different drive cycles, performance levels, and applied powertrain technologies. Following Soltic it is shown that if fuel usage and traction work are both expressed in terms of cycle average power, a wide range of drive cycles collapse to a single transfer function, where cycle average traction power captures the drive cycle and the vehicle size. If this transfer function is then normalized by weight, i.e. by working in cycle average power/weight (P/W), a linear model is obtained where the offset is mainly a function of rated performance and applied technology. A final normalization by rated power/weight as the primary performance metric further collapses the data to express the cycle average fuel power/rated power ratio as a function of cycle average traction power/rated power ratio. This final transfer function is mainly a function of technology. It was used to estimate the effectiveness of technologies deployed by manufacturers to improve fuel consumption. Compared to the naturally aspirated PFI engines and six-speed automatic transmissions of a decade ago, three different combinations of downsized turbo or Atkinson engines, with either 8+ speed transmissions or CVTs achieve similar substantial improvements in efficiency. The useful work or power definition is expanded to include electrical power for customer functions, and power to drive the air conditioning, so that the model can be applied to ‘real world’ driving.&lt;/div&gt;&lt;/div&gt;

Coupled transfer function model for the evaluation of implanted cables safety in MRI.

Multiple medical-device leads implanted next to each other are often encountered in clinical practice. The aim of this work is to study a coupled transfer function model to evaluate the safety of these coupled leads submitted to the RF field of a 1.5T MRI scanner for a constant distance between both leads. The effect of coupling on the heating of 2 cables with different termination conditions is evaluated experimentally. The coupled and single transfer functions are determined experimentally and used to predict the relative temperature increases of both cables alone and coupled. Two different coupled models, an additive model and a global model, are proposed. The coupled transfer functions are also simulated. The coupling between cables has a strong influence on the resulting heating at the electrodes. The coupled additive transfer function model is a relevant tool to evaluate the heating of coupled leads separated by a constant distance. The global model underestimates the heating in one of the coupled cases by about 30%. The measured coupled transfer functions coincide with the simulated models. It is necessary to take into account the coupling effect between leads to evaluate the safety of implanted devices. This work shows that, in the case of 2 cables separated by a constant distance, that an experimentally determined coupled transfer function allows estimation of the heating of the 2 electrodes for a given incident field. Further work should take into account the in vivo varying distance between the 2 cables.

Optimum frequency identification of anomalous geomagnetic signal related to earthquake precursor in Sumatra Island

Many scientific studies has detected ULF (ultra-low frequency) emission before an earthquake. An earlier study of Loma Prieta 7.1 M earthquake in 1989 shows ULF anomaly ranged between 0.01-10 Hz before an earthquake. A similar study of Kushiro earthquake 6.4 Mw shows that the ULF anomaly can be detected at a frequency range of 0.022-0.1 Hz. Furthermore, a study conducted in Sumatra Island from 2007-2012 shows the ULF anomaly at 0.01-0.06 Hz. Newer study on the 2009 Padang earthquake and Mentawai 2010 earthquake shows ULF emission between 0.012-0.022 Hz. Based on the aforementioned researches, a study is conducted on frequency range of 0.01-0.09 Hz to identify the optimum ULF frequency. Study conducted in this case uses magnetic diurnal variation data from Sumatra region from 2017 to 2018, especially earthquakes recorded at Gunung Sitoli (GSI), and Sicincin (SCI) stations. Previous studies above provide an overview of ULF ranges associated with earthquakes. Based on all above, an analysis is conducted to find the precursors using data of past earthquake events by utilizing Fast Fourier Transform to transform time-domain data to frequency domain, bandpass filters to eliminate noise, power ratio of Z/H to determine the time window, and Single Station Transfer Function to determine the location window. Lastly, moving average is used to assist determination of time window. Magnetic anomalies between 0.01-0.03 Hz, with amplitude exceeding monthly average, were observed before the earthquakes. Analysis in this frequency range shows occurence of earthquake 5-6 days after geomagnetic anomalies were detected. This study shows that location window prediction is possible with 100% accuracy. Therefore, 0.01-0.03 is currently the optimum frequency for precursor analysis.

Prediction of the number dengue hemorrhagic fever patients in district Jombang Regency using transfer function model approach

Transfer function describes the values of future prediction from output series (Yt) based on its past value and also based on one or more input series (Xt) as the dependent variables. Single input transfer function model is a transfer function model that use one variable as input series (Xt).Then, this single input transfer function model was applied to make the model and forecast the number of dengue hemorrhagic fever (DHF) cases (Yt) in Jombang based on rainfall (Xt). From the model, it couldbe described that the number of dengue hemorrhagic fever cases in a month was affected by rainfall on that month, rainfall two month earlier, rainfall twelve month earlier, rainfall thirteen month earlier, the number of dengue hemorrhagic fever cases a month earlier, the number of dengue hemorrhagic fever cases twelve month earlier, the number of dengue hemorrhagic fever cases thirteen month earlier, and also residual value on that month. Based on the transfer function model result, it the number of dengue hemorrhagic fever cases in Jombang could be predicted for next 20 months. After comparing the prediction result and the actual data, we obtained that almost all the prediction results (75%) were valid.

Transfer functions for flow predictions in wall-bounded turbulence

Three methods are evaluated to estimate the streamwise velocity fluctuations of a zero-pressure-gradient turbulent boundary layer of momentum-thickness-based Reynolds number up to $Re_{\unicode[STIX]{x1D703}}\simeq 8200$, using as input velocity fluctuations at different wall-normal positions. A system identification approach is considered where large-eddy simulation data are used to build single and multiple-input linear and nonlinear transfer functions. Such transfer functions are then treated as convolution kernels and may be used as models for the prediction of the fluctuations. Good agreement between predicted and reference data is observed when the streamwise velocity in the near-wall region is estimated from fluctuations in the outer region. Both the unsteady behaviour of the fluctuations and the spectral content of the data are properly predicted. It is shown that approximately 45 % of the energy in the near-wall peak is linearly correlated with the outer-layer structures, for the reference case $Re_{\unicode[STIX]{x1D703}}=4430$. These identified transfer functions allow insight into the causality between the different wall-normal locations in a turbulent boundary layer along with an estimation of the tilting angle of the large-scale structures. Differences in accuracy of the methods (single- and multiple-input linear and nonlinear) are assessed by evaluating the coherence of the structures between wall-normally separated positions. It is shown that the large-scale fluctuations are coherent between the outer and inner layers, by means of an interactions which strengthens with increasing Reynolds number, whereas the finer-scale fluctuations are only coherent within the near-wall region. This enables the possibility of considering the wall-shear stress as an input measurement, which would more easily allow the implementation of these methods in experimental applications. A parametric study was also performed by evaluating the effect of the Reynolds number, wall-normal positions and input quantities considered in the model. Since the methods vary in terms of their complexity for implementation, computational expense and accuracy, the technique of choice will depend on the application under consideration. We also assessed the possibility of designing and testing the models at different Reynolds numbers, where it is shown that the prediction of the near-wall peak from wall-shear-stress measurements is practically unaffected even for a one order of magnitude change in the corresponding Reynolds number of the design and test, indicating that the interaction between the near-wall peak fluctuations and the wall is approximately Reynolds-number independent. Furthermore, given the performance of such methods in the prediction of flow features in turbulent boundary layers, they have a good potential for implementation in experiments and realistic flow control applications, where the prediction of the near-wall peak led to correlations above 0.80 when wall-shear stress was used in a multiple-input or nonlinear scheme. Errors of the order of 20 % were also observed in the determination of the near-wall spectral peak, depending on the employed method.

An evaluation of high frequency turbidity as a proxy for riverine total phosphorus concentrations

Surface water eutrophication resulting from excessive phosphorus (P) inputs is one of today's most challenging environmental issues. Riverine total phosphorus (TP) concentrations have high temporal variability, which complicates flux estimation. We evaluated the usefulness of high frequency in-situ turbidity measurements as a proxy for TP in Sävjaån, a river draining a mixed land use catchment (722 km2) in central Sweden. Turbidity was monitored every 10th–15th minute during 6 consecutive years (2012–2017). Linear regression showed a good relationship between high frequency turbidity and TP (r2 = 0.64) and could hence be used for comparison of flux estimation methods. Predictive power of the turbidity-TP relationship was not improved by adding seasons, hydrograph rising/falling limb or high/low stream discharge to the model which argues for a single transfer function relating turbidity and TP. Both TP and turbidity were log-normally distributed. However, flux estimates were sensitive to data transformation; predicted TP concentrations and fluxes based on log-transformed data were biased towards lower concentrations and fluxes compared to non-transformed data. In five of six years grab sample and high frequency estimated TP fluxes were similar (grab sample estimates −10% to +13% P transport compared to high frequency flux estimates). The exception was in 2013, when a 50-year spring flood occurred, and the grab sample estimated flux was 56% larger than that estimated from high frequency data. Thus, the flux comparisons were mostly affected by stream discharge, which underlines the importance of capturing high discharge episodes with, e.g. in situ sensors. While uncertainties regarding the use of turbidity as a proxy for TP remain, it is clear that credible water chemistry data can be obtained with current high frequency sensors. We conclude that high frequency data can be used to better understand catchment response to external pressures and gain insights into water quality that will be missed with grab sampling.

Sequences Domain Impedance Modeling of Three-Phase Grid-Connected Converter Using Harmonic Transfer Matrices

The sequence-domain impedance using harmonic linearization technique can well describe the harmonic behavior of the interconnected system consisting of the grid and converter. However, fast phase-locked loop (PLL) design, unbalanced current controller structure will cause the unneglectable off-diagonal components in impedance matrix of converter. Due to the frequency coupling and sequence coupling effect in the sequence domain, the traditional single input single output transfer function lacks the capability to accurately express this frequency shift relationship. Therefore, in this paper, the harmonic transfer matrix (HTM) is used to model the frequency shift existing in the sequence-domain impedance model. By unifying positive sequence and negative sequence components, the complexity of impedance model derivation can be reduced. The linear time-periodic system is transformed to a linear time-invariant system in harmonic domain. And then, Nyquist criteria is applied to analyze the stability of the interconnected system. Finally, simulation results verify the proposed HTM-based sequence-domain impedance modeling method.

A practical method for the consistent identification of a module in a dynamical network

We present a new and simple method for the identification of a single transfer function that is embedded in a dynamical network. In existing methods the consistent identification of the desired transfer function relies on the positive definiteness of the spectral density matrix of the vector of node signals, and it typically requires knowledge of information about the topology and the excitation of the whole network. The positivity condition is on the internal signals and therefore can not be guaranteed a priori; in addition it is not necessary. The new method of this paper provides simple conditions on which nodes to excite and which nodes to measure in order to produce a consistent estimate of the desired transfer function. Just as importantly, it requires knowledge of the local topology and excitation only.

HESS Opinions: The complementary merits of competing modelling philosophies in hydrology

Abstract. In hydrology, two somewhat competing philosophies form the basis of most process-based models. At one endpoint of this continuum are detailed, high-resolution descriptions of small-scale processes that are numerically integrated to larger scales (e.g. catchments). At the other endpoint of the continuum are spatially lumped representations of the system that express the hydrological response via, in the extreme case, a single linear transfer function. Many other models, developed starting from these two contrasting endpoints, plot along this continuum with different degrees of spatial resolutions and process complexities. A better understanding of the respective basis as well as the respective shortcomings of different modelling philosophies has the potential to improve our models. In this paper we analyse several frequently communicated beliefs and assumptions to identify, discuss and emphasize the functional similarity of the seemingly competing modelling philosophies. We argue that deficiencies in model applications largely do not depend on the modelling philosophy, although some models may be more suitable for specific applications than others and vice versa, but rather on the way a model is implemented. Based on the premises that any model can be implemented at any desired degree of detail and that any type of model remains to some degree conceptual, we argue that a convergence of modelling strategies may hold some value for advancing the development of hydrological models.