Order Lag Research Articles

Continuous-time identification of grey-box and black-box models of an industrial oven

The design of temperature controllers is impaired by the limited accuracy of the models employed for thermal systems, which are commonly estimated from uninformative data, such as step responses, due to the restrictive experimental design connected to the long duration of the experiments. This paper focuses on modelling an industrial convection oven following different rationales. Three continuous-time models are proposed and compared: a grey-box parametric thermal network model, a black-box parametric first order lag plus time delay model, and a black-box non-parametric model based on reproducing kernel Hilbert spaces. These are all estimated and validated on step response experimental data. Lastly, the pros and cons of each model are highlighted.

STGC-GNNs: A GNN-based traffic prediction framework with a spatial–temporal Granger causality graph

Accurate representation of the temporal dynamics of traffic flow traveling in the road network is the key to traffic prediction, it is therefore important to model the spatial dependence of the road network. The essence of spatial dependence is to accurately describe how traffic information transmission is affected by other nodes in the road network, and the GNN-based traffic prediction model, as a benchmark for traffic prediction, has become the most common method for the ability to model spatial dependence by transmitting traffic information with the message passing mechanism. However, existing methods model a local and static spatial dependence, which cannot transmit the global-dynamic traffic information (GDTi) required for long-term prediction. The challenge is the difficulty of detecting the precise transmission of GDTi due to the uncertainty of individual transport, especially for long-term transmission. In this paper, we propose a new hypothesis: GDTi behaves macroscopically as a transmitting causal relationship (TCR) underlying traffic flow, which remains stable under dynamic changing traffic flow. We further propose spatial–temporal Granger causality (STGC) to express TCR, which models global and dynamic spatial dependence. To model global transmission, we model the causal order and causal lag of TCR’s global transmission by a spatial–temporal alignment algorithm. To capture dynamic spatial dependence, we approximate the stable TCR underlying dynamic traffic flow by a Granger causality test. The experimental results on three backbone models show that using STGC to model the spatial dependence has better results than the original model for 45 min and 1 h long-term prediction.

Balanced Truncation of $k$-Positive Systems

This paper considers balanced truncation of discrete-time Hankel $k$-positive systems, characterized by Hankel matrices whose minors up to order $k$ are nonnegative. Our main result shows that if the truncated system has order $k$ or less, then it is Hankel totally positive ($\infty$-positive), meaning that it is a sum of first order lags. This result can be understood as a bridge between two known results: the property that the first-order truncation of a positive system is positive ($k=1$), and the property that balanced truncation preserves state-space symmetry. It provides a broad class of systems where balanced truncation is guaranteed to result in a minimal internally positive system.

Highly Variable Paracetamol Pharmacokinetics After Multiple Oral Dosing in Frail Older People: A Population Pharmacokinetic Analysis.

Paracetamol pharmacokinetics (PK) is highly variable in older fit adults after intravenous administration. Frailty and oral administration likely result in additional variability. The aim was to determine oral paracetamol PK and variability in geriatric inpatients. A population PK analysis, using NONMEM7.2, was performed on 245 paracetamol samples in 40 geriatric inpatients (median age 87 [range 80-95] years, bodyweight 66.4 [49.3-110] kg, 92.5% frail [Edmonton Frail Scale]). All subjects received paracetamol 1000mg as tablet (72.5%) or granulate (27.5%) three times daily. Simulations of dosing regimens (1000mg every 6 hours [q6h] or q8h) were performed to determine target attainment, using mean steady-state concentration (Css-mean) of 10mg/L as target. A one-compartment model with first order absorption and lag time best described the data. The inter-individual variability was high, with absorption rate constant containing the highest variability. The inter-individual variability could not be explained by covariates. Simulations of 1000mg q6h and q8h resulted in a Css-mean of 10.8 [25-75th percentiles 8.2-12.7] and 8.13 [6.3-9.6]mg/L, respectively, for the average geriatric inpatient. The majority of the population remained off-target (22.2% [q6h] and 52.2% [q8h] <8mg/L; 31.3 [q6h] and 7.6% [q8h] >12mg/L). A population of average geriatric inpatients achieved target Css-mean with paracetamol 1000mg q6h, while q8h resulted in underexposure for the majority of them. Due to high unexplained variability, a relevant proportion remained either above or below the target concentration of 10mg/L. Research focusing on PK, efficacy and safety is needed to recommend dosing regimens.

Early warning systems and rapid response systems for the prevention of patient deterioration on acute adult hospital wards.

Early warning systems and rapid response systems for the prevention of patient deterioration on acute adult hospital wards.

Development of tuning free SISO PID controllers for First Order Plus Time Delay (FOPTD) and First Order Lag Plus Integral Plus Time Delay model (FOLIPD) systems based on partial model matching and experimental verification

This work aims to introduce a tuning-free PID controller for stable FOPTD and FOLIPD systems. The objective was achieved using a partial model-matching strategy; matching the coefficients of corresponding powers of s of the closed loop response of the model to the desired closed loop transfer function. Closed-loop performance is evaluated by considering a unit step change in the process model and compared the results with other methods reported earlier in the literature. Input and output performances were evaluated using error analyses and total variation. The robustness of the proposed method was assessed via incorporation of uncertainties in the process model parameters. The proposed method was also experimentally validated for FOPTD model using a temperature controlled lab. It was concluded that the method was analytically derived and model based with a key advantage that the resultant PID required no tuning parameter.

Frequency Estimation from Compressed Measurements of a Sinusoid in Moving-Average Colored Noise

Frequency estimation of a single sinusoid in colored noise has received a considerable amount of attention in the research community. Taking into account the recent emergence and advances in compressive covariance sensing (CCS), the aim of this work is to combine the two disciplines by studying the effects of compressed measurements of a single sinusoid in moving-average colored noise on its frequency estimation accuracy. CCS techniques can recover the second-order statistics of the original uncompressed signal from the compressed measurements, thereby enabling correlation-based frequency estimation of single tones in colored noise using higher order lags. Acceptable accuracy is achieved for moderate compression ratios and for a sufficiently large number of available compressed signal samples. It is expected that the proposed method would be advantageous in applications involving resource-limited systems such as wireless sensor networks.

Thermal Performance of a Convective Functionally Graded Fin Using Fractional Non-Fourier Heat Conduction

To analyze the thermal performance of longitudinal fins made of functionally graded materials, this article studies the transient heat transfer in a longitudinally graded fin with power-law thermal conductivity in a convective ambiance using a fractional heat conduction model. This model has an advantage over the Fourier heat conduction in describing the anomalous heat diffusion and non-Fourier effect, and in avoiding the infinite velocity of heat waves and abrupt change of temperature. For heat shock at the base, instantaneous temperature response in an axially graded fin surrounded by convective fluid is obtained through numerical inversion of the Laplace transform. The effects of non-Fourier parameters such as the fractional order and phase lag of heat flux (relaxation time), and the gradient index of the thermal conductivity on the temperature distribution and fin efficiencies are analyzed and shown graphically. Two definitions of instantaneous fin efficiency are discussed for homogeneous and longitudinally graded fins. The occurrence of heat convection leads to a subdiffusion term, and the temperature change exhibits a significant difference when adopting the fractional-order model and the integer-order model. The obtained results are of great benefit to the design of enhancing the thermal performance of extended surfaces.

Constrained neural adaptive predictive control of SMES for dynamic performance improvement of power systems

For dynamic performance improvement of modern power systems, the use of fast acting energy systems like superconducting magnetic energy storage (SMES) is imperative. In this paper, incorporation of a small rating SMES in a solar and wind power penetrated multi-area power system is proposed. A non-linear neural adaptive predictive controller is used to generate an optimal power command taking into account the converter rating and energy level constraints of SMES unit. The SMES is represented by a control relevant model comprising of a first order lag compensator cascaded by an integrator to translate the hardware constraints pertaining to its coil current into modified power constraints. Moreover for avoiding the sudden SMES outage, the power thresholds are forcibly varied as the SMES current reaches near its maximum and minimum values. The uprightness of the designed scheme is illustrated by simulation studies performed on a three area power system.

Trend Analysis of Rainfall Time Series in Shanxi Province, Northern China (1957–2019)

Changes in rainfall play an important role in agricultural production, water supply and management, and social and economic development in arid and semi-arid regions. The objective of this study was to examine the trend of rainfall series from 18 meteorological stations for monthly, seasonal, and annual scales in Shanxi province over the period 1957–2019. The Mann–Kendall (MK) test, Spearman’s Rho (SR) test, and the Revised Mann–Kendall (RMK) test were used to identify the trends. Sen’s slope estimator (SSE) was used to estimate the magnitude of the rainfall trend. An autocorrelation function (ACF) plot was used to examine the autocorrelation coefficients at various lags in order to improve the trend analysis by the application of the RMK test. The results indicate remarkable differences with positive and negative trends (significant or non-significant) depending on stations. The largest number of stations showing decreasing trends occurred in March, with 10 out of 18 stations at the 10%, 5%, and 1% levels. Wutai Shan station has strong negative trends in January, March, April, November, and December at the level of 1%. In addition, Wutai Shan station also experienced a significant decreasing trend over four seasons at a significance level of 1% and 10%. On the annual scale, there was no significant trend detected by the three identification methods for most stations. MK and SR tests have similar power for detecting monotonic trends in rainfall time series data. Although similar results were obtained by the MK/SR and RMK tests in this study, in some cases, unreasonable trends may be provided by the RMK test. The findings of this study could benefit agricultural production activities, water supply and management, drought monitoring, and socioeconomic development in Shanxi province in the future.

Stability and direction of Hopf bifurcations of a cyclical growth model with two-time delays and one-delay dependent coefficients

• We study the impact of two discrete-time delays on the basic Goodwin growth cycle model. • We study a delayed differential equation system with discrete-time delays and delay-dependent coefficients depending only on one of the time delay. • Having chosen the time delays as bifurcation parameters, we study the stability-switching properties of the transcendental characteristic equation. • We analyze the direction and stability of Hopf bifurcation by means of the first Lyapunov coefficient. This paper deals with the impact of two discrete-time delays on the basic Goodwin growth cycle model. The former concerns the existence of a finite time delay for building capital goods as suggested by Kalecki. The latter pertains to the wage lag hypothesis. This is because, taking the current change of the employment rate into account, workers and capitalists bargain new wage periodically. There are no examples in the literature on the Goodwin model of the use of both those lags in order to explore the GDP dynamics. From the analytical point-of-view, what we obtain is a delayed differential equation system with discrete-time delays and delay-dependent coefficients depending only on one of the time delays. Having chosen the time delays as bifurcation parameters, we study the stability-switching properties of the transcendental characteristic equation resulting from the stability analysis and the direction of the Hopf bifurcations. Although the system with no lag displays a stable focus, the introduction of the two lags preserves the stable solution only for particular combinations of parameters and length of the lags. In any other case, instability prevails and regular cycles or chaotic fluctuations emerge. Finally, we provide the analytical results with the necessary economic interpretations.

Are driver's licenses issued within 3 years of cancer diagnosis a valid source of BMI data?

Overweight and obesity are risk factors for several cancers; however, population-based cancer registries do not routinely collect data on body mass index (BMI). This study evaluated the utility of supplementing cancer registry data with BMI data derived from driver's license records. We linked self-reported height and weight data from driver's license records to directly measured values, obtained via medical record abstraction, in a sample of 712 adult Iowa residents with cancer diagnosed during 2007-2012. Matched BMI values were subjected to a comprehensive evaluation of quantitative and categorical measures of agreement between data sources. Driver's license issue dates preceded diagnosis dates in 60.7% of cases, with time lags ranging from 3.0years pre-diagnosis to 2.9years post-diagnosis. Statistical analysis of agreement between continuous BMI values and ordinal BMI categories yielded an overall intraclass correlation estimate of 0.79 (95% confidence interval [CI] 0.77, 0.82) and an overall weighted kappa estimate of 0.63 (95% CI 0.59, 0.68), respectively. Subgroup analyses indicated reduced reliability among obesity-related cancers, particularly multiple myeloma, ovarian cancer, and pancreatic cancer. Neither measurement order nor time lag significantly affected agreement between BMI values. These findings suggest that self-reported driver's license data provide a reasonable approximation of BMI, but are less precise than interview- and questionnaire-based methods. Furthermore, the degree of bias is seemingly unaffected by measurement order and time lag, but appears to become more pronounced as BMI itself increases.

Photo-Thermoelastic Model with Time-Fractional of Higher Order and Phase Lags for a Semiconductor Rotating Materials

In this work, a modified generalized fractional photothermeolastic model is constructed on the basis of the fractional calculus technique. For the considered model, Fourier law is introduced using the Taylor series expansion of higher time-fractional. The formulated model is an extension to the thermoelastic theories proposed by Lord–Shulman Lord and Shulman (J. Mech. Phys. Solid 15:299-309, 1967). Tzou (J Heat Transfer 117: 8-16, 1995) and fractional thermoelastic model introduced by Ezzat (Applied Mathematical Modelling 35:4965-4978, 2011). The model is then implemented to investigate photothermoelastic interaction in a rotating semiconductor half-space stressed by magnetic field. The numerical results of the effects of some physical functions are illustrated graphically to estimate the influences of the fractional parameter, the rotation parameter, and the higher-order time-fractional. It is shown that these parameters have a required significant influence on the physical fields.

Dynamic regularization discriminant local preserving projection method for fault diagnosis

Due to the high dimensionality, serial correlation, and nonlinearity of industrial process data, the primary task for diagnosing fault is to extract key fault features from fault datasets. In this paper, to obtain much more inherent fault information, a dynamic regularization discriminant local preserving projection approach (DRDLPP) based on feature reduction is put forward to diagnose fault, which addresses the small sample size problem of discriminant local preserving projection (DLPP) by incorporating the regularization term into the objective function of DLPP. The enhanced performance of DRDLPP for fault diagnosis over conventional diagnostic approaches mostly benefits from two aspects: One aspect is that DRDLPP can discover local manifold fault information hidden in original sample space by preserving the local neigborhood structure of data; The other aspect is that DRDLPP has the remarkable capacity to capture dynamic information by extending the observation vector with previous observation vectors. What is more, the information criterion function is utilized to capture the optimal dimensionality reduction order and time lag of DRDLPP method. The experimental results of the Tennessee Eastman process demonstrate that the proposed DRDLPP approach provides a better visual performance and achieve lower misclassification rates in fault diagnosis.

The sequential collaborative relationship between economic growth and carbon emissions in the rapid urbanization of the Pearl River Delta.

In a rapid urbanization context, socio-economic development has caused large increases in carbon emissions. In this study, various techniques such as cointegration analysis, vector autoregression, and decoupling elastic function methods are applied to analyze the sequential collaborative relationship between economic development and carbon emissions in the process of urbanization in terms of the time-series lag relationship and the decoupling relationship. The main findings are as follows: (1) urbanization and carbon emissions displayed a temporal correlation relation with a lag of order 4, according to stability tests, and (2) the development of urbanization, economic growth, and changes in land use may be responsible for the time lag in carbon emissions. Furthermore, the mechanisms behind the effect of urbanization on carbon emissions are investigated to assist future carbon emissions reduction efforts. (3) From 1990 to 2014, carbon emissions and economic development showed a temporal evolution trend of "weak decoupling-expansionary coupling-weak decoupling" in the Pearl River Delta region, and there was an overall weak decoupling state: carbon emissions increased with growth in economic development, but the emissions growth rate was lower than the speed of economic development. (4) From 1990 to 2014, economic development showed a trend of sustained growth in the Pearl River Delta region, and differences were detected in the decoupling status between carbon emissions and economic development at different times. The overall decoupling status of the nine cities in the region was one of weak decoupling; however, the decoupling index, carbon emissions, and economic development levels displayed differences, whereby cities with high carbon emissions and high economic development levels were not necessarily the cities in which environmental pressures from economic development were the most severe. Our results have important theoretical and practical significance as they clarify the impact of economic development on carbon emissions in the process of urbanization, as well as the carbon emissions reduction work that must be undertaken in urban systems.

Generalized Fractional Heat Conduction in a One-Dimensional Functionally Graded Material Layer

Functionally graded materials (FGMs) have been widely used. This work studies a heat conduction problem in an FGM layer with different exponential gradients. Based on a generalized fractional heat conduction theory with phase lag of heat flux, a mixed initial-boundary value problem is solved. Analytical expression for temperature change in the Laplace transform domain is derived. Numerical results of the transient temperature response in the time domain are evaluated by applying a numerical inversion of the Laplace transform. Two representative boundary conditions related to given temperature or heat convective transfer are discussed. For different Biot numbers, the effects of phase lag of heat flux, fractional order, and material properties on temperature field are illustrated graphically. A comparison of the temperature fields based on the non-Fourier model and classic Fourier model is made. The obtained results show that wave-like behaviors may occur for the generalized fractional heat transfer, which does not occur for the classical Fourier heat conduction. The material properties play an important role in the heat transfer process. The derived results are of benefit to the design of materials for thermoresistance and abstraction of heat.

Dynamic Minimax Probability Machine-Based Approach for Fault Diagnosis Using Pairwise Discriminate Analysis

Fault diagnosis plays a key role in the safe and efficient operation of industrial processes. With the emerging big data era, the analytic methods based on probabilistic representations have attracted growing research interest. In this brief, a dynamic minimax probability machine (DMPM) approach based on the framework of probabilistic representations is proposed for diagnosing process faults, without imposing any assumptions on data distributions. In addition, an information criterion is put forward to determine the optimal dimensionality reduction order and time lags of DMPM. The proposed DMPM-based method allows for the enhanced performance of fault diagnosis due to the following advantages over conventional diagnostic approaches. First, DMPM maximizes the pairwise separation probability between each pair of faulty data sets, directly yielding improved discriminatory power in the projected space. Second, the proposed approach is less likely to be influenced by “outlier” classes since its objective function is a summation of probabilities, thereby enabling it to be beneficial for the classification of imbalanced data. Third, DMPM has superior capability on capturing dynamic information from the process data by augmenting observation vectors with time lags. The effectiveness of the proposed approach is demonstrated on the Tennessee Eastman process.

Simplified Machine Diagnosis Techniques with Absolute Deterioration Factor by Utilizing the Second Order Autocorrelation Function

Among many amplitude parameters, Kurtosis and Bicoherence are recognized to be the sensitive good parameters for machine diagnosis. In this paper, simplified calculation method of coefficient of autocorrelation function of 1st order lag is introduced, and new deterioration factor of correlation of four variables is introduced consecutively. New deterioration factor is an absolute index of deterioration factor. Three cases in which the rolling elements number is nine, twelve and sixteen are examined and compared. Varying N, the number of data, its characteristics are examined. When N is smaller, sensitivity is better. Therefore this parameter can be used as an index for the machine diagnosis of early failure stage especially.

FPN estimation based nonuniformity correction for infrared imaging system

In this paper, to compensate for the fixed pattern noise (FPN) of infrared imaging system, a novel scene-based nonuniformity correction method is proposed based on FPN estimation. The FPN is supposed to be equal to the offset of detectors in IRFPA and is estimated based on the temporal filtering results of adjacent pixel difference. The temporal filters we used are the one order lag filter and mean filter. At the same time, the threshold constraint is introduced to select the candidate pixels of the original images for the estimation of FPN. This leads to the less interference of the details in scenes and the temporarily still scenes, thus our proposed method performs well on the actual scene. Besides this, the low computational complexity, simplicity of implementation and good real-time performance make our proposed method more suitable for hardware implementation. Experiments are conducted with three infrared video sequences to evaluate the performance of our proposed method and other two related methods, the correction results and quality indexes show that the performance of our proposed method is the best among these three methods.

Analysis of the Preference Shift of Customer Brand Selection and its Matrix Structure : Expansion of its Block Matrix to the Third Order Lag and Compression of the Variables

Analysis of the Preference Shift of Customer Brand Selection and its Matrix Structure : Expansion of its Block Matrix to the Third Order Lag and Compression of the Variables