Steady-state Sensitivity Research Articles

Pseudorotation Adjoint-Based Aerodynamic and Aeroacoustic Optimization Method for Isolated Rotors

The present study proposes a pseudorotation adjoint-based aerodynamic and aeroacoustic optimization method for the application on isolated rotors with both accuracy and efficiency. The pseudorotation adjoint-based optimization methodology incorporates two innovative techniques: i) a hybrid computational fluid dynamics–computational aeroacoustics method closely integrating with Reynolds-averaged Navier–Stokes equations under a rotating reference frame within a pseudorotation moving-medium Ffowcs Williams-Hawkings formulation to evaluate aerodynamic performance and tonal noise, and ii) a unified architecture for steady-state adjoint-based sensitivity analyses of both aerodynamics and aeroacoustics leveraging the pseudorotation approach, thereby facilitating effective multi-objective weighted optimizations within one comprehensive framework. The proposed pseudorotation steady adjoint-based optimization method is applied to a bidiscipline optimization problem of rotor blades compared with our previous on-the-fly unsteady adjoint method. Results of the comparative study demonstrate that the pseudorotation steady approach exhibits good agreement with the unsteady approach in predicting aerodynamics and aeroacoustics as well as their sensitivity derivatives. Furthermore, the steady adjoint optimization demonstrates its capability in achieving an optimum rotor design that closely resembles the outcome from unsteady adjoint optimization while exhibiting a 20-fold acceleration in computational time. These results highlight the potential of this proposed pseudorotation adjoint-based optimization method in efficiently exploring fundamental principles governing high aerodynamic performance and low tonal noise emissions for isolated rotors.

Benchmarking methods for computing local sensitivities in ordinary differential equation models at dynamic and steady states.

Estimating parameters of dynamic models from experimental data is a challenging, and often computationally-demanding task. It requires a large number of model simulations and objective function gradient computations, if gradient-based optimization is used. In many cases, steady-state computation is a part of model simulation, either due to steady-state data or an assumption that the system is at steady state at the initial time point. Various methods are available for steady-state and gradient computation. Yet, the most efficient pair of methods (one for steady states, one for gradients) for a particular model is often not clear. In order to facilitate the selection of methods, we explore six method pairs for computing the steady state and sensitivities at steady state using six real-world problems. The method pairs involve numerical integration or Newton's method to compute the steady-state, and-for both forward and adjoint sensitivity analysis-numerical integration or a tailored method to compute the sensitivities at steady-state. Our evaluation shows that all method pairs provide accurate steady-state and gradient values, and that the two method pairs that combine numerical integration for the steady-state with a tailored method for the sensitivities at steady-state were the most robust, and amongst the most computationally-efficient. We also observed that while Newton's method for steady-state computation yields a substantial speedup compared to numerical integration, it may lead to a large number of simulation failures. Overall, our study provides a concise overview across current methods for computing sensitivities at steady state. While our study shows that there is no universally-best method pair, it also provides guidance to modelers in choosing the right methods for a problem at hand.

Characterize the high-temperature steady-state rheological behavior and Arrhenius activation of PEEK via strain rate jump tensile tests

Polyetheretherketone (PEEK) is a high-performance thermoplastic polymer with diverse industrial applications, such as aerospace, automotive, electronics, and medical devices. However, systematic research on its high-temperature rheological characteristics is inadequate. In this study, strain rate jump tensile tests were introduced to examine the steady-state rheology phenomena and strain rate sensitivity of PEEK at four different temperatures and nine different strain rates. Theoretical analysis based on the free volume theory and the Arrhenius law was also carried out to further analyze the transition of PEEK from Newtonian flow to non-Newtonian flow. Results indicate that PEEK materials exhibit a transition from Newtonian flow to non-Newtonian flow similar to metal materials at high temperatures. The transition point from Newtonian flow to non-Newtonian flow is marked by the emergence of steady-state rheology and its characteristic stress. Theoretical analysis demonstrates that the transition of PEEK is in accordance with the Arrhenius low. Moreover, its apparent activation energy (1.42 eV) is significantly lower than that of metal materials (5.28 eV), indicating a lower energy barrier and an easier transition. The strain rate sensitivity index correlates negatively with rising temperatures, especially at lower rates. This study enhances understanding of PEEK's rheological characteristics at high temperatures, aiding the development and application of high-performance thermoplastic materials.

Design of a Steady-State Adjustment Method and Sensitivity Analysis for an ORC System with Plate Heat Exchangers

Design of a Steady-State Adjustment Method and Sensitivity Analysis for an ORC System with Plate Heat Exchangers

Vibration and force properties of an actuator formed from a piezoelectric stack within a frame structure

This paper examines the vibration and force properties of an actuator formed from a piezoelectric stack within a frame structure. Such configuration avoids the use of the traditional “earth-connected” support and allows the convenient attachment of the actuator to structures, such as power transformer tanks. The steady-state sensitivity of the actuator is analyzed, which comprised a linear frequency response function of the actuator system and a steady-state line frequency spectra of the transducer force at the frequency of the input voltage and its odd harmonics. The sensitivity is first analyzed by examining the forces transmitted to a rigid base structure through the stack and two legs of the frame when the actuator is excited by a single-frequency voltage input. The magnitude of the steady-state sensitivity at the frequency of the input voltage is approximately 15 dB higher than that at the other frequencies. The force transmitted through the piezoelectric stack is approximately twice as large as that through the two frame legs and with opposite phase. Next, the properties of transmitted forces when the rigid base structure is replaced by a beam and a plate of infinite size are also investigated. The interaction between the actuator and the elastic base structure has little effect on the magnitudes of the transmitted forces except at the resonace frequency of the actuator structure. However, the induced structural response is greatly affected and should be considered when describing the excitation capacity of the actuator. This capacity could be illustrated by the power flow between the actuator and the base structure and by the spatial distribution of the structural vibration induced by the actuator.

Study of electrochemical biosensor for determination of glucose based on Prussian blue/gold nanoparticles-chitosan nanocomposite film sensing interface

A highly electroactive bilayer composite film sensing interface of Prussian blue (PB)/gold nanoparticles-chitosan (AuNPs-CS) was modified on Au electrode through electrochemical deposition and coating method followed by integrating glucose oxidase (GOx) into the interfacial matrix to fabricate a high-performance glucose biosensor. The excellent electrocatalytic ability of the PB/AuNPs-CS composite film sensing interface for H2O2 was evaluated, which has a broad linear response of 0.01–7.95 mM, with a low detection limit (LOD) 0.269 μM and a high sensitivity of 511.82 μA·mM−1·cm−2. The enhanced electrocatalytic activity of this sensing interface for H2O2 is attributed to the protection from the network CS film to PB and the synergistic effect of PB and AuNPs. Consequently, an electrochemical biosensing interface was constructed with GOx immobilized as a model enzyme. The PB/GOx-AuNPs-CS biosensing nanocomposite film was capable of a fast steady-state response time (within 2 s) and high sensitivity to glucose with a wide linear range of: 0.025–2.00 mM (R 2 = 0.99), with a sensitivity of 40.41 μA·mM−1·cm−2 and a LOD of 1.62 μM; and 2.00–6.50 mM (R 2 = 0.98), with a sensitivity of 8.90 μA·mM−1·cm−2 and a LOD of 7.16 μM. The biosensor has good anti-interference and selectivity, which provides a promising wide linear range platform for clinical blood glucose detection in the future.

Reliability analysis of a two-unit‏ ‏standby system under Marshall–Olkin dependency

PurposeOne of the common approaches to improve systems reliability is using standby redundancy. Although many works are available in the literature on the applications of standby redundancy, the system components are assumed to be independent of each other. But, in reality, the system components can be dependent on one another, causing the failure of each component to affect the failure rate of the remaining active components. In this paper, a standby two-unit system is considered, assuming a dependency between the switch and its associated active component.Design/methodology/approachThis paper assumes that the failures between the switch and its associated active component follow the Marshall–Olkin exponential bivariate exponential distribution. Then, the reliability analysis of the system is done using the continuous-time Markov chain method.FindingsThe derived equations application to determine the system steady-state availability, system reliability and sensitivity analysis on the mean time to failure is demonstrated using a numerical illustration.Originality/valueAll previous models assumed independency between the switch and the associated active unit in the standby redundancy approach. In this paper, the switch and its associated component are assumed to be dependent on each other.

Vertex results for the robust analysis of uncertain biochemical systems

We consider the problem of assessing the sensitivity of uncertain biochemical systems in the presence of input perturbations (either constant or periodic) around a stable steady state. In particular, we propose approaches for the robust sensitivity analysis of systems with uncertain parameters assumed to take values in a hyper-rectangle. We highlight vertex results, which allow us to check whether a property is satisfied for all parameter choices in the hyper-rectangle by simply checking whether it is satisfied for all parameter choices at the vertices of the hyper-rectangle. We show that, for a vast class of systems, including (bio)chemical reaction networks with mass-action kinetics, the system Jacobian has a totally multiaffine structure (namely, all minors of the Jacobian matrix are multiaffine functions of the uncertain parameters), which can be exploited to obtain several vertex results. We consider different problems: robust non-singularity; robust stability of the steady-state; robust steady-state sensitivity analysis, in the case of constant perturbations; robust frequency-response sensitivity analysis, in the presence of periodic perturbations; and robust adaptation analysis. The developed theory is then applied to gain insight into some examples of uncertain biochemical systems, including the incoherent feed-forward loop, the coherent feed-forward loop, the Brusselator oscillator and the Goldbeter oscillator.

Adaptive real-time grid operation via Online Feedback Optimization with sensitivity estimation

In this paper we propose an approach based on an Online Feedback Optimization (OFO) controller with grid input–output sensitivity estimation for real-time grid operation, e.g., at subsecond time scales. The OFO controller uses grid measurements as feedback to update the value of the controllable elements in the grid, and track the solution of a time-varying AC Optimal Power Flow (AC-OPF). Instead of relying on a full grid model, e.g., grid admittance matrix, OFO only requires the steady-state sensitivity relating a change in the controllable inputs, e.g., power injections set-points, to a change in the measured outputs, e.g., voltage magnitudes. Since an inaccurate sensitivity may lead to a model-mismatch and jeopardize the performance, we propose a recursive least-squares estimation that enables OFO to learn the sensitivity from measurements during real-time operation, turning OFO into a model-free approach. We analytically certify the convergence of the proposed OFO with sensitivity estimation, and validate its performance on a simulation using the IEEE 123-bus test feeder, and comparing it against a state-of-the-art OFO with constant sensitivity.

Clinical and Metabolic Characterization of Adults With Type 2 Diabetes by Age in the Glycemia Reduction Approaches in Diabetes: A Comparative Effectiveness Study (GRADE) Cohort

OBJECTIVE Differences in type 2 diabetes phenotype by age are described, but it is not known whether these differences are seen in a more uniformly defined adult population at a common early stage of care. We sought to characterize age-related clinical and metabolic characteristics of adults with type 2 diabetes on metformin monotherapy, prior to treatment intensification. RESEARCH DESIGN AND METHODS In the Glycemia Reduction Approaches in Diabetes: A Comparative Effectiveness Study (GRADE), participants were enrolled who had type 2 diabetes duration <10 years, had HbA1c 6.8–8.5%, and were on metformin monotherapy. Participants were randomly assigned to one of four additional glucose-lowering medications. We compared baseline clinical and metabolic characteristics across age categories (<45, 45 to <55, 55 to <65, and ≥65 years) using ANOVA and Pearson χ2 tests. RESULTS Within the GRADE cohort (n = 5,047), we observed significant differences by age, with younger adults having greater racial diversity, fewer medications for common comorbidities, lower prevalence of CVD, higher weight and BMI, and more pronounced hyperglycemia and diabetic dyslipidemia and with metabolic profile indicating lower insulin sensitivity (inverse fasting insulin [1/(fasting insulin)], HOMA of steady-state insulin sensitivity, Matsuda index) and inadequate β-cell response (oral disposition index) (P < 0.05 across age categories). CONCLUSIONS Clinical and metabolic characteristics of type 2 diabetes differ by age within the GRADE cohort. Younger adults exhibit more prominent obesity-related characteristics, including higher obesity levels and lower insulin sensitivity and β-cell compensation. Given the increasing burden of type 2 diabetes and complications, particularly among younger populations, these age-related distinctions may inform risk factor management approaches and treatment priorities. Further study will determine whether age-related differences impact response to therapy.

The Impact of Pancreatic Head Resection on Blood Glucose Homeostasis in Patients with Chronic Pancreatitis.

Background: Chronic pancreatitis (CP) often leads to recurrent pain as well as exocrine and/or endocrine pancreatic insufficiency. This study aimed to investigate the effect of pancreatic head resections on glucose metabolism in patients with CP. Methods: Patients who underwent pylorus-preserving pancreaticoduodenectomy (PPPD), Whipple procedure (cPD), or duodenum-preserving pancreatic head resection (DPPHR) for CP between January 2011 and December 2020 were retrospectively analyzed with regard to markers of pancreatic endocrine function including steady-state beta cell function (%B), insulin resistance (IR), and insulin sensitivity (%S) according to the updated Homeostasis Model Assessment (HOMA2). Results: Out of 141 pancreatic resections for CP, 43 cases including 31 PPPD, 2 cPD and 10 DPPHR, met the inclusion criteria. Preoperatively, six patients (14%) were normoglycemic (NG), 10 patients (23.2%) had impaired glucose tolerance (IGT) and 27 patients (62.8%) had diabetes mellitus (DM). In each subgroup, no significant changes were observed for HOMA2-%B (NG: p = 0.57; IGT: p = 0.38; DM: p = 0.1), HOMA2-IR (NG: p = 0.41; IGT: p = 0.61; DM: p = 0.18) or HOMA2-%S (NG: p = 0.44; IGT: p = 0.52; DM: p = 0.51) 3 and 12 months after surgery, respectively. Conclusion: Pancreatic head resections for CP, including DPPHR and pancreatoduodenectomies, do not significantly affect glucose metabolism within a follow-up period of 12 months.

Virtual inertia emulation and RoCoF control of a microgrid with high renewable power penetration

High renewable power (RP) penetration in a microgrid (MG) reduces the inertia of the MG. As a result, small load perturbation, or weather dependent fluctuations in RP generation, causes a high rate of change of frequency (RoCoF) and severe frequency instability problems. To cope with such issues, virtual inertia (VI) needs to be emulated in the MG for RoCoF and frequency control of a low-inertia MG. An MG consisting of thermal, wind, and solar photovoltaic power plants has been considered for the present study. In the proposed work, Genetic Algorithm (GA) optimized derivative-type VI control system has been designed considering both inertia and damping in the VI loop along with an energy storage device. The RoCoF and frequency responses of the MG using the proposed VI control strategy have been studied for variations in loads, weather dependent inputs, and MG parameters. Additionally, mathematical analysis has been provided to highlight the significance of adding a VI loop on steady-state stability and sensitivity of the MG. Furthermore, the performance of the proposed controller has been examined by comparing it with numerous pre-existing VI control topologies from recent literature for the same MG.

Overlaid positive and negative feedback loops shape dynamical properties of PhoPQ two-component system.

Bacteria use two-component systems (TCSs) to sense environmental conditions and change gene expression in response to those conditions. To amplify cellular responses, many bacterial TCSs are under positive feedback control, i.e. increase their expression when activated. Escherichia coli Mg2+ -sensing TCS, PhoPQ, in addition to the positive feedback, includes a negative feedback loop via the upregulation of the MgrB protein that inhibits PhoQ. How the interplay of these feedback loops shapes steady-state and dynamical responses of PhoPQ TCS to change in Mg2+ remains poorly understood. In particular, how the presence of MgrB feedback affects the robustness of PhoPQ response to overexpression of TCS is unclear. It is also unclear why the steady-state response to decreasing Mg2+ is biphasic, i.e. plateaus over a range of Mg2+ concentrations, and then increases again at growth-limiting Mg2+. In this study, we use mathematical modeling to identify potential mechanisms behind these experimentally observed dynamical properties. The results make experimentally testable predictions for the regime with response robustness and propose a novel explanation of biphasic response constraining the mechanisms for modulation of PhoQ activity by Mg2+ and MgrB. Finally, we show how the interplay of positive and negative feedback loops affects the network's steady-state sensitivity and response dynamics. In the absence of MgrB feedback, the model predicts oscillations thereby suggesting a general mechanism of oscillatory or pulsatile dynamics in autoregulated TCSs. These results improve the understanding of TCS signaling and other networks with overlaid positive and negative feedback.

Circadian Potency Spectrum with Extended Exposure to Polychromatic White LED Light under Workplace Conditions.

Electric light has enabled humans to conquer the night, but light exposure at night can disrupt the circadian timing system and is associated with a diverse range of health disorders. To provide adequate lighting for visual tasks without disrupting the human circadian timing system, a precise definition of circadian spectral sensitivity is required. Prior attempts to define the circadian spectral sensitivity curve have used short (≤90-min) monochromatic light exposures in dark-adapted human subjects or in vitro dark-adapted isolated retina or melanopsin. Several lines of evidence suggest that these dark-adapted circadian spectral sensitivity curves, in addition to 430- to 499-nm (blue) wavelength sensitivity, may include transient 400- to 429-nm (violet) and 500- to 560-nm (green) components mediated by cone- and rod-originated extrinsic inputs to intrinsically photosensitive retinal ganglion cells (ipRGCs), which decay over the first 2 h of extended light exposure. To test the hypothesis that the human circadian spectral sensitivity in light-adapted conditions may have a narrower, predominantly blue, sensitivity, we used 12-h continuous exposures of light-adapted healthy human subjects to 6 polychromatic white light-emitting diode (LED) light sources with diverse spectral power distributions at recommended workplace levels of illumination (540 lux) to determine their effect on the area under curve of the overnight (2000–0800 h) salivary melatonin. We derived a narrow steady-state human Circadian Potency spectral sensitivity curve with a peak at 477 nm and a full-width half-maximum of 438 to 493 nm. This light-adapted Circadian Potency spectral sensitivity permits the development of spectrally engineered LED light sources to minimize circadian disruption and address the health risks of light exposure at night in our 24/7 society, by alternating between daytime circadian stimulatory white light spectra and nocturnal circadian protective white light spectra.

Stopped-Flow Calcium Kinetics of Hypertrophic Cardiomyopathy-Associated Troponin T Mutations

Hypertrophic cardiomyopathy (HCM) is a complex genetic disorder of the cardiac sarcomere affecting 1/500 individuals worldwide. The cardiac thin filament (CTF) protein, cardiac troponin T (cTnT), is known to play a critical role in the regulation of contraction, and mutations in cTnT often cause HCM. This study focuses on 4 HCM-causing, clinically relevant point mutations located within the cTnT N-terminus (R92L/Q/W and I79N) which are each associated with distinct phenotypes and disease severity. Despite this, they exhibit comparable changes in steady-state calcium sensitivity of both force generation and myosin ATPase activity. Thus, we monitored the rates of calcium association to and dissociation from IAANS-labeled, Cys-substituted cardiac troponin C in CTFs to explain the comparable changes in steady-state calcium sensitivity. We and others previously characterized mutation-specific differences in calcium dissociation rates for the R92 mutations in CTFs. I79N CTFs significantly increased the rate of calcium dissociation from 116.0±3.2s−1 measured in WT CTFs to 136.1±6.1s−1. The observed calcium association rates to WT, R92L, R92W, and I79N CTFs were measured over a range of calcium concentrations (2.5µM-20µM) and were found to be 9.88±2.051 x106 M−1s−1, 9.141±1.94 x106 M−1s−1, 31.37±2.948 x106 M−1s−1, and 28.2±2.736 x106 M−1s−1, respectively. Both I79N and R92W, but not R92L, significantly increased the rate of calcium association compared to WT CTFs. Furthermore, both I79N and R92W, but not R92L, trend with increased responsiveness to artificially evoked calcium transients compared to WT. These data show that in addition to changing the rate of calcium dissociation, mutations in cTnT can significantly alter the rate of calcium association to affect CTF calcium sensitivity. Together this suggests that alterations in CTF calcium kinetics may represent a highly mutation-specific mechanism of disease initiation and are thus a target for potential therapeutic intervention.

Piezoresistive Carbon Nanofiber-Based Cilia-Inspired Flow Sensor.

Evolving over millions of years, hair-like natural flow sensors called cilia, which are found in fish, crickets, spiders, and inner ear cochlea, have achieved high resolution and sensitivity in flow sensing. In the pursuit of achieving such exceptional flow sensing performance in artificial sensors, researchers in the past have attempted to mimic the material, morphological, and functional properties of biological cilia sensors, to develop MEMS-based artificial cilia flow sensors. However, the fabrication of bio-inspired artificial cilia sensors involves complex and cumbersome micromachining techniques that lay constraints on the choice of materials, and prolongs the time taken to research, design, and fabricate new and novel designs, subsequently increasing the time-to-market. In this work, we establish a novel process flow for fabricating inexpensive, yet highly sensitive, cilia-inspired flow sensors. The artificial cilia flow sensor presented here, features a cilia-inspired high-aspect-ratio titanium pillar on an electrospun carbon nanofiber (CNF) sensing membrane. Tip displacement response calibration experiments conducted on the artificial cilia flow sensor demonstrated a lower detection threshold of 50 µm. Furthermore, flow calibration experiments conducted on the sensor revealed a steady-state airflow sensitivity of 6.16 mV/(m s−1) and an oscillatory flow sensitivity of 26 mV/(m s−1), with a lower detection threshold limit of 12.1 mm/s in the case of oscillatory flows. The flow sensing calibration experiments establish the feasibility of the proposed method for developing inexpensive, yet sensitive, flow sensors; which will be useful for applications involving precise flow monitoring in microfluidic devices, precise air/oxygen intake monitoring for hypoxic patients, and other biomedical devices tailored for intravenous drip/urine flow monitoring. In addition, this work also establishes the applicability of CNFs as novel sensing elements in MEMS devices and flexible sensors.

Calculation and analysis of the steady-state line ampacity weather sensitivity coefficients

The continuous increase in electrical power demand entails the need for larger ratings of overhead lines. For spatial, economic and ecological reasons, contemporary solutions are focused on incrementing the ratings of existing lines. One of these solutions is the real-time determination of line ampacity according to the measured or predicted weather and/or line parameters. The paper is focused on a novel calculation procedure and analysis of the steady-state line ampacity (SSLA) weather sensitivity coefficients (WSCs). The calculation of WSCs is based on the sensitivity analysis of the methodology for the SSLA given in Cigre N° 601 Technical Brochure. On the one hand these WSCs allow a fast estimate of the potential in the introduction of real-time ampacity calculation concept. On the other hand they give a good basis on the requirements for the measurement equipment installed in contemporary dynamical line rating systems (DLRSs). The interrelations between the WSCs and the SSLA are investigated using correlation and regression analysis. Finally, according to the typical design parameters of overhead lines the WSCs and their interrelations with the SSLA are calculated and analysed for typical aluminium steel-reinforced conductors (ACSRs) present in the Croatian transmission system.

Modelling and investigating the impact of asynchronous inertia of induction motor on power system frequency response

Besides synchronous inertia, asynchronous inertia of induction motor also widely exists in power systems, but its effect on system frequency response has not been well studied. A simplified transfer function model of induction motor is derived based on the detailed model. The model is regarded as a decaying proportion of the consumed power to the frequency deviation. Three key features of the model are the immediate proportion, the steady-state proportion and the decaying time constant. Their affecting factors are also studied. Then the model is added to the system frequency response model to study the effect of induction motor. There are three key factors of induction motor affecting frequency response, the sensitivity of electromagnetic torque to slip, the sensitivity of mechanical load torque to rotor speed, and the inertia. Their effects are analytically analyzed. The asynchronous inertia only affects the maximum frequency deviation, and a large inertia reduces the maximum frequency deviation. However, it is acceptable to neglect the asynchronous inertia and represent the induction motor with static model considering steady-state frequency sensitivity. The derived conclusions are validated with simulation results.

A finite state projection method for steady-state sensitivity analysis of stochastic reaction networks.

Consider the standard stochastic reaction network model where the dynamics is given by a continuous-time Markov chain over a discrete lattice. For such models, estimation of parameter sensitivities is an important problem, but the existing computational approaches to solve this problem usually require time-consuming Monte Carlo simulations of the reaction dynamics. Therefore, these simulation-based approaches can only be expected to work over finite time-intervals, while it is often of interest in applications to examine the sensitivity values at the steady-state after the Markov chain has relaxed to its stationary distribution. The aim of this paper is to present a computational method for the estimation of steady-state parameter sensitivities, which instead of using simulations relies on the recently developed stationary finite state projection algorithm [Gupta et al., J. Chem. Phys. 147, 154101 (2017)] that provides an accurate estimate of the stationary distribution at a fixed set of parameters. We show that sensitivity values at these parameters can be estimated from the solution of a Poisson equation associated with the infinitesimal generator of the Markov chain. We develop an approach to numerically solve the Poisson equation, and this yields an efficient estimator for steady-state parameter sensitivities. We illustrate this method using several examples.

STATSSCANDLEPLOT: A NEW WAY OF MONITORING OPERATIONAL PERFORMANCE INDICATORS

ABSTRACT Operational KPIs play an extremely important role in the process industry, aiding in decision making. However, they need to be reliably calculated to be representative. The present work presents a schematic methodology for the calculation of these KPIs, including techniques of steady-state detection, denoising, error propagation and sensitivity analysis, presented, as far as it is known, in the form of a new graphical tool proposed by the authors named StatSSCandlePlot. The methodology was applied in a real case study of a gas fired boiler in which the indicator studied was its efficiency evaluated by the Stack Loss Method. From the StatSSCandlePlot it was possible to identify the trends of the indicator, the portion of each window in the steady-state, the values to be considered from the indicator and, in a complementary way, to identify the variable that most influences the variation of the indicator, through the sensitivity analysis.