Error Propagation Analysis Research Articles

An Analytical Framework for Error Propagation Effects in Multiprocess Manufacturing

Analysis of multisource errors accompanying process execution and study of the propagation effects of the corresponding multiprocess manufacturing process are the basic prerequisites for optimizing the generation process and improving the quality of the product. This paper proposes an analytical framework for error propagation effects in multiprocess manufacturing, which completely covers error source analysis, mathematical calculation of error propagation accumulation, and description of error propagation effects, which can provide better support for error traceability, error propagation monitoring, and error dissipation in manufacturing production. First of all, establish the process state model into the features of the manufacturing level, analyze the type of multisource error, and its mode of action when executing the process operation; second, establish the mathematical calculation model of error propagation accumulation based on state space equation is established, so as to realize calculation and analysis of error propagation; and finally, establish the link graph and link matrix of error propagation influence in multiprocess manufacturing process are established to further reveal the scope and path of error propagation influence. In this section of the case study, a plate cover part had been taken as an example, the multisource error in its manufacturing was analyzed, and the propagation and accumulation of these error values are obtained by state space and state transition theory. On this basis, the link graph and its corresponding link matrix were used to explicitly describe the error propagation effects during the multiprocess manufacturing of the example part. The example analysis illustrated the proposed error analysis framework could analyze and calculate the multisource error of multiprocess manufacturing and visually describe the error propagation effects, which showed the effectiveness and feasibility of the proposed method framework.

Accuracy of key performance indicators in solar-assisted heating systems due to measurement uncertainties

In this paper, the influence of measurement uncertainties on the key performance indicators fsav and FSC in solar-assisted heating systems is investigated. The impact of temperature, volumetric flow rate, and irradiance sensors with different measurement accuracies is analysed with a combination of Gaussian error propagation and Monte Carlo Analysis. To identify the sensor equipment with best cost–benefit-ratio (BCBR), different sensor combinations are investigated. If fsav and FSC are to be measured, additional sensors must be installed. The resulting costs range from 250€ for an inexpensive equipment to 330€ for recommended BCBR equipment and up to 780€ for the maximum accuracy equipment. For smaller economically dimensioned systems the use of inexpensive sensors results in large uncertainties, e.g. fˆsav=(15.2±13.7)%. The uncertainties for larger systems are significantly lower, e.g. fˆsav=(56.7±6.3)%. This is true as well if better sensors are used. Regardless of the system’s size, with the BCBR sensor equipment the resulting expanded uncertainties can be reduced by 60% (relative) compared to the results with the inexpensive sensor equipment. With maximum accuracy sensor equipment the resulting expanded uncertainties can even be reduced by 77% (relative). The results show the importance of a carefully selected sensor equipment and the influence of the system’s size. Inexpensive sensors can lead to large uncertainty ranges for the important key performance indicators fsav and FSC. Thus, these key figures effectively cannot be used for assessing the performance of a solar-assisted heating system.

Robust two-colour pyrometry uncertainty analysis to acquire spatially-resolved measurements

Two-colour pyrometry (2CP) has been used over several decades to study engine-relevant combustion processes, but results are generally regarded as qualitative or semi-quantitative. In many current 2CP systems, large measurement errors are introduced by parallax because the two measured wavelengths are not from the same line of sight. This work presents a spatially-resolved 2CP system with the objective of quantifying and reducing measurement uncertainty. An optical setup that eliminates parallax in 2CP is used together with pixel-by-pixel calibration of the camera sensor to increase measurement accuracy. Primary uncertainty terms are identified, and an error propagation analysis is performed to compute uncertainties in the final results of soot temperature, soot concentration parameter, KL, and soot mass. These methodologies are applied to investigate an auto-igniting fuel spray in a constant pressure flow rig at diesel-like conditions of high ambient pressure and temperature. Results show bias uncertainty of around 200 K (≈10%) for temperature and about 40%–60% for KL. High uncertainty was found to occur on the diffusion flame front where both optical thickness and soot concentrations are small. However, these uncertain measurement zones with relatively low soot concentrations contribute minimally to the total soot mass present in the reacting jet during the temporal evolution of the flame.

One‐Shot Active Learning for Globally Optimal Battery Electrolyte Conductivity**

AbstractNon‐aqueous aprotic battery electrolytes need to perform well over a wide range of temperatures in practical applications. Herein we present a one‐shot active learning study to find all conductivity optima, confidence bounds, and relating formulation trends in the temperature range from −30 °C to 60 °C. This optimization is enabled by a high‐throughput formulation and characterization setup guided by one‐shot active learning utilizing robust and heavily regularized polynomial regression. Whilst there is an initially good agreement for intermediate and low temperatures, there is a need for the active learning step to improve the model for high temperatures. Optimized electrolyte formulations likely correspond to the highest physically possible conductivities within this formulation system when compared to literature data. A thorough error propagation analysis yields a fidelity assessment of conductivity measurements and electrolyte formulation.

Influence of the Signal-To-Noise Ratio on Variance of Chromophore Concentration Quantification in Broadband Near-Infrared Spectroscopy

This study presented a theoretical or analytical approach to quantify how the signal-to-noise ratio (SNR) of a near infrared spectroscopy (NIRS) device influences the accuracy on calculated changes of oxy-hemoglobin (Δ[HbO]), deoxy-hemoglobin (Δ[HHb]), and oxidized cytochrome c oxidase (Δ[oxCCO]). In theory, all NIRS experimental measurements include variations due to thermal or electrical noise, drifts, and disturbance of the device. Since the computed concentration results are highly associated with device-driven variations, in this study, we applied the error propagation analysis to compute the variability or variance of Δ[HbO], Δ[HHb], and Δ[oxCCO] depending on the system SNR. The quantitative expressions of variance or standard deviations of changes in chromophore concentrations were derived based on the error propagation analysis and the modified Beer-Lambert law. In order to compare and confirm the derived variances versus those from the actual measurements, we conducted two sets of broadband NIRS (bbNIRS) measurements using a solid tissue phantom and the human forearm. A Monte Carlo framework was also executed to simulate the bbNIRS data under two physiological conditions for further confirmation of the theoretical analysis. Finally, the confirmed expression for error propagation was utilized for quantitative analyses to guide optimal selections of wavelength ranges and different wavelength combinations for minimal variances of Δ[HbO], Δ[HHb], and Δ[oxCCO] in actual experiments.

Improve the accuracy of vehicle velocity estimation based on low-cost GPS/IMU by GPS course angle

Vehicle velocity is an important parameter for vehicle dynamics control. Global Positioning System (GPS) and inertial measurement unit (IMU) information can be used for velocity estimation by taking advantage of each other through fusion. However, if GPS velocity is used as the only measurement like classic GPS/INS, it will cause a large velocity estimation error or even divergence. This paper, from the perspective of system observability, proves that the GPS course angle (GCA) plays an important role in vehicle velocity estimation based on low-cost GPS/IMU. Firstly, construct the velocity estimation algorithm in the vehicle coordinate system directly. Then, according to the characteristics of different working conditions, the observability of the system without GCA is fully analyzed from the Lie derivative-based observability proof and the observability basic definition. The results show that the weak observability of the yaw angle is the most serious threat in vehicle velocity estimation. After fusing the GCA, the yaw angle potential divergence can be suppressed and the estimation accuracy of velocity will be improved. Even though roll and pitch are still unobservable under some conditions after augmenting GCA, the error propagation analysis shows that their estimation errors have little effect on velocity estimation, so the accurate estimation of velocity can be guaranteed. Finally, the indispensable of GCA in velocity estimation based on low-cost GPS/IMU is verified by Carsim-Simulink joint simulations and vehicle tests.

UNCERTAINTY MODELING FOR POINT CLOUD-BASED AUTOMATIC INDOOR SCENE RECONSTRUCTION BY STRICT ERROR PROPAGATION ANALYSIS

Abstract. Accurate digital representation of indoor facilities is a key component for the generation of building twins. 3D indoor scenes are often reconstructed from 3D point clouds obtained by various measurement techniques, which usually show different accuracy characteristics. During the reconstruction process, the uncertainties of data and intermediate products propagate into the accuracy of the vectorized model. Although point clouds-based 3D building modeling has been a hot topic of research for at least two decades, a thorough analysis of error propagation for this problem from a geodetic point of view is still underrepresented. In this contribution, we propose an analytical approach to estimate the uncertainty of 3D modeling results using the analytic approach based on first-order Taylor-series expansion. A general model for the input data is established and the uncertainty expressions of all computed products are symbolically derived. We estimate the uncertainty of 3D data fitting, followed by the derivation of vectorized building parameters and their covariance matrices. The results of the theoretical approaches are tested on real data presenting an indoor scene. The practical example is illustrated, thoroughly analysed, and quantified.

Limits of the precision in refractive results after cataract surgery

Background and objectiveIn order to improve refractive results in cataract surgery with an intraocular lens implant, it is important to know the sources of error as well as the limit of this process. Therefore, the objective of the present work is to approximate the theoretical limit in the precision in the refractive result after cataract surgery with the currently available means and to assess the impact of different sources of error in this process. Materials and methodsWe conducted a search of the literature to determine the variability provided by each component of the process. Based on the Barrett Universal-II formula, we performed an error propagation analysis. The theoretical limit was defined as the situation in which the refractive result is only affected by the variability in the parameters introduced in the formula, the tolerance of the intraocular lens and the subjective refraction. ResultsThe main contributors to the error were (1) intraoperative and postoperative variability variables not considered by the formulas (49.33%), (2) postoperative subjective refraction (38.29%), (3) mean keratometry (5.98%) and (4) the variability in the labelling of the power of the intraocular lens (5.09%). The theoretical limit obtained for the intraocular lens calculation with the means available today was 91.9% of the eyes between ±0.50D. ConclusionsWe found a theoretical limit for the intraocular lens calculation of 91.9% of the eyes between ±0.50D. Approaching the precision limit described in the study requires the use of optical biometrics and state-of-the-art formulas, a reproducible surgical technique, and the compensation of systematic errors by adjusting constants.

Límites de la precisión en el resultado refractivo tras la cirugía de cataratas

Background and objectiveIn order to improve refractive results in cataract surgery with an intraocular lens implant, it is important to know the sources of error as well as the limit of this process. Therefore, the objective of the present work is to approximate the theoretical limit in the precision in the refractive result after cataract surgery with the currently available means and to assess the impact of different sources of error in this process. Materials and methodsWe conducted a search of the literature to determine the variability provided by each component of the process. Based on the Barrett Universal-II formula, we performed an error propagation analysis. The theoretical limit was defined as the situation in which the refractive result is only affected by the variability in the parameters introduced in the formula, the tolerance of the intraocular lens and the subjective refraction. ResultsThe main contributors to the error were: 1. Intraoperative and postoperative variability variables not considered by the formulas (49.33%). 2. Postoperative subjective refraction (38.29%). 3. Mean keratometry (5.98%), and 4. the variability in the labelling of the power of the intraocular lens (5.09%). The theoretical limit obtained for the intraocular lens calculation with the means available today was 91.9% of the eyes between + -0.50D. ConclusionsWe found a theoretical limit for the intraocular lens calculation of 91.9% of the eyes between + -0.50D. Approaching the precision limit described in the study requires the use of optical biometrics and state-of-the-art formulas, a reproducible surgical technique, and the compensation of systematic errors by adjusting constants.

Development and validation of a new n-dodecane-n-butanol-PAH reduced mechanism under diesel engine-relevant conditions

In this work, a new n-dodecane-n-butanol-polycyclic aromatic hydrocarbon (PAH) reduced mechanism that consists of 105 species and 584 reactions was developed to model the combustion and soot characteristics of diesel, n-butanol and its blends. The current mechanism was formulated by merging a n-dodecane and PAH reduced mechanism to a n-butanol reduced mechanism that was developed through the direct relation graph with error propagation (DRGEP), isomer lumping and reaction pathway analysis (RPA) methods. Good predictions were obtained when the mechanism was validated against the ignition delay (ID) times, species concentrations in jet-stirred reactor (JSR) and premixed flame and laminar flame speed. Moreover, the non-reacting liquid and vapour penetration lengths of Bu0, Bu20 and Bu40 (0 vol%, 20 vol% and 40 vol% n-butanol blended in n-dodecane) at ambient temperatures of 800 K, 850 K and 900 K were well predicted with a maximum deviation of 4%. The ID and flame lift-off length (FLOL) deviated with a maximum value of 20% and 12%, respectively. As compared to the measurements, the peak soot volume fraction (SVF) of Bu0 fuel at ambient temperatures of 850 K and 900 K were reasonably predicted with maximum deviations of 1.0 ppm and 0.3 ppm, respectively. At higher n-butanol blending ratios and at lower ambient temperatures, soot was reduced significantly due to lower equivalence ratio, lower flame temperature and the high oxygen content which suppressed the formation of soot precursor species.

Construction of reduced chemical mechanisms orientated toward specific applications: a case study of primary reference fuel

Due to the specific prediction requirements in combustion simulations, the reduced chemical mechanism developed focusing on particular applications is usually needed. A systematic method for chemical mechanism reduction orientated toward specific applications is proposed in this work. The reduction process is divided into two parts for large-molecule fuels, including the reduction of the fuel-specific sub-mechanism and the reduction of the C0–C4 sub-mechanisms. In the first part, path sensitivity analysis and global sensitivity analysis are used to identify the key reaction classes in the fuel-specific sub-mechanism, and then the rate of production (ROP) analysis and genetic algorithm are utilised to recognise the representative reactions with the maximum flux in the key reaction classes and optimise the reaction rate coefficients within their uncertainties. For the second part, the directed relation graph with error propagation and sensitivity analysis (DRGEPSA) is employed to reduce the C0–C4 sub-mechanisms. And then, the genetic algorithm with binary variables is applied to further reduce the pathways of the small-molecule reactions targeted at ignition delay times in shock tubes, major species (fuel, O2, CO, and CO2) profiles in jet-stirred reactors, and laminar flame speeds, respectively. Finally, reaction lumping is conducted by identifying the quasi-steady-state (QSS) species. Based on a detailed mechanism of primary reference fuel (PRF) consisting of 2,870 species and 9,233 reactions, three reduced models orientated toward specific applications, including ModelST with 42 species and 82 reactions targeted at the ignition timings in shock tubes (ST), ModelJSR with 43 species and 79 reactions targeted at the major species concentrations in jet-stirred reactors (JSR), and ModelLPF with 41 species and 69 reactions targeted at laminar flame speeds in laminar premixed flames (LPF) are constructed, respectively. The validation results indicate that all the three reduced mechanisms can achieve good predictions in their featured specific applications.

Accurate Statistical BER Analysis of DFE Error Propagation in the Presence of Residual ISI

This brief discusses the limitation of previously published statistical decision feedback equalizer (DFE) models when residual inter-symbol interference (ISI) is present and proposes a method that overcomes this limitation. The paper presents an accurate closed-form expression for the DFE with residual ISI and additive white Gaussian noise (AWGN). The analysis is extended to 4-level pulse amplitude modulation (PAM-4) to cover serial links of current interest. The results verify that the proposed model estimates an accurate bit error rate (BER).

Error and Uncertainty Propagation Analysis on the Model of Containment Leakagerate

Error and Uncertainty Propagation Analysis on the Model of Containment Leakagerate

Density Evolution for Noise Propagation Analysis in Biological Networks

Accurate prediction of noise propagation in biological networks is key to understanding faithful signal propagation in gene networks as well as for designing noise-tolerant synthetic gene circuits. Knowledge on how biological fluctuations propagate up the development ladder of biological systems is currently lacking. Similarly, little research effort has been devoted to the analysis of error propagation in biological networks. To capture and characterize error evolution, this paper considers a Boolean network (BN) model representation of a biological network such that nodes on the graph represent diverse biological entities, e.g., proteins, genes, messenger-RNAs, etc. In addition, the network edges capture the interactions between nodes. By conducting a density evolution analysis on the graphical model based on node functionalities, a recursive closed-form expression for error propagation is derived. Subsequently, the recursive equation allows us to obtain a necessary condition to guarantee noise-error elimination in dynamic discrete gene networks. Our analytical formulations provide a step toward achieving optimal network parameters for resilience against variability or noise in biology.

Development of a reduced multi-component chemical kinetic mechanism for the combustion modelling of diesel-biodiesel-gasoline mixtures

In this study, a compact combined reaction mechanism for diesel-biodiesel-gasoline mixtures (CDBG) is developed, comprising n-heptane, methyl butanoate (MB) and methyl decanoate (MD) as well as toluene and isooctane to represent the combustion characteristics of diesel, biodiesel and gasoline fuels, respectively. The mechanisms are separately reduced prior to combining by means of directed relation graph (DRG), directed relation graphs with error propagation (DRGEP) and full species sensitivity analysis (FSSA). The reduced mechanisms are then combined, and extensive validations are carried out for closed homogenous reactor application under the following conditions: T = 600–1700 K, P = 1–50 atm, and equivalence ratios (Φ) of 0.25–1.5 (156 setups in total). To boost the accuracy of the CDBG mechanism, cross-reaction analysis is performed to identify the important intermediate species and reactions. The identified species and reactions are subsequently integrated into the CDBG mechanism, resulting in significant improvements in ID timings up to 30%, 18% and 16% for the CDBG sub-mechanisms of diesel, biodiesel and gasoline, respectively. In addition, Arrhenius rate constant optimisation is also employed to further improve the ignition behaviour of the proposed kinetic mechanism. The results revealed that the dual implementation of the cross-reaction analysis and Arrhenius rate constant optimisation diminished the maximum associated errors considerably, down to 14.6%, 16.9% and 14.9% for the CDBG sub-mechanisms of diesel, biodiesel and gasoline, respectively. Concisely, the best results achieved at T = 600–1700 K were P = 41 atm and Φ=1, P = 1,4 atm and Φ=1, and P = 50 bar and Φ=0.3 for diesel, biodiesel and gasoline surrogates, respectively.

Reduction and optimization for combustion mechanism of dimethyl ether–air mixtures

AbstractAs an alternative fuel, dimethyl ether (DME) has attracted much attention due to its high efficiency and low emission. In this study, first, a skeletal mechanism of DME is obtained using a directed relation graph with error propagation (DRGEP) and sensitivity analysis (SA). Then the Arrhenius preexponential factors of the selected reactions in the skeletal mechanism are adjusted by the particle swarm optimization (PSO) algorithm to improve the prediction accuracy. Finally, an optimized mechanism with 30 species and 65 elementary reactions is proposed to describe the combustion of DME–air mixtures. This reaction mechanism is validated against the experimental data of ignition delay time, species concentration, and laminar flame speed, covering a wide range of initial temperatures (298–1600 K), pressures (1.0–60 bar), and equivalence ratios (0.5–2.0). Comparing the previous skeletal mechanisms, the optimized mechanism can excellently reproduce the experiment results, especially in the prediction of the ignition delay time of low‐temperature zone and laminar flame speed of high‐pressure conditions. It means that this mechanism corresponds to higher precision and more extensive applicability.

Error propagation and conditioning analysis of DNS data of turbulent viscoelastic channel flows

In the context of drag reduction phenomenon, direct numerical simulation (DNS) of turbulent viscoelastic flows is a very useful tool able to provide information that is not possible with experiments and that can be used for modeling purposes. A rare and challenging task is to provide measures for statistical errors that are present in DNS data. In the present communication, we employ a method to quantify the statistical convergence of the DNS turbulent viscoelastic channel flows from the unbalance on the mean momentum equation. In addition, we conduct a conditioning analysis of the resultant numerical linear system of this problem. We compare results from different research groups. We found that DNS databases of viscoelastic flows can induce high error propagation in the mean velocity. As a consequence, larger sampling times are needed to achieve a statistically converged Reynolds stress tensor. The conditioning analysis has shown that elasticity enhances conditioning. • We discuss the DNS importance for turbulence modeling. • Uncertainty and statistical error are analyzed in the DNS context. • Equations for mean viscoelastic turbulence (VT) are ill-conditioned. • Error propagation in the mean velocity field related to VT is high. • Statistical quantities, like Reynolds stress, in VT need to be more converged.

Automated Transformation of uml/sysml Behavioral Diagrams for Stochastic Error Propagation Analysis of Autonomous Systems

Abstract Modern technical systems consist of heterogeneous components, including mechanical parts, hardware, and the extensive software part that allows the autonomous system operation. The heterogeneity and autonomy require appropriate models that can describe the mutual interaction of the components. uml and sysml are widely accepted candidates for system modeling and model-based analysis in early design phases, including the analysis of reliability properties. uml and sysml models are semiformal. Thus, transformation methods to formal models are required. Recently, we introduced a stochastic dual-graph error propagation model (DEPM). This model captures the control and data flow structures of a system and allows the computation of advanced risk metrics using probabilistic model checking techniques. This article presents a new automated transformation method of an annotated state machine diagram (SMD), extended with activity diagrams (ADs), to a hierarchical DEPM. This method will help reliability engineers to keep error propagation models up to date and ensure their consistency with the available system models. The capabilities and limitations of the transformation algorithm are described in detail and demonstrated on a complete model-based error propagation analysis of an autonomous medical patient table (MPT).

Analytical investigation into error propagation of power spectral density transmissibility (PSDT) based on coherence function

Power spectral density transmissibility (PSDT) has attracted widespread interests because it is insensitive to the nature of excitation and has no demand for measuring the input. The classical spectral estimation procedure is usually subject to measurement and spectral leakage errors, which might cause distortion in the estimation of PSDT. This study investigates how the error of PSD estimation propagates into PSDT estimation based on analytical approximation formulas. Based on perturbation theory in tandem with statistical moments of the ratio of random variables, both first- and second-order asymptotic expressions of the mean and variance of PSDT estimation are derived in terms of coherence functions, PSDT measurements, and the number of averages. Given these theoretical findings, it is further revealed that the variance of PSDT estimation around the system poles approaches zero, and the variances of the magnitude and phase of the mode shape decrease to local minima. The performance of the analytical error propagation formulas is validated through numerical and field test data. Parametric studies into the effects of recording durations, window types, and reference outputs on the statistics of PSDT estimation and mode shape estimation are also conducted.

Regional soft error vulnerability and error propagation analysis for GPGPU applications

Regional soft error vulnerability and error propagation analysis for GPGPU applications