Fourier Amplitude Sensitivity Test Method Research Articles

Twinning quality sensors in wastewater treatment process via optimized echo state network-based soft sensors

The presence of a large amount of quality-related but hard-to-measure variables usually makes effective monitoring of industrial processes difficult, and even impossible. Soft computing techniques and digital twins can revolutionize standard approaches to solve this issue, even though industrial data are frustrated by nonlinearity, disturbances, and dynamic behaviors. In this light, this paper proposes a data-driven soft sensor with the help of the Fourier amplitude sensitivity test (FAST) and improved probabilistic regularized echo state network (IPRESN), then to twin the quality hardware sensors. Within this framework, the initial step is to rely on the FAST method to measure the collaborated importance of multiple process variables with respect to each quality variable. This quantification facilitates the selection of auxiliary variables for the training of IPRESN. Furthermore, a probabilistic regularization method is learned to improve the robust performance of the echo state network (ESN) by re-designing a new objective function to minimize the mean and variance of the modeling error. Additionally, the whale optimization algorithm (WOA) is improved and then used to optimize the critical hyper-parameters of ESN, thus mitigating the risks associated with suboptimal hyperparameter selection. The effectiveness of the proposed method is verified through a Benchmark Simulation Model 2 (BSM2) and a full-scale wastewater treatment plant data set. The findings show the potential of the proposed method in facilitating digital twin implementations for hardware sensors.

Data-driven multi-step robust prediction of TBM attitude using a hybrid deep learning approach

A robust multi-step TBM attitude prediction approach named convolutional gated-recurrent-unit neural network (C-GRU) is proposed in this research and the random balance design Fourier amplitude sensitivity test method is used for sensitivity analysis to reveal the interaction between input and output of the C-GRU model. A tunnel construction project in Singapore is taken as an example to prove the robustness and effectiveness of the proposed approach. Results indicate that the length of the output sequence of the model can maintain high robustness and accuracy within 21 steps. In the 21-step prediction, the highest R2 can reach 0.9652 while the mean R2 is 0.9004 even though some attitude parameter is with large fluctuations. Each step in the 21-step prediction can maintain a stable accuracy. The data of the past 11 time steps of the TBM attitude parameters are the most sensitive. The proposed method has higher accuracy and robustness than state-of-art time-series based methods.

Global sensitivity analysis of hydrodynamic lubrication performance for textured surfaces

The computational model of textured surfaces is highly nonlinear, and the texturing parameters interact with each other. The Fourier Amplitude Sensitivity Test(FAST) method was introduced to calculate the first-order sensitivity indices of texturing parameters to the tribological characteristics. Results show that both the inlet suction and the cumulative effect influence the tribological performance, but which mechanism plays the leading role is related to the convergence ratio. Besides, the texture density along the velocity direction is the most crucial geometric parameter; the effects of the cell size and the bottom profile are negligible. The sensitivity indices provide a novel perspective to quantify the influence of input on the output and the FAST method proved ideally suited to the texturing model.

Dynamic performance and sensitivity of grid-connected hydropower station under uncertain disturbance

The grid-connected operating condition of hydropower station is a common operation mode to provide electric energy for the load side. This paper investigates the dynamic performance and sensitivity of grid-connected hydropower station (GCHS) under uncertain disturbance. Firstly, the nonlinear uncertain model of GCHS under uncertain disturbance is established. Then, the dynamic performance of GCHS is studied when the governor parameters change under certain step disturbance, periodic disturbance and uncertain random disturbance, respectively. Finally, based on the sensitivity index of the uncertain output obtained from the extended Fourier amplitude sensitivity test method, the sensitivity of the uncertain random disturbance at different input positions is studied. The results indicate that the GCHS under periodic disturbances or random disturbances have more complex dynamic performance than that under certain step disturbance. Under periodic disturbance, the forced oscillations and high frequency resonances are generated in dynamic response of GCHS. Under the uncertain random disturbance, the system of GCHS always presents random oscillation. The state variables q H , z, qP, y, x s , x t , and δ of GCHS are the most sensitive to uncertain disturbances, which are introduced at the generator or surge tank. The uncertain disturbances have significant interaction on the dynamic response of GCHS.

Weight Loss Function for the Cooperative Inversion of Atmospheric Duct Parameters

Low-altitude atmospheric ducts are abnormal atmospheric phenomena in the troposphere, impacting the operation of microwave or ultrashort wave radio systems. Therefore, the real-time acquisition of low-altitude atmospheric duct parameters is essential to ensure the successful operation of radio systems. Remote sensing methods based on deep learning are, presently, the most important tools to infer duct parameters. In a traditional deep learning loss function, different duct parameters adopt the same weight coefficient. This study establishes a weight loss function and proposes a method for determining the weight coefficient based on the extended Fourier amplitude sensitivity test method. Based on Global Navigation Satellite System (GNSS) occultation signals, the cooperative inversion model of atmospheric duct parameters is established. Test results show that our proposed loss function was feasible, effective, and yielded a higher inversion accuracy than the traditional loss function.

Assembly deviation modelling to predict and trace the geometric accuracy of the precision motion system of a CNC machine tool

Geometric accuracy is the direct embodiment of the assembly deviation of a precision motion system. This paper proposes a novel methodology for predicting the geometric accuracy induced by assembly deviation of a precision motion system and tracing the sensitivity of the assembly deviation with respect to geometric accuracy terms. The small displacement torsor is first characterized as the periodic function of the assembly deviation and dimension parameters of the components of ball-screw feeding system, the vector constraint relationship of the parallel assembly of the feeding system is established, and a spatial propagate model of the assembly deviation for the feeding system is then constructed. A random balance design and Fourier amplitude sensitivity test method are introduced to trace the effect of each assembly feature on the geometric accuracy. The experiments were performed on a single-axis feeding system to verify the effectiveness of the proposed method. This method has the advantage that the mapping relationship between the assembly deviation and geometric accuracy with respect to the instructed position is quantified, and the assembly and adjustment is pertinent to the traceability analysis. The model has the potential to accurately allocate and maintain the machining centre.

Global sensitivity analysis of wheat grain yield and quality and the related process variables from the DSSAT-CERES model based on the extended Fourier Amplitude Sensitivity Test method

A crop growth model, integrating genotype, environment, and management factor, was developed to serve as an analytical tool to study the influence of these factors on crop growth, production, and agricultural planning. A major challenge of model application is the optimization and calibration of a considerable number of parameters. Sensitivity analysis (SA) has become an effective method to identify the importance of various parameters. In this study, the extended Fourier Amplitude Sensitivity Test (EFAST) approach was used to evaluate the sensitivity of the DSSAT-CERES model output responses of interest to 39 crop genotype parameters and six soil parameters. The outputs for the SA included grain yield and quality (take grain protein content (GPC) as an indicator) at maturity stage, as well as leaf area index, aboveground biomass, and aboveground nitrogen accumulation at the critical process variables. The key results showed that: (1) the influence of parameter bounds on the sensitivity results was slight and less than the impacts from the significance of the parameters themselves; (2) the sensitivity parameters of grain yield and GPC were different, and the sensitivity of the interactions between parameters to GPC was greater than those between the parameters to grain yield; and (3) the sensitivity analyses of some process variables, including leaf area index, aboveground biomass, and aboveground nitrogen accumulation, should be performed differently. Finally, some parameters, which improve the model's structure and the accuracy of the process simulation, should not be ignored when maturity output as an objective variable is studied.

Global sensitivity analysis of static characteristics of tilting-pad journal bearing to manufacturing tolerances

A tiny difference between nominal dimension and actual processing dimension in the range of manufacturing tolerance can vary the performance of journal bearing. For minimizing this variation, sensitivity analysis is usually conducted. In present paper, the variance-based global sensitivity analysis was introduced to deal with the uncertainty quantification problem for a five-pad journal bearing. By using Fourier Amplitude Sensitivity Test (FAST) method, the first-order sensitivity indices of static characteristics including capacity, power loss and inlet flow were analyzed and evaluated for five normal distributed processing parameters: pad internal radius, shaft radius, pivot radius, pivot position and pad angular extent. The FAST method was proved perfectly suited to the bearing model. The quantitative sensitivities of output to each input parameter were obtained.

Global sensitivity analysis of the APSIM-Oryza rice growth model under different environmental conditions

This study conducted the global sensitivity analysis of the APSIM-Oryza rice growth model under eight climate conditions and two CO2 levels using the extended Fourier Amplitude Sensitivity Test method. Two output variables (i.e. total aboveground dry matter WAGT and dry weight of storage organs WSO) and twenty parameters were analyzed. The ±30% and ±50% perturbations of base values were used as the ranges of parameter variation, and local fertilization and irrigation managements were considered. Results showed that the influential parameters were the same under different environmental conditions, but their orders were often different. Climate conditions had obvious influence on the sensitivity index of several parameters (e.g. RGRLMX, WGRMX and SPGF). In particular, the sensitivity index of RGRLMX was larger under cold climate than under warm climate. Differences also exist for parameter sensitivity of early and late rice in the same site. The CO2 concentration did not have much influence on the results of sensitivity analysis. The range of parameter variation affected the stability of sensitivity analysis results, but the main conclusions were consistent between the results obtained from the ±30% perturbation and those obtained the ±50% perturbation in this study. Compared with existing studies, our study performed the sensitivity analysis of APSIM-Oryza under more environmental conditions, thereby providing more comprehensive insights into the model and its parameters.

Global Sensitivity Analysis of Large Reaction Mechanisms Using Fourier Amplitude Sensitivity Test

Global sensitivity analysis (GSA) of large chemical reaction mechanisms remains a challenge since the model with uncertainties in the large number of input parameters provides large dimension of input parameter space and tends to be difficult to evaluate the effect of input parameters on model outputs. In this paper, a criterion for frequency selection to input parameter is proposed so that Fourier amplitude sensitivity test (FAST) method can evaluate the complex model with a low sample size. This developed FAST method can establish the relationship between the number of input parameters and sample size needed to measure sensitivity indices with high accuracy. The performance of this FAST method which can allow both the qualitative and quantitative analysis of complex systems is validated by a H2/air combustion model and a CH4/air combustion model. This FAST method is also compared with other GSA methods to illustrate the features of this FAST method. The results show that FAST method can evaluate the reaction systems with low sample size, and the sensitivity indices obtained from the FAST method can provide more important information which the variance-based GSA methods cannot obtain. FAST method can be a remarkably effective tool for the modelling and diagnosis of large chemical reaction.

Developing a robust assessment system for the passive design approach in the green building rating scheme of Hong Kong

This paper proposed a renovated passive design assessment system for green building labelling based on robust energy end-use statistics, different global sensitivity analysis methods, modelling experiments and a detailed case study. The developed system is only applied to cooling and lighting related criteria, which are mainly influenced by selected passive design strategies. After a preliminary definition of the assessment framework and total available credits, the priorities of different sub-criteria are derived from sensitivity analyses of a generic building model with screening-based, variance-based and regression methods. Adjustment of assessment criteria is also performed according to significance tests and post optimization analyses. Furthermore, performance and grading scales are formulated with baseline requirements, optimization results and local sensitivity analyses. Eventually, the FAST (Fourier Amplitude Sensitivity Test) method is proved to generate the most appropriate weighting system considering the consistence of the credit prediction with the traditional whole building simulation approach. Findings from this research can guide decision-makers in the construction industry to obtain an optimized preliminary design by properly allocating resources and investments under a prescriptive evaluation approach starting from the early planning stage. The research design can also be applied to determine the assessment system for other performance-based criteria in a green building assessment scheme.

Key geometric error extraction of machine tool based on extended Fourier amplitude sensitivity test method

Machining accuracy is a very important index to measure the performance of NC machine tools, and how to improve the machining accuracy grabs the attention of both manufacturers and users. Since the geometric errors are intercoupling and are one of the main factors affecting machining accuracy of machine tools, in this paper, a new method for extracting key geometric errors based on the screw theory and extended Fourier amplitude sensitivity test (EFAST) method was proposed. First, screw theory was introduced, and the machining accuracy modeling of a three-axis vertical machining center (VMC) was established. Then, in order to analyze the coupling effects between geometric errors by high-dimensional nonlinear model, EFAST global sensitivity analysis method was adopted to help in extracting the main geometric errors. An illustration example on a three-axis VMC shows that the proposed method is effective and can be helpful to improve the geometric accuracy of machine tool.

Accurate evaluation of sensitivity for calibration between a LiDAR and a panoramic camera used for remote sensing

Computer-based reconstruction models can be used to approximate urban environments. These models are usually based on several mathematical approximations and the usage of different sensors, which implies dependency on many variables. The sensitivity analysis presented in this paper is used to weigh the relative importance of each uncertainty contributor into the calibration of a panoramic camera–LiDAR system. Both sensors are used for three-dimensional urban reconstruction. Simulated and experimental tests were conducted. For the simulated tests we analyze and compare the calibration parameters using the Monte Carlo and Latin hypercube sampling techniques. Sensitivity analysis for each variable involved into the calibration was computed by the Sobol method, which is based on the analysis of the variance breakdown, and the Fourier amplitude sensitivity test method, which is based on Fourier’s analysis. Sensitivity analysis is an essential tool in simulation modeling and for performing error propagation assessments.

Global sensitivity analysis of analytical vibroacoustic transmission models

Noise reduction issues arise in many engineering problems. One typical vibroacoustic problem is the transmission loss (TL) optimisation and control. The TL depends mainly on the mechanical parameters of the considered media. At early stages of the design, such parameters are not well known. Decision making tools are therefore needed to tackle this issue. In this paper, we consider the use of the Fourier Amplitude Sensitivity Test (FAST) for the analysis of the impact of mechanical parameters on features of interest. FAST is implemented with several structural configurations. FAST method is used to estimate the relative influence of the model parameters while assuming some uncertainty or variability on their values. The method offers a way to synthesize the results of a multiparametric analysis with large variability. Results are presented for transmission loss of isotropic, orthotropic and sandwich plates excited by a diffuse field on one side. Qualitative trends found to agree with the physical expectation. Design rules can then be set up for vibroacoustic indicators. The case of a sandwich plate is taken as an example of the use of this method inside an optimisation process and for uncertainty quantification.

Global Quantitative Sensitivity Analysis and Compensation of Geometric Errors of CNC Machine Tool

A quantitative analysis to identify the key geometric error elements and their coupling is the prerequisite and foundation for improving the precision of machine tools. The purpose of this paper is to identify key geometric error elements and compensate for geometric errors accordingly. The geometric error model of three-axis machine tool is built on the basis of multibody system theory; and the quantitative global sensitivity analysis (GSA) model of geometric error elements is constructed by using extended Fourier amplitude sensitivity test method. The crucial geometric errors are identified; and stochastic characteristics of geometric errors are taken into consideration in the formulation of building up the compensation strategy. The validity of geometric error compensation based on sensitivity analysis is verified on a high-precision three-axis machine tool with open CNC system. The experimental results show that the average compensation rates along theX,Y, andZdirections are 59.8%, 65.5%, and 73.5%, respectively. The methods of sensitivity analysis and geometric errors compensation presented in this paper are suitable for identifying the key geometric errors and improving the precision of CNC machine tools effectively.

Comparison of Sensitivity Analysis Methods in Building Energy Assessment

Sensitivity analysis is an important tool in building energy assessment to determine the key factors influencing energy use or carbon emissions for buildings. This research is focused on comparing the characteristics of four global sensitivity analysis: SRC (standardized regression coefficient), Morris design, extended FAST (Fourier Amplitude Sensitivity Test) and TGP (treed Gaussian process) method. A retail building located at Harbin (China) is used as a case study to demonstrate the advantages and drawbacks for these four methods. The results indicate that the TGP method (one of meta-modelling approaches) is the best choice in terms of both accuracy and computationally cost. Note that the TGP method needs more time to calculate the sensitivity index although it needs only moderate time for running building energy models. At least two fundamentally different methods for sensitivity analysis are recommended to be performed to provide more robust results in building energy assessment.

Thermal Behavior of Green Roof in Reunion Island: Contribution Towards a Net Zero Building

A green roof is an option for improving a building thermal comfort. The investigation is here performed within the specific climate context of Reunion Island in south hemisphere. This type of roof system involves choice difficulties for plant species that are more favorable to establish that comfort.The objective of this work is to simulate the dynamic behavior of this system towards external requests in wet tropical zones and vis-à-vis influences of certain number of physical parameters related to this system.As long as possible, authors used the electrical analogy method to establish a mathematical model associated to the studied system. Based on this model, a Matlab computing code was finalized. Weather data of Reunion Island were used for simulations; the green roof potential and benefit were highlighted by surveying the temperature gain and the heat flux crossing the roof as well as the energy saving performance. Furthermore, the energy consumption being surveyed while doing sensitivity analysis with Fourier Amplitude Sensitivity Test method, the most influential parameters of the model were identified.Full scale experimental results are provided and consisting in monitoring green roof on the top of a public building. According to the results, we can assert that the green roof decreases heat flux entering through the roof during the day and restrains the restoration of accumulated heat at night. Indeed, the support on which the plantation ground bases affects the building thermal insulation.The experimental data are also conducted to prove the effectiveness of thermal insulation by green roofs in reducing temperature in the building between 5̊C and 7̊C in relation to plants type and the canopy Leaf Area Index (LAI).A comparison of experimental values and model results is done. Among other uses, this code can be used as a tool for choosing the plants and the drain materials to be experimented on the green roof. The results offer hints to optimize the design and thermal performance of extensive green roofs.

Modeling and Global Sensitivity Analysis of a Solar Powered Air Cooling System Using Liquid Desiccant

Solar energy technology is an option for energy saving in building air conditioning. A theoretical investigation of an open cycle solar air cooling system using aqueous Lithium Chloride solution as liquid desiccant is presented in this paper. The purpose of this work is to analyze the influences of both internal loads and external forcing, on the studied system by developing a computational code related to its mathematical model. The simulation results justify the choice of the system design. Indeed, it was highlighted that the higher is the outdoor temperature; the better is the coefficient of performance (COP) of the system. Furthermore, a global sensitivity analysis of the system model, achieved using Fourier Amplitude Sensitivity Test method, allowed us to identify the most influential factors that were ranked in a decreasing order of their influence degree on the system COP. Hence, key factors to be controlled for improving the system overall performance are specified.

A new approach to visualizing time-varying sensitivity indices for environmental model diagnostics across evaluation time-scales

Assessing the time-varying sensitivity of environmental models has become a common approach to understand both the value of different data periods for estimating specific parameters, and as part of a diagnostic analysis of the model structure itself (i.e. whether dominant processes are emerging in the model at the right times and over the appropriate time periods). It is not straightforward to visualize these results though, given that the window size over which the time-varying sensitivity is best integrated generally varies for different parameters. In this short communication we present a new approach to visualizing such time-varying sensitivity across time scales of integration. As a case study, we estimate first order sensitivity indices with the FAST (Fourier Amplitude Sensitivity Test) method for a typical conceptual rainfall–runoff model. The resulting plots can guide data selection for model calibration, support diagnostic model evaluation and help to define the timing and length of spot gauging campaigns in places where long-term calibration data are not yet available.

Parameter sensitivity analysis of crop growth models based on the extended Fourier Amplitude Sensitivity Test method

Sensitivity analysis (SA) has become a basic tool for the understanding, application and development of models. However, in the past, little attention has been paid to the effects of the parameter sample size and parameter variation range on the parameter SA and its temporal properties. In this paper, the corn crop planted in 2008 in the Yingke Oasis of northwest China is simulated based on meteorological observation data for the inputs and statistical data for the parameters. Furthermore, using the extended Fourier Amplitude Sensitivity (EFAST) algorithm, SA is performed on the 47 crop parameters of the WOrld FOod STudies (WOFOST) crop growth models. A deep analysis is conducted, including the effects of the parameter sample size and variation range on the parameter SA, the temporal properties and the multivariable output issues of SA. The results show that sample size highly affects the convergence of the sensitivity indices. Two types of parameter variation ranges are used for the analysis, and the results show that the sensitive parameters of the two parameter spaces are distinctly different. In addition, taking the storage organ biomasses at the different growth stages as the objective output, the time-dependent characteristics of the parameter sensitivity are discussed. The results show that several sensitive parameters exist in the grain biomass throughout the entire development stage. In addition, analyzing the twelve sensitive parameters has proven that although certain parameters have no effect on the final yield, they play key roles in certain growth stages, and the importance of these parameters gradually increases. Finally, the sensitivity analyses of different state variable outputs are performed, including the biomass, yield, leaf area index, and transpiration coefficient. The results suggest that the sensitive parameters of various variable processes differ. This study highlights the importance of considering multiple characteristics of the model parameters and the responses of the models in specific phenological stages.