Output Error Model Research Articles

Code-Aware Prompting: A Study of Coverage-Guided Test Generation in Regression Setting using LLM

Testing plays a pivotal role in ensuring software quality, yet conventional Search Based Software Testing (SBST) methods often struggle with complex software units, achieving suboptimal test coverage. Recent work using large language models (LLMs) for test generation have focused on improving generation quality through optimizing the test generation context and correcting errors in model outputs, but use fixed prompting strategies that prompt the model to generate tests without additional guidance. As a result LLM-generated testsuites still suffer from low coverage. In this paper, we present SymPrompt, a code-aware prompting strategy for LLMs in test generation. SymPrompt’s approach is based on recent work that demonstrates LLMs can solve more complex logical problems when prompted to reason about the problem in a multi-step fashion. We apply this methodology to test generation by deconstructing the testsuite generation process into a multi-stage sequence, each of which is driven by a specific prompt aligned with the execution paths of the method under test, and exposing relevant type and dependency focal context to the model. Our approach enables pretrained LLMs to generate more complete test cases without any additional training. We implement SymPrompt using the TreeSitter parsing framework and evaluate on a benchmark challenging methods from open source Python projects. SymPrompt enhances correct test generations by a factor of 5 and bolsters relative coverage by 26% for CodeGen2. Notably, when applied to GPT-4, SymPrompt improves coverage by over 2x compared to baseline prompting strategies.

The implementation of a proposed deep-learning algorithm to classify music genres

Abstract To improve the classification effect of music genres in the digital music era, the article employs deep-learning algorithms to improve the performance of the classification of music genres. An auxiliary (estimated) model is constructed to estimate the amount of unmeasured data in the dual-rate system to enhance the recognition effect of music features. Moreover, a dual-rate output error model to identify such impacts is proposed to eliminate the impact of corrupt data caused by the estimation, which eventually leads to the further improvement of the proposed model called dual-rate multi-innovation forgetting gradient algorithm based on the auxiliary model. In addition, the article employs linear time-varying forgetting factors to improve the stability of the system, advances the recognition effect of music features through enhancement processing, and combines a deep-learning algorithm to construct a classification system of music genres. The result shows that the classification of the music genre system based on a deep-learning algorithm has a good music genre classification effect.

Identification of heat exchanger process through Hammerstein and polynomial models

Process industries extensively use heat exchangers in their operations, playing a crucial role in various sectors by facilitating efficient heat transfer, conserving energy, and reducing operational costs. This paper focuses on identifying and validating the system model, with the primary task of designing the controller involving the determination of the mathematical representation of the system. The First Order Plus Dead Time (FODT) model, derived from basic principles, is used to represent the system. To analyze the system’s behavior and construct a suitable controller, model development is essential, achieved by constructing principles models using energy balance equations to identify the heat exchanger process. Data collected from the model are utilized in the identification process, with the temperature at the outlet of the hot air blower being the controlled variable in this investigation. The research aims to determine the mathematical model based on time versus temperature data acquired from the Heat Exchanger. Various system identification methods, such as Hammerstein Wiener (HW), Auto Regressive with Exogenous Input (ARX), Box-Jenkins (BJ), Output-Error (OE), and Auto Regressive Moving Average with Exogenous Input (ARMAX) models, are implemented for the heat exchanger. The models obtained undergo validation, and the best-fit model closest to the physical system is considered for controller design. After conducting the analysis, it was found that the Output-Error (OE) model outperforms other models in terms of achieving the best fit.

An online battery–state of charge estimation method using the varying forgetting factor recursive least square - unscented Kalman filter algorithm on electric vehicles

Accurate and fast estimation of the state of charge is important for the battery management system of electric vehicles. This paper proposes a method to estimate the state of charge of Lithium-ion batteries by the <span lang="EN-US">variable</span> forgetting factor recursive least square (VFFRLS) – unscented Kalman filter (UKF) algorithm in real-time without the off-line battery testing data. Since the state observation requires an accurate model, an equivalent circuit model was constructed. Then, the VFFRLS algorithm is used to identify online the battery model parameters based on voltage and current measurements. An advantage of this algorithm is that it requires less initial information and shorter identification time than offline parameter identification. After the model parameters are well identified, the unscented Kalman filter estimates the state of charge and minimizes noise characteristics and uncertainty in the parameter identification process. The VFFRLS algorithm applied in this paper has shown a good result with the model output error of less than 1%, and the identification achieves real-time response. The state of charge obtained by the UKF algorithm has shown satisfactory estimation results with fast convergence speed and small errors. The UKF filter provides the results with a 1.5% error from the reference and converges after 10 cycles.

Development of a fed-batch-scale anaerobic co-digestion control system based on multivariable output error state space and model predictive control

This paper describes a feeding control system for fed-batch-scale anaerobic co-digestion. The proposed system is based on the multivariable output error state space and uses model predictive control to regulate the biogas flow output of anaerobic co-digestion. This control system combines predictive modeling, receding-horizon optimization, and state feedback. An accurate linear model of anaerobic co-digestion is obtained through the multivariable output error state space method using experimental data, and the accuracy of the model is evaluated using a goodness-of-fit index and the root mean square error. After augmenting the model, a predictive control system is established. The system states are observed through a Kalman filter, and the constrained receding-horizon optimization problem is solved using quadratic programming. Finally, the stability of the control system is demonstrated from both open- and closed-loop perspectives. The control system is then constructed and used in actual experiments, with the target flow output set at 100 NmL/h. The final flow output indicates that the control system achieves good control performance. This research enables the biogas output of anaerobic co-digestion to be controlled from a linear perspective through a concise control algorithm with strong practical application prospects.

Quantitative analysis and cancellation of rotating modulation noise in gravity gradient measurement

Rotating accelerometer gravity gradiometer (RAGG) is an important instrument for auxiliary navigation and mineral exploration. The turntable in RAGG modulates the gravity gradient signal to a high frequency to avoid the influence of low-frequency noise. In order to quantitatively analyze and cancel the rotating modulation noise in gravity gradient measurement, the theoretical RAGG output error model with rotating modulation noise is derived and experimentally verified on a high-precision air-bearing turntable. The experimental results indicate that the dominant rotating modulation noise is turntable vibration noise, which results from the supply pressure fluctuations revealed by further analysis. Based on the rotating modulation noise characteristics, a deep neural network (DNN) is trained to cancel the rotating modulation noise from the RAGG output. Positively, the root-mean-square error (RMSE) of the trained DNN output is 1.7 E in sample data. Furthermore, a gravity gradient calibration platform is established to validate the effectiveness of this method by generating a gravity gradient signal with the same frequency as the rotating modulation noise and amplitude of 100 E. After cancelling the noise by the trained DNN, the RMSE of RAGG output reduced from 94 E to 7.7 E, while the RMSE of the result processed by wavelet analysis remains at 87 E. These results demonstrate that the trained DNN successfully cancels 92% of the rotating modulation noise in actual RAGG measurement without affecting the gravity gradient signal.

Regional climate models and bias correction methods for rainfall-runoff modeling in Katar watershed, Ethiopia

Systematic errors in regional climate models (RCMs) hinder their implementation and lead to uncertainties in regional hydrological climate change studies. As a result, checking the accuracy of climate model simulations and applying bias correction are preliminary methods for achieving consistent findings. Therefore, identifying suitable RCM models for bias correction is important for providing reliable inputs for evaluating climate change impacts. The impacts of bias correction methods on streamflow were assessed on the Katar catchment within the Lake Ziway subbasin using coordinated regional climate downscaling experiments with a spatial resolution of 50 km (CORDEX-44) RCMs through the Integrated Hydrological Modelling System (IHMS) version 6.3. This study evaluated fourteen RCM models under five precipitation and three temperature bias correction methods for the Katar catchment. Statistical approaches, such as bias (PBIAS), the root mean square error (RMSE), the mean absolute error (MAE), the coefficient of variation (CV), the coefficient of determination (R2), and the relative volume error (RVE), are used for performance analysis. GERICS-MPI, RAC4-NOAA-2G, and CCLM4-NCCR-AFR-22 have better performances for both rainfall and temprature. The empirical cumulative distribution function (ECDF) method performed best in removing bias from the frequency-based statistics of rainfall and streamflow, followed by the power transformation (PT), distribution mapping (DM), local intensity scaling (LOCI), and linear scaling (LS) methods. Specifically, for temperature, the VARI and DM methods perform better in frequency-based statistics than the LS method. The performance of hydrological modeling is strongly affected by the selection of rainfall bias correction methods. In addition, the effect of the temperature bias correction method was not significant. The adequacy of the BCM depends on the RCM models and regional context. Therefore, the BCM implementation procedure can be adapted from region to region. This study revealed that the performance of the RCM models differed and that the errors in the RCM model outputs were reduced by the use of bias correction methods.

Differentiable multi-ridge regression for system identification

Regularization aims to shrink model parameters, reducing complexity and overfitting risk. Traditional methods like LASSO and Ridge regression, limited by a single regularization hyperparameter, can restrict bias-variance trade-off adaptability. This paper addresses system identification in a multi-ridge regression framework, where an l2-penalty on the model coefficients is introduced, and a different regularization hyperparameter is assigned to each model parameter. To compute the optimal hyperparameters, a cross-validation-based criterion is optimized through gradient descent. Autoregressive and Output Error models are considered. The former requires formulating a regularized least-squares problem. The identification of the latter class is more challenging and is addressed by adopting regularized instrumental variable methods to ensure a consistent parameter estimation.

Parameter estimation of the systems with irregularly missing data by using sequentially parallel distributed adaptive signal processing architecture

This paper considers problems related to output error models for output data estimation and parameter identification in missing output data systems. In this regard, a new sequentially parallel distributed adaptive signal processing method with the implementation of a low complexity least squares algorithm is introduced to estimate the parameters of an auxiliary model relative to the original system, as well as handling irregularly missing output data in a stochastic framework. The validation of the proposed distributed architecture using the low complexity least squares algorithm is presented in terms of computational complexity and processing time. Measurement results show that the proposed architecture using the low complexity least squares approach provides fast convergence, parallel linear computational complexity, and significantly reduced processing time compared to the sequentially operated recursive least square (RLS) algorithm for parameter identification in missing output data systems. Finally, the effectiveness of the low complexity least squares algorithm is tested with a system example

Momentum‐innovation recursive least squares identification algorithm for a servo turntable system based on the output error model

AbstractIn this article, the parameter identification problem of the output error model is investigated under the application requirement of online parameter identification of a two‐degree‐of‐freedom servo turntable system. To eliminate the influence of colored noise in the observed output signal of the output error model on the algorithm identification accuracy, the momentum factor is introduced into the innovation term of the recursive least squares algorithm, and the momentum‐innovation recursive least squares (MI‐RLS) algorithm is proposed. Further, to improve the convergence speed and identification accuracy of the algorithm while avoiding increasing the algorithm complexity significantly, a reframed multi‐innovation strategy is introduced, and a momentum reframed multi‐innovation least squares (MR‐MILS) algorithm is developed. After analyzing the complexity of the proposed algorithms, the convergence performances of the two algorithms are verified using the theory of martingale convergence, and the results show that the reframed multi‐innovation strategy can accelerate the convergence speed of the MR‐MILS algorithm. The effectiveness of the proposed identification approach is demonstrated via simulation results.

Online Identification of Mechanical Systems Using the Simplified Output Error Model

Online Identification of Mechanical Systems Using the Simplified Output Error Model

Evolving Neuro-Fuzzy Systems-Based Design of Experiments in Process Identification

This paper presents a new design of experiment approach based on an evolving neuro-fuzzy model. The input of the process is proposed by a space-filling method that uses a sequence of step functions to maximise the coverage of the antecedent clusters in the input space of the evolving model, which is called the heuristic step sequence (HSS). When the system reaches a steady state, a new rule is added, existing rules are merged based on the similarity of the consequent transfer functions, and a new optimal excitation is calculated. The output error model structure was chosen because it assumes a noise distribution common to real processes and is suitable for identification, while the step function input signal is one of the most commonly used signals in identification and control. A filtered recursive least squares method is used to identify the consequent parameters of the output error models and the optimisation filter is adapted based on the the confidence interval of the local model. Evaluations were performed on a Hammerstein type model comparing the HSS method with a staircase excitation and on a real plate heat-exchanger pilot plant. The experiments show that the proposed HSS method outperforms the staircase excitation and can be used to identify nonlinear dynamical systems of Hammerstein-Wiener type.

Identification of Nonlinear Systems Using the Hammerstein-Wiener Model with Improved Orthogonal Functions

Hammerstein-Wiener systems present a structure consisting of three serial cascade blocks. Two are static nonlinearities, which can be described with nonlinear functions. The third block represents a linear dynamic component placed between the first two blocks. Some of the common linear model structures include a rational-type transfer function, orthogonal rational functions (ORF), finite impulse response (FIR), autoregressive with extra input (ARX), autoregressive moving average with exogenous inputs model (ARMAX), and output-error (O-E) model structure. This paper presents a new structure, and a new improvement is proposed, which is consisted of the basic structure of Hammerstein-Wiener models with an improved orthogonal function of Müntz-Legendre type. We present an extension of generalised Malmquist polynomials that represent Müntz polynomials. Also, a detailed mathematical background for performing improved almost orthogonal polynomials, in combination with Hammerstein-Wiener models, is proposed. The proposed approach is used to identify the strongly nonlinear hydraulic system via the transfer function. To compare the results obtained, well-known orthogonal functions of the Legendre, Chebyshev, and Laguerre types are exploited.

What to Do When the F10.7 Goes Out?

AbstractThe solar radio flux at 10.7 cm, known as F10.7, is a critical operational space weather index. However, without a clear backup, any interruption to the service can result in substantial errors in model outputs. In this paper we show the impact of one such outage in March 2022 on the models TIE‐GCM and NeQuick, and present a number of alternative solutions that could be used for future outages. The analysis is extended to the F10.7 time series since 1951 and the approach resulting in the smallest reconstruction error of F10.7 uses the solar radio flux observations at alternative wavelengths (the best giving a percentage error of 3.1%). Alternatively, use of Sunspot Number, a regular, robust alternative observation, results in a mean percentage error of 8.2% and is also a reliable fallback solution. Additionally, analysis of the error on the use of the conversion between the 12‐month rolling sunspot number (R12) and its conversion to F10.7 is included.

The data-filtering based bias compensation recursive least squares identification for multi-input single-output systems with colored noises

For the multi-input single-output (MISO) system corrupted by colored noise, we transform the original system model into a new MISO output error model with white noise through data filtering technology. Based on the newly obtained model and the bias compensation principle, a novel data filtering-based bias compensation recursive least squares (BCRLS) identification algorithm is developed for identifying the parameters of the MISO system with colored noise disturbance. Unlike the exiting BCRLS method for the MISO system (see, in Section 3), without computing the complicated noise correlation functions, still the proposed method can achieve the unbiased parameters estimation of the MISO system in the case of colored process noises. The proposed algorithm simplifies the implementation of and further expands the application scope of the existing BCRLS method. Three numerical examples clearly illustrate the validity of and the good performances of the proposed method, including its superiority over the BCRLS method and so on.

Grid-to-Point Deep-Learning Error Correction for the Surface Weather Forecasts of a Fine-Scale Numerical Weather Prediction System

Forecasts of numerical weather prediction models unavoidably contain errors, and it is a common practice to post-process the model output and correct the error for the proper use of the forecasts. This study develops a grid-to-multipoint (G2N) model output error correction scheme which extracts model spatial features and corrects multistation forecasts simultaneously. The model was tested for an operational high-resolution model system, the precision rapid update forecasting system (PRUFS) model, running for East China at 3 km grid intervals. The variables studied include 2 m temperature, 2 m relative humidity, and 10 m wind speed at 311 standard ground-based weather stations. The dataset for training G2N is a year of historical PRUFS model outputs and the surface observations of the same period and the assessment of the G2N performance are based on the output of two months of real-time G2N. The verification of the real-time results shows that G2N reduced RMSEs of the 2 m temperature, 2 m relative humidity, and 10 m wind speed forecast errors of the PRUFS model by 19%, 24%, and 42%, respectively. Sensitivity analysis reveals that increasing the number of the target stations for simultaneous correction helps to improve the model performance and reduces the computational cost as well indicating that enhancing the loss function with spatial regional meteorological structure is helpful. On the other hand, adequately selecting the size of influencing grid areas of the model input is also important for G2N to incorporate enough spatial features of model forecasts but not to include the information from the grids far from the correcting areas. G2N is a highly efficient and effective tool that can be readily implemented for real-time regional NWP models.

Radiative cooling scale method for correcting hourly surface air temperature error in numerical weather prediction models

AbstractGlobally, a variety of numerical weather prediction (NWP) models are employed by national agencies. However, the derived outputs from these models are generally inadequate for precise cultivation management due to bias error. This study uses observational data acquired over several months to develop an equation for correcting surface air temperature (SAT) error in NWP model outputs. With the proposed method, model outputs are converted into potential temperature to cancel the influence of differences between computational elevation and real elevation. The potential temperature errors in the NWP model outputs are corrected using a linear regression equation in which a radiative cooling scale (RCS) serves as the independent variable. The RCS is computed using air temperature observed at a nearby meteorological observation station, together with upper‐level pressure data from the NWP model. Versions of the correction models are developed for specific situations: day, night, and upper‐level meteorology, classified into six groups. In an application of the proposed method, the root mean square error (RMSE) of the corrected SAT output from a global spectral model operated by the Japan Meteorological Agency (JMA) was 1.2–1.6 K; the RMSE of the corrected SAT output from a nonhydrostatic model operated by the JMA was 1.2–1.5 K. The proposed method corrected the NWP model SAT output errors to a level of accuracy similar to that of data corrected using the Kalman filtering technique without the requirement for constant observation at the target site.

Input Spectrum Design for Identification of a Thermostat System

This paper considers the shaping of the amplitude spectra of perturbation signals for the identification of a thermostat system. The current approach in control engineering practice utilizes flat spectrum signals, which may not result in the highest possible accuracy. This research aims to investigate the effectiveness of optimal signals with amplitude spectra designed using two state-of-the-art software approaches, namely the model-based optimal signal excitation 2 (MOOSE2) design and the optimal excitation (optexcit) design, in improving estimation accuracy. Such a comparison on a real system is currently lacking. In particular, there exists a research gap on how the combined choice of signal and model structure affects performance measures. In this research, two model structures are used, which are the autoregressive with exogenous input (ARX) and the output error (OE) model structures. Four performance measures are compared, namely the determinant of the covariance matrix of the parameter estimates and the minimum error, mean error and maximum error in the frequency response. Results show that the optimal signals are effective in reducing the determinant of the covariance matrix and the maximum error in the frequency response for the thermostat system, when applied in combination with the ARX model structure. The flat spectrum signal remains very useful as a general broadband perturbation signal as it provides a good overall fit of the frequency response. The findings from this work highlight the benefits of applying optimal signals especially if the identification results are to be used for control, since these signals improve key performance measures which have direct implications on controller design.

Time-domain system identification of Li-ion batteries from non-zero initial conditions

Electrochemical Impedance Spectroscopy (EIS) allows characterizing electrochemical behavior of Lithium-ion batteries. However, it requires the battery to be at a relaxed state which is quite time-consuming during data acquisition process at different State-Of-Charge (SOC) levels. A time relaxation is usually observed of about 1h at each SOC level. In the prospect to reduce the measurement time, this paper presents a time-domain identification method using non-zero initial conditions of a fractional-order equivalent circuit model (FO-ECM). A two-stage iterative algorithm is developed. It estimates at one stage the system free response, due to the past initialization, and the system forced response due to the input/output signal. It uses, at the second stage, an output error model to estimate model parameters. The algorithm is iterated until convergence. The proposed identification algorithm is applied to identify a Li-ion battery FO-ECM using experimental data.

Closed-loop identification of multi-axis active magnetic bearing systems based on decentralized and decoupling control

In response to the open-loop instability of magnetic bearing systems, this paper develops a closed-loop identification method to obtain an accurate plant model for controller design. The identification method is based on a decentralized and decoupling control architecture, which allows the decoupling of the multi-input-multi-output (MIMO) system into two single-input-single-output (SISO) systems for simplifying the identification process. The identification uses a pseudo-random binary sequence as the excitation signal. A parameterized model is obtained through a parameter estimation algorithm based on the output error model. To ensure that the model prediction error can converge during the computation process, a filter is incorporated into the estimation algorithm. The filter can be synthesized systematically by solving a set of linear matrix inequalities. The performance of the proposed closed-loop identification method is firstly verified by simulations. Then it is implemented on a five-axis magnetic bearing platform and the parameterized model obtained from the identification is compared to the experimental frequency response.