Least-squares Research Articles

Seasonal variations of permanent stations in close vicinity to tectonic plate boundaries

Abstract With the increasing use and popularity of GNSS, there is a growing emphasis on understanding the characteristics of the signals and the impact on their outputs. This article provides an analysis of the daily solution of Iceland permanent GNSS stations daily time series in near proximity to tectonic plate boundaries, aiming to investigate seasonal changes in coordinate values. As a part of the study, the data are prepared, and a function is fitted using the method of least squares, providing for further analysis coefficients and the quality of fit. The research reveals no unequivocal correlation between location and the height of annual amplitudes, except for the stations situated on the Vatnajökull ice cap. It consistently demonstrates higher seasonal changes compared to others, which indicates the influence of snow and water load. Excluding these results, the annual displacement for horizontal components is approximately 1 mm, while the average yearly amplitude for vertical components is almost 5 mm. The results concerned with the Up generally exhibit larger values compared to the other components. It is observed that the mean station variations are higher for the Eurasian plate. The quality of the fit, with regard to outliers and RMSE, does not demonstrate a correlation between the duration of the time series. Furthermore, the average percentage of detected outlier observations is higher for the North American plate.

A Bayesian Shrinkage Approach for the Inverse Weibull Distribution under the Type-II Censoring Schemes

One main challenge in the application of the lifetime distribution models, such as inverse Weibull (IW) distribution is the need for an appropriate estimation method based on experimental conditions. When prior information and certain guessed values are available for model parameters the Bayesian shrinkage (BS) method becomes a valuable approach in this situation. This study considered the BS estimation method in the two-parameter IW distribution under the squared error loss function (SELF) and the type-II censored data. The maximum likelihood (ML), the least squares (LS), and Bayes estimation methods were also examined for a comparative study. Due to the complexity of calculations, the Lindley approach was utilized to approximate the Bayes estimates. The BS estimates were derived and a score test for the guessed value was presented. Additionally, a Monte Carlo simulation was conducted to evaluate the efficiency of all estimation methods. Furthermore, a real data set was implemented to illustrate and compare the BS estimates with the other estimates. The simulation study indicated the consistency of the estimators. The numerical studies also demonstrated that the BS estimators outperform the others.

Statistical analysis of absolute photopeak efficiency of clover HPGe detectors

The variation of absolute photopeak efficiency of an array of clover HPGe detectors as a function of γ-ray energy has been obtained using statistical model analysis. Machine learning technique has been implemented for determining the energy-dependent polynomial of photopeak efficiency. The distribution of parameters of the best-fit model has been deduced by incorporating Markov chain Monte Carlo method working with the basic framework of Bayesian analysis which also provides the correlation between the parameters. This method has the advantage of calculating the posterior probability distribution by maximizing the likelihood function of the experimental data over standard least-squares method. Excellent agreement among the results procured from machine learning, Markov chain Monte Carlo, and least-squares method has been achieved and the correct prediction of the nature of the variation extrapolation region as well as interpolation region has been discussed.

A least-squares framework for developing interval type-2 fuzzy semantics

The developing of IT2 fuzzy semantics is critical for computing with words (CWW), but exiting approaches lack flexibility and fail to adapt user’s diversified demands. The study proposes a least-squares framework for designing CWW encoders that construct interval type-2 fuzzy sets (IT2 FSs) to represent the semantic meanings of linguistic words. In the least-squares framework, an CWW encoder is characterized by two elements: an intra-uncertain semantic mapping and an inter-uncertain semantic family. The intra-uncertain semantic mapping transforms data intervals into type-1 fuzzy sets (T1 FSs), then an optimal IT2 FS is derived from the inter-uncertain semantic family using the least-squares method. Furthermore, several intra-uncertain semantic mappings are introduced, and a compatibility measure is defined to facilitate model selection. The least-squares framework benefits from the flexible selection of intra-uncertain semantic mappings and least-squares optimization-based construction of IT2 FSs. In experiments, the least-squares framework is applied to handle real-world online survey data and the large-scale online review data set of a Chinese life service review site, Dianping.com. Compared to the enhanced interval approach and the Hao-Mendel approach, the least-squares framework shows its favorable efficiency in experiments and statistical tests, and adapts to user-defined intra- and inter-uncertain semantic families.

Efficacy and Safety of Sotatercept Across Ranges of Cardiac Index in Patients with Pulmonary Arterial Hypertension: A Pooled Analysis of PULSAR and STELLAR

BackgroundThis analysis compared effects of the activin signaling inhibitor, sotatercept, across pulmonary arterial hypertension (PAH) subgroups stratified by baseline cardiac index (CI). MethodsPooled data from PULSAR (N=106; NCT03496207) and STELLAR (N=323; NCT04576988) were analyzed using two different CI thresholds, < and ≥ 2.0 L/min/m2 or 2.5 L/min/m2. Median differences in change from baseline at week 24 were evaluated using Hodges-Lehmann (HL) estimator and mean differences by least squares (LS), with 95% confidence intervals and p-values; p=0.05 was significant. Categorial endpoints and time-to-clinical worsening were analyzed by Cochran-Mantel-Haenszel and Cox model (hazard ratio (HR), respectively, without multiplicity adjustment. ResultsOf 429 participants, 51 and 378 had CI <2.0 L/min/m2 and ≥ 2.0 L/min/m2, respectively, whereas 179 and 250 had CI <2.5 L/min/m2 and ≥ 2.5 L/min/m2, respectively. Across all CI subgroups, sotatercept vs placebo significantly improved median 6-minute walk distance (range: 33.9 to 63.7 m: p<0.001), pulmonary vascular resistance (range: -202.8 to -395.4 dyn•s•cm-5; p≤0.002), and N-terminal pro-B-type natriuretic peptide (range: -317.3 to -1041.2 pg/mL; p<0.001). LS means showed reductions in pulmonary and right atrial pressures, decreased right ventricular size and enhanced tricuspid annular plane systolic excursion/ systolic pulmonary artery pressure in all subgroups. Sotatercept significantly delayed time to first occurrence of death or a worsening event in the subset of participants with CI ≥2.5 (HR 0.12; p<0.001), ≥2.0 (HR 0.13; p<0.001), and <2.5 (HR 0.21; p<0.001) L/min/m2. Improvements in World Health Organization functional class (all p<0.050) and European Society of Cardiology/European Respiratory Society risk score (all p<0.001) were seen within each subgroup. ConclusionsEfficacy and safety were consistent across baseline CI subgroups, supporting use of sotatercept in PAH patients irrespective of baseline cardiac hemodynamics.

A Novel Algorithm for Precise Orbit Determination Using a Single Satellite Laser Ranging System Within a Single Arc for Space Surveillance and Tracking

A satellite laser ranging (SLR) system uses lasers to measure the range from ground stations to space objects with millimeter-level precision. Recent advances in SLR systems have increased their use in space surveillance and tracking (SST). The problem we are addressing, the precise orbit determination (POD) using one-dimensional range observations within a single arc, is challenging owing to infinite solutions because of limited observability. Therefore, general orbit determination algorithms struggle to achieve reasonable accuracy. The proposed algorithm redefines the cost value for orbit determination by leveraging residual tendencies in the POD process. The tendencies of residuals are quantified as R-squared values using Fourier series fitting to determine velocity vector information. The algorithm corrects velocity vector errors through the grid search method and least squares (LS) with a priori information. This approach corrects all six dimensions of the state vectors, comprising position and velocity vectors, utilizing only one dimension of the range observations. Simulations of three satellites using real data validate the algorithm. In all cases, the errors of the two-line element data (three-dimensional position error of 1 km and velocity error of 1 m/s, approximately) used as the initial values were reduced by tens of meters and the cm/s level, respectively. The algorithm outperformed the general POD algorithm using only the LS method, which does not effectively reduce errors. This study offers a more efficient and accurate orbit determination method, which improves the safety, cost efficiency, and effectiveness of space operations.

Quality of care of oncological patients with home parenteral nutrition

PurposeTransferring adult cancer patients from the hospital to the home environment for home parenteral nutrition (HPN) can be challenging. There is limited real-world data on how those affected perceive this situation. Our aim was to assess the quality of life (QoL) on HPN and the benefits and burdens from the cancer patient's perspective.MethodsThis observational study from Germany examined the QoL on HPN on the basis of the Functional Assessment of Cancer Therapy – G questionnaire (FACT-G). The benefits and burdens of HPN were assessed using predefined questions and answers tailored to the situation of this patient group.Results139 adults with advanced solid tumors in a palliative setting at 10 hospitals in Germany were eligible for the study. The follow-up was 12 weeks. At week 4, the Least-square (LS) mean (95% CI) change from baseline in the total FACT-G score was 0.9 (-2.4; 4.2) points, indicating QoL stability. HPN was associated with few complications, with a low rate of hospital readmission due to catheter-related issues (3.8%; n = 5). In the patient assessment of the benefits of HPN, the LS mean values at Week 4 ranged between 7.6 and 8.5 on a 10-point Likert scale. The most commonly perceived burden was "restricted mobility".ConclusionWith thorough preparation for home parenteral nutrition, the transition from hospital to home care environment works well. QoL is largely maintained through HPN, and cancer patients perceive this situation as not or minimally burdensome alongside their underlying disease, although many patients found the limited mobility to be a burden.Trial Registration numberNCT03425435 / Date of registration: February 01, 2018.

The Uncoupling of Disease Activity from Joint Structural Progression in Patients with Rheumatoid Arthritis Treated with Filgotinib.

While modern treatments can prevent progressive bone destruction in patients with rheumatoid arthritis (RA) achieving clinical remission, it is unclear whether residual clinical activity may cause or be associated with progressive joint damage. This post hoc analysis evaluated the association between clinical disease activity and structural progression in patients with RA treated with filgotinib (FIL) in FINCH 1 (NCT02889796). Patients with RA and inadequate response to methotrexate (MTX) use were randomized 3:3:2:3 to FIL 200mg (FIL200) or FIL 100mg (FIL100) once daily, adalimumab 40mg biweekly, or placebo, all with background MTX. We evaluated the change from baseline (CFB) in modified total Sharp score (mTSS), erosion score, and joint space narrowing score among patients achieving Clinical Disease Activity Index (CDAI) remission (CDAI ≤ 2.8), low disease activity (LDA; 2.8 < CDAI ≤ 10), medium disease activity (MDA; 10 < CDAI ≤ 22), and high disease activity (HDA; CDAI > 22) at 24weeks. At week 24, the least squares (LS) mean CFB in mTSS was similarly low across treatments among patients who achieved CDAI remission (range 0.00-0.11) or LDA (n = 285 and 575, respectively). In patients with MDA and HDA (n = 471 and 157, respectively), smaller LS mean CFB in mTSS was seen in the FIL200 group vs. the placebo group (P < 0.05 for both). RA clinical remission and LDA achievement were associated with suppressed progression of joint destruction over 24weeks in all treatment groups. Only FIL200 significantly inhibited joint damage compared with placebo in patients with MDA or HDA, indicating an uncoupling of clinical disease activity and structural progression in patients receiving FIL200. NCT02889796.

An Automatic Solution for Registration Between Single-Image and Point Cloud in Manhattan World Using Line Primitives

2D-3D registration is increasingly being applied in various scientific and engineering scenarios. However, due to appearance differences and cross-modal discrepancies, it is demanding for image and point cloud registration methods to establish correspondences, making 2D-3D registration highly challenging. To handle these problems, we propose a novel and automatic solution for 2D-3D registration in Manhattan world based on line primitives, which we denote as VPPnL. Firstly, we derive the rotation matrix candidates by establishing the vanishing point coordinate system as the link of point cloud principal directions to camera coordinate system. Subsequently, the RANSAC algorithm, which accounts for the clustering of parallel lines, is employed in conjunction with the least-squares method for translation vectors estimation and optimization. Finally, a nonlinear least-squares graph optimization method is carried out to optimize the camera pose and realize the 2D-3D registration and point colorization. Experiments on synthetic data and real-world data illustrate that our proposed algorithm can address the problem of 2D-3D direct registration in the case of Manhattan scenes where images are limited and sparse.

The Huber estimation for UMAR model with imprecise observations

A nonlinear uncertain time series model was proposed which was defined as the uncertain max-autoregressive (UMAR) model. After the model is established, we pay more attention to its corresponding prediction and analysis. Before that, the estimation of unknown parameters is the top priority of a series of work. So, this paper presents the Huber estimation to estimate the unknown parameters. Then, the residual analysis and relevant prediction are discussed. Furthermore, the data of China's unemployed population, from 2002 to 2021 via the State Statistical Bureau, are used to verify the feasibility of the model and the Huber estimation. So, the relevant comparison with uncertain autoregressive (UAR) model are given to verify the practicability of the UMAR model under the Huber estimation. In addition, the relevant comparative analysis are given to present that the Huber estimation has better robustness than the least square (LS) estimation when the outliers appear.

Enhanced Lissajous-based algorithm for phase-measuring in two-step phase-shifting fringe projection profilometry

Two-step phase-shifting profilometry is widely used in many applications due to its good trade-off between measurement resolution and efficiency. In this technique, however, it is not easy to accurately calculate fringe phases from only two available fringe patterns, especially when these patterns have nonuniform or even discontinuous background intensities, modulations, or fringe phases. To solve this problem, we propose in this paper an enhanced Lissajous-based algorithm. With it, intensity pairs within the neighborhood of a point form a Lissajous trajectory if their backgrounds and modulations are assumed to be constant. Fitting this Lissajous curve enables us to roughly estimate fringe phase at this point, and a linearized algorithm is suggested here for alleviating the computational complexity. After that, we provide a least-squares method to correct the errors caused by the uneven background intensities by modeling them as linearly varying values within the neighborhood. Further, from the residuals of the above step, the edges and discontinuities in the fringe patterns, where a piecewise algorithm generally have large errors, can be detected. The fringe phases at these edges are recalculated by using forward or backward extrapolations. Simulation and experimental results demonstrate this proposed algorithm to have a relatively high measurement accuracy in two-step phase-shifting fringe projection profilometry.

Abstract 4136334: Treatment Satisfaction With an “Inclisiran First” Implementation Strategy Versus Usual Care in Patients With Atherosclerotic Cardiovascular Disease

Background: Despite the availability of effective lipid-lowering therapies (LLTs), most patients (pts) with ASCVD do not meet guideline-recommended LDL-C goals. In VICTORION-INITIATE (NCT04929249), an “inclisiran first” (IF) strategy of adding inclisiran immediately on failure to achieve LDL-C &lt;70 mg/dL, despite maximally tolerated statin therapy, in pts with ASCVD led to significantly higher LDL-C goal attainment vs usual care (UC) at Day 330. Objective: To evaluate change from baseline to Day 330 in pt-reported treatment satisfaction with an IF implementation strategy vs UC in pts with ASCVD enrolled in VICTORION-INITIATE. Methods: VICTORION-INITIATE, a Phase 3b, open-label, prospective trial, was conducted at 45 representative clinical sites across 20 US states. Pts randomized 1:1 (stratified by insurance status) received inclisiran 284 mg (300 mg inclisiran sodium) at Days 0, 90, and 270 plus UC or UC alone (lipid management directed by treating physicians). We evaluated change from baseline to Day 330 in pt-reported satisfaction with IF vs UC using the validated 11-question Treatment Satisfaction Questionnaire for Medication (TSQM)-II comprising 4 domains (effectiveness, side effects, convenience, and global satisfaction) scored from 0–100. As a post-hoc analysis of a pre-specified exploratory endpoint, we analyzed the difference in least-squares (LS) mean change in TSQM-II domain scores for IF vs UC using ANCOVA with baseline scores as a covariate. Results: We randomized 450 patients: median age 67 years, 30.9% female, 25.8% with a history of statin intolerance. From baseline to Day 330, difference in LS mean change (95% confidence interval) in TSQM-II scores for IF (n=139) vs UC (n=105) was significant (p&lt;0.001) for effectiveness (10.4 [5.4, 15.5]), convenience (10.5 [5.8, 15.2]), and global satisfaction (12.1 [7.2, 16.9]). Statistical comparison was not applicable for the side effects domain at Day 330 due to the small sample size (IF: n=6, UC: n=7). On Day 330, mean scores for IF exceeded UC for each TSQM-II question (Figure). Conclusions: An IF implementation strategy resulted in significantly greater change from baseline to Day 330 across multiple domains of pt-reported treatment satisfaction vs UC.

A Comparison of Battery Equivalent Circuit Model Parameter Extraction Approaches Based on Electrochemical Impedance Spectroscopy

This paper presents three approaches to estimating the battery parameters of the electrical equivalent circuit model (ECM) based on electrochemical impedance spectroscopy (EIS); these approaches are referred to as (a) least squares (LS), (b) exhaustive search (ES), and (c) nonlinear least squares (NLS). The ES approach is assisted by the LS method for the rough determination of the lower and upper bound of the ECM parameters, and the NLS approach is incorporated with the Monte Carlo run such that different initial guesses can be assigned to improve the goodness of EIS fitting. The proposed approaches are validated using both simulated and real EIS data. Compared to the LS approach, the ES and NLS approaches show better fitting accuracy at various noise levels, whereas in both the validation using simulated EIS data and actual EIS data collected from LG 18650 and Molicel 21700 batteries, the NLS approach shows better fitting accuracy than that of LS and ES approaches. In all cases, compared with the ES approach, the computational time of the NLS approach is significantly faster, and compared with the LS approach, the NLS approach shows a minimal difference in computational time and considerably better fitting performance.

Synergistic Effect of Influence Factors on Ammonia Volatilization in Fertilizer Solution: A Laboratory Experiment

Ammonia volatilization, which is one of the main ways that nitrogen gas is released from farmland, restricts promotion of the utilization of nitrogen fertilizer and contains some potential environmental risks. To investigate the general pattern of ammonia volatilization under actual paddy field conditions, we designed an indoor simulated system to measure the amount of ammonia volatilized within a single time period by controlling the pH and concentration of NH4+ (c(NH4+)) in the solution, the gas–liquid interfacial gas velocity, and the ambient temperature. In this paper, the influence of these factors, the synergistic effect on ammonia volatilization, and their quantitative relationship are discussed. We used solutions of ammonium bicarbonate (SAB) and diammonium phosphate (SDP) for the simulation experiments, and the results showed that there is a significant linear relationship between the amount of ammonia volatilization and c(NH4+). The correlation coefficients were between 0.9214 to 0.9897 and 0.8932 to 0.9904 for SAB and SDP, respectively. The quantitative relationship between temperature and pH and the influence factor (CIF) and the initial ammonia volatilization fluxes (IAVFs) was analyzed by the least-squares method, and the degrees of polynomial were one and two, respectively. The regression equations of the SAB and SDP among the amount of ammonia volatilization with the concentration of ammonium nitrogen, the temperature, and the pH were calculated by using MATLAB. Considering the effects of temperature and pH on the CIF and IAVFs under individual conditions, we used a binary cubic model to fit the relationship between temperature and pH to the CIF and IAVFs. The simulation results showed that the correlation coefficients between the CIF and IAVFs for SAB were 0.9980 and 0.9680, respectively, and the correlation coefficients were 0.9946 and 0.9708 for SDP, respectively. The quantitative equation took into account the coefficient of determination and degrees of polynomial, and the ammonia volatilization fluxes can be calculated by using these equations.

Scaling relations between mass components and rotational velocity in disk galaxies

Abstract In this study, we re-evaluate the baryonic Tully–Fisher relation (BTFR) by analyzing the correlations between maximum rotational velocity and various mass components, including stellar mass, atomic hydrogen (H i) mass, baryonic mass, and dark matter mass in a sample of 141 disk galaxies from the SPARC (Spitzer Photometry and Accurate Rotation Curves) database, augmented by recent data on stellar and dark matter masses. We apply multiple statistical methods, including Monte Carlo orthogonal distance regression (MCODR), Monte Carlo least-squares (MCLS), and traditional least-squares (LS), to assess the impact of different fitting techniques on the derived scaling relations between the mass components (stellar, H i, and dark matter) and maximum rotational velocities of these galaxies. We find that the selection of statistical methods significantly influences the derived slopes and intercepts the relation between maximum rotational velocity and mass components. The MCODR method that accounts for errors in both variables consistently produces steeper slopes, suggesting a stronger correlation between stellar mass and rotational dynamics compared to other methods. In contrast, the MCLS method tends to yield flatter slopes, highlighting the sensitivity of this approach to outliers. Despite the variations in slope and intercept across different methods, the fundamental relation between baryonic mass and rotational velocity remains robust. We have also compared dark matter mass derived from different halo models [NFW (Navarro–Frenk–White) versus combined NFW + Dekel–Zhao profiles] and noted that the slope from the NFW profile is slightly steeper than that from the combined profile, highlighting the sensitivity of scaling relations to the selection of halo model. Overall, this study reinforces the robustness of the BTFR across different mass components in disk galaxies while emphasizing the critical role of statistical methods and dark matter profiles in analyzing galactic dynamics.

Unbiased and reproducible liver MRI-PDFF estimation using a scan protocol-informed deep learning method.

To estimate proton density fat fraction (PDFF) from chemical shift encoded (CSE) MR images using a deep learning (DL)-based method that is precise and robust to different MR scanners and acquisition echo times (TEs). Variable echo times neural network (VET-Net) is a two-stage framework that first estimates nonlinear variables of the CSE-MR signal model, to posteriorly estimate water/fat signal components using the least-squares method. VET-Net incorporates a vector with TEs as an auxiliary input, therefore enabling PDFF calculation with any TE setting. A single-site liver CSE-MRI dataset (188 subjects, 4146 axial slices) was considered, which was split into training (150 subjects), validation (18), and testing (20) subsets. Testing subjects were scanned using several protocols with different TEs, which we then used to measure the PDFF reproducibility coefficient (RDC) at two regions of interest (ROIs): the right posterior and left hepatic lobes. An open-source multi-site and multi-vendor fat-water phantom dataset was also used for PDFF bias assessment. VET-Net showed RDCs of 1.71% and 1.04% on the right posterior and left hepatic lobes, respectively, across different TEs, which was comparable to a reference graph cuts-based method (RDCs = 1.71% and 0.86%). VET-Net also showed a smaller PDFF bias (-0.55%) than graph cuts (0.93%) when tested on a multi-site phantom dataset. Reproducibility (1.94% and 1.59%) and bias (-2.04%) were negatively affected when the auxiliary TE input was not considered. VET-Net provided unbiased and precise PDFF estimations using CSE-MR images from different hardware vendors and different TEs, outperforming conventional DL approaches. Question Reproducibility of liver PDFF DL-based approaches on different scan protocols or manufacturers is not validated. Findings VET-Net showed a PDFF bias of -0.55% on a multi-site phantom dataset, and RDCs of 1.71% and 1.04% at two liver ROIs. Clinical relevance VET-Net provides efficient, in terms of scan and processing times, and unbiased PDFF estimations across different MR scanners and scan protocols, and therefore it can be leveraged to expand the use of MRI-based liver fat quantification to assess hepatic steatosis.

Consideration of spectral interference in total reflection X-ray fluorescence analysis using a limited number of calibration samples: Case study of ocean polymetallic nodules

A novel approach for quantitative analysis in total-reflection X-ray fluorescence (TXRF) which can be employed for the samples with complex matrices inducing overlapping spectral signals in the scenario of limited availability of standard samples is proposed. The approach is based on the least squares (LS) decomposition of real spectra into the weighted sum of simulated individual element subspectra and requires only a single sample of matrix-matched reference material. Oceanic polymetallic nodules and crusts, having complex mineral matrix and containing high concentrations of overlapping elements, were chosen to demonstrate the feasibility of the approach in quantification of 11 elements. The comparison of the results obtained with LS decomposition, internal standard and linear calibration with three standard samples was performed. It was demonstrated that the performance of the proposed approach and of the linear calibration was better than that of internal standard for most of the elements; however, the proposed method requires only a single standard sample.

Mathematical Modeling of Biogas Production in Sanitary Landfills

Objective: The objective of this study is to evaluate the biogas production potential in sanitary landfills using the Verhulst mathematical model, which is employed to represent natural phenomena constrained by a saturation point. Theoretical Framework: It was based on references on energy use from waste, possible conversion routes, in addition to mathematical models that estimate the energy potential for biogas generation. Method: The methodology adopted for this research involves the use of data collected in an experimental cell, subsequently applying the De Verhulst model through a regression with minimization of errors using the Least Squares Method (LSM). Results and Discussion: The results indicated that the developed model correlates well with the observed data, demonstrating its suitability as a predictive model for biogas production. Research Implications: The research contributes to the construction of a theoretical framework for the adaptation, elaboration and use of mathematical models to predict the energy potential in the generation of biogas in landfills. Originality/Value: This study contributes to the literature by using a population growth model (Verhulst) to predict landfill biogas production.

Combining long short-term memory and shape superposition for estimating moving load-induced global responses of bridges

Recently, a method of estimating the global responses of bridges was introduced, by combining a deep neural network (DNN) and shape superposition method (SSM). This DNN-SSM model demonstrated superior performance to the traditional estimation method based on the least-squares method. However, the application and validation of this approach have been restricted to static problems. For bridges, the dynamic effect induced by the moving load requires consideration. Therefore, this study proposes a long short-term memory (LSTM)-SSM model to improve the estimation performance for dynamic global responses. The LSTM-SSM model consists of LSTM layers, followed by fully connected DNN layers and a post-process part based on SSM. Limited displacement, slope, and strain data were used as the inputs, and the global displacement, slope, and strain were estimated. To validate the effectiveness and improvement of the LSTM-SSM model, a numerical model of a cable-stayed bridge was used to compare the proposed model with the previously developed DNN-SSM model. The validation results indicated that the LSTM-SSM model can provide more accurate estimates of the dynamic global response than DNN-SSM models. Finally, a technique for structural safety monitoring based on the proposed method was introduced.

Real-time calibration of magnetometers based on the recursive least squares method

Abstract A real-time calibration method for magnetometers based on the recursive least squares (RLS) algorithm is proposed to address the issues of large data processing and lack of real-time performance in the calibration of magnetometers in complex magnetic environments using the traditional least squares (LS) algorithm. Firstly, an error model for the magnetometer is established. Then, using this error model as the measurement equation, the current measurement value is iterated from the previous measurement value through least squares iteration to update the state parameters. Finally, the effectiveness of the algorithm was verified by shaking the magnetometer in a “figure-eight” pattern. Experiments have shown that compared with the traditional least squares algorithm, the recursive least squares algorithm requires less data processing and offers faster calculation speed. Compared to LS calibration, the standard deviation of the magnetic vector modulus obtained from RLS calibration decreased by 24.4%, 17.4%, and 23.2% in three different environments, respectively. Additionally, by performing real-time detection and analysis of the state covariance matrix, it was determined that the calibration process is essentially complete after 3500 iterations.